- Email: [email protected]
Imaging brain tumour microstructure
Accepted Manuscript Imaging brain tumour microstructure Markus Nilsson, Elisabet Englund, Filip Szczepankiewicz, Danielle van Westen, Pia C. Sundgren PII:
S1053-8119(18)30395-1
DOI:
10.1016/j.neuroimage.2018.04.075
Reference:
YNIMG 14922
To appear in:
NeuroImage
Received Date: 19 May 2017 Revised Date:
27 April 2018
Accepted Date: 30 April 2018
Please cite this article as: Nilsson, M., Englund, E., Szczepankiewicz, F., van Westen, D., Sundgren, P.C., Imaging brain tumour microstructure, NeuroImage (2018), doi: 10.1016/j.neuroimage.2018.04.075. This is a PDF file of an unedited manuscript that has been accepted for publication. As a service to our customers we are providing this early version of the manuscript. The manuscript will undergo copyediting, typesetting, and review of the resulting proof before it is published in its final form. Please note that during the production process errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain.
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Imaging brain tumour microstructure
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Markus Nilssona, Elisabet Englundb, Filip Szczepankiewiczc, Danielle van Westena, d, Pia C Sundgrena a
Clinical Sciences Lund, Radiology, Lund University, Lund, Sweden
b
Division of Oncology and Pathology, Department of Clinical Sciences, Lund, Lund University,
Skåne University Hospital, Lund, Sweden CR Development AB, Lund, Sweden
d
Image and Function, Skåne University Hospital, 22185 Lund, Sweden
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Corresponding author Markus Nilsson
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Lund, Sweden
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Lund University
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Clinical Sciences Lund Department of Radiology
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c
Email: [email protected] Telephone: +46 70 25 23 745
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ACCEPTED MANUSCRIPT Abstract Imaging is an indispensable tool for brain tumour diagnosis, surgical planning, and follow-up. Definite diagnosis, however, often demands histopathological analysis of microscopic features of tissue samples, which have to be obtained by invasive means. A non-invasive alternative may be to probe corresponding microscopic tissue characteristics by MRI, or so called ‘microstructure imaging’.
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The promise of microstructure imaging is one of ‘virtual biopsy’ with the goal to offset the need for invasive procedures in favour of imaging that can guide pre-surgical planning and can be repeated longitudinally to monitor and predict treatment response. The exploration of such methods is motivated by the striking link between parameters from MRI and tumour histology, for example the correlation between the apparent diffusion coefficient and cellularity. Recent microstructure imaging
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techniques probe even more subtle and specific features, providing parameters associated to cell shape, size, permeability, and volume distributions. However, the range of scenarios in which these
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techniques provide reliable imaging biomarkers that can be used to test medical hypotheses or support clinical decisions is yet unknown. Accurate microstructure imaging may moreover require acquisitions that go beyond conventional data acquisition strategies. This review covers a wide range of candidate microstructure imaging methods based on diffusion MRI and relaxometry, and explores
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advantages, challenges, and potential pitfalls in brain tumour microstructure imaging.
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Introduction Tumours in the brain and the central nervous system are found in approximately 250 000 patients yearly across the world (Ferlay et al., 2015), with an age-adjusted incidence rate in adults of approximately 25 in 100 000 in the USA (Ostrom et al., 2014). Brain metastases are approximately half as common (Smedby et al., 2009; Stelzer, 2013). Among primary intracranial tumours, the most
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common types are meningiomas and gliomas (Fig. 1). Meningioma tumours are often curable by gross resection, and the five-year survival rate is approximately 65% (Ostrom et al., 2014). Glioma treatment and survival depends on the subtype (Ricard et al., 2012), with five-year survival rates of 94% for pilocytic astrocytomas to only 5% for glioblastomas (Ostrom et al., 2014). Survival for
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patients with brain metastases is shorter than for those with primary brain tumours (Nayak et al., 2012).
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Imaging plays a pivotal role in brain tumour diagnosis, surgical planning, and follow-up. The initial work-up for suspected brain malignancy consists primarily of computed tomography (CT) due to ease of access, but magnetic resonance imaging (MRI) is the standard imaging modality for brain tumours. Clinical protocols yield morphological images and typically include T2-weighted (T2W), fluidattenuated inversion recovery (FLAIR), and gadolinium-enhanced T1-weighted (Gd-T1w) imaging. FLAIR and T2W outline the tumour lesion and oedema, while gadolinium enhancement on the GdT1w contrast shows regions of blood-brain-barrier disruption (Fig. 2). This type of morphological
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imaging is often the basis for primary diagnosis of brain tumours, however, detailed characterisation such as grading can be challenging by morphological imaging only. For example, some high-grade gliomas may not demonstrate the expected gadolinium enhancement, while low-grade gliomas occasionally do (Scott et al., 2002). Approximately 10% of glioblastoma and 30% of anaplastic
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astrocytomas lack gadolinium enhancement. Therefore, imaging may be insufficient for definitive diagnosis of all brain tumours, which motivates biopsies and histological examination, in particular
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for gliomas (Dhermain et al., 2010; Waldman et al., 2009). Biopsy-based histology is thus critical for tumour diagnosis, although ensuring that biopsies are obtained from the most relevant tissue can be challenging (Jackson et al., 2001). The development of new treatment techniques pose further challenges to clinical imaging (Walbert and Mikkelsen, 2011). For example, concurrent treatment, often with radiotherapy and chemotherapy, is associated with so called pseudo-progression (Kruser et al., 2013), where imaging may misleadingly suggest tumour progression due to a transient increase in size and/or a brighter appearance than on pre-treatment MRI (Hygino da Cruz et al., 2011). Conversely, bevacizumab treatment can lead to pseudo-response, where imaging indicates reduced oedema and gadolinium enhancement despite an actual tumour progression (Hygino da Cruz et al., 2011). Gamma knife
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ACCEPTED MANUSCRIPT therapy is associated with a high incidence of radiation necrosis (Korytko et al., 2006), which has similar morphological characteristics as recurrent tumour (Kruser et al., 2013). Imaging techniques that go beyond conventional morphological MRI may overcome these challenges and microstructure imaging by MRI has been proposed as a candidate for this. Microstructure MRI characterizes tissue preoperatively in situ and provides images of the whole tumour rather than of a
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few biopsy samples and, as such, it can avoid mistakes from inadequately targeted biopsy. It may also improve diagnosis by guiding the biopsy and might even replace a biopsy in situations where these are too risky. Moreover, microstructure MRI can be repeated over time and facilitates longitudinal monitoring without elevated risk. In this review, we will provide an overview of histopathology of intracranial tumours and review non-invasive MRI techniques that enable mapping of quantities or
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imaging biomarker related to tissue microstructure. Microstructure imaging is a field of rapid development, and we will cover the current directions and state-of-the-art examples, and outline
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challenges to be addressed by future research.
Histopathological assessment and tumour typing For intra vitam (‘during life’) diagnosis by microscopy, tumour tissue must be obtained by either biopsy or tumour resection (as part of tumour reduction). Tissue is generally provided fresh, frozen, or
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fixed in 4% formaldehyde solution, cut in representative portions, and embedded in paraffin. Sections with a thickness of 4 µm are then processed and stained to visualize microscopic features of the tissue, as described below.
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Staining
Hematoxylin and eosin (HE) staining highlights cell membranes, cytoplasm, and nuclei (Fig. 3). In
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gliomas, the tumour cells are delineated. Vessels and components of bleeding, fibrosis, and necrosis are also visualized. Inflammatory activity, as shown by lymphocytic infiltrates, may also be seen. Cell proliferation, indicating tumour activity and growth potential, is estimated by mitotic counts. For meningiomas, the Elastica Van Gieson (EVG) staining demonstrates vital tumour vis-a-vis fibrous tissue and adjacent brain. The staining is relevant for detection of meningioma infiltration of either the dura, the skull or inwards to the brain, the latter being important since brain invasion alone connotes an atypical meningioma of WHO grade II (Louis et al., 2016). EVG can also depict tumour invasion of vessels, which reflects an accelerated tumour growth and serves as a warning of explosive spread. The tumour grading is further corroborated by the marker for cell cycle activity Ki67 that identifies all cells but the G0 stage (resting) cells – hence indicating the level of proliferation in the
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ACCEPTED MANUSCRIPT tumour. Most normal glial cells can be identified by the antibody against glial fibrillary acidic protein (GFAP), although there are important exceptions (Reifenberger et al., 1987). The GFAP staining also visualizes brain invasion in meningiomas, because these tumours do not express glial marker features and thus stand out negatively against a background of positive brain tissue (Fig. 3D). Immunostainings and molecular analyses have recently become important for glioma diagnostics. A
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reason is that although glioma presence can be certified with a predominantly positive GFAP staining, the degree of malignancy in high grade gliomas does not correlate well with number of proliferating cells, as shown by Ki67 and number of mitoses. This is because most of the cell population may be in transition to cell death and no longer proliferating, despite of or resulting from the tumour being
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highly malignant. Immunostainings such as ATRX, TP53, IDH1, BRAF V600E, and H3K27M can then be used to enhance the diagnostic potential. These stainings point to different pathogenetic steps in tumour development and can hence guide the choice of specific treatment strategies. For example,
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the staining against antigen H3K27M can reveal a specific glioma subtype associated with a worse prognosis than other similar gliomas (Buczkowicz et al., 2014). Molecular analyses can further complement immunostainings for full diagnosis by enabling identification of one of several possible IDH mutations. For example, a complete co-deletion in 1p19q will reveal an oligodendroglioma in a sample that in the pathologist's eyes is an astrocytoma (Capper et al., 2011), hence altering both the prognosis and the therapeutic plan.
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Cell organisation and tissue structure
Glioma microstructure varies considerably between and within each type and malignancy grade (Fig. 3). Low grade gliomas are often composed of groups of loosely scattered cells insidiously infiltrating
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the surrounding brain (Zetterling et al., 2016). There, a mild reactive gliosis can be perceived by the presence of large reactive astrocytes with symmetrically branching extensions and homogenous nuclei
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that attest the non-tumour quality of these glial cells. More intense gliosis—and oedema seen with HE staining as the presence of small microvacuoles in the matrix between cells—generally indicates high grade glioma. In contrast to the diffuse low grade gliomas, high grade gliomas often have a central core of more or less compact tumour with a border pushing against, and compressing the surroundings – a feature explained by rapid tumour growth. However, despite having a tumour core, high grade gliomas may exhibit a loose structure with seemingly low cell cohesivity (Fig. 3B, bottom). This is not only due to necrosis, but also due to grouped assembling of small cells on the one hand, and assembling of large multinuclear bizarre cells on the other. The latter can have cytoplasms 30–40 times larger than those of neighbouring small tumour cells. The lack of tissue cohesivity points to a variety of cell clones. Gliomas can also be indicated by proliferation of tumour vessels, which are often malfunctioning leading to leakage of plasma, proteins, and blood.
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ACCEPTED MANUSCRIPT Meningioma morphology also varies between subtypes, but less so within each type (Fig. 3C–D). The structural subtypes, with some correspondence to malignancy degree, range from compact and hard tissue filled with cell-depleted collagen and calcification between scattered tumour cells, via cell-rich tumours full of spindle-formed cells in packed bundles, to loose architecture of less cohesive cells forming papillary or even glioma-like patterns (see Bi et al., 2016). Proliferation marker in a biopsy of a meningioma relates more closely to malignancy degree than for gliomas. For example, malignant
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meningiomas with necrosis and increased number of mitoses have higher Ki67 indices than the benign ones. However, there are exceptions: meningiomas that exhibit brain invasion behaviour (Fig. 3D) are since 2016 regarded as of intermediate malignance grade even in the absence of other features
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of malignancy (Louis et al., 2016).
Candidate microstructure imaging techniques
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We will here review methods that yield parameter maps associated to features of the microscopic structure of tissue. This type of microstructure imaging make use of diffusion and relaxation-weighted MRI. However, MRI itself produces only signal intensities. Parameter maps are obtained from these by solving an inverse problem, in which a number of parameters are estimated. Because the number of ways the tumour microstructure can vary is large, the problem is often ill posed meaning that we cannot necessarily recover all relevant features of the tumour microstructure in the estimated
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parameters. We thus refer to the reviewed set of methods as “candidate” techniques to acknowledge that the methods may need further theoretical, technical, biological, and clinical validation. Four aspects will be considered for each method: (i) key assumptions and their justifications, (ii) the requirements on the acquisition protocol, (iii) the level of evidence for associating the estimated
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parameters to features of tumour tissue quantified by independent techniques such as microscopy, and (iv) the scientific and clinical usefulness of the technique. Finally, we will discuss challenges to be addressed by future research: model validity, the use of parameters as imaging biomarkers, and unmet
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clinical needs.
Cellular microstructure by diffusion MRI Diffusion MRI (dMRI) probes tissue microstructure by measuring effects on the MR signal intensity from water diffusion with magnetic field gradients. A plethora of different methods have been developed to quantify dMRI data: quantification of the apparent diffusion coefficient (ADC) (Le Bihan et al., 1986), diffusion tensor imaging (DTI) (Basser et al., 1994), diffusional kurtosis imaging (DKI) (Jensen et al., 2005), diffusional variance decomposition (DIVIDE) (Lasič et al., 2014; Szczepankiewicz et al., 2016), composite hindered and restricted model of diffusion (CHARMED) (Assaf and Basser, 2005), axon diameter imaging techniques (D. C. Alexander et al., 2010; Assaf et al., 2008), neurite orientation and density imaging (NODDI) (H. Zhang et al., 2012), to name a few. 6
ACCEPTED MANUSCRIPT These methods fall into two broad categories that use what we will refer to as “signal representations” and “biophysical models”, inspired by the nomenclature in (Novikov et al., 2018). Methods using signal representations include, for example DTI and DKI, and make few, or no, assumptions about the tissue composition, but provide descriptive statistics of the diffusion process (Yablonskiy and Sukstanskii, 2010). Such methods are not constructed with the intent of capturing specific microstructure parameters, but are reviewed here because of the large amount of studies correlating
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their parameters to microstructure features in tumours and their potential use to provide imaging biomarkers. The other class of methods use biophysical models constructed with the intent of enabling estimation of explicit microstructure features such as the intracellular volume fraction, and may offer the most direct route towards microstructure imaging of tumours. Although promising,
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there are still few applications in brain tumours. Diffusion tensor imaging
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Brain tissue exhibits anisotropy, meaning that the ADC depends on the direction of the diffusion encoding. This anisotropy can be analysed with DTI, which provides a measure of the degree of anisotropy in terms of the fractional anisotropy (FA) in addition to a directionally-averaged ADC known as the mean diffusivity (MD) (Basser and Pierpaoli, 1996). Analysis of the FA in the brain has become widely used in neuroscience (Jones et al., 2012), but its role in tumour imaging is less clear because the FA does not quantify diffusion anisotropy at the microscopic level but rather at the
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“macroscopic” voxel level. Hence, the FA is a product of both microscopic anisotropy and orientation coherence (A. L. Alexander et al., 2001; Szczepankiewicz et al., 2015). Since both healthy brain tissue and brain tumours exhibit high orientation dispersion within typical imaging voxels (Jeurissen et al., 2012; Szczepankiewicz et al., 2016; J. Zhang et al., 2007), the FA is not a specific measure of
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microscopic diffusion anisotropy and will thus not pass our mark of being a specific microstructure parameter. In special cases, however, detection of the microscopic diffusion anisotropy either by high-
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resolution DTI or so-called b-tensor encoding can be used to quantify relevant microstructure features in both glioma and meningioma tumours (Szczepankiewicz et al., 2016; J. Zhang et al., 2007). Diffusion anisotropy also serves as the basis of tractography, which reconstructs streamlines that reveal the location of nerve fibres bundles in the brain (Ciccarelli et al., 2008; Mori and van Zijl, 2002), with potential applications in neurosurgical planning (Dimou et al., 2013; Potgieser et al., 2014). Here, the goal is to inform the surgeon on the location of important nerve fibres relative to the tumour (e.g. Fig. 6) so that damage to vital functions can be minimised (Coenen et al., 2001; Hou et al., 2012; Romano et al., 2009). However, the accuracy of DTI-based tractograpy is limited in regions with crossing fibres, but techniques using higher b-values and high angular resolution can address this problem (Frank, 2001; Tournier et al., 2011) and can contribute to more accurate presurgical planning (McDonald et al., 2013; Mormina et al., 2015). 7
ACCEPTED MANUSCRIPT Cellularity and the apparent diffusion coefficient The simplest—and arguably the most common—dMRI method determines the so-called ADC parameter by assuming that the diffusion-weighted signal follows a mono-exponential attenuation (Le Bihan et al., 1986; Stejskal and Tanner, 1965) (1)
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S = exp(–b ADC).
Quantification of the ADC is thus remarkably simple (Fig. 4B). In the presence of anisotropy, a rotationally invariant ADC can be obtained by averaging it across at least three orthogonal encoding directions (Basser and Pierpaoli, 1996; Uluğ and van Zijl, 1999), or obtained as the MD from DTI.
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Without any further mathematical modelling, it is natural to hypothesise that dense tissue with high cellularity and a reduced interstitial space has a lower apparent diffusivity than a tissue with low cellularity. This hypothesised association between the ADC and tumour cellularity has been observed
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in several studies (Barajas et al., 2010; Chenevert et al., 2000; Doskaliyev et al., 2012; Ellingson et al., 2010; Gauvain et al., 2001; Ginat et al., 2012; Gupta et al., 2000; Hayashida et al., 2006; Kono et al., 2001; Matsumoto et al., 2009; Sugahara et al., 1999), although contradictory findings have also been reported (Jenkinson et al., 2009; Sadeghi et al., 2008). A meta-analysis by Chen et al (2013a) found an average correlation coefficient of r = –0.57 across 28 studies for the relationship between the ADC and the cellularity, determined ex situ, of non-treated human tumours (of both the brain and
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other organs). ADC thus has a clear association to the tumour microstructure. However, a multiplicity of mechanisms other than cellularity are known to also influence the ADC (Morse et al., 2007), including membrane permeability (Badaut et al., 2011). To disentangle the different microstructural
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contributions to the ADC, more sophisticated methods are warranted. Two principal applications of ADC quantification have been investigated: treatment monitoring, and tumour differentiation. Treatment monitoring addresses the clinical need for early detection of
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treatment efficacy, and utilizes the fact that ADC responds to changes in tumour cellularity already days or weeks after initiation of treatment (Chenevert et al., 2000), in contrast to volumetric changes which manifest much later. Effective treatment causes necrosis or cell lysis. Both reduce the cellularity, and result in increased ADC. The ADC may thus be a marker for treatment efficacy (Mardor et al., 2003; Ross et al., 2003). However, the relationship between treatment-induced apoptosis and ADC response may be complex (Morse et al., 2007), and brain tumours are often heterogeneous (Fig. 2, Fig. 3) which can make ADC assessments unreliable. The so-called functional diffusion map was proposed as a solution to this problem (Moffat et al., 2005). In this approach, posttreatment parameter maps are registered to pre-treatment maps, and the fractional volume of positive and negative ADC change following treatment is assessed (Fig. 5). Large volumes with ADC increases were indicative of successful treatment (Moffat et al., 2005). The approach, which has also 8
ACCEPTED MANUSCRIPT been referred to as parametric response mapping (PRM) (Galbán et al., 2009), was covered in a recent review (Galban et al., 2017). Tumour differentiation can, in some cases, be done based on the ADC alone. For example, ADC values of dysembryoplastic neuroepithelial tumours are substantially higher than those of more common tumours: 2.55±0.14 µm2/ms, compared to 1.53±0.15 µm2/ms for grade II astrocytomas or
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1.08±0.16 µm2/ms for grade IV glioblastomas (Yamasaki et al., 2005). The ADC can also be used to separate tumour subgroups, albeit with lower sensitivity. For example, the minimum ADC in glioblastoma subgroup of astrocytomas were lower than in the anaplastic subgroup: 0.83±0.14 versus 1.1±0.2 µm2/ms (Higano et al., 2006). For glioma subtypes, small but detectable differences between
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low-grade astrocytomas and oligodendrocytomas have been reported: 1.17±0.17 versus 1.03±0.08 µm2/ms, for the 10th percentile of a whole-tumour histogram (Tozer et al., 2007).
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Diffusion kurtosis imaging
ADC quantification and DTI both rely on the use of relatively low b-values (approximately 1000 s/mm2), but the use of multiple b-values over a larger interval can improve tumour differentiation and monitoring (Falk Delgado et al., 2018; Kang et al., 2011; Vandendries et al., 2014). However, the signal does not decay monoexponentially as required for Eq. 1 to be valid and simple ADC quantification with high b-values will yield a parameter highly dependent on the experimental
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conditions (e.g. maximal b-value). Diffusional kurtosis imaging (DKI) is a natural extension of DTI (Jensen et al., 2005), that permits joint analysis of low and high b-value data (Fig 4C). In one dimension, the analysis is based on the following relation (Jensen et al., 2005; Yablonskiy et al.,
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S(b) = exp(–b MD + 1/6 b2 MD2 MK).
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This approach provides maps of the mean kurtosis (MK) in addition to the mean diffusion (MD; Fig. 7). In essence, the kurtosis captures the amount by which the signal departs from monoexponential attenuation (Fig. 4C). A tensor-based kurtosis analysis is also available (Jensen et al., 2005), which allows the assessment of the kurtosis in any direction, for example, the directions radial and axial to a nerve fiber (Hui et al., 2008). However, the difference between the radial and axial kurtosis is low in most brain tumours (Van Cauter et al., 2012) and assessment of axial and radial tensor components in tissues with low voxel-scale anisotropy, such as tumours, is prone to bias due to the so-called eigenvalue sorting problem (Basser and Pajevic, 2000; Martin et al., 1999). Assessment of the kurtosis tensor may thus not be particularly useful in brain tumours, except for the purpose of obtaining rotation invariant
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ACCEPTED MANUSCRIPT estimates of MK. This can be achieved by fast acquisition protocols for full tensor analysis (Hansen et al., 2013; Lätt et al., 2010; Tietze et al., 2015). DKI has been applied in the context of tumour grading. Raab et al (2010) reported gradually increasing values of MK from grade II astrocytomas, grade III astrocytomas, and glioblastomas, to normal appearing white matter (NAWM), spanning the range from 0.48±0.02 in the grade II tumours
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to 1.14±0.01 in NAWM (mean ± standard error). The progression towards higher MK with higher grade has also been reported by other studies (Raja et al., 2016; Van Cauter et al., 2012). Although not all studies find differences between grade II and grades III gliomas (Delgado et al., 2017), a recent meta-analysis showed that DKI has high diagnostic accuracy in separating low from high grade gliomas (Falk Delgado et al., 2018). Paediatric applications have also been investigated with DKI.
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values of from 0.62 to 0.97 in grade II and grade IV tumours.
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Winfeld et al (2013) reported MK values increasing with grade in paediatric brain neoplasm, with
Although the kurtosis tends to increase with tumour grade, the mean kurtosis is not specific to any single feature of the tissue microstructure. It is assessed from the deviation of monoexponential attenuation at higher b-values, but as Fig. 4E–G shows, this signal feature is affected by both experimental and tissue variables. Nevertheless, DKI parameters have been related to microstructure features of tumours with positive results. For example, MK in gliomas correlated with proliferation marker Ki-67, total vascular area, and tumour cell density (Li et al., 2016). To further understand the
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kurtosis, it is instructive to apply the notion that a voxel can be subdivided into smaller components, all with approximately Gaussian diffusion but with separate ADC values. This allows the kurtosis to be expressed as the normalized intra-voxel variance in ADC (VADC) (Jensen et al., 2005; Yablonskiy
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et al., 2003): MK = 3 VADC / MD2
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High VADC can arise from two distinct sources: anisotropy with orientation dispersion or intra-voxel variance in isotropic diffusivity (Eriksson et al., 2013; Lasič et al., 2014; Szczepankiewicz et al., 2016; Westin et al., 2016). Expressed in terms of microstructure, these effects originate from two separate sources: elongated cell structures with high orientation dispersion and heterogeneous cell density on the voxel level (see e.g. Fig. 3B, bottom), respectively (Szczepankiewicz et al., 2016). These two different microstructure features contribute to the kurtosis in different degrees in different types of tumours (Figure 8). Note that this analysis assumes that the intra-compartment kurtosis is small, which may only be conditionally true (Jespersen et al., 2017). The kurtosis can become more specific to the microstructure features by separating the two sources contributing to the VADC using so-called b-tensor encoding (Lasič et al., 2014; Topgaard, 2016; Westin
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ACCEPTED MANUSCRIPT et al., 2016; 2014). This approach utilizes custom gradient waveforms to shape the diffusion encoding b-tensor. Conventional diffusion encoding yields linear b-tensors, double diffusion with orthogonal gradients yields planar b-tensors, and custom gradient waveforms can yield arbitrary b-tensor shapes (Westin et al., 2016; 2014). Specificity to the kurtosis components is obtained by combining any two types of b-tensor shapes, such as linear and planar (Jespersen et al., 2013; Lawrenz et al., 2010) or linear and spherical (Lasič et al., 2014; Szczepankiewicz et al., 2016). The principle for separating
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kurtosis components with linear and spherical encoding is shown in Figure 4H and 4J, and is based on the idea that with spherical encoding, only variations in the isotropic diffusivity contribute to VADC, whereas with linear encoding, it also captures contributions from anisotropy. Formally, this enables separation of the isotropic kurtosis (MKI) from the anisotropic kurtosis (MKA) (Szczepankiewicz et
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al., 2016; Westin et al., 2016). These two components otherwise contribute to the total kurtosis according to
(4)
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MK = MKI + b∆2 MKA
where b∆ is the shape of the b-tensor. For conventional linear b-tensor encoding b∆ = 1, for spherical encoding b∆ = 0, and for planar encoding b∆ = –1/2 (Eriksson et al., 2015). These specific kurtosis components have been associated to specific features from histology: MKI to intra-voxel variation in cell density and MKA to the average structure anisotropy, e.g., cell eccentricity (Fig. 8C) (Szczepankiewicz et al., 2016). Also note the MKA parameter is a more specific marker of anisotropy
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than FA from DTI, because MKA is not conflated by orientation dispersion (Jespersen et al., 2013; Lasič et al., 2014; Szczepankiewicz et al., 2015).
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Stretched exponential
Methods other than DKI have also been used to analyse high b-value brain tumour data. Kwee et al (2010) applied the stretched exponential representation (Bennett et al., 2003) to estimate the
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distributed diffusion coefficient (DDC) and the hetereogeneity index (α) from high b-value data in high-grade gliomas, and found that α was lower in the tumours than in most of the normal brain tissue. Bai et al (2016) compared diffusion parameters obtained from multiple methods (e.g. ADC, DTI, DKI, stretched exponential), and found significant differences between glioma tumours of different grades in all parameters except FA. The best grading performance was found for α and MK. Biophysical models Methods that estimate parameters with a defined meaning, such as the intracellular volume fraction or cell sizes, are based on biophysical models. Each method comprises its own set of details, as reviewed previously (D. C. Alexander et al., 2017; Nilsson et al., 2013b; Reynaud, 2017), but most decompose
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ACCEPTED MANUSCRIPT the signal into separate components for the vascular (v), intracellular (i) and extracellular (e) spaces, and use a signal model given by S/S0 = fv Sv(·) + fi Si(·) + fe Se(·)
(5)
where fv, fi and fe are the signal fractions of vascular, intracellular and extracellular water,
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respectively, and Sv(·), Si(·), and Se(·) are functions describing the signal attenuation in the corresponding spaces. Some methods omit the vascular component, others add a component for cerebrospinal fluid or free water. Parameter estimation is performed by finding the model parameters, for example, fv, fi and fe and associated parameters describing corresponding signal functions, that best
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predict the acquired signal data.
A very simple type of biophysical model could be built by assuming the vascular fraction to be negligible (fv = 0), constrain the remaining fractions to unity (fi + fe = 1), assume diffusion within cells
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to be completely restricted in impermeable cells so that Si = 1 regardless of the level of diffusion encoding, and employ a tortuosity assumption whereby the extracellular diffusivity could be computed from the intracellular signal fraction according to, for example, De(fi) ≈ (1 – fi2/3) D0,
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where D0 is the bulk diffusivity, which could be constrained to by a priori information (for example,
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D0 = 3 µm2/ms as for free water at body temperature). This parallel-series tortuosity model was proposed by (Szafer et al., 1995), and is based on the rationale that the extracellular apparent diffusivity is lower in a dense than in a loose cellular environment. The signal model would then be given by
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S(b)/S0 = fi + (1 – fi) exp(–b [1 – fi2/3] D0).
(7)
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Since this model has only one free parameter (fi), it could, in principle, be used to rephrase the ADC as an intracellular water fraction (e.g. ‘cell density index’). Biophysical models can also be extended to include more free parameters in order to capture, for example, distributions of cellular sizes (Assaf et al., 2008; Packer and Rees, 1972), several distinctly different cell components (D. C. Alexander et al., 2010; Stanisz et al., 1997), and vascular components (Panagiotaki et al., 2014). To illustrate a very general approach, we could model the vascular component by Sv(b) = exp(–b D*)
(8)
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ACCEPTED MANUSCRIPT thereby adding one parameter, D*, to describe the pseudo-diffusion in flowing blood (Le Bihan et al., 1988). Intracellular diffusion could be described by integrating the signal across multiple compartments of different sizes = ∫ | , exp− |
(9)
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where p(x | d, s) is the probability distribution of cell sizes, described its mean (d) and variance (s), and Di[x | g(t)] describes how the apparent diffusivity of the compartment depend on the gradient waveform, g(t). For details on ways of modelling Di, see references (Nilsson et al., 2013b; 2017; described by = exp− , |
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Reynaud, 2017; Stepisnik, 1993; Wang et al., 1995). Finally, the extracellular signal could be
(10)
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where , | describes how the extracellular apparent diffusivity depend on the gradient waveform (Novikov et al., 2014; Xu et al., 2014). This adds another two parameters, D∞ and β, describing the long-time extracellular diffusivity and a presumed linear frequency-dependence of the extracellular diffusivity, respectively. In total, this very general model contains eight free parameters (fi, fe,, fv, D*, d, s, D∞, β), of which seven would be free, considering that fi + fe + fv = 1. On top of this, one could imagine including another component capturing water within axons, relevant in the case of
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infiltrative glioma, but this would add at least another four more parameters, describing the intraaxonal axial diffusivity, principal fibre direction (two polar angles), and the level of axonal orientation dispersion.
The capacity of a model to fit the signal generally increases with the number of free parameters. This
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concept is central to machine learning (Goodfellow et al., 2016), but is explored also in biophysical modelling in dMRI (Ferizi et al., 2014; Panagiotaki et al., 2012). In practise, the signal rarely
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contains enough information to support reliable estimation of more than a handful of meaningful parameters (Ferizi et al., 2015; Novikov et al., 2016a). In the absence of anisotropy, data acquired with multiple b-values in the range of up to approximately 2500 s/mm2 can at most support the estimation of two parameters regardless of the number of b-values used (Kiselev 2007 and 2017). Models with more than two free parameters risk becoming degenerate, meaning that measured data will be equally well fitted by multiple combinations of model parameters, which often results in noisy and un-interpretable parameter maps. This so-called degeneracy is not unique to dMRI but is encountered also in other scientific fields that use exponential analysis (Istratov and Vyvenko, 1999). Degeneracy can be tackled by two principal approaches. The first is to reduce the number of free parameters by introducing constraints, for example, assuming specific values or functional dependencies of some parameters. An obvious risk with this approach is that parameter bias will 13
ACCEPTED MANUSCRIPT result whenever these constraints are invalid. For example, see (Lampinen et al., 2017a). The second and more desirable approach is to acquire more independent information by extending the acquisition protocols, sometimes referred to as “orthogonal measurements” (Novikov et al., 2016a) or multidimensional encoding (Topgaard, 2016). Examples of such encoding dimensions applied to tumours are the diffusion time (Reynaud, 2017) and the b-tensor shape (Szczepankiewicz et al., 2016), and their effect on the signal is illustrated in Figure 4. With this background, we will now
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cover many of the present biophysical models used for microstructure imaging. Methods for estimating neurite density
Several contemporary methods aim at estimation of the ‘neurite density’ (Jespersen et al., 2010;
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2007), and two approaches have been tailored for clinical acquisition protocols: the neurite orientation dispersion and density imaging technique (NODDI) (H. Zhang et al., 2012), and the two-component spherical mean technique (SMT) (Kaden et al., 2016). The “standard model” behind both of these
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techniques is intrinsically degenerate (Jelescu et al., 2016; Novikov et al., 2016b), which necessitates the application of constraints. NODDI, for example, includes assumptions on the diffusivity and the microscopic anisotropy of ‘neurites’ and a link between the extracellular diffusivity and the ‘neurite density’ via a so-called tortuosity assumption. However, these constraints appear to be incongruent with the diffusion in both healthy and tumour tissue (Jelescu et al., 2016; Lampinen et al., 2017a; Novikov et al., 2016a), which leads to biased parameter estimates (Lampinen et al., 2017a). Despite
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this limitation, NODDI has been applied to analyse brain tumour data (Wen et al., 2015), but the estimated ‘neurite density’ should be interpreted with care because the model can yield high ‘neurite density’ even in the known absence of neurites (Lampinen et al., 2017a). This pitfall is particularly relevant in tumours where there is a high intra-voxel variation in cell density (Fig. 3). Contributions
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from this effect can, however, not be separated from contributions of dispersed neurites and so these two effects are conflated in a single ‘neurite density index’, unless b-tensor encoding is applied. This
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type of degeneracy is illustrated in Figure 4H–J. The biexponential model
The biexponential model features fractions of water undergoing ‘fast’ and ‘slow’ diffusion and has three free parameters: ffast, Dfast, Dslow, representing the fast diffusion fraction, the fast diffusion coefficient, and the slow diffusion coefficient. It is expressed as S/S0 = ffast exp(–b Dfast) + fslow exp(–b Dslow).
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The fourth parameter fslow is given by the constraint that ffast + fslow = 1. In the context of dMRI in peripheral nerves, with diffusion encoding perpendicular to the nerve fibre structures, the ffast and fslow parameters were associated to extra-axonal and intra-axonal water fractions, respectively (Assaf and 14
ACCEPTED MANUSCRIPT Cohen, 2000). In the brain, however, orientation dispersion—present in most brain tissues—prevents the use of this simple interpretation (Nilsson et al., 2012; H. Zhang et al., 2012). The biexponential model has been used to characterize brain tumours (Maier et al., 2001), and to study treatment response (Mardor et al., 2003). However, clinically acquired dMRI data rarely supports accurate estimation of the three microstructure parameters (Kiselev, 2017; Kiselev and
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Il'yasov, 2007). The degeneracy of the biexponential model can be mitigated by constraining one of its parameter to a predetermined value, reducing the number of free parameters from three to two, but this procedure results in biased parameters devoid of their connection to underlying microstructure (Mulkern et al., 2017).
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Beyond the b-value: Size estimation by time-dependent diffusion
To support estimation of more than two microstructure features in tumours, the acquisition must
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include variation of more factors than just the b-value1. Figure 4E and 4F illustrates how variation of the diffusion time contributes to a change in the signal curves and how it relates to the underlying microstructure. We refer to such advanced acquisition protocols as multidimensional microstructure imaging techniques. These permit, for example, cell size estimation by acquiring data with multiple diffusion times or by gradients oscillating with different frequencies (Assaf et al., 2008; Schachter et al., 2000; Stanisz et al., 1997; Xu et al., 2014). However, the use of such techniques in brain tumours
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begun only recently, and thus the available data is still limited. Therefore, we also review selected examples of such techniques applied to tumours outside of the brain. The VERDICT (Vascular, Extracellular, and Restricted Diffusion for Cytometry in Tumors) approach uses data acquired with multiple diffusion times to estimate the intracellular volume fraction and cell
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size (Panagiotaki et al., 2014). So far, VERDICT has only been applied to xenograft models of colorectal cancer and prostate cancer (Panagiotaki et al., 2014; 2015), where it enabled MRI-based
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inference of the tumour cellularity, which could differentiate tumours that were indistinguishable by the ADC alone. Time-dependent diffusion––the basis for a VERDICT type of analysis––has also been demonstrated in a xenograft glioblastoma model (Hope et al., 2016). Another analysis approach referred to as IMPULSED (Imaging Microstructural Parameters Using Limited Spectrally Edited Diffusion) utilizes oscillating gradients to probe time-dependent diffusion (Jiang et al., 2016), and enables estimation of cell sizes and cellularity scores in animal models of colon cancer (Fig. 9). Oscillating gradients can be used to probe diffusion at very short diffusion times, which enables assessment of the geometrical features of cell structures such as the surface to
1
Tissues with large vascular components may be an exception, where the exceptionally fast pseudo-diffusion of flowing blood can contribute with sufficient information for another parameter to be captured at low b-values
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ACCEPTED MANUSCRIPT volume ratio (Schachter et al., 2000). Reynaud et al (2015) applied oscillating gradients in a murine glioma model and quantified geometric restrictions by their surface to volume ratio. Corresponding experiments in brain tumour patients have to our knowledge not yet been published. However, Baron et al (2015) used oscillating gradients in stroke patients to investigate the reduced diffusion in stroke lesions, and found swelling and beading of neuronal structures to be key elements for explaining the
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ADC reduction in stroke. Even state-of-the art approaches for cell size estimation have limitations, however. No method can accurately estimate cell sizes below approximately 3–5 microns from intra-cellular time-dependent diffusion with clinical scanners (Nilsson et al., 2017), because the difference in signal attenuation at
(compare Fig. 4E and 4F).
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Time-dependent diffusion for estimation of exchange
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different diffusion times, which the models translates to sizes, is negligible for small structures
Cell membranes are generally permeable to water and assessment of the permeability could be of importance in tumours because the permeability may be related to the migration of malignant astrocytes (McCoy and Sontheimer, 2007). It may also influence the formation and extent of vasogenic brain oedema (Papadopoulos and Verkman, 2007).
Membrane permeability can be estimated from dMRI measurements (Andrasko, 1976; Kärger, 1969).
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Conventional dMRI is, however, not specific to water exchange (Nilsson et al., 2013c), because effects of exchange are entangled with effects of restricted diffusion. This is illustrated in Figure 4E and 4G, which shows that the presence of restricted diffusion leads to increased signal intensities at high b-values, whereas the opposite effect if found in the presence of exchange. In other words: a
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change in signal for longer diffusion times may be due to restricted diffusion, exchange, or a mixture of the two. To disentangle these effects, more advanced encoding strategies are warranted.
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Filter exchange imaging uses a double diffusion encoding experiment with variable mixing times to assess the so-called apparent exchange rate (AXR; see Fig. 10) (Lasič et al., 2011). Where cells are small, the AXR can be expected to be specific to exchange because it relies on a double diffusion encoding experiment, but for larger structures (e.g. above 10 µm) it can become coupled to effects of restricted diffusion (Ulloa et al., 2017). The AXR has been demonstrated to vary approximately linear with the ground truth exchange rate (Tian et al., 2017), and to be elevated for increased levels of urea membrane channels (which cotransports water) in a rat brain (Schilling et al., 2016). The AXR has been measured in the human brain, in the breast, and in glioma and meningioma brain tumour patients (Lampinen et al., 2017b; Lasič et al., 2016; Nilsson et al., 2013a). Results showed, for example, that gliomas exhibit higher AXR than meningiomas (Lampinen et al., 2017b).
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ACCEPTED MANUSCRIPT Translating an AXR value to an exchange time or membrane permeability is not trivial and requires additional measurements or assumptions on fractional water populations and relaxivities (Åslund et al., 2009; Eriksson et al., 2017). Assuming equal amounts of intra- and extracellular water, and that all intra-cellular components contributed to the exchange, the results in Lampinen et al (2017) predict exchange times of 2 and 4 seconds in gliomas and meningiomas, respectively. Conventional diffusion MRI is typically performed with diffusion times of below 100 ms, which would place such
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measurements in the “slow exchange regime” where effects of exchange can be neglected. However, this should be regarded as a probable hypothesis rather than a verified truth. Tissue fractions by relaxation MRI
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Brian tumours generally have longer T2 relaxation times than brain tissue, but there are also differences between tumour types. For example, Oh et al (2005) found T2-relaxation times at 1.5 T
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for gliomas that were significantly longer than those for meningiomas and metastases (160±31 versus 125±31 ms). In oedema, T2 values were generally longer than 200 ms. Preclinical results on experimental tumour models have also demonstrated longer T2 relaxation times in the tumours than in normal tissue (Eis et al., 1995; Sun et al., 2004).
Quantification of the average T2 relaxation time can provide valuable information about tumours. Hattingen et al (2013) investigated patients with recurrent glioblastoma, and suggested that
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comparisons of quantitative T2 measurements between baseline and follow-up can reveal tumour progression (T2 increase) or tumour treatment response (T2 decrease). This may not be surprising given the strong relationship between T2 and ADC (Oh et al., 2005), and the correspondence between ADC, cellularity, and treatment response (Chen et al., 2013; Chenevert et al., 2000; Moffat et al.,
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2005). Moreover, (Lescher et al., 2014) demonstrated that tumour progression was detected earlier on quantitative T1 and T2 differential maps (follow-up minus baseline) than with conventional imaging, and Ellingson et al (2015) showed that T2 quantification can aid quantification of non-enhancing
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tumour burden for use in prediction of survival. However, due to large heterogeneity of brain tumours, T2 quantification in itself may not enable tumour differentiation. For example, it cannot differentiate between benign and malignant astrocytomas (Kjaer et al., 1991). Microstructure imaging could exploit compartmental differences in T2-relaxation times to estimate proton densities in each compartment rather than relaxation-weighted signal fractions. In normal brain tissue, analysis of the T2 decay curve (signal versus TE) reveal up to three distinct components associated with myelin, tissue water, and cerebrospinal fluid with T2-relaxation times at 1.5 T in the ranges of 10–20 ms, 50–600 ms, and above 1000 ms (Whittall et al., 1997). The tissue water itself, however, appears to have small but potentially detectable differences in T2 between intra- and extracellular spaces (Veraart et al., 2017). In experimental glioma tissue, tissue components with 17
ACCEPTED MANUSCRIPT distinctly different T2-relaxation times have been reported (Hoehn-Berlage et al., 1992). For example, Dortch et al (2009) investigated a glioblastoma tumour model at 7 T and found two components with T2 relaxation times of 21±5.4 ms and 76±9.3 ms, where the short-lived component represented a small fraction of the signal (6.8±6.2%). Contralateral grey matter exhibited approximately monoexponential decay with a T2 relaxation time of 49±2.3 ms. Multiexponential T2 decay has also
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been reported in human brain tumours at 1.5 T (Kjaer et al., 1991; Schad et al., 1989). The underlying physiological origin of the observed T2 components in tumours is still unknown, but this effect will be necessary to include in compartment models for accurate quantification of compartmental proton densities rather than signal fractions. Although this type of diffusion-relaxation correlations has already been applied in porous media to study for example cheese (Godefroy and
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Vascular microstructure by perfusion MRI
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Callaghan, 2003), corresponding in vivo applications in tumours are scarce.
Angiogenesis is the process by which new blood vessels are formed. It plays an essential role in tumour growth, and imaging perfusion and vascular microstructure by MRI is important for tumour diagnosis and monitoring (Waldman et al., 2009). Dynamic contrast-enhanced MRI (DCE-MRI) makes use of contrast injection to enable estimation of parameters that relate to the microvascular permeability, and blood flow, blood volume fraction. DCE-MRI techniques were covered in a recent
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review by Heye et al (2014), and here, we will cover diffusion-based methods that do not require injection of exogenous agents to estimate parameters associated to the blood volume. Intra-voxel incoherent motion
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On the scale of a voxel, capillaries are near-randomly oriented and their associated distribution of flow directions will thus be approximately random. In dMRI experiments, blood in the capillaries will thus appear to exhibit pseudodiffusion with a very high ADC (Le Bihan et al., 1988), which yields a
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distinct signal impression at low b-values (Fig. 4D). The intra-voxel incoherent motion (IVIM) approach use this phenomenon to estimate the so-called perfusion fraction from dMRI data using a biexponential approach:
S(b) = f exp(–b D*) + (1–f) exp(–b D)
(12)
where f is the perfusion fraction, D* the pseudo-diffusion coefficient of blood, and D is the tissue diffusivity. Due to the very high value of D*, the perfusion fraction is attenuated already at moderate b-values and thus IVIM relies on the use of low b-values to capture the perfusion fraction. If performed carefully, IVIM can yield useful information on tumour perfusion (Fig. 11). Federau et al (2014) evaluated the perfusion fraction in different types of brain lesions, and found results
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ACCEPTED MANUSCRIPT concurrent with expectations: hyperperfusion in high grade gliomas and meningiomas, and hypoperfusion in acute ischemia and in the necrotic part of a glioblastoma. Moreover, perfusion fractions in high-grade gliomas have been reported to be higher than in low-grade gliomas (Shen et al., 2016; Togao et al., 2016). Higher perfusion fractions have also been reported in recurrent glioblastomas compared to treatment-responding ones (Kim et al., 2014). However, it is still unclear whether the perfusion fraction from IVIM contributes with clinically relevant information. Compared
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to the ADC, for example, it did not add substantially to prediction of 2-year survival in gliomas (Federau et al., 2016) or to the differentiation of high and low grade tumours (Shen et al., 2016). The product of f and D* did, however, improve the differentiation (Shen et al., 2016). The perfusion fraction may also help differentiating primary central nervous system lymphoma (PCNSL) and
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glioblastomas (Suh et al., 2014; Yamashita et al., 2016).
In the context of compartment models, we referred to the fact that modelling must deal with the ill-
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posed nature of the dMRI experiment (Kiselev, 2017), and that this is a problem for all exponential analyses (Istratov and Vyvenko, 1999). IVIM employs a biexponential model and results are thus either highly sensitive to noise, or conversely, to the constraints applied to mitigate the noise sensitivity. Constraints often lead to bias and IVIM is not immune to this limitation. For example, perfusion fractions as high as 30% have been reported in normal white matter (Hu et al., 2014; Lin et al., 2015), well above the expected values of 5% or lower, which suggests the use of invalid
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constraints. In particular, the estimated perfusion fraction is easily confounded by the presence of the cerebrospinal fluid (CSF) that also exhibits fast diffusion (Bisdas and Klose, 2015). This problem can be mitigated by supressing the CSF by an inversion recovery prepared sequence (Federau and O'Brien, 2015). Multidimensional encoding that enable varying the level of flow compensation in addition to the b-value could also contribute to more accurate estimation of the perfusion fraction
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(Ahlgren et al., 2016; Wetscherek et al., 2014).
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Challenges for brain tumour microstructure imaging Model validity
The promise of microstructure imaging is to produce parameter maps reflecting clinically relevant cell-level tissue properties non-invasively, across whole organs, in a way that allows repeated measurements for monitoring (D. C. Alexander et al., 2017). One may ask whether microstructure imaging may even enable measurements of tissue quantities, using these terms as defined in the International Vocabulary of Metrology (2012): a quantity is a property of a body (e.g. a piece of tissue) and a measurement is the process of experimentally obtaining quantity values that can reasonably be attributed to a quantity. Since a property is invariant to the measurement modality,
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ACCEPTED MANUSCRIPT quantity values should be too. Microstructure imaging offers the hope of enabling measurements of tissue quantities of tumours, such as the cellularity or cell sizes, based on MRI only (Jiang et al., 2016; Panagiotaki et al., 2014). Microstructure imaging relies on three foundations: acquisition strategies that encode information about the desired tissue quantities into the magnetic-resonance signal, forward models that predict the
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dependence of the signal from the tissue quantities, and procedures to estimate quantity values by fitting the forward models to the signal. The acquisition is of particular importance: using multiple and moderate b-values (e.g. multi-shell dMRI) is enough to probe just two parameters (Kiselev, 2017; Kiselev and Il'yasov, 2007), and it is unlikely that these can be reasonably attributed any single tissue quantity. Multidimensional encoding strategies are thus warranted to encode more information into
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the signal (Fig. 4). Successful examples include the use of multiple diffusion times to probe cell sizes (Jiang et al., 2016; Panagiotaki et al., 2014), variable b-tensor shapes to probe cell shapes
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(Szczepankiewicz et al., 2016), and variable flow-compensation to probe perfusion (Ahlgren et al., 2016). Even with multidimensional encoding, however, the number of independent tissue quantities that can affect the signal may still exceed the number of parameters required to represent the signal data. In other words, many tissue quantities map to few observable parameters. For example, the intracellular proton density and volume fraction both contribute to the intracellular signal fraction, and cannot be decomposed without data acquisitions that go beyond regular dMRI.
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Microstructure imaging methods that use biophysical models often address the problem of many-tofew mappings by the use of constraints that fix the values of some quantities, or compute them from functional relationships with other quantities. For example, the tortuosity constraint defines a relationship between the extracellular diffusivity and the cell density. The validity of such constraints
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is of utmost concern, because estimated quantity values cannot be reasonably attributed to any single tissue quantity when invalid constraints are applied (Novikov et al., 2018), as demonstrated in the
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case of neurite density mapping in tumours (Lampinen et al., 2017a). Without knowing that the applied constraints are valid in the tumours being investigated, results may be misinterpreted. Therefore, the first challenge is to verify the validity of microstructure imaging methods in a relevant set of brain tumours prior to relying on them for interpretations. Tools for testing assumptions have been described (Novikov et al., 2018). For example, the parameters produced with a valid biophysical model should depend only marginally and in a predicable manner on variations in the experimental protocol (e.g. the set of b-values or diffusion times employed). The use of models can also be analysed philosophically, and to do so we borrow terminology and concepts from (Frigg and Hartmann, 2018). A model is here analysed as a representation of a target system. Discussions on validity then begin by a definition of this target system. For signal models such as DTI and DKI, the signal itself is the target of the model. For biophysical models, the 20
ACCEPTED MANUSCRIPT interaction between the tissue microstructure and the MR experiment is the target. Interpreting increased ADC as reduced cellularity also involves a model, although with linguistic rather than mathematical entities (e.g. high cell density leads to more obstructions to the diffusion and thus a reduced ADC). Model validity concerns whether the model represents the target system accurately enough for the task at hand. The scientific realist may argue that a valid model has entities (e.g. the ‘intracellular volume fraction’ in a biophysical model) with near-identical counterparts in the target
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system (cancerous tissue). Opponents could argue that the biophysical models we have discussed are always false, as their entities are Galilean idealizations, meaning that they involve deliberate distortions of the reality (e.g. assuming that axons are like cylinders, or that cell bodies are like spheres). Models can be false in different ways, however, and Wimsatt (1987) listed these in terms of
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increasing seriousness: a model is false because it (i) has only local applicability, (ii) is so idealised that its entities have no counterparts in nature, (iii) is incomplete meaning that it leaves out variables with explanatory power, (iv) is so incomplete that it provides erroneous descriptions of the
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interactions in the target system, or (v) gives a completely wrong-headed picture of reality. Most, if not all, models discussed herein are invalid up to the third level, since they leave out parameters such as the proton density or relaxivity in each compartment because, at present, there are no multimodal protocols available that allows precise estimation of such parameters from data. That may change in the future. Meanwhile, even false models can be useful, for example, to provide imaging biomarkers.
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Usefulness as imaging biomarkers
An imaging parameter with a strong association to a property of medical interest may be regarded as a quantitative imaging biomarker, which is defined as an “objective characteristic derived from an in vivo image measured on a ratio or interval scale as an indicator of normal biological processes,
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pathogenic processes or a response to a therapeutic intervention” (Kessler et al., 2015). When developing a new image biomarker, two translational gaps must be bridged (O'Connor et al., 2017).
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The first gap concerns establishing the biomarker as a useful tool for applied medical research, for example as a surrogate endpoint in treatment studies, and the second gap concerns the ascension of the biomarker into a clinical decision making tool. Bridging the first gap requires validation of the imaging biomarker on the technical, biological, and clinical arenas. Technical validation assesses, among other factors, repeatability (that the method yields the same value under the same conditions) and reproducibility (it yields the same value under different conditions, e.g. different scanners). Identification of the intervals within which accurate and reproducible measurements can be expected is thus an important step along the road of turning a microstructure imaging parameter into an imaging biomarker. Biological validation ensures that the imaging biomarker is associated to a tissue quantity within the specific validated context. Such validation can be performed by correlating the imaging biomarker to a tissue quantity obtained with independent means such as histology or another
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ACCEPTED MANUSCRIPT imaging technique. Biological validation can also be performed by testing whether the imaging biomarker responds as expected to changes in the quantity. For example, we may verify that a parameter thought to be associated with cellularity actually decrease in a tumour following successful treatment. Clinical validation assesses whether the method can discriminate clinically interesting conditions, for example tumours of low and high grade. The limitations of the imaging-biomarker approach are that the experimental conditions must be fixed (“operationalized”) between validation
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and application and that the validation must be repeated for any new contexts (e.g. another type of tumour). The second challenge for the microstructure imaging community is to allocate resources to validate its parameters as imaging biomarkers in cancer research. Inspiring examples of such validation work are provided below.
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The ADC is the microstructural imaging biomarker that has been most extensively validated. Technical validation has shown high repeatability and reproducibility of ADC quantification
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(Malyarenko et al., 2012; Pfefferbaum et al., 2003). Biological validation has shown a strong association between ADC and cellularity in a wide range brain tumours, comprising gliomas, meningioma, lymphomas, brain metastasis and paediatric brain tumours, with correlation coefficients (r) in the range –0.54 to –0.77 (Barajas et al., 2010; Chenevert et al., 2000; Doskaliyev et al., 2012; Ellingson et al., 2010; Gauvain et al., 2001; Ginat et al., 2012; Gupta et al., 2000; Hayashida et al., 2006; Kono et al., 2001; Sugahara et al., 1999). Clinical validation has shown increases in the ADC
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following successful treatment (Hamstra et al., 2005; Hein et al., 2004; Mardor et al., 2003; Pope et al., 2009), presumably due to treatment-induced reductions in cellularity (Chenevert et al., 2000). However, the ADC have several limitations as an imaging biomarker. Technically, the measurement procedure has not been sufficiently well operationalized with standards for the acquisition protocol (Padhani et al., 2009), for example, regarding diffusion times which we know can affect the ADC.
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Accuracy is hampered in multi-centre studies due to gradient nonlinearity issues (Malyarenko et al., 2016). Biologically, the association between ADC and cellularity is also far from perfect, as expected
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since factors other than the cellularity also affects the ADC. Approaches for microstructure imaging based on biophysical models have also been validated, although not as extensively and often only on preclinical systems. Such validation results may not always translate well to clinical systems. For example, measurements of the axon diameter from dMRI agreed well with histology-based estimates in animal models both ex vivo and in vivo (Assaf et al., 2008; Barazany et al., 2009). The agreement was, however, lost in the translation to the human brain and clinical MRI scanners, where the diameter was grossly overestimated (D. C. Alexander et al., 2010). A probable reason is that the hardware available at clinical MRI scanners does not support estimation of diameters below 3–5 microns (Nilsson et al., 2017), while most axons in the human brain are below 1-2 microns (Aboitiz et al., 1992). Nevertheless, preliminary biological validation
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ACCEPTED MANUSCRIPT studies indicate that imaging biomarkers from multidimensional microstructure imaging methods perform better in tumours than the ADC. For example, such imaging biomarkers and histology correlated very well in the case of cellularity in a colorectal cancer xenograft model (r = 0.81) (Jiang et al., 2016), and in the case of cell shapes (r = 0.95) and cell density heterogeneity (r = 0.83) in human meningioma and glioma tumours (Szczepankiewicz et al., 2016). Biological validation studies have also shown plausible associations between imaging biomarkers of water exchange and the cell
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membrane permeability. Åslund et al (2009) demonstrated that the exchange rate detected by double diffusion encoding varied with temperature as expected, and Schilling et al (2016) showed that the expression of membrane channels co-transporting water increased the detected exchange rates, as expected. Similar causality-based biological validation tests have been performed also for IVIM, by
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subjecting volunteers to variable levels of hypercapnia-induced vasodilation, known to increase brain perfusion, and observing a concurrent change in the perfusion fraction (Federau et al., 2012). In general, however, too few studies have tested the technical, biological, and clinical validity of
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imaging biomarkers from methods based on biophysical models. Unmet clinical needs
From a clinical perspective, there are also numerous challenges. For example, reduced diffusion after treatment is typically associated with viable tumour and progressive disease, but it can also be the result of successful bevacizumab treatment (Mong et al., 2012). This challenge may potentially be
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addressed by incorporating perfusion data and the spatial extent of the region with restricted diffusion (Farid et al., 2013). Early prediction of tumour response to treatment is another clinically important challenge, and the parametric response maps has shown promise (Ellingson et al., 2010; Galbán et al., 2009; Moffat et al., 2005). However, the approach relies on accurate image registration of pre- and
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post-treatment image volumes. This can be challenging when there are geometric distortions and mass effects (Ellingson et al., 2012). A potential solution, apart from improving image registration, may be
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to model and predict tumour growth using functional information on cell proliferation and hypoxia on addition to microstructure information (Atuegwu et al., 2012). Yet another challenge is the grading of glioma, in particular separating between grade II and grade III gliomas. Here, multi-parametric approaches including both spectroscopy, diffusion, and perfusion may be helpful (Caulo et al., 2014; Di Costanzo et al., 2006), and integrating these into a joint microstructure analysis framework would probably enable faster acquisitions. DKI has also shown promise in this regard (Falk Delgado et al., 2018). Finally, infiltration of low-grade glioma can be very subtle, and low concentration of tumour cells can be found far beyond the regions where there are changes in morphological MRI sequences (Zetterling et al., 2016). More accurate imaging techniques are thus warranted to detect low levels of tumour cells scattered around the main tumour, which would address unmet neurosurgical needs regarding determination of tumour resection regions.
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Conclusions Microstructure imaging techniques aim to inform researchers, oncologists and radiologists about tissue features on the cell level without relying on invasive procedures. A simple, yet powerful, example is the relationship between the ADC and cellularity, which can be used to detect dense tumours, as well as to probe the efficacy of treatment over time. As a true measure of cellularity,
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however, the ADC remains inadequate because it is confounded by unrelated tissue features, and depend on the experimental setup. Multidimensional microstructure imaging techniques that encode more information and could together with microstructure modelling provide imaging biomarkers that report directly on tissue quantities, with negligible dependency on the experimental design within
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defined limits. Examples of such techniques use variable diffusion time to probe the cell sizes; multiple b-tensor shapes to separate cell shapes from orientation dispersion; filter exchange imaging to estimate the effects of exchange; and variable echo and repetition times to facilitate estimation of
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compartmental proton densities rather than relaxation-weighted signal fractions. Microstructure imaging will reach maturity when all relevant effects are identified and quantified accurately from the MRI data. Progress requires more clinical data, and comprehensive validation studies to verify that the estimated parameters correspond to the intended microstructure features in a reproducible and robust fashion. Although “virtual biopsy” is a challenge yet to be met, emerging techniques have already provided more specific microstructure parameters than what can be obtained from ADC
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quantification alone.
Funding information
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This research was supported by the Swedish Research Council (grant no. 2016-03443), the Swedish Foundation for Strategic Research (grant no. AM13-0090), Crafoord foundation (grant no. 20160990), the Swedish Cancer Society (grant no. CAN2016/365), and Random Walk Imaging AB
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(grant no. MN15).
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Resonance Medicine 65, 1532–1556. Tozer, D.J., Jäger, H.R., Danchaivijitr, N., Benton, C.E., Tofts, P.S., Rees, J.H., Waldman, A.D., 2007. Apparent diffusion coefficient histograms may predict low-grade glioma subtype. NMR Biomed 20, 49–57. doi:10.1002/nbm.1091 Ulloa, P., Methot, V., Koch, M.A., 2017. Experimental validation of a bias in apparent exchange rate measurement. Current Directions in Biomedical Engineering 3. doi:10.1515/cdbme-2017-0112 Uluğ, A.M., van Zijl, P.C., 1999. Orientation-independent diffusion imaging without tensor diagonalization: anisotropy definitions based on physical attributes of the diffusion ellipsoid. J Magn Reson Imaging 9, 804–813. Van Cauter, S., Veraart, J., Sijbers, J., Peeters, R.R., Himmelreich, U., De Keyzer, F., Van Gool, S.W., Van Calenbergh, F., De Vleeschouwer, S., Van Hecke, W., Sunaert, S., 2012. Gliomas: diffusion kurtosis MR imaging in grading. Radiology 263, 492–501. doi:10.1148/radiol.12110927 Vandendries, C., Ducreux, D., Lacroix, C., Ducot, B., Saliou, G., 2014. Statistical analysis of multi-b factor diffusion weighted images can help distinguish between vasogenic and tumor-infiltrated edema. J Magn Reson Imaging 40, 622–629. doi:10.1002/jmri.24399 Veraart, J., Novikov, D.S., Fieremans, E., 2017. TE dependent Diffusion Imaging (TEdDI) distinguishes between compartmental T2 relaxation times. NeuroImage. doi:10.1016/j.neuroimage.2017.09.030 Walbert, T., Mikkelsen, T., 2011. Recurrent high-grade glioma: a diagnostic and therapeutic challenge. Expert Rev Neurother 11, 509–518. doi:10.1586/ern.11.37 Waldman, A.D., Jackson, A., Price, S.J., Clark, C.A., Booth, T.C., Auer, D.P., Tofts, P.S., Collins, D.J., Leach, M.O., Rees, J.H., National Cancer Research Institute Brain Tumour Imaging Subgroup, 2009. Quantitative imaging biomarkers in neuro-oncology. Nature Publishing Group 6, 445–454. doi:10.1038/nrclinonc.2009.92 Wang, L., Caprihan, A., Fukushima, E., 1995. The narrow-pulse criterion for pulsed-gradient spinecho diffusion measurements. J Magn Reson A 117, 209–219. Wen, Q., Kelley, D.A.C., Banerjee, S., Lupo, J.M., Chang, S.M., Xu, D., Hess, C.P., Nelson, S.J., 2015. Clinically feasible NODDI characterization of glioma using multiband EPI at 7 T. Neuroimage Clin 9, 291–299. doi:10.1016/j.nicl.2015.08.017 Westin, C.-F., Knutsson, H., Pasternak, O., Szczepankiewicz, F., Ozarslan, E., van Westen, D., Mattisson, C., Bogren, M., O'Donnell, L.J., Kubicki, M., Topgaard, D., Nilsson, M., 2016. Qspace trajectory imaging for multidimensional diffusion MRI of the human brain. NeuroImage 135, 345–362. doi:10.1016/j.neuroimage.2016.02.039 Westin, C.F., Szczepankiewicz, F., Pasternak, O., Özarslan, E., Topgaard, D., Knutsson, H., Nilsson, M., 2014. Measurement Tensors in Diffusion MRI: Generalizing the Concept of Diffusion Encoding. Med Image Comput Comput Assist Interv 8675, 209–216. Wetscherek, A., Stieltjes, B., Laun, F.B., 2014. Flow-compensated intravoxel incoherent motion diffusion imaging. Magn Reson Med 74, 410–419. doi:10.1002/mrm.25410 Whittall, K.P., MacKay, A.L., Graeb, D.A., Nugent, R.A., Li, D.K., Paty, D.W., 1997. In vivo measurement of T2 distributions and water contents in normal human brain. Magnetic Resonance Medicine 37, 34–43. Wimsatt, W., 1987. False Models as Means to Truer Theories, in: Neutral Models in Biology. pp. 23– 55. Winfeld, M., Jensen, J., Adisetiyo, V., Fieremans, E., Helpern, J., Karajannis, M., Allen, J., Gardner, S., Milla, S., 2013. Differentiating high and low grade pediatric brain tumors using diffusional kurtosis imaging. Journal of Pediatric … 2, 301–305. doi:10.1007/s00330-009-1493-4 Xu, J., Li, H., Harkins, K.D., Jiang, X., Xie, J., Kang, H., Does, M.D., Gore, J.C., 2014. Mapping mean axon diameter and axonal volume fraction by MRI using temporal diffusion spectroscopy. NeuroImage 103C, 10–19. doi:10.1016/j.neuroimage.2014.09.006 Yablonskiy, D.A., Bretthorst, G.L., Ackerman, J.J.H., 2003. Statistical model for diffusion attenuated MR signal. Magn Reson Med 50, 664–669. doi:10.1002/mrm.10578 Yablonskiy, D.A., Sukstanskii, A.L., 2010. Theoretical models of the diffusion weighted MR signal. NMR Biomed 23, 661–681. Yamasaki, F., Kurisu, K., Satoh, K., Arita, K., Sugiyama, K., Ohtaki, M., Takaba, J., Tominaga, A., 35
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Hanaya, R., Yoshioka, H., Hama, S., Ito, Y., Kajiwara, Y., Yahara, K., Saito, T., Thohar, M.A., 2005. Apparent diffusion coefficient of human brain tumors at MR imaging. Radiology 235, 985–991. doi:10.1148/radiol.2353031338 Yamashita, K., Hiwatashi, A., Togao, O., Kikuchi, K., Kitamura, Y., Mizoguchi, M., Yoshimoto, K., Kuga, D., Suzuki, S.O., Baba, S., Isoda, T., Iwaki, T., Iihara, K., Honda, H., 2016. Diagnostic utility of intravoxel incoherent motion mr imaging in differentiating primary central nervous system lymphoma from glioblastoma multiforme. J Magn Reson Imaging 44, 1256–1261. doi:10.1002/jmri.25261 Zetterling, M., Roodakker, K.R., Berntsson, S.G., Edqvist, P.-H., Latini, F., Landtblom, A.-M., Pontén, F., Alafuzoff, I., Larsson, E.-M., Smits, A., 2016. Extension of diffuse low-grade gliomas beyond radiological borders as shown by the coregistration of histopathological and magnetic resonance imaging data. J Neurosurg 1–12. doi:10.3171/2015.10.JNS15583 Zhang, H., Schneider, T., Wheeler-Kingshott, C.A., Alexander, D.C., 2012. NODDI: practical in vivo neurite orientation dispersion and density imaging of the human brain. NeuroImage 61, 1000– 1016. doi:10.1016/j.neuroimage.2012.03.072 Zhang, J., van Zijl, P.C.M., Laterra, J., Salhotra, A., Lal, B., Mori, S., Zhou, J., 2007. Unique patterns of diffusion directionality in rat brain tumors revealed by high-resolution diffusion tensor MRI. Magn Reson Med 58, 454–462. doi:10.1002/mrm.21371
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Figure 1. Distribution of primary brain tumours, by type (left) and gliomas by subtype
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(right). Data were compiled from Ostrom et al (2014).
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Figure 2. Clinical MRI, of a WHO grade IV glioblastoma, showing a T2W image (A), gadolinium enhanced T1W image (B), FLAIR image
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(C), and an ADC map (D).
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Figure 3. Histology examples from brain tumours, showing HE staining unless indicated otherwise. (A) Diffuse astrocytoma infiltrating white matter exhibiting oedema and mild reactive gliosis. Bottom panel shows a magnified part of the top panel. (B) Glioblastoma with high cell density (top) and highly variable cell density (bottom), the latter with necrosis and thromb-occluded vessels. (C) Fibroblastic meningioma showing elongated cell structures that run in different directions.
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(D) Meningioma with brain invasion as depicted by GFAP staining (top) and HE staining (bottom), which also show reactive
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gliosis adjacent to the protruding tumour noduli. Notice the large heterogeneity in cell structures between the four examples.
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Figure 4. Overview of dMRI methods, showing relationships between MR signal intensity, encoding strategy, microstructure features. Methods A-D are based on conventional diffusion encoding that vary the diffusion-encoding strength b by increasing the amplitudes of the encoding gradients (blue in panel A). Higher b-values result in stronger signal
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attenuation and a change in image contrast (A, inset). The signal-versus-b curve from a tumour region shows a distinct pattern that can be used to compute different parameters. The apparent diffusion coefficient (ADC) is assessed from the slope of the signal attenuation curve at low a b-value, often 1000 s/mm2 (panel B). Diffusional kurtosis imaging utilizes higher bvalues, and assess the departure of the signal curve from monoexponential attenuation (panel C; blue region between dashed and solid line). The intra-voxel incoherent motion approach estimates the perfusion fraction (f) from the small overshoot of
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the signal at low b-values (panel D, red region in inset). Methods E-G go beyond conventional dMRI and also varies the diffusion time (distance between blue gradients). The separation of the curves between short and long diffusion times (td) can be used to assess cell sizes (panel E), however, this separation vanishes for small sizes (F) and there is therefore a minimal
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size that can be accurately assessed—referred to as the resolution limit (Nilsson et al., 2017). Increasing the diffusion time in presence of membrane permeability and water exchange has the opposite effect on the signal compared to that of restricted diffusion (panel G), which can give rise to a degenerate problem that can be solved by double diffusion encoding (Lasič et al., 2011). Panels H–J show three cases that may appear identical with conventional DKI, but that can be distinguished by tensor-valued diffusion encoding. Panel H shows signal-versus-b curves from a system comprised of randomly oriented and elongated cells, similar to a meningioma sample (top, colour-coded FA). The curves diverge for so-called linear tensor encoding (upper curve) and spherical-tensor encoding (lower curve). Panel I shows a case where the linear and spherical tensor encoded curves overlap because the system was comprised of isotropic diffusion tensors only (panel I, bottom right). This represents the situation in a glioma, which shows considerable variation in ADC within a small region as evidenced from magnetic resonance microscopy (Panel I, top right), from (Gonzalez-Segura et al., 2011). Panel J show a case where the curvature (‘kurtosis’) in the upper signal curve is due to both microscopic anisotropy (green) and isotropic heterogeneity (yellow), where tensor-encoding can be used to disentangle the separate contributions.
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Figure 6. Pre-surgical tractography. Thalamic or basal ganglia tumours and positions of the pyramidal tract. The left column show the tumour location types. The right column demonstrates the relative positions of the dislocated pyramidal
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tract. Green circles indicate tumours and purple circles indicate the tract location. The middle three columns show typical cases. This type of analysis may aid surgeons in determining the location of the pyramidal tract preoperatively. Reproduced
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from Hou et al (2012).
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Figure 5. Parametric response mapping. MRI is performed both before and after treatment, after which the image volumes
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are coregistered. The response map can be computed for different parameters and here it is shown for the ADC. It shows regions in which there were no substantial change in ADC in green, substantial decrease post treatment in blue, increase in red. The fractional volumes of ADC increase and decrease may predict treatment response already weeks after treatment
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initiation (Moffat et al., 2005). Figure courtesy of Björn Lampinen.
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Figure 7. Morphological MRI and DKI in a glioblastoma patient. The first two techniques provide morphological images,
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whereas DKI provides quantitative parameter maps.
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Figure 8. Separation of kurtosis components by diffusional variance decomposition (DIVIDE).
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parameter maps of the total, anisotropic and isotropic kurtosis (MKT, MKA, MKI, respectively) in meningioma and glioma tumours, along with the signal-versus-b curves observed in the tumours. The separation between signal curves acquired with
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linear tensor encoding (LTE) and spherical tensor encoding (STE) in the meningioma suggests a high diffusional anisotropy. No such separation is seen in the glioma, although both LTE and STE are curved, indicating a high isotropic variance. This showcases that tumours may appear similar when considering only conventional diffusion encoding (LTE), but that they can be distinguished when employing different shapes of the b-tensor (LTE vs STE). Panel B shows quantitative microscopy of the corresponding tissue, where the meningioma exhibits high structure anisotropy due to its elongated cell structures,
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whereas the glioma shows a high variability in cell density—both features are congruent with the results seen in dMRI. In panel C, the microscopic anisotropy and isotropic heterogeneity estimated from dMRI and quantitative microscopy are compared. The resulting parameters exhibit a strong correlation across the different tumours. The association indicates that
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the kurtosis components MKA and MKI reflect specific and separate features of the tissue. These features cannot be decomposed by conventional DKI based on LTE only. The figure was adapted from Szczepankiewicz et al. (2016) published by Elsevier.
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Figure 9. Parameter maps from IMPULSED, in a colorectal xenograft model, from Jiang et al (2016). Top row shows HE stained histological images. Other maps show conventional ADC map, and IMPULSED-derived parametric maps overlaid on T2weighted MR images. These comprise apparent cellularity in terms of the MRI-derived density, the cell size, intracellular volume fraction, extracellular diffusivity, intracellular diffusivity, and extracellular structural coefficient βex.
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Figure 10. Filter exchange imaging, is based on a double diffusion encoding sequence (panel A). An initial diffusion filter is followed by a mixing block, and finally, a detection block used to observe the ADC. Image acquisition is done using echo-planar imaging (EPI). The magnetization is stored longitudinally during the mixing block, which enables the use of long mixing times without substantial signal loss. Panel B illustrates the principles
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of the FEXI protocol. Intracellular water exhibit slow diffusion (red), whereas extracellular water exhibit fast diffusion (blue). Application of the diffusion filter preferentially attenuates the extracellular water component, leading to a reduction of the observed ADC (dashed line). Subsequent exchange during the mixing leads to a gradual reappearance of signal-bearing water in the extracellular space. With increasing mixing time, the ADC thus approaches its equilibrium value, with a rate given by the AXR. Panel C show images from a typical
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meningioma (top), atypical meningioma (middle), and a glioma (bottom). Left column shows T1W-images, and
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the right column AXR parameter maps. Modified from Nilsson et al (2013) and Lampinen et al (2017).
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Figure 11. Example of IVIM in a glioblastoma patient. Panels A–C show an axial T2-weighted image, T1-weighted post
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gadolinium, and cerebral blood volume from DSC-MRI. Panels D–F show IVIM parameter maps of the perfusion fraction (f), the apparent diffusivity of the pseudodiffusing blood (D*), and the product between the two. Panel G show a signalversus-b curve where the perfusion fraction is shown as the signal overshoot at low b-values. Adapted from Federau et al (2014).
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Conflict of interest statement MN declares research support from Random Walk Imaging (formerly Colloidal Resource), and patent applications in Sweden (1250453-6 and 1250452-8), USA (61/642 594 and 61/642 589), and PCT (SE2013/050492 and SE2013/050493). FS has been employed at Random Walk Imaging. Remaining
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authors declare no conflict of interest.
S1053-8119(18)30395-1
DOI:
10.1016/j.neuroimage.2018.04.075
Reference:
YNIMG 14922
To appear in:
NeuroImage
Received Date: 19 May 2017 Revised Date:
27 April 2018
Accepted Date: 30 April 2018
Please cite this article as: Nilsson, M., Englund, E., Szczepankiewicz, F., van Westen, D., Sundgren, P.C., Imaging brain tumour microstructure, NeuroImage (2018), doi: 10.1016/j.neuroimage.2018.04.075. This is a PDF file of an unedited manuscript that has been accepted for publication. As a service to our customers we are providing this early version of the manuscript. The manuscript will undergo copyediting, typesetting, and review of the resulting proof before it is published in its final form. Please note that during the production process errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain.
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Imaging brain tumour microstructure
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Markus Nilssona, Elisabet Englundb, Filip Szczepankiewiczc, Danielle van Westena, d, Pia C Sundgrena a
Clinical Sciences Lund, Radiology, Lund University, Lund, Sweden
b
Division of Oncology and Pathology, Department of Clinical Sciences, Lund, Lund University,
Skåne University Hospital, Lund, Sweden CR Development AB, Lund, Sweden
d
Image and Function, Skåne University Hospital, 22185 Lund, Sweden
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Corresponding author Markus Nilsson
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Lund, Sweden
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Lund University
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Clinical Sciences Lund Department of Radiology
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c
Email: [email protected] Telephone: +46 70 25 23 745
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ACCEPTED MANUSCRIPT Abstract Imaging is an indispensable tool for brain tumour diagnosis, surgical planning, and follow-up. Definite diagnosis, however, often demands histopathological analysis of microscopic features of tissue samples, which have to be obtained by invasive means. A non-invasive alternative may be to probe corresponding microscopic tissue characteristics by MRI, or so called ‘microstructure imaging’.
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The promise of microstructure imaging is one of ‘virtual biopsy’ with the goal to offset the need for invasive procedures in favour of imaging that can guide pre-surgical planning and can be repeated longitudinally to monitor and predict treatment response. The exploration of such methods is motivated by the striking link between parameters from MRI and tumour histology, for example the correlation between the apparent diffusion coefficient and cellularity. Recent microstructure imaging
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techniques probe even more subtle and specific features, providing parameters associated to cell shape, size, permeability, and volume distributions. However, the range of scenarios in which these
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techniques provide reliable imaging biomarkers that can be used to test medical hypotheses or support clinical decisions is yet unknown. Accurate microstructure imaging may moreover require acquisitions that go beyond conventional data acquisition strategies. This review covers a wide range of candidate microstructure imaging methods based on diffusion MRI and relaxometry, and explores
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advantages, challenges, and potential pitfalls in brain tumour microstructure imaging.
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Introduction Tumours in the brain and the central nervous system are found in approximately 250 000 patients yearly across the world (Ferlay et al., 2015), with an age-adjusted incidence rate in adults of approximately 25 in 100 000 in the USA (Ostrom et al., 2014). Brain metastases are approximately half as common (Smedby et al., 2009; Stelzer, 2013). Among primary intracranial tumours, the most
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common types are meningiomas and gliomas (Fig. 1). Meningioma tumours are often curable by gross resection, and the five-year survival rate is approximately 65% (Ostrom et al., 2014). Glioma treatment and survival depends on the subtype (Ricard et al., 2012), with five-year survival rates of 94% for pilocytic astrocytomas to only 5% for glioblastomas (Ostrom et al., 2014). Survival for
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patients with brain metastases is shorter than for those with primary brain tumours (Nayak et al., 2012).
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Imaging plays a pivotal role in brain tumour diagnosis, surgical planning, and follow-up. The initial work-up for suspected brain malignancy consists primarily of computed tomography (CT) due to ease of access, but magnetic resonance imaging (MRI) is the standard imaging modality for brain tumours. Clinical protocols yield morphological images and typically include T2-weighted (T2W), fluidattenuated inversion recovery (FLAIR), and gadolinium-enhanced T1-weighted (Gd-T1w) imaging. FLAIR and T2W outline the tumour lesion and oedema, while gadolinium enhancement on the GdT1w contrast shows regions of blood-brain-barrier disruption (Fig. 2). This type of morphological
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imaging is often the basis for primary diagnosis of brain tumours, however, detailed characterisation such as grading can be challenging by morphological imaging only. For example, some high-grade gliomas may not demonstrate the expected gadolinium enhancement, while low-grade gliomas occasionally do (Scott et al., 2002). Approximately 10% of glioblastoma and 30% of anaplastic
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astrocytomas lack gadolinium enhancement. Therefore, imaging may be insufficient for definitive diagnosis of all brain tumours, which motivates biopsies and histological examination, in particular
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for gliomas (Dhermain et al., 2010; Waldman et al., 2009). Biopsy-based histology is thus critical for tumour diagnosis, although ensuring that biopsies are obtained from the most relevant tissue can be challenging (Jackson et al., 2001). The development of new treatment techniques pose further challenges to clinical imaging (Walbert and Mikkelsen, 2011). For example, concurrent treatment, often with radiotherapy and chemotherapy, is associated with so called pseudo-progression (Kruser et al., 2013), where imaging may misleadingly suggest tumour progression due to a transient increase in size and/or a brighter appearance than on pre-treatment MRI (Hygino da Cruz et al., 2011). Conversely, bevacizumab treatment can lead to pseudo-response, where imaging indicates reduced oedema and gadolinium enhancement despite an actual tumour progression (Hygino da Cruz et al., 2011). Gamma knife
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ACCEPTED MANUSCRIPT therapy is associated with a high incidence of radiation necrosis (Korytko et al., 2006), which has similar morphological characteristics as recurrent tumour (Kruser et al., 2013). Imaging techniques that go beyond conventional morphological MRI may overcome these challenges and microstructure imaging by MRI has been proposed as a candidate for this. Microstructure MRI characterizes tissue preoperatively in situ and provides images of the whole tumour rather than of a
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few biopsy samples and, as such, it can avoid mistakes from inadequately targeted biopsy. It may also improve diagnosis by guiding the biopsy and might even replace a biopsy in situations where these are too risky. Moreover, microstructure MRI can be repeated over time and facilitates longitudinal monitoring without elevated risk. In this review, we will provide an overview of histopathology of intracranial tumours and review non-invasive MRI techniques that enable mapping of quantities or
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imaging biomarker related to tissue microstructure. Microstructure imaging is a field of rapid development, and we will cover the current directions and state-of-the-art examples, and outline
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challenges to be addressed by future research.
Histopathological assessment and tumour typing For intra vitam (‘during life’) diagnosis by microscopy, tumour tissue must be obtained by either biopsy or tumour resection (as part of tumour reduction). Tissue is generally provided fresh, frozen, or
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fixed in 4% formaldehyde solution, cut in representative portions, and embedded in paraffin. Sections with a thickness of 4 µm are then processed and stained to visualize microscopic features of the tissue, as described below.
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Staining
Hematoxylin and eosin (HE) staining highlights cell membranes, cytoplasm, and nuclei (Fig. 3). In
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gliomas, the tumour cells are delineated. Vessels and components of bleeding, fibrosis, and necrosis are also visualized. Inflammatory activity, as shown by lymphocytic infiltrates, may also be seen. Cell proliferation, indicating tumour activity and growth potential, is estimated by mitotic counts. For meningiomas, the Elastica Van Gieson (EVG) staining demonstrates vital tumour vis-a-vis fibrous tissue and adjacent brain. The staining is relevant for detection of meningioma infiltration of either the dura, the skull or inwards to the brain, the latter being important since brain invasion alone connotes an atypical meningioma of WHO grade II (Louis et al., 2016). EVG can also depict tumour invasion of vessels, which reflects an accelerated tumour growth and serves as a warning of explosive spread. The tumour grading is further corroborated by the marker for cell cycle activity Ki67 that identifies all cells but the G0 stage (resting) cells – hence indicating the level of proliferation in the
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ACCEPTED MANUSCRIPT tumour. Most normal glial cells can be identified by the antibody against glial fibrillary acidic protein (GFAP), although there are important exceptions (Reifenberger et al., 1987). The GFAP staining also visualizes brain invasion in meningiomas, because these tumours do not express glial marker features and thus stand out negatively against a background of positive brain tissue (Fig. 3D). Immunostainings and molecular analyses have recently become important for glioma diagnostics. A
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reason is that although glioma presence can be certified with a predominantly positive GFAP staining, the degree of malignancy in high grade gliomas does not correlate well with number of proliferating cells, as shown by Ki67 and number of mitoses. This is because most of the cell population may be in transition to cell death and no longer proliferating, despite of or resulting from the tumour being
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highly malignant. Immunostainings such as ATRX, TP53, IDH1, BRAF V600E, and H3K27M can then be used to enhance the diagnostic potential. These stainings point to different pathogenetic steps in tumour development and can hence guide the choice of specific treatment strategies. For example,
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the staining against antigen H3K27M can reveal a specific glioma subtype associated with a worse prognosis than other similar gliomas (Buczkowicz et al., 2014). Molecular analyses can further complement immunostainings for full diagnosis by enabling identification of one of several possible IDH mutations. For example, a complete co-deletion in 1p19q will reveal an oligodendroglioma in a sample that in the pathologist's eyes is an astrocytoma (Capper et al., 2011), hence altering both the prognosis and the therapeutic plan.
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Cell organisation and tissue structure
Glioma microstructure varies considerably between and within each type and malignancy grade (Fig. 3). Low grade gliomas are often composed of groups of loosely scattered cells insidiously infiltrating
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the surrounding brain (Zetterling et al., 2016). There, a mild reactive gliosis can be perceived by the presence of large reactive astrocytes with symmetrically branching extensions and homogenous nuclei
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that attest the non-tumour quality of these glial cells. More intense gliosis—and oedema seen with HE staining as the presence of small microvacuoles in the matrix between cells—generally indicates high grade glioma. In contrast to the diffuse low grade gliomas, high grade gliomas often have a central core of more or less compact tumour with a border pushing against, and compressing the surroundings – a feature explained by rapid tumour growth. However, despite having a tumour core, high grade gliomas may exhibit a loose structure with seemingly low cell cohesivity (Fig. 3B, bottom). This is not only due to necrosis, but also due to grouped assembling of small cells on the one hand, and assembling of large multinuclear bizarre cells on the other. The latter can have cytoplasms 30–40 times larger than those of neighbouring small tumour cells. The lack of tissue cohesivity points to a variety of cell clones. Gliomas can also be indicated by proliferation of tumour vessels, which are often malfunctioning leading to leakage of plasma, proteins, and blood.
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ACCEPTED MANUSCRIPT Meningioma morphology also varies between subtypes, but less so within each type (Fig. 3C–D). The structural subtypes, with some correspondence to malignancy degree, range from compact and hard tissue filled with cell-depleted collagen and calcification between scattered tumour cells, via cell-rich tumours full of spindle-formed cells in packed bundles, to loose architecture of less cohesive cells forming papillary or even glioma-like patterns (see Bi et al., 2016). Proliferation marker in a biopsy of a meningioma relates more closely to malignancy degree than for gliomas. For example, malignant
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meningiomas with necrosis and increased number of mitoses have higher Ki67 indices than the benign ones. However, there are exceptions: meningiomas that exhibit brain invasion behaviour (Fig. 3D) are since 2016 regarded as of intermediate malignance grade even in the absence of other features
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of malignancy (Louis et al., 2016).
Candidate microstructure imaging techniques
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We will here review methods that yield parameter maps associated to features of the microscopic structure of tissue. This type of microstructure imaging make use of diffusion and relaxation-weighted MRI. However, MRI itself produces only signal intensities. Parameter maps are obtained from these by solving an inverse problem, in which a number of parameters are estimated. Because the number of ways the tumour microstructure can vary is large, the problem is often ill posed meaning that we cannot necessarily recover all relevant features of the tumour microstructure in the estimated
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parameters. We thus refer to the reviewed set of methods as “candidate” techniques to acknowledge that the methods may need further theoretical, technical, biological, and clinical validation. Four aspects will be considered for each method: (i) key assumptions and their justifications, (ii) the requirements on the acquisition protocol, (iii) the level of evidence for associating the estimated
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parameters to features of tumour tissue quantified by independent techniques such as microscopy, and (iv) the scientific and clinical usefulness of the technique. Finally, we will discuss challenges to be addressed by future research: model validity, the use of parameters as imaging biomarkers, and unmet
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clinical needs.
Cellular microstructure by diffusion MRI Diffusion MRI (dMRI) probes tissue microstructure by measuring effects on the MR signal intensity from water diffusion with magnetic field gradients. A plethora of different methods have been developed to quantify dMRI data: quantification of the apparent diffusion coefficient (ADC) (Le Bihan et al., 1986), diffusion tensor imaging (DTI) (Basser et al., 1994), diffusional kurtosis imaging (DKI) (Jensen et al., 2005), diffusional variance decomposition (DIVIDE) (Lasič et al., 2014; Szczepankiewicz et al., 2016), composite hindered and restricted model of diffusion (CHARMED) (Assaf and Basser, 2005), axon diameter imaging techniques (D. C. Alexander et al., 2010; Assaf et al., 2008), neurite orientation and density imaging (NODDI) (H. Zhang et al., 2012), to name a few. 6
ACCEPTED MANUSCRIPT These methods fall into two broad categories that use what we will refer to as “signal representations” and “biophysical models”, inspired by the nomenclature in (Novikov et al., 2018). Methods using signal representations include, for example DTI and DKI, and make few, or no, assumptions about the tissue composition, but provide descriptive statistics of the diffusion process (Yablonskiy and Sukstanskii, 2010). Such methods are not constructed with the intent of capturing specific microstructure parameters, but are reviewed here because of the large amount of studies correlating
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their parameters to microstructure features in tumours and their potential use to provide imaging biomarkers. The other class of methods use biophysical models constructed with the intent of enabling estimation of explicit microstructure features such as the intracellular volume fraction, and may offer the most direct route towards microstructure imaging of tumours. Although promising,
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there are still few applications in brain tumours. Diffusion tensor imaging
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Brain tissue exhibits anisotropy, meaning that the ADC depends on the direction of the diffusion encoding. This anisotropy can be analysed with DTI, which provides a measure of the degree of anisotropy in terms of the fractional anisotropy (FA) in addition to a directionally-averaged ADC known as the mean diffusivity (MD) (Basser and Pierpaoli, 1996). Analysis of the FA in the brain has become widely used in neuroscience (Jones et al., 2012), but its role in tumour imaging is less clear because the FA does not quantify diffusion anisotropy at the microscopic level but rather at the
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“macroscopic” voxel level. Hence, the FA is a product of both microscopic anisotropy and orientation coherence (A. L. Alexander et al., 2001; Szczepankiewicz et al., 2015). Since both healthy brain tissue and brain tumours exhibit high orientation dispersion within typical imaging voxels (Jeurissen et al., 2012; Szczepankiewicz et al., 2016; J. Zhang et al., 2007), the FA is not a specific measure of
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microscopic diffusion anisotropy and will thus not pass our mark of being a specific microstructure parameter. In special cases, however, detection of the microscopic diffusion anisotropy either by high-
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resolution DTI or so-called b-tensor encoding can be used to quantify relevant microstructure features in both glioma and meningioma tumours (Szczepankiewicz et al., 2016; J. Zhang et al., 2007). Diffusion anisotropy also serves as the basis of tractography, which reconstructs streamlines that reveal the location of nerve fibres bundles in the brain (Ciccarelli et al., 2008; Mori and van Zijl, 2002), with potential applications in neurosurgical planning (Dimou et al., 2013; Potgieser et al., 2014). Here, the goal is to inform the surgeon on the location of important nerve fibres relative to the tumour (e.g. Fig. 6) so that damage to vital functions can be minimised (Coenen et al., 2001; Hou et al., 2012; Romano et al., 2009). However, the accuracy of DTI-based tractograpy is limited in regions with crossing fibres, but techniques using higher b-values and high angular resolution can address this problem (Frank, 2001; Tournier et al., 2011) and can contribute to more accurate presurgical planning (McDonald et al., 2013; Mormina et al., 2015). 7
ACCEPTED MANUSCRIPT Cellularity and the apparent diffusion coefficient The simplest—and arguably the most common—dMRI method determines the so-called ADC parameter by assuming that the diffusion-weighted signal follows a mono-exponential attenuation (Le Bihan et al., 1986; Stejskal and Tanner, 1965) (1)
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S = exp(–b ADC).
Quantification of the ADC is thus remarkably simple (Fig. 4B). In the presence of anisotropy, a rotationally invariant ADC can be obtained by averaging it across at least three orthogonal encoding directions (Basser and Pierpaoli, 1996; Uluğ and van Zijl, 1999), or obtained as the MD from DTI.
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Without any further mathematical modelling, it is natural to hypothesise that dense tissue with high cellularity and a reduced interstitial space has a lower apparent diffusivity than a tissue with low cellularity. This hypothesised association between the ADC and tumour cellularity has been observed
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in several studies (Barajas et al., 2010; Chenevert et al., 2000; Doskaliyev et al., 2012; Ellingson et al., 2010; Gauvain et al., 2001; Ginat et al., 2012; Gupta et al., 2000; Hayashida et al., 2006; Kono et al., 2001; Matsumoto et al., 2009; Sugahara et al., 1999), although contradictory findings have also been reported (Jenkinson et al., 2009; Sadeghi et al., 2008). A meta-analysis by Chen et al (2013a) found an average correlation coefficient of r = –0.57 across 28 studies for the relationship between the ADC and the cellularity, determined ex situ, of non-treated human tumours (of both the brain and
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other organs). ADC thus has a clear association to the tumour microstructure. However, a multiplicity of mechanisms other than cellularity are known to also influence the ADC (Morse et al., 2007), including membrane permeability (Badaut et al., 2011). To disentangle the different microstructural
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contributions to the ADC, more sophisticated methods are warranted. Two principal applications of ADC quantification have been investigated: treatment monitoring, and tumour differentiation. Treatment monitoring addresses the clinical need for early detection of
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treatment efficacy, and utilizes the fact that ADC responds to changes in tumour cellularity already days or weeks after initiation of treatment (Chenevert et al., 2000), in contrast to volumetric changes which manifest much later. Effective treatment causes necrosis or cell lysis. Both reduce the cellularity, and result in increased ADC. The ADC may thus be a marker for treatment efficacy (Mardor et al., 2003; Ross et al., 2003). However, the relationship between treatment-induced apoptosis and ADC response may be complex (Morse et al., 2007), and brain tumours are often heterogeneous (Fig. 2, Fig. 3) which can make ADC assessments unreliable. The so-called functional diffusion map was proposed as a solution to this problem (Moffat et al., 2005). In this approach, posttreatment parameter maps are registered to pre-treatment maps, and the fractional volume of positive and negative ADC change following treatment is assessed (Fig. 5). Large volumes with ADC increases were indicative of successful treatment (Moffat et al., 2005). The approach, which has also 8
ACCEPTED MANUSCRIPT been referred to as parametric response mapping (PRM) (Galbán et al., 2009), was covered in a recent review (Galban et al., 2017). Tumour differentiation can, in some cases, be done based on the ADC alone. For example, ADC values of dysembryoplastic neuroepithelial tumours are substantially higher than those of more common tumours: 2.55±0.14 µm2/ms, compared to 1.53±0.15 µm2/ms for grade II astrocytomas or
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1.08±0.16 µm2/ms for grade IV glioblastomas (Yamasaki et al., 2005). The ADC can also be used to separate tumour subgroups, albeit with lower sensitivity. For example, the minimum ADC in glioblastoma subgroup of astrocytomas were lower than in the anaplastic subgroup: 0.83±0.14 versus 1.1±0.2 µm2/ms (Higano et al., 2006). For glioma subtypes, small but detectable differences between
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low-grade astrocytomas and oligodendrocytomas have been reported: 1.17±0.17 versus 1.03±0.08 µm2/ms, for the 10th percentile of a whole-tumour histogram (Tozer et al., 2007).
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Diffusion kurtosis imaging
ADC quantification and DTI both rely on the use of relatively low b-values (approximately 1000 s/mm2), but the use of multiple b-values over a larger interval can improve tumour differentiation and monitoring (Falk Delgado et al., 2018; Kang et al., 2011; Vandendries et al., 2014). However, the signal does not decay monoexponentially as required for Eq. 1 to be valid and simple ADC quantification with high b-values will yield a parameter highly dependent on the experimental
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conditions (e.g. maximal b-value). Diffusional kurtosis imaging (DKI) is a natural extension of DTI (Jensen et al., 2005), that permits joint analysis of low and high b-value data (Fig 4C). In one dimension, the analysis is based on the following relation (Jensen et al., 2005; Yablonskiy et al.,
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2003)
S(b) = exp(–b MD + 1/6 b2 MD2 MK).
(2)
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This approach provides maps of the mean kurtosis (MK) in addition to the mean diffusion (MD; Fig. 7). In essence, the kurtosis captures the amount by which the signal departs from monoexponential attenuation (Fig. 4C). A tensor-based kurtosis analysis is also available (Jensen et al., 2005), which allows the assessment of the kurtosis in any direction, for example, the directions radial and axial to a nerve fiber (Hui et al., 2008). However, the difference between the radial and axial kurtosis is low in most brain tumours (Van Cauter et al., 2012) and assessment of axial and radial tensor components in tissues with low voxel-scale anisotropy, such as tumours, is prone to bias due to the so-called eigenvalue sorting problem (Basser and Pajevic, 2000; Martin et al., 1999). Assessment of the kurtosis tensor may thus not be particularly useful in brain tumours, except for the purpose of obtaining rotation invariant
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ACCEPTED MANUSCRIPT estimates of MK. This can be achieved by fast acquisition protocols for full tensor analysis (Hansen et al., 2013; Lätt et al., 2010; Tietze et al., 2015). DKI has been applied in the context of tumour grading. Raab et al (2010) reported gradually increasing values of MK from grade II astrocytomas, grade III astrocytomas, and glioblastomas, to normal appearing white matter (NAWM), spanning the range from 0.48±0.02 in the grade II tumours
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to 1.14±0.01 in NAWM (mean ± standard error). The progression towards higher MK with higher grade has also been reported by other studies (Raja et al., 2016; Van Cauter et al., 2012). Although not all studies find differences between grade II and grades III gliomas (Delgado et al., 2017), a recent meta-analysis showed that DKI has high diagnostic accuracy in separating low from high grade gliomas (Falk Delgado et al., 2018). Paediatric applications have also been investigated with DKI.
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values of from 0.62 to 0.97 in grade II and grade IV tumours.
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Winfeld et al (2013) reported MK values increasing with grade in paediatric brain neoplasm, with
Although the kurtosis tends to increase with tumour grade, the mean kurtosis is not specific to any single feature of the tissue microstructure. It is assessed from the deviation of monoexponential attenuation at higher b-values, but as Fig. 4E–G shows, this signal feature is affected by both experimental and tissue variables. Nevertheless, DKI parameters have been related to microstructure features of tumours with positive results. For example, MK in gliomas correlated with proliferation marker Ki-67, total vascular area, and tumour cell density (Li et al., 2016). To further understand the
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kurtosis, it is instructive to apply the notion that a voxel can be subdivided into smaller components, all with approximately Gaussian diffusion but with separate ADC values. This allows the kurtosis to be expressed as the normalized intra-voxel variance in ADC (VADC) (Jensen et al., 2005; Yablonskiy
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et al., 2003): MK = 3 VADC / MD2
(3)
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High VADC can arise from two distinct sources: anisotropy with orientation dispersion or intra-voxel variance in isotropic diffusivity (Eriksson et al., 2013; Lasič et al., 2014; Szczepankiewicz et al., 2016; Westin et al., 2016). Expressed in terms of microstructure, these effects originate from two separate sources: elongated cell structures with high orientation dispersion and heterogeneous cell density on the voxel level (see e.g. Fig. 3B, bottom), respectively (Szczepankiewicz et al., 2016). These two different microstructure features contribute to the kurtosis in different degrees in different types of tumours (Figure 8). Note that this analysis assumes that the intra-compartment kurtosis is small, which may only be conditionally true (Jespersen et al., 2017). The kurtosis can become more specific to the microstructure features by separating the two sources contributing to the VADC using so-called b-tensor encoding (Lasič et al., 2014; Topgaard, 2016; Westin
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ACCEPTED MANUSCRIPT et al., 2016; 2014). This approach utilizes custom gradient waveforms to shape the diffusion encoding b-tensor. Conventional diffusion encoding yields linear b-tensors, double diffusion with orthogonal gradients yields planar b-tensors, and custom gradient waveforms can yield arbitrary b-tensor shapes (Westin et al., 2016; 2014). Specificity to the kurtosis components is obtained by combining any two types of b-tensor shapes, such as linear and planar (Jespersen et al., 2013; Lawrenz et al., 2010) or linear and spherical (Lasič et al., 2014; Szczepankiewicz et al., 2016). The principle for separating
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kurtosis components with linear and spherical encoding is shown in Figure 4H and 4J, and is based on the idea that with spherical encoding, only variations in the isotropic diffusivity contribute to VADC, whereas with linear encoding, it also captures contributions from anisotropy. Formally, this enables separation of the isotropic kurtosis (MKI) from the anisotropic kurtosis (MKA) (Szczepankiewicz et
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al., 2016; Westin et al., 2016). These two components otherwise contribute to the total kurtosis according to
(4)
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MK = MKI + b∆2 MKA
where b∆ is the shape of the b-tensor. For conventional linear b-tensor encoding b∆ = 1, for spherical encoding b∆ = 0, and for planar encoding b∆ = –1/2 (Eriksson et al., 2015). These specific kurtosis components have been associated to specific features from histology: MKI to intra-voxel variation in cell density and MKA to the average structure anisotropy, e.g., cell eccentricity (Fig. 8C) (Szczepankiewicz et al., 2016). Also note the MKA parameter is a more specific marker of anisotropy
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than FA from DTI, because MKA is not conflated by orientation dispersion (Jespersen et al., 2013; Lasič et al., 2014; Szczepankiewicz et al., 2015).
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Stretched exponential
Methods other than DKI have also been used to analyse high b-value brain tumour data. Kwee et al (2010) applied the stretched exponential representation (Bennett et al., 2003) to estimate the
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distributed diffusion coefficient (DDC) and the hetereogeneity index (α) from high b-value data in high-grade gliomas, and found that α was lower in the tumours than in most of the normal brain tissue. Bai et al (2016) compared diffusion parameters obtained from multiple methods (e.g. ADC, DTI, DKI, stretched exponential), and found significant differences between glioma tumours of different grades in all parameters except FA. The best grading performance was found for α and MK. Biophysical models Methods that estimate parameters with a defined meaning, such as the intracellular volume fraction or cell sizes, are based on biophysical models. Each method comprises its own set of details, as reviewed previously (D. C. Alexander et al., 2017; Nilsson et al., 2013b; Reynaud, 2017), but most decompose
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ACCEPTED MANUSCRIPT the signal into separate components for the vascular (v), intracellular (i) and extracellular (e) spaces, and use a signal model given by S/S0 = fv Sv(·) + fi Si(·) + fe Se(·)
(5)
where fv, fi and fe are the signal fractions of vascular, intracellular and extracellular water,
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respectively, and Sv(·), Si(·), and Se(·) are functions describing the signal attenuation in the corresponding spaces. Some methods omit the vascular component, others add a component for cerebrospinal fluid or free water. Parameter estimation is performed by finding the model parameters, for example, fv, fi and fe and associated parameters describing corresponding signal functions, that best
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predict the acquired signal data.
A very simple type of biophysical model could be built by assuming the vascular fraction to be negligible (fv = 0), constrain the remaining fractions to unity (fi + fe = 1), assume diffusion within cells
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to be completely restricted in impermeable cells so that Si = 1 regardless of the level of diffusion encoding, and employ a tortuosity assumption whereby the extracellular diffusivity could be computed from the intracellular signal fraction according to, for example, De(fi) ≈ (1 – fi2/3) D0,
(6)
where D0 is the bulk diffusivity, which could be constrained to by a priori information (for example,
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D0 = 3 µm2/ms as for free water at body temperature). This parallel-series tortuosity model was proposed by (Szafer et al., 1995), and is based on the rationale that the extracellular apparent diffusivity is lower in a dense than in a loose cellular environment. The signal model would then be given by
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S(b)/S0 = fi + (1 – fi) exp(–b [1 – fi2/3] D0).
(7)
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Since this model has only one free parameter (fi), it could, in principle, be used to rephrase the ADC as an intracellular water fraction (e.g. ‘cell density index’). Biophysical models can also be extended to include more free parameters in order to capture, for example, distributions of cellular sizes (Assaf et al., 2008; Packer and Rees, 1972), several distinctly different cell components (D. C. Alexander et al., 2010; Stanisz et al., 1997), and vascular components (Panagiotaki et al., 2014). To illustrate a very general approach, we could model the vascular component by Sv(b) = exp(–b D*)
(8)
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ACCEPTED MANUSCRIPT thereby adding one parameter, D*, to describe the pseudo-diffusion in flowing blood (Le Bihan et al., 1988). Intracellular diffusion could be described by integrating the signal across multiple compartments of different sizes = ∫ | , exp− |
(9)
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where p(x | d, s) is the probability distribution of cell sizes, described its mean (d) and variance (s), and Di[x | g(t)] describes how the apparent diffusivity of the compartment depend on the gradient waveform, g(t). For details on ways of modelling Di, see references (Nilsson et al., 2013b; 2017; described by = exp− , |
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Reynaud, 2017; Stepisnik, 1993; Wang et al., 1995). Finally, the extracellular signal could be
(10)
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where , | describes how the extracellular apparent diffusivity depend on the gradient waveform (Novikov et al., 2014; Xu et al., 2014). This adds another two parameters, D∞ and β, describing the long-time extracellular diffusivity and a presumed linear frequency-dependence of the extracellular diffusivity, respectively. In total, this very general model contains eight free parameters (fi, fe,, fv, D*, d, s, D∞, β), of which seven would be free, considering that fi + fe + fv = 1. On top of this, one could imagine including another component capturing water within axons, relevant in the case of
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infiltrative glioma, but this would add at least another four more parameters, describing the intraaxonal axial diffusivity, principal fibre direction (two polar angles), and the level of axonal orientation dispersion.
The capacity of a model to fit the signal generally increases with the number of free parameters. This
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concept is central to machine learning (Goodfellow et al., 2016), but is explored also in biophysical modelling in dMRI (Ferizi et al., 2014; Panagiotaki et al., 2012). In practise, the signal rarely
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contains enough information to support reliable estimation of more than a handful of meaningful parameters (Ferizi et al., 2015; Novikov et al., 2016a). In the absence of anisotropy, data acquired with multiple b-values in the range of up to approximately 2500 s/mm2 can at most support the estimation of two parameters regardless of the number of b-values used (Kiselev 2007 and 2017). Models with more than two free parameters risk becoming degenerate, meaning that measured data will be equally well fitted by multiple combinations of model parameters, which often results in noisy and un-interpretable parameter maps. This so-called degeneracy is not unique to dMRI but is encountered also in other scientific fields that use exponential analysis (Istratov and Vyvenko, 1999). Degeneracy can be tackled by two principal approaches. The first is to reduce the number of free parameters by introducing constraints, for example, assuming specific values or functional dependencies of some parameters. An obvious risk with this approach is that parameter bias will 13
ACCEPTED MANUSCRIPT result whenever these constraints are invalid. For example, see (Lampinen et al., 2017a). The second and more desirable approach is to acquire more independent information by extending the acquisition protocols, sometimes referred to as “orthogonal measurements” (Novikov et al., 2016a) or multidimensional encoding (Topgaard, 2016). Examples of such encoding dimensions applied to tumours are the diffusion time (Reynaud, 2017) and the b-tensor shape (Szczepankiewicz et al., 2016), and their effect on the signal is illustrated in Figure 4. With this background, we will now
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cover many of the present biophysical models used for microstructure imaging. Methods for estimating neurite density
Several contemporary methods aim at estimation of the ‘neurite density’ (Jespersen et al., 2010;
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2007), and two approaches have been tailored for clinical acquisition protocols: the neurite orientation dispersion and density imaging technique (NODDI) (H. Zhang et al., 2012), and the two-component spherical mean technique (SMT) (Kaden et al., 2016). The “standard model” behind both of these
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techniques is intrinsically degenerate (Jelescu et al., 2016; Novikov et al., 2016b), which necessitates the application of constraints. NODDI, for example, includes assumptions on the diffusivity and the microscopic anisotropy of ‘neurites’ and a link between the extracellular diffusivity and the ‘neurite density’ via a so-called tortuosity assumption. However, these constraints appear to be incongruent with the diffusion in both healthy and tumour tissue (Jelescu et al., 2016; Lampinen et al., 2017a; Novikov et al., 2016a), which leads to biased parameter estimates (Lampinen et al., 2017a). Despite
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this limitation, NODDI has been applied to analyse brain tumour data (Wen et al., 2015), but the estimated ‘neurite density’ should be interpreted with care because the model can yield high ‘neurite density’ even in the known absence of neurites (Lampinen et al., 2017a). This pitfall is particularly relevant in tumours where there is a high intra-voxel variation in cell density (Fig. 3). Contributions
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from this effect can, however, not be separated from contributions of dispersed neurites and so these two effects are conflated in a single ‘neurite density index’, unless b-tensor encoding is applied. This
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type of degeneracy is illustrated in Figure 4H–J. The biexponential model
The biexponential model features fractions of water undergoing ‘fast’ and ‘slow’ diffusion and has three free parameters: ffast, Dfast, Dslow, representing the fast diffusion fraction, the fast diffusion coefficient, and the slow diffusion coefficient. It is expressed as S/S0 = ffast exp(–b Dfast) + fslow exp(–b Dslow).
(11)
The fourth parameter fslow is given by the constraint that ffast + fslow = 1. In the context of dMRI in peripheral nerves, with diffusion encoding perpendicular to the nerve fibre structures, the ffast and fslow parameters were associated to extra-axonal and intra-axonal water fractions, respectively (Assaf and 14
ACCEPTED MANUSCRIPT Cohen, 2000). In the brain, however, orientation dispersion—present in most brain tissues—prevents the use of this simple interpretation (Nilsson et al., 2012; H. Zhang et al., 2012). The biexponential model has been used to characterize brain tumours (Maier et al., 2001), and to study treatment response (Mardor et al., 2003). However, clinically acquired dMRI data rarely supports accurate estimation of the three microstructure parameters (Kiselev, 2017; Kiselev and
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Il'yasov, 2007). The degeneracy of the biexponential model can be mitigated by constraining one of its parameter to a predetermined value, reducing the number of free parameters from three to two, but this procedure results in biased parameters devoid of their connection to underlying microstructure (Mulkern et al., 2017).
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Beyond the b-value: Size estimation by time-dependent diffusion
To support estimation of more than two microstructure features in tumours, the acquisition must
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include variation of more factors than just the b-value1. Figure 4E and 4F illustrates how variation of the diffusion time contributes to a change in the signal curves and how it relates to the underlying microstructure. We refer to such advanced acquisition protocols as multidimensional microstructure imaging techniques. These permit, for example, cell size estimation by acquiring data with multiple diffusion times or by gradients oscillating with different frequencies (Assaf et al., 2008; Schachter et al., 2000; Stanisz et al., 1997; Xu et al., 2014). However, the use of such techniques in brain tumours
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begun only recently, and thus the available data is still limited. Therefore, we also review selected examples of such techniques applied to tumours outside of the brain. The VERDICT (Vascular, Extracellular, and Restricted Diffusion for Cytometry in Tumors) approach uses data acquired with multiple diffusion times to estimate the intracellular volume fraction and cell
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size (Panagiotaki et al., 2014). So far, VERDICT has only been applied to xenograft models of colorectal cancer and prostate cancer (Panagiotaki et al., 2014; 2015), where it enabled MRI-based
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inference of the tumour cellularity, which could differentiate tumours that were indistinguishable by the ADC alone. Time-dependent diffusion––the basis for a VERDICT type of analysis––has also been demonstrated in a xenograft glioblastoma model (Hope et al., 2016). Another analysis approach referred to as IMPULSED (Imaging Microstructural Parameters Using Limited Spectrally Edited Diffusion) utilizes oscillating gradients to probe time-dependent diffusion (Jiang et al., 2016), and enables estimation of cell sizes and cellularity scores in animal models of colon cancer (Fig. 9). Oscillating gradients can be used to probe diffusion at very short diffusion times, which enables assessment of the geometrical features of cell structures such as the surface to
1
Tissues with large vascular components may be an exception, where the exceptionally fast pseudo-diffusion of flowing blood can contribute with sufficient information for another parameter to be captured at low b-values
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ACCEPTED MANUSCRIPT volume ratio (Schachter et al., 2000). Reynaud et al (2015) applied oscillating gradients in a murine glioma model and quantified geometric restrictions by their surface to volume ratio. Corresponding experiments in brain tumour patients have to our knowledge not yet been published. However, Baron et al (2015) used oscillating gradients in stroke patients to investigate the reduced diffusion in stroke lesions, and found swelling and beading of neuronal structures to be key elements for explaining the
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ADC reduction in stroke. Even state-of-the art approaches for cell size estimation have limitations, however. No method can accurately estimate cell sizes below approximately 3–5 microns from intra-cellular time-dependent diffusion with clinical scanners (Nilsson et al., 2017), because the difference in signal attenuation at
(compare Fig. 4E and 4F).
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Time-dependent diffusion for estimation of exchange
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different diffusion times, which the models translates to sizes, is negligible for small structures
Cell membranes are generally permeable to water and assessment of the permeability could be of importance in tumours because the permeability may be related to the migration of malignant astrocytes (McCoy and Sontheimer, 2007). It may also influence the formation and extent of vasogenic brain oedema (Papadopoulos and Verkman, 2007).
Membrane permeability can be estimated from dMRI measurements (Andrasko, 1976; Kärger, 1969).
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Conventional dMRI is, however, not specific to water exchange (Nilsson et al., 2013c), because effects of exchange are entangled with effects of restricted diffusion. This is illustrated in Figure 4E and 4G, which shows that the presence of restricted diffusion leads to increased signal intensities at high b-values, whereas the opposite effect if found in the presence of exchange. In other words: a
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change in signal for longer diffusion times may be due to restricted diffusion, exchange, or a mixture of the two. To disentangle these effects, more advanced encoding strategies are warranted.
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Filter exchange imaging uses a double diffusion encoding experiment with variable mixing times to assess the so-called apparent exchange rate (AXR; see Fig. 10) (Lasič et al., 2011). Where cells are small, the AXR can be expected to be specific to exchange because it relies on a double diffusion encoding experiment, but for larger structures (e.g. above 10 µm) it can become coupled to effects of restricted diffusion (Ulloa et al., 2017). The AXR has been demonstrated to vary approximately linear with the ground truth exchange rate (Tian et al., 2017), and to be elevated for increased levels of urea membrane channels (which cotransports water) in a rat brain (Schilling et al., 2016). The AXR has been measured in the human brain, in the breast, and in glioma and meningioma brain tumour patients (Lampinen et al., 2017b; Lasič et al., 2016; Nilsson et al., 2013a). Results showed, for example, that gliomas exhibit higher AXR than meningiomas (Lampinen et al., 2017b).
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ACCEPTED MANUSCRIPT Translating an AXR value to an exchange time or membrane permeability is not trivial and requires additional measurements or assumptions on fractional water populations and relaxivities (Åslund et al., 2009; Eriksson et al., 2017). Assuming equal amounts of intra- and extracellular water, and that all intra-cellular components contributed to the exchange, the results in Lampinen et al (2017) predict exchange times of 2 and 4 seconds in gliomas and meningiomas, respectively. Conventional diffusion MRI is typically performed with diffusion times of below 100 ms, which would place such
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measurements in the “slow exchange regime” where effects of exchange can be neglected. However, this should be regarded as a probable hypothesis rather than a verified truth. Tissue fractions by relaxation MRI
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Brian tumours generally have longer T2 relaxation times than brain tissue, but there are also differences between tumour types. For example, Oh et al (2005) found T2-relaxation times at 1.5 T
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for gliomas that were significantly longer than those for meningiomas and metastases (160±31 versus 125±31 ms). In oedema, T2 values were generally longer than 200 ms. Preclinical results on experimental tumour models have also demonstrated longer T2 relaxation times in the tumours than in normal tissue (Eis et al., 1995; Sun et al., 2004).
Quantification of the average T2 relaxation time can provide valuable information about tumours. Hattingen et al (2013) investigated patients with recurrent glioblastoma, and suggested that
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comparisons of quantitative T2 measurements between baseline and follow-up can reveal tumour progression (T2 increase) or tumour treatment response (T2 decrease). This may not be surprising given the strong relationship between T2 and ADC (Oh et al., 2005), and the correspondence between ADC, cellularity, and treatment response (Chen et al., 2013; Chenevert et al., 2000; Moffat et al.,
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2005). Moreover, (Lescher et al., 2014) demonstrated that tumour progression was detected earlier on quantitative T1 and T2 differential maps (follow-up minus baseline) than with conventional imaging, and Ellingson et al (2015) showed that T2 quantification can aid quantification of non-enhancing
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tumour burden for use in prediction of survival. However, due to large heterogeneity of brain tumours, T2 quantification in itself may not enable tumour differentiation. For example, it cannot differentiate between benign and malignant astrocytomas (Kjaer et al., 1991). Microstructure imaging could exploit compartmental differences in T2-relaxation times to estimate proton densities in each compartment rather than relaxation-weighted signal fractions. In normal brain tissue, analysis of the T2 decay curve (signal versus TE) reveal up to three distinct components associated with myelin, tissue water, and cerebrospinal fluid with T2-relaxation times at 1.5 T in the ranges of 10–20 ms, 50–600 ms, and above 1000 ms (Whittall et al., 1997). The tissue water itself, however, appears to have small but potentially detectable differences in T2 between intra- and extracellular spaces (Veraart et al., 2017). In experimental glioma tissue, tissue components with 17
ACCEPTED MANUSCRIPT distinctly different T2-relaxation times have been reported (Hoehn-Berlage et al., 1992). For example, Dortch et al (2009) investigated a glioblastoma tumour model at 7 T and found two components with T2 relaxation times of 21±5.4 ms and 76±9.3 ms, where the short-lived component represented a small fraction of the signal (6.8±6.2%). Contralateral grey matter exhibited approximately monoexponential decay with a T2 relaxation time of 49±2.3 ms. Multiexponential T2 decay has also
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been reported in human brain tumours at 1.5 T (Kjaer et al., 1991; Schad et al., 1989). The underlying physiological origin of the observed T2 components in tumours is still unknown, but this effect will be necessary to include in compartment models for accurate quantification of compartmental proton densities rather than signal fractions. Although this type of diffusion-relaxation correlations has already been applied in porous media to study for example cheese (Godefroy and
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Vascular microstructure by perfusion MRI
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Callaghan, 2003), corresponding in vivo applications in tumours are scarce.
Angiogenesis is the process by which new blood vessels are formed. It plays an essential role in tumour growth, and imaging perfusion and vascular microstructure by MRI is important for tumour diagnosis and monitoring (Waldman et al., 2009). Dynamic contrast-enhanced MRI (DCE-MRI) makes use of contrast injection to enable estimation of parameters that relate to the microvascular permeability, and blood flow, blood volume fraction. DCE-MRI techniques were covered in a recent
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review by Heye et al (2014), and here, we will cover diffusion-based methods that do not require injection of exogenous agents to estimate parameters associated to the blood volume. Intra-voxel incoherent motion
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On the scale of a voxel, capillaries are near-randomly oriented and their associated distribution of flow directions will thus be approximately random. In dMRI experiments, blood in the capillaries will thus appear to exhibit pseudodiffusion with a very high ADC (Le Bihan et al., 1988), which yields a
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distinct signal impression at low b-values (Fig. 4D). The intra-voxel incoherent motion (IVIM) approach use this phenomenon to estimate the so-called perfusion fraction from dMRI data using a biexponential approach:
S(b) = f exp(–b D*) + (1–f) exp(–b D)
(12)
where f is the perfusion fraction, D* the pseudo-diffusion coefficient of blood, and D is the tissue diffusivity. Due to the very high value of D*, the perfusion fraction is attenuated already at moderate b-values and thus IVIM relies on the use of low b-values to capture the perfusion fraction. If performed carefully, IVIM can yield useful information on tumour perfusion (Fig. 11). Federau et al (2014) evaluated the perfusion fraction in different types of brain lesions, and found results
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ACCEPTED MANUSCRIPT concurrent with expectations: hyperperfusion in high grade gliomas and meningiomas, and hypoperfusion in acute ischemia and in the necrotic part of a glioblastoma. Moreover, perfusion fractions in high-grade gliomas have been reported to be higher than in low-grade gliomas (Shen et al., 2016; Togao et al., 2016). Higher perfusion fractions have also been reported in recurrent glioblastomas compared to treatment-responding ones (Kim et al., 2014). However, it is still unclear whether the perfusion fraction from IVIM contributes with clinically relevant information. Compared
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to the ADC, for example, it did not add substantially to prediction of 2-year survival in gliomas (Federau et al., 2016) or to the differentiation of high and low grade tumours (Shen et al., 2016). The product of f and D* did, however, improve the differentiation (Shen et al., 2016). The perfusion fraction may also help differentiating primary central nervous system lymphoma (PCNSL) and
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glioblastomas (Suh et al., 2014; Yamashita et al., 2016).
In the context of compartment models, we referred to the fact that modelling must deal with the ill-
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posed nature of the dMRI experiment (Kiselev, 2017), and that this is a problem for all exponential analyses (Istratov and Vyvenko, 1999). IVIM employs a biexponential model and results are thus either highly sensitive to noise, or conversely, to the constraints applied to mitigate the noise sensitivity. Constraints often lead to bias and IVIM is not immune to this limitation. For example, perfusion fractions as high as 30% have been reported in normal white matter (Hu et al., 2014; Lin et al., 2015), well above the expected values of 5% or lower, which suggests the use of invalid
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constraints. In particular, the estimated perfusion fraction is easily confounded by the presence of the cerebrospinal fluid (CSF) that also exhibits fast diffusion (Bisdas and Klose, 2015). This problem can be mitigated by supressing the CSF by an inversion recovery prepared sequence (Federau and O'Brien, 2015). Multidimensional encoding that enable varying the level of flow compensation in addition to the b-value could also contribute to more accurate estimation of the perfusion fraction
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(Ahlgren et al., 2016; Wetscherek et al., 2014).
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Challenges for brain tumour microstructure imaging Model validity
The promise of microstructure imaging is to produce parameter maps reflecting clinically relevant cell-level tissue properties non-invasively, across whole organs, in a way that allows repeated measurements for monitoring (D. C. Alexander et al., 2017). One may ask whether microstructure imaging may even enable measurements of tissue quantities, using these terms as defined in the International Vocabulary of Metrology (2012): a quantity is a property of a body (e.g. a piece of tissue) and a measurement is the process of experimentally obtaining quantity values that can reasonably be attributed to a quantity. Since a property is invariant to the measurement modality,
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ACCEPTED MANUSCRIPT quantity values should be too. Microstructure imaging offers the hope of enabling measurements of tissue quantities of tumours, such as the cellularity or cell sizes, based on MRI only (Jiang et al., 2016; Panagiotaki et al., 2014). Microstructure imaging relies on three foundations: acquisition strategies that encode information about the desired tissue quantities into the magnetic-resonance signal, forward models that predict the
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dependence of the signal from the tissue quantities, and procedures to estimate quantity values by fitting the forward models to the signal. The acquisition is of particular importance: using multiple and moderate b-values (e.g. multi-shell dMRI) is enough to probe just two parameters (Kiselev, 2017; Kiselev and Il'yasov, 2007), and it is unlikely that these can be reasonably attributed any single tissue quantity. Multidimensional encoding strategies are thus warranted to encode more information into
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the signal (Fig. 4). Successful examples include the use of multiple diffusion times to probe cell sizes (Jiang et al., 2016; Panagiotaki et al., 2014), variable b-tensor shapes to probe cell shapes
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(Szczepankiewicz et al., 2016), and variable flow-compensation to probe perfusion (Ahlgren et al., 2016). Even with multidimensional encoding, however, the number of independent tissue quantities that can affect the signal may still exceed the number of parameters required to represent the signal data. In other words, many tissue quantities map to few observable parameters. For example, the intracellular proton density and volume fraction both contribute to the intracellular signal fraction, and cannot be decomposed without data acquisitions that go beyond regular dMRI.
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Microstructure imaging methods that use biophysical models often address the problem of many-tofew mappings by the use of constraints that fix the values of some quantities, or compute them from functional relationships with other quantities. For example, the tortuosity constraint defines a relationship between the extracellular diffusivity and the cell density. The validity of such constraints
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is of utmost concern, because estimated quantity values cannot be reasonably attributed to any single tissue quantity when invalid constraints are applied (Novikov et al., 2018), as demonstrated in the
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case of neurite density mapping in tumours (Lampinen et al., 2017a). Without knowing that the applied constraints are valid in the tumours being investigated, results may be misinterpreted. Therefore, the first challenge is to verify the validity of microstructure imaging methods in a relevant set of brain tumours prior to relying on them for interpretations. Tools for testing assumptions have been described (Novikov et al., 2018). For example, the parameters produced with a valid biophysical model should depend only marginally and in a predicable manner on variations in the experimental protocol (e.g. the set of b-values or diffusion times employed). The use of models can also be analysed philosophically, and to do so we borrow terminology and concepts from (Frigg and Hartmann, 2018). A model is here analysed as a representation of a target system. Discussions on validity then begin by a definition of this target system. For signal models such as DTI and DKI, the signal itself is the target of the model. For biophysical models, the 20
ACCEPTED MANUSCRIPT interaction between the tissue microstructure and the MR experiment is the target. Interpreting increased ADC as reduced cellularity also involves a model, although with linguistic rather than mathematical entities (e.g. high cell density leads to more obstructions to the diffusion and thus a reduced ADC). Model validity concerns whether the model represents the target system accurately enough for the task at hand. The scientific realist may argue that a valid model has entities (e.g. the ‘intracellular volume fraction’ in a biophysical model) with near-identical counterparts in the target
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system (cancerous tissue). Opponents could argue that the biophysical models we have discussed are always false, as their entities are Galilean idealizations, meaning that they involve deliberate distortions of the reality (e.g. assuming that axons are like cylinders, or that cell bodies are like spheres). Models can be false in different ways, however, and Wimsatt (1987) listed these in terms of
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increasing seriousness: a model is false because it (i) has only local applicability, (ii) is so idealised that its entities have no counterparts in nature, (iii) is incomplete meaning that it leaves out variables with explanatory power, (iv) is so incomplete that it provides erroneous descriptions of the
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interactions in the target system, or (v) gives a completely wrong-headed picture of reality. Most, if not all, models discussed herein are invalid up to the third level, since they leave out parameters such as the proton density or relaxivity in each compartment because, at present, there are no multimodal protocols available that allows precise estimation of such parameters from data. That may change in the future. Meanwhile, even false models can be useful, for example, to provide imaging biomarkers.
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Usefulness as imaging biomarkers
An imaging parameter with a strong association to a property of medical interest may be regarded as a quantitative imaging biomarker, which is defined as an “objective characteristic derived from an in vivo image measured on a ratio or interval scale as an indicator of normal biological processes,
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pathogenic processes or a response to a therapeutic intervention” (Kessler et al., 2015). When developing a new image biomarker, two translational gaps must be bridged (O'Connor et al., 2017).
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The first gap concerns establishing the biomarker as a useful tool for applied medical research, for example as a surrogate endpoint in treatment studies, and the second gap concerns the ascension of the biomarker into a clinical decision making tool. Bridging the first gap requires validation of the imaging biomarker on the technical, biological, and clinical arenas. Technical validation assesses, among other factors, repeatability (that the method yields the same value under the same conditions) and reproducibility (it yields the same value under different conditions, e.g. different scanners). Identification of the intervals within which accurate and reproducible measurements can be expected is thus an important step along the road of turning a microstructure imaging parameter into an imaging biomarker. Biological validation ensures that the imaging biomarker is associated to a tissue quantity within the specific validated context. Such validation can be performed by correlating the imaging biomarker to a tissue quantity obtained with independent means such as histology or another
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ACCEPTED MANUSCRIPT imaging technique. Biological validation can also be performed by testing whether the imaging biomarker responds as expected to changes in the quantity. For example, we may verify that a parameter thought to be associated with cellularity actually decrease in a tumour following successful treatment. Clinical validation assesses whether the method can discriminate clinically interesting conditions, for example tumours of low and high grade. The limitations of the imaging-biomarker approach are that the experimental conditions must be fixed (“operationalized”) between validation
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and application and that the validation must be repeated for any new contexts (e.g. another type of tumour). The second challenge for the microstructure imaging community is to allocate resources to validate its parameters as imaging biomarkers in cancer research. Inspiring examples of such validation work are provided below.
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The ADC is the microstructural imaging biomarker that has been most extensively validated. Technical validation has shown high repeatability and reproducibility of ADC quantification
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(Malyarenko et al., 2012; Pfefferbaum et al., 2003). Biological validation has shown a strong association between ADC and cellularity in a wide range brain tumours, comprising gliomas, meningioma, lymphomas, brain metastasis and paediatric brain tumours, with correlation coefficients (r) in the range –0.54 to –0.77 (Barajas et al., 2010; Chenevert et al., 2000; Doskaliyev et al., 2012; Ellingson et al., 2010; Gauvain et al., 2001; Ginat et al., 2012; Gupta et al., 2000; Hayashida et al., 2006; Kono et al., 2001; Sugahara et al., 1999). Clinical validation has shown increases in the ADC
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following successful treatment (Hamstra et al., 2005; Hein et al., 2004; Mardor et al., 2003; Pope et al., 2009), presumably due to treatment-induced reductions in cellularity (Chenevert et al., 2000). However, the ADC have several limitations as an imaging biomarker. Technically, the measurement procedure has not been sufficiently well operationalized with standards for the acquisition protocol (Padhani et al., 2009), for example, regarding diffusion times which we know can affect the ADC.
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Accuracy is hampered in multi-centre studies due to gradient nonlinearity issues (Malyarenko et al., 2016). Biologically, the association between ADC and cellularity is also far from perfect, as expected
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since factors other than the cellularity also affects the ADC. Approaches for microstructure imaging based on biophysical models have also been validated, although not as extensively and often only on preclinical systems. Such validation results may not always translate well to clinical systems. For example, measurements of the axon diameter from dMRI agreed well with histology-based estimates in animal models both ex vivo and in vivo (Assaf et al., 2008; Barazany et al., 2009). The agreement was, however, lost in the translation to the human brain and clinical MRI scanners, where the diameter was grossly overestimated (D. C. Alexander et al., 2010). A probable reason is that the hardware available at clinical MRI scanners does not support estimation of diameters below 3–5 microns (Nilsson et al., 2017), while most axons in the human brain are below 1-2 microns (Aboitiz et al., 1992). Nevertheless, preliminary biological validation
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ACCEPTED MANUSCRIPT studies indicate that imaging biomarkers from multidimensional microstructure imaging methods perform better in tumours than the ADC. For example, such imaging biomarkers and histology correlated very well in the case of cellularity in a colorectal cancer xenograft model (r = 0.81) (Jiang et al., 2016), and in the case of cell shapes (r = 0.95) and cell density heterogeneity (r = 0.83) in human meningioma and glioma tumours (Szczepankiewicz et al., 2016). Biological validation studies have also shown plausible associations between imaging biomarkers of water exchange and the cell
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membrane permeability. Åslund et al (2009) demonstrated that the exchange rate detected by double diffusion encoding varied with temperature as expected, and Schilling et al (2016) showed that the expression of membrane channels co-transporting water increased the detected exchange rates, as expected. Similar causality-based biological validation tests have been performed also for IVIM, by
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subjecting volunteers to variable levels of hypercapnia-induced vasodilation, known to increase brain perfusion, and observing a concurrent change in the perfusion fraction (Federau et al., 2012). In general, however, too few studies have tested the technical, biological, and clinical validity of
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imaging biomarkers from methods based on biophysical models. Unmet clinical needs
From a clinical perspective, there are also numerous challenges. For example, reduced diffusion after treatment is typically associated with viable tumour and progressive disease, but it can also be the result of successful bevacizumab treatment (Mong et al., 2012). This challenge may potentially be
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addressed by incorporating perfusion data and the spatial extent of the region with restricted diffusion (Farid et al., 2013). Early prediction of tumour response to treatment is another clinically important challenge, and the parametric response maps has shown promise (Ellingson et al., 2010; Galbán et al., 2009; Moffat et al., 2005). However, the approach relies on accurate image registration of pre- and
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post-treatment image volumes. This can be challenging when there are geometric distortions and mass effects (Ellingson et al., 2012). A potential solution, apart from improving image registration, may be
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to model and predict tumour growth using functional information on cell proliferation and hypoxia on addition to microstructure information (Atuegwu et al., 2012). Yet another challenge is the grading of glioma, in particular separating between grade II and grade III gliomas. Here, multi-parametric approaches including both spectroscopy, diffusion, and perfusion may be helpful (Caulo et al., 2014; Di Costanzo et al., 2006), and integrating these into a joint microstructure analysis framework would probably enable faster acquisitions. DKI has also shown promise in this regard (Falk Delgado et al., 2018). Finally, infiltration of low-grade glioma can be very subtle, and low concentration of tumour cells can be found far beyond the regions where there are changes in morphological MRI sequences (Zetterling et al., 2016). More accurate imaging techniques are thus warranted to detect low levels of tumour cells scattered around the main tumour, which would address unmet neurosurgical needs regarding determination of tumour resection regions.
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Conclusions Microstructure imaging techniques aim to inform researchers, oncologists and radiologists about tissue features on the cell level without relying on invasive procedures. A simple, yet powerful, example is the relationship between the ADC and cellularity, which can be used to detect dense tumours, as well as to probe the efficacy of treatment over time. As a true measure of cellularity,
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however, the ADC remains inadequate because it is confounded by unrelated tissue features, and depend on the experimental setup. Multidimensional microstructure imaging techniques that encode more information and could together with microstructure modelling provide imaging biomarkers that report directly on tissue quantities, with negligible dependency on the experimental design within
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defined limits. Examples of such techniques use variable diffusion time to probe the cell sizes; multiple b-tensor shapes to separate cell shapes from orientation dispersion; filter exchange imaging to estimate the effects of exchange; and variable echo and repetition times to facilitate estimation of
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compartmental proton densities rather than relaxation-weighted signal fractions. Microstructure imaging will reach maturity when all relevant effects are identified and quantified accurately from the MRI data. Progress requires more clinical data, and comprehensive validation studies to verify that the estimated parameters correspond to the intended microstructure features in a reproducible and robust fashion. Although “virtual biopsy” is a challenge yet to be met, emerging techniques have already provided more specific microstructure parameters than what can be obtained from ADC
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quantification alone.
Funding information
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This research was supported by the Swedish Research Council (grant no. 2016-03443), the Swedish Foundation for Strategic Research (grant no. AM13-0090), Crafoord foundation (grant no. 20160990), the Swedish Cancer Society (grant no. CAN2016/365), and Random Walk Imaging AB
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(grant no. MN15).
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Figure 1. Distribution of primary brain tumours, by type (left) and gliomas by subtype
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(right). Data were compiled from Ostrom et al (2014).
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Figure 2. Clinical MRI, of a WHO grade IV glioblastoma, showing a T2W image (A), gadolinium enhanced T1W image (B), FLAIR image
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(C), and an ADC map (D).
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Figure 3. Histology examples from brain tumours, showing HE staining unless indicated otherwise. (A) Diffuse astrocytoma infiltrating white matter exhibiting oedema and mild reactive gliosis. Bottom panel shows a magnified part of the top panel. (B) Glioblastoma with high cell density (top) and highly variable cell density (bottom), the latter with necrosis and thromb-occluded vessels. (C) Fibroblastic meningioma showing elongated cell structures that run in different directions.
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(D) Meningioma with brain invasion as depicted by GFAP staining (top) and HE staining (bottom), which also show reactive
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gliosis adjacent to the protruding tumour noduli. Notice the large heterogeneity in cell structures between the four examples.
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Figure 4. Overview of dMRI methods, showing relationships between MR signal intensity, encoding strategy, microstructure features. Methods A-D are based on conventional diffusion encoding that vary the diffusion-encoding strength b by increasing the amplitudes of the encoding gradients (blue in panel A). Higher b-values result in stronger signal
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attenuation and a change in image contrast (A, inset). The signal-versus-b curve from a tumour region shows a distinct pattern that can be used to compute different parameters. The apparent diffusion coefficient (ADC) is assessed from the slope of the signal attenuation curve at low a b-value, often 1000 s/mm2 (panel B). Diffusional kurtosis imaging utilizes higher bvalues, and assess the departure of the signal curve from monoexponential attenuation (panel C; blue region between dashed and solid line). The intra-voxel incoherent motion approach estimates the perfusion fraction (f) from the small overshoot of
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the signal at low b-values (panel D, red region in inset). Methods E-G go beyond conventional dMRI and also varies the diffusion time (distance between blue gradients). The separation of the curves between short and long diffusion times (td) can be used to assess cell sizes (panel E), however, this separation vanishes for small sizes (F) and there is therefore a minimal
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size that can be accurately assessed—referred to as the resolution limit (Nilsson et al., 2017). Increasing the diffusion time in presence of membrane permeability and water exchange has the opposite effect on the signal compared to that of restricted diffusion (panel G), which can give rise to a degenerate problem that can be solved by double diffusion encoding (Lasič et al., 2011). Panels H–J show three cases that may appear identical with conventional DKI, but that can be distinguished by tensor-valued diffusion encoding. Panel H shows signal-versus-b curves from a system comprised of randomly oriented and elongated cells, similar to a meningioma sample (top, colour-coded FA). The curves diverge for so-called linear tensor encoding (upper curve) and spherical-tensor encoding (lower curve). Panel I shows a case where the linear and spherical tensor encoded curves overlap because the system was comprised of isotropic diffusion tensors only (panel I, bottom right). This represents the situation in a glioma, which shows considerable variation in ADC within a small region as evidenced from magnetic resonance microscopy (Panel I, top right), from (Gonzalez-Segura et al., 2011). Panel J show a case where the curvature (‘kurtosis’) in the upper signal curve is due to both microscopic anisotropy (green) and isotropic heterogeneity (yellow), where tensor-encoding can be used to disentangle the separate contributions.
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Figure 6. Pre-surgical tractography. Thalamic or basal ganglia tumours and positions of the pyramidal tract. The left column show the tumour location types. The right column demonstrates the relative positions of the dislocated pyramidal
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tract. Green circles indicate tumours and purple circles indicate the tract location. The middle three columns show typical cases. This type of analysis may aid surgeons in determining the location of the pyramidal tract preoperatively. Reproduced
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Figure 5. Parametric response mapping. MRI is performed both before and after treatment, after which the image volumes
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are coregistered. The response map can be computed for different parameters and here it is shown for the ADC. It shows regions in which there were no substantial change in ADC in green, substantial decrease post treatment in blue, increase in red. The fractional volumes of ADC increase and decrease may predict treatment response already weeks after treatment
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initiation (Moffat et al., 2005). Figure courtesy of Björn Lampinen.
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Figure 7. Morphological MRI and DKI in a glioblastoma patient. The first two techniques provide morphological images,
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whereas DKI provides quantitative parameter maps.
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Figure 8. Separation of kurtosis components by diffusional variance decomposition (DIVIDE).
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parameter maps of the total, anisotropic and isotropic kurtosis (MKT, MKA, MKI, respectively) in meningioma and glioma tumours, along with the signal-versus-b curves observed in the tumours. The separation between signal curves acquired with
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linear tensor encoding (LTE) and spherical tensor encoding (STE) in the meningioma suggests a high diffusional anisotropy. No such separation is seen in the glioma, although both LTE and STE are curved, indicating a high isotropic variance. This showcases that tumours may appear similar when considering only conventional diffusion encoding (LTE), but that they can be distinguished when employing different shapes of the b-tensor (LTE vs STE). Panel B shows quantitative microscopy of the corresponding tissue, where the meningioma exhibits high structure anisotropy due to its elongated cell structures,
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whereas the glioma shows a high variability in cell density—both features are congruent with the results seen in dMRI. In panel C, the microscopic anisotropy and isotropic heterogeneity estimated from dMRI and quantitative microscopy are compared. The resulting parameters exhibit a strong correlation across the different tumours. The association indicates that
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the kurtosis components MKA and MKI reflect specific and separate features of the tissue. These features cannot be decomposed by conventional DKI based on LTE only. The figure was adapted from Szczepankiewicz et al. (2016) published by Elsevier.
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Figure 9. Parameter maps from IMPULSED, in a colorectal xenograft model, from Jiang et al (2016). Top row shows HE stained histological images. Other maps show conventional ADC map, and IMPULSED-derived parametric maps overlaid on T2weighted MR images. These comprise apparent cellularity in terms of the MRI-derived density, the cell size, intracellular volume fraction, extracellular diffusivity, intracellular diffusivity, and extracellular structural coefficient βex.
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Figure 10. Filter exchange imaging, is based on a double diffusion encoding sequence (panel A). An initial diffusion filter is followed by a mixing block, and finally, a detection block used to observe the ADC. Image acquisition is done using echo-planar imaging (EPI). The magnetization is stored longitudinally during the mixing block, which enables the use of long mixing times without substantial signal loss. Panel B illustrates the principles
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of the FEXI protocol. Intracellular water exhibit slow diffusion (red), whereas extracellular water exhibit fast diffusion (blue). Application of the diffusion filter preferentially attenuates the extracellular water component, leading to a reduction of the observed ADC (dashed line). Subsequent exchange during the mixing leads to a gradual reappearance of signal-bearing water in the extracellular space. With increasing mixing time, the ADC thus approaches its equilibrium value, with a rate given by the AXR. Panel C show images from a typical
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meningioma (top), atypical meningioma (middle), and a glioma (bottom). Left column shows T1W-images, and
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the right column AXR parameter maps. Modified from Nilsson et al (2013) and Lampinen et al (2017).
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Figure 11. Example of IVIM in a glioblastoma patient. Panels A–C show an axial T2-weighted image, T1-weighted post
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gadolinium, and cerebral blood volume from DSC-MRI. Panels D–F show IVIM parameter maps of the perfusion fraction (f), the apparent diffusivity of the pseudodiffusing blood (D*), and the product between the two. Panel G show a signalversus-b curve where the perfusion fraction is shown as the signal overshoot at low b-values. Adapted from Federau et al (2014).
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Conflict of interest statement MN declares research support from Random Walk Imaging (formerly Colloidal Resource), and patent applications in Sweden (1250453-6 and 1250452-8), USA (61/642 594 and 61/642 589), and PCT (SE2013/050492 and SE2013/050493). FS has been employed at Random Walk Imaging. Remaining
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authors declare no conflict of interest.