Volume transition analysis: A new approach to resolve reclassification of brain tissue in repeated MRI scans

Journal of Neuroscience Methods 243 (2015) 78–83

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Short communication

Volume transition analysis: A new approach to resolve reclassification of brain tissue in repeated MRI scans Anja Teuber a,∗ , Jan-Gerd Tenberge b , Harald Kugel c , Michael Deppe b , Klaus Berger a , Heike Wersching a a

Institute of Epidemiology and Social Medicine, University of Münster, Albert-Schweitzer-Campus 1, 48149 Münster, Germany Department of Neurology, University Hospital Münster, Albert-Schweitzer-Campus 1, 48149 Münster, Germany c Department of Clinical Radiology, University Hospital Münster, Albert-Schweitzer-Campus 1, 48149 Münster, Germany b

h i g h l i g h t s

g r a p h i c a l

a b s t r a c t

• Brain • • • •

tissue segmentations of repeated cerebral MRI scans are compared. A new approach to resolve tissue type reclassifications is introduced. Voxel inflows from and outflows towards adjacent tissue volumes are quantified. Three scan–rescan scenarios imitate data basis of various applications. Monodirectional net flows increase with longer timespan and scanner switch.

a r t i c l e

i n f o

Article history: Received 30 October 2014 Received in revised form 23 January 2015 Accepted 24 January 2015 Available online 18 February 2015 Keywords: MRI Brain volume Reliability Image segmentation

a b s t r a c t Background: Variability in brain tissue volumes derived from magnetic resonance images is attributable to various sources. In quantitative comparisons it is therefore crucial to distinguish between biologically and methodically conditioned variance and to take spatial accordance into account. New method: We introduce volume transition analysis as a method that not only provides details on numerical and spatial accordance of tissue volumes in repeated scans but also on voxel shifts between tissue types. Based on brain tissue probability maps, mono- and bidirectional voxel shifts can be examined by explicitly separating volume transitions into source and target. We apply the approach to a set of subject data from repeated intra-scanner (one week and 30 month interval) as well as inter-scanner measurements. Results: In all measurement scenarios, we found similar inter-class transitions of 9.9–15.9% of intracranial volume. The percentage of monodirectional net volume transition however increases from 0.3% in short term intra-scanner to 1.6% in long term intra-scanner and 9.3% in inter-scanner comparisons.

Abbreviations: MRI, magnetic resonance imaging; GM, grey matter; WM, white matter; CSF, cerebrospinal fluid; ICV, intracranial volume; DoM, distance over mean; DC, Dice’s coefficient; VOI, volume of interest; OLS, ordinary least square; MAD, median absolute deviation. ∗ Corresponding author. Tel.: +49 251 83 56086; fax: +49 251 83 55300. E-mail address: [email protected] (A. Teuber). http://dx.doi.org/10.1016/j.jneumeth.2015.01.028 0165-0270/© 2015 Elsevier B.V. All rights reserved.

A. Teuber et al. / Journal of Neuroscience Methods 243 (2015) 78–83

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Comparison with existing methods: Unlike most routinely used variability measures volume transition analysis is able to monitor reclassifications and thus to quantify not only balanced flows but also the amount of monodirectional net flows between tissue classes. The approach is independent from group analysis and can thus be applied in as few as two images. Conclusions: The proposed method is an easily applicable tool that is useful in discovering intra-individual brain changes and assists in separating biological from technical variance in structural brain measures. © 2015 Elsevier B.V. All rights reserved.

1. Introduction Magnetic resonance imaging (MRI) of the brain is used in medical research and increasingly in epidemiologic studies with assumedly healthy community-dwelling individuals examined repeatedly over large periods of time. Image-derived structural brain measures thereby serve as outcomes, mediators or surrogate markers for various physiological processes, such as maturation or ageing, as well as for pathological processes particularly in degenerative and neuropsychiatric diseases. Accordingly, the precise classification and quantification of brain tissue volumes – consisting of brain parenchyma, which is subdivided into grey matter (GM) and white matter (WM), and cerebrospinal fluid (CSF) – from MR data is a non-negligible core task of medical image analysis. Well-known biological factors that influence brain tissue volumes are sex and age. Women generally show smaller brain tissue volumes, although their brain parenchymal fraction (i.e. the ratio of brain parenchymal volume to total intracranial volume) is higher than in men (Littmann et al., 2006). Regarding age, a continuous decline in parenchyma volume is assumed after the age of 35 years, starting with a decrease of about 0.2% per year and accelerating gradually to an annual brain volume loss of 0.5% and more in people over 60 years of age (Fotenos et al., 2005; Hedman et al., 2012; Good et al., 2001). Even independent from sex and age, brain tissue volumes also underly a large inter-individual physiologic variability of about 10% (coefficient of variation) (Courchesne et al., 2000). Further sources of variability are present at all levels of image acquisition and processing. They arise from the subject (e.g. movements during scan, including breathing and pulsation of the CSF, or hydration status (Duning et al., 2005)), the scanner (field strength, gradients or hardware instability (Jovicich et al., 2009; Shuter et al., 2008; Lüders et al., 2002)) and analysis (segmentation algorithm (de Boer et al., 2010; Eggert et al., 2012; Klauschen et al., 2009) and normalisation method (O’Brien et al., 2011, 2006)). In order to quantify and provide valid interpretations of subtle inter-individual differences or intra-individual changes over time, high reproducibility and accuracy in acquisition and analysis of brain volumes are crucial. Regarding image processing, MR image segmentation methods are being continuously improved, with recently developed algorithms for brain tissue segmentation yielding generally low variability in brain volume measures (de Boer et al., 2010). However, low variability does not necessarily correspond to good reliability as numerically small variances can mask considerable systematic voxel shifts among separated tissue classes. Settings with repeated measurements of the same subject – like longitudinal data assessment in the course of a study, follow-up examinations of patients, or reliability tests – provide the opportunity to keep track of these voxel shifts and separate biological from technical variance. We here suggest an easily applicable method (volume transition analysis) that provides information on differences as well as similarities in brain tissue volumes obtained from spatial tissue probability maps as returned by every commonly used segmentation software. We illustrate the benefit of this approach in subjects repeatedly examined for a reliability

check prior to a large-scale neuroimaging study (Teismann et al., 2014). 2. Theory Commonly used software packages for tissue segmentation take a grey-value image G ∈ Rnx ×ny ×nz of the brain as input and return spatial probability maps Pt ∈ Rnx ×ny ×nz for each tissue class, i.e. the probability (pt )xyz ∈ [0, 1] of belonging to the particular tissue class t is assigned to every voxel/matrix element of the image. By default, the considered tissue classes are GM (t = g), WM (t = w) and CSF (t = f). The overall tissue volume Vt is calculated as sum over all voxels Vt = Vvox ·



(pt )xyz ,

x,y,z

Vvox being the voxel’s volume. The comparison of brain tissue volumes in repeated measurements G(1) and G(2) can be done in various ways. The aim in each case is to calculate parameters that quantify similarities as well as differences rather than to spatially present variances, since voxel based statistics is not meaningful when comparing as few as two images. (1) (2) Variation measures of overall tissue volumes Vt and Vt like the distance over mean (DoM) (1)

DoM t =

2·|Vt

(1)

Vt

(2)

− Vt | (2)

+ Vt

do not contain any spatial information and therefore carry the risk of concealing considerable differences between images G(1) and G(2) . If, for example, the amount of tissue is similar in both scans whereas the contributing voxels in the tissue probability maps have a poor spatial overlap, the DoM will be low in spite of the fact that many of the voxels accounting for the total volume are of different spatial origin. (1) (2) Similarity measures of tissue probability maps Pt and Pt like the Dice’s coefficient (DC) (Dice, 1945; Sorensen, 1948) DCt =

2·



(1)

x,y,z



(2)

min((pt )xyz , (pt )xyz )

x,y,z

(1)

(2)

[(pt )xyz + (pt )xyz ]

take spatial overlap into account, but results depend on the size of the intersection as well as on the variation of overall tissue volumes. DoM and DC analysis is beneficial in confirming good reliability since a low DoMt accompanied by a high DCt is indicative of close similarity of the amount and spatial distribution of the corresponding tissue t. In case of non-negligible technically or biologically conditioned changes, however, this analysis does not directly allow for a meaningful interpretation of the observed change in one particular tissue volume. In order to accomplish this, the knowledge of changes in the remaining tissue volumes is required. In other words, DoM and DC analysis considers each tissue class individually, i.e. the initial algorithmic work step of the evaluation

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disregards the contentual and accordingly mathematical correlation among different tissue classes. Only an additional deductive work step, which combines various pieces of information, allows conclusions about the global alterations and the interrelation of different tissues. Volume transition analysis precisely profits from interdependency of volume measures among different tissue classes to specify the differences between images G(1) and G(2) in more detail. From a biological point of view, the sum Vg + Vw + Vf should be constant in adult subjects as it represents the intracranial volume (ICV). Thus, deviating segmentation results of images G(1) and G(2) can be considered as volume transition between the three tissue classes. In the following, a forth non-brain class n (including bone, skin and other non-brain tissues) will be carried along such that (pg )xyz + (pw )xyz + (pf )xyz + (pn )xyz = 1 ∀ x, y, z

(2)

to encounter for technical variations in the distinction of brain and non-brain tissue. However, we restrict our calculations to a volume of interest (VOI) containing only those voxels, that share brain tis(1) (2) sue in at least one of the two images, i.e. (pn )xyz < 1 or (pn )xyz < 1. Let q be the number of the associated voxels and hence V = q · Vvox the total size of the VOI. Volume transitions can be approached by tracing back the tissue (2) (2) volume fraction vt = Vt /V of class t in the second image to the (1)

corresponding tissue volume fraction vt of class t in the first image as well as to the tissue volume fractions of any other tissue class in the first image. The resulting multivariate multiple regression model is

⎛

v(2) g

⎞

⎛

ˇgg

ˇwg

ˇfg

ˇgn

ˇwn

ˇfn

⎞ ⎛ (1) ⎞ vg ⎟ ⎟ ⎜ ⎟ ˇnw ⎟ ⎜ v(1) w ⎟ ⎜ ⎟· ⎜ ⎟ ⎟ ˇnf ⎠ ⎜ v(1) ⎟ ⎝ f ⎠

v(2) n





ˇnn

with transition coefficients (ˇtt ). Based on two images only, the transition matrix B is not unique. Nevertheless, the most likely coefficients can be estimated by analysing the observed tissue partitioning in approximately 1.5 million voxels. The multivariate multiple regression model for a single voxel is

⎞ (2)

⎛

pg

⎜ (2) ⎟ ⎜ pw ⎟ ⎜ ⎟ ⎜ (2) ⎟ ⎜p ⎟ ⎝ f ⎠

pg

 xyz +

(1)

pn

xyz

xyz

 . A straightforward way of including an appropriate error term  estimating the transition matrix is the ordinary least square (OLS) technique, where calculations can be performed for each outcome individually, i.e. solving

⎛ ⎜ ⎜ ⎝

(2)

(pt )1 .. .

⎞

⎛

⎟ ⎜ ⎟=⎜ ⎠ ⎝

(2)



(pt )q



 (2) p t



(1)

(pg )1 .. .

(pg )(1) q

(1)

Vt q · Vvox

with the result that coefficients ( ˇtt ) quantify shares of the whole VOI, meaning

  ˇ  = 1. In the resulting matrix  B, the diagonal t,t tt

elements  ˇtt give the recurrence rate of tissue t, subsuming the volume fraction that was and remains in tissue class t. Their sum is the overall recurrence rate. The non-diagonal elements provide information on volume transitions. Beside their extent, the sym-

t, t  t = / t

3. Material and methods In order to demonstrate the benefit of volume transition analysis we created three different data scenarios each based on a different assumption regarding numerical and spatial variability of segmentation results:

⎞ (1)

⎜ (1) ⎟ ⎜ pw ⎟ ⎜ ⎟ = B·⎜ ⎟ ⎜ p(1) ⎟ ⎝ f ⎠

(2)

pn

ˇtt →  ˇtt = ˇtt ·

1  · |ˇtt −  ˇt t |. 2

v(1) n

B

⎛

every column of second scan, i.e. contributes to Vt  . Accordingly,   = 1 ∀ t. ˇ transition coefficients adds up to 100%,  tt t To ensure better comparability, matrix entries can be scaled according to

ˇtt in comparison to  ˇt t , is important. Equally large metry, i.e.  entries correspond to bidirectional volume exchange, whereas an increasing difference between entries indicates more monodirectional volume transition, i.e. higher net flow. The overall net flow is quantified as

ˇng

⎜ (2) ⎟ ⎜ ⎜ vw ⎟ ⎜ ˇgw ˇww ˇfw ⎜ ⎟ ⎜ (2) ⎟ = ⎜ ⎜v ⎟ ⎜ ˇ ˇwf ˇff ⎝ f ⎠ ⎝ gf

(1)  t = (P(1) P(1) )−1 P(1) · p  (2) for all tissue classes t by ˇ denott with P (1) ing the transpose of matrix P . It should be noticed that the hereby estimated transition matrix reveals global trends whereas locally deviant transitions are deliberately smoothed out. Reversely transferring the coefficients to confined anatomical regions or even to single voxels is not valid and not intended by volume transition analysis. Voxel-based data, i.e. their percentage composition of tissue, are used regardless of the spatial position of the voxels to each other or their anatomical meaning. This approach brings about a broad data basis and allows for the estimation of a set of parameters that provide, as covered below, more elaborate information about the global changes between scan and rescan. Transition coefficient (ˇtt ) is interpreted as percentage of tissue (1) volume Vt in the first scan that changed to tissue class t in the

(1)

(1)

(pw )1

(pf )1

.. .

.. . (1)

(pw )q

P

.. . (1)

 (1)

(1)

(pn )1

(pf )q

⎞

⎛

ˇgt

⎞

⎜ ⎟ ⎟ ⎜ ˇwt ⎟ ⎟  ⎟·⎜ ⎠ ⎜ ˇ ⎟ + t ft ⎠ ⎝ (1)

(pn )q

nt

ˇ

 ˇ t

(1) Short term intra-scanner measurements: Morphological brain changes can practically be excluded. The expected variability in numerical volume measures is randomly distributed, low and should arise from subject- and scanner-related variables as mentioned in Section 1. Only small spatial deviations are expected. (2) Long term intra-scanner measurements: The extent of numerical and spatial variability is expected to be higher compared to scenario (1). Segmentation results might have changed systematically due to updates of scanner software, hardware replacements or the like. Morphological brain changes are possible. (3) Short term inter-scanner measurements: Segmentation results are expected to change systematically due to scanner switch, whereas morphological alterations can practically be excluded. Changes can be reflected in numerical as well as spatial deviations.

A. Teuber et al. / Journal of Neuroscience Methods 243 (2015) 78–83

3.1. Subjects and data acquisition We made use of two different MR data sets: for inter-scanner measurements 12 volunteers (5 women, median age 33 years, age range 26–69 years) underwent two MRI sessions in two different MR systems within 48 h. For intra-scanner measurements additional 5 volunteers (4 women, median age 48 years, age range 41–53 years) underwent three MRI sessions in the same scanner with identical protocols within time intervals of 3–7 days and of about 30 month. The employed scanner systems were a Philips Intera (used for intra-scanner measurements) and a Siemens Trio, both with 3.0 T field strength. In both scanners a 3D T1-weighted gradient echo sequence with magnetisation preparation finally yielded images with an isotropic voxel resolution of 1 mm3 . Technical details about MR systems and acquisition parameters are summarised in Appendix A. Standard MRI exclusion criteria were applied. All participants provided written informed consent before starting the MRI session. The ethics committee of the Westphalian Chamber of Physicians approved the study. 3.2. Image processing Image segmentation has been done by using the freely available and established algorithm of the VBM8 toolbox1 (r435) for SPM8 (Statistical Parametric Mapping2 ) run with Matlab R2012b. All T1-weighted images were processed with the Estimate and Write module choosing low dimensional spatial normalisation and apart from that keeping the default options. The calculated tissue maps of subject’s personal scan and rescan were spatially aligned by a rigid body transformation that was previously estimated based on the original images. 3.3. Data analysis For each scan–rescan scenario and each subject, we calculated the distance over mean (DoM) of overall tissue volumes and the Dice’s coefficient (DC) of tissue probability maps and we estimated the transition matrix. Matrix entries with absolute value lower than 0.001 are reported as zero. Due to the low number of subjects, the results are reported as median over the cohort and the median absolute deviation (MAD)3 as robust measure for statistical spread. Volume transition analysis includes about 1.5 million data points and therefore all p-values numerically equal zero. Since they are not interpretable as significance measures in a meaningful way, none of them is reported. 4. Results and discussion 4.1. Short term intra-scanner scenario Median DoM and median DC and their MAD are presented in Table 1. As shown in Fig. 1, the volume differences are randomly distributed around zero for every tissue class.

1 2 3

http://dbm.neuro.uni-jena.de/vbm/. http://www.fil.ion.ucl.ac.uk/spm/. The median absolute deviation (MAD) is defined as

81

Table 1 Median distance over mean (DoM) and Dice’s coefficient (DC), with median absolute deviation (MAD) in each case, for the short term intra-scanner scenario (1), the long term intra-scanner scenario (2) and the short-term inter-scanner scenario (3). Scenario

GM

WM

CSF

ICV

(1)

DoM DC

1.0 ± 0.8 % 89.6 ± 1.3 %

0.8 ± 0.4 % 93.6 ± 0.5 %

1.5 ± 0.8 % 83.4 ± 3.6 %

0.1 ± 0.1 % 98.8 ± 0.1 %

(2)

DoM DC

1.3 ± 0.8 % 87.8 ± 1.1 %

0.5 ± 0.5 % 92.3 ± 0.8 %

1.5 ± 2.1 % 81.9 ± 1.5 %

0.7 ± 0.4 % 98.6 ± 0.1 %

(3)

DoM DC

2.2 ± 1.7 % 83.5 ± 1.0 %

10.4 ± 1.3 % 89.6 ± 0.7 %

8.3 ± 8.5 % 71.6 ± 8.0 %

2.4 ± 1.6 % 98.1 ± 0.4 %

GM: grey matter; WM: white matter; CSF: cerebrospinal fluid; ICV: intracranial volume.

The estimated volume transition matrix is

⎛

92.0 ± 0.5 1 ⎜ 4.0 ± 0.3 B= ·⎝ 4.1 ± 0.7 100

4.6 ± 0.2 95.7 ± 0.3

9.9 ± 1.8 84.6 ± 1.5 5.6 ± 0.4

4.3 ± 0.8

⎞ ⎟

26.0 ± 1.8 ⎠ 68.7 ± 1.9

After translation into percentages of the total considered volume (VOI), it follows

⎛

38.3 ± 3.1 1 1.7 ± 0.1 ⎜  B= ·⎝ 1.7 ± 0.2 100

1.7 ± 0.4 33.1 ± 3.5

1.8 ± 0.2 16.3 ± 1.5 1.1 ± 0.1

0.2 ± 0.1

⎞ ⎟

0.9 ± 0.1 ⎠ 2.5 ± 0.1

resulting in a recurrence rate of 90.1%.4 Thus, based on a mean VOI of 1529 ± 193 ml in our subjects, about 151 ml of brain tissue is assigned to a different class in scan versus rescan. However, the net flow makes up only about 4% of these tissue shifts (0.4% of total VOI). In line with this low net flow, the small and clearly symmetric non-diagonal elements confirm the implications of common comparison methods, i.e. minor and bidirectional volume transitions as well as high spatial accordance. Our DoM and DC values are comparable to previously published findings (de Boer et al., 2010). 4.2. Long term intra-scanner scenario Median DoM and median DC and their MAD are presented in Table 1. All volume differences are randomly distributed around zero (Fig. 1). The estimated volume transition matrix is

⎛

89.3 ± 1.5 1 ⎜ 5.0 ± 0.2 ·⎝ B= 5.9 ± 0.6 100

5.8 ± 0.5 94.6 ± 0.6

8.8 ± 2.1 84.2 ± 0.6 7.1 ± 2.4

5.8 ± 3.2

⎞ ⎟

26.2 ± 3.1 ⎠ 67.0 ± 3.1

After translation into percentages of the total VOI, it follows

⎛

37.5 ± 2.7 1 ⎜ 2.2 ± 0.1  B= ·⎝ 2.5 ± 0.2 100

2.0 ± 0.0 32.7 ± 3.3

1.7 ± 0.5 16.4 ± 1.5 1.4 ± 0.4

0.2 ± 0.1

⎞ ⎟

0.9 ± 0.3 ⎠ 2.3 ± 0.2

resulting in a recurrence rate of 88.9%. Thus on average, about 170 ml of brain tissue is reclassified in scan versus rescan. Net flow is about 15% of these tissue shifts (1.6% of total VOI). The persistently high recurrence rate is in line with low DoM and high DC values, whereas increasingly asymmetric non-diagonal

MADy = 1.4826 · median|y −  y|, where  y denotes cohort median of y and the scale factor of 1.4826 ensures that MAD approaches standard deviation in large samples with normally distributed y.

4 This and all subsequently reported numerical values in the continuous text are directly calculated from non-rounded transition coefficients and thus differ to some extent from results that can be calculated from the presented matrices.

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A. Teuber et al. / Journal of Neuroscience Methods 243 (2015) 78–83

Fig. 1. Bland–Altman plots showing volume differences versus volume means of (in columns) grey matter (GM), white matter (WM), cerebrospinal fluid (CSF) and intracranial volume (ICV) for (in rows) the short term intra-scanner scenario (1), the long term intra-scanner scenario (2) and the short term inter-scanner scenario (3). Horizontal lines indicate median difference (dash-dotted) and median ± MAD (dashed).

elements point towards monodirectional volume transitions, particularly from GM to CSF. The GM → CSF net flow of 0.8% in the timespan of 30 months (in combination with constant WM volumes) corresponds well to the annual age-related brain volume decline of 0.2–0.5% that is reported in the literature (Fotenos et al., 2005; Hedman et al., 2012; Good et al., 2001), thereby suggesting a biological tissue shift (atrophy). 4.3. Short term inter-scanner scenario Median DoM and median DC and their MAD are presented in Table 1. As shown in Fig. 1, the differences in GM volumes are randomly distributed around zero. By contrast, the segmentation algorithm identified systematically larger WM, smaller CSF and slightly larger intracranial volumes in Siemens images compared to Philips scans. The estimated volume transition matrix is

⎛

87.3 ± 2.0 1 ⎜ 11.4 ± 0.8 ·⎝ B= 2.2 ± 1.1 100

2.8 ± 0.6 97.2 ± 0.5

24.5 ± 8.1

11.3 ± 3.9

3.9 ± 1.5

48.5 ± 5.4

⎞

⎟ 73.0 ± 6.6 39.2 ± 3.4 ⎠

After translation into percentages of the total VOI, it follows

⎛

37.7 ± 2.1 1 ⎜ 4.9 ± 0.4  B= ·⎝ 1.0 ± 0.5 100

1.0 ± 0.3 32.7 ± 2.5

3.9 ± 1.2 11.0 ± 3.4 0.7 ± 0.3

0.6 ± 0.3

resulting in a recurrence rate of 84.1%. Accordingly, about 242 ml of brain tissue is reclassified in scan versus rescan. In this scenario, net flow makes up about 59% of this tissue shifts (9.3% of total VOI) corresponding to a monodirectional volume transition of 142 ml. Exemplarily for one subject, a graphical representation of the quantified volume transitions is provided in Appendix A. In comparison with intra-scanner scenarios, clearly higher DoM values, differing distributions of volume differences and lower DC values point to a systematical deviation between segmentation results of Philips and Siemens scans. Volume transition analysis is able to clarify this observation in a consistent way. For example, about 16.5% non-similarity in GM maps according to the DC (equal to approximately 7.2% of VOI) are traceable to almost 4% net outflow towards WM and about 3.5% net inflow from CSF and the non-brain class. Balanced inflows and outflows explain low DoM for GM in this scenario.

⎞ ⎟

2.3 ± 0.6 ⎠ 2.8 ± 0.2

4.4. Comprehensive results The results of volume transition analysis are reasonable regarding characteristic as well as extent: first, the above given B confirm our implications from the characteristics of matrices  assumptions regarding numerical and spatial variability of segmentation results as stated in Section 3. Second, the values of DoM and DC (converted into percentages of total VOI in each case) can precisely be deduced from the estimated matrix elements, i.e. the DoM of tissue class t follows from the DoM of the appropriate column

A. Teuber et al. / Journal of Neuroscience Methods 243 (2015) 78–83

    ˇ  and row sum ˇ  whereas the DC of tissue class t t tt t t t        ˇ − ˇt t  of absolute net inflows follows from the sum / t  tt t ,t =

83

from and net outflows towards other tissue classes. In addition, the transition coefficients proved to be robust within the cohorts, indicated by low statistical spread (MAD values).

project are the radprax Institute of Diagnostics and Research Münster (Petra Eickhoff), Jürgen Wellmann and Ernst Riepenhausen. The study was funded by grants of the German Federal Ministry of Research and Education (BMBF, grants FKZ-01ER0816 and FKZ01ER1205) and by the Neuromedical Foundation Münster (Stiftung Neuromedizin).

5. Conclusion

Appendix A. Supplementary Material

Volume transition analysis provides clear comprehensive information about differences and similarities of brain tissue volumes from repeated MRI examinations of the same subject. The calculated transition matrix contains commonly used quantitative measures like the distance over mean and Dice’s coefficient and, moreover, estimates the magnitude of balanced bidirectional interclass transitions that are otherwise not directly resolvable. Net flows are explicitly separated into source and target and thus can hint at morphological changes in a descriptive way. In contrast to DoM and DC analysis, volume transition analysis incorporates the contentual and mathematical relation between the different tissue classes by modelling volume differences as inter-class transitions. Since each possible transition is represented by one parameter, proceeding volume transitions are distinctly separated and misinterpretation of (accidentally) low/high variability or reliability measures is avoided. Volume transition analysis has the distinction of being based on the evaluation of approximately two times 1.5 million data points already at individual level. Consequently, it offers the opportunity to investigate differences between repeated scans of a single subject. In contrast, essentially voxelbased approaches such as voxel-based morphometry take full effect only at group level. The presented approach reveals an overall trend of volume transitions as it pools all voxel data without distinction in as few as 16 parameters. Actual changes in certain spatial regions easily can be under- or overestimated. If further knowledge about the subject suggests marked transitions in confined brain regions, the volume of interest can be selected accordingly or volume transition analysis can be extended to consider different transitions matrices for different regions. Upcoming studies should investigate the numerical properties of volume transition analysis in detail. Simulated MR data can help to confirm the validity and interpretation of transition coefficients especially regarding morphological changes. Furthermore, evolving from OLS estimation technique to the minimisation of total least square errors can assure exact reversibility of the approach when swapping scan and rescan. The proposed method is a handy and computationally cheap tool that is based on standard statistical methods. The range of application covers data exploration and quality assurance (i.e. scanning for outliers) in a variety of settings. The results are robust across individual subjects, so that, presumably, group comparisons of transition coefficients are quite possible. At any rate, volume transition analysis is useful in discovering intra-individual brain changes and assists to separate biological from technical variance in structural brain measures.

Supplementary material associated with this article can be found, in the online version, at http://dx.doi.org/10.1016/ j.jneumeth.2015.01.028.

sum

Acknowledgements We would like to thank all study participants for their time and engagement. Our data could not have been acquired without the personal commitment of Nina Nagelmann (Department of Clinical Radiology, Münster) – particular thanks to her. Further supporters of this

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