Scalp and skull influence on near infrared photon propagation in the Colin27 brain template

NeuroImage 85 (2014) 136–149

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Scalp and skull influence on near infrared photon propagation in the Colin27 brain template Gary E. Strangman ⁎, Quan Zhang, Zhi Li Neural Systems Group, Massachusetts General Hospital/Harvard Medical School, Charlestown, MA, USA

a r t i c l e

i n f o

Article history: Accepted 18 April 2013 Available online 7 May 2013 Keywords: Near-infrared spectroscopy NIRS Monte Carlo simulation Scalp thickness Skull thickness

a b s t r a c t Near-infrared neuromonitoring (NIN) is based on near-infrared spectroscopy (NIRS) measurements performed through the intact scalp and skull. Despite the important effects of overlying tissue layers on the measurement of brain hemodynamics, the influence of scalp and skull on NIN sensitivity are not well characterized. Using 3555 Monte Carlo simulations, we estimated the sensitivity of individual continuous-wave NIRS measurements to brain activity over the entire adult human head by introducing a small absorption perturbation to brain gray matter and quantifying the influence of scalp and skull thickness on this sensitivity. After segmenting the Colin27 template into five tissue types (scalp, skull, cerebrospinal fluid, gray matter and white matter), the average scalp thickness was 6.9 ± 3.6 mm (range: 3.6–11.2 mm), while the average skull thickness was 6.0 ± 1.9 mm (range: 2.5–10.5 mm). Mean NIN sensitivity – defined as the partial path length through gray matter divided by the total photon path length – ranged from 0.06 (i.e., 6% of total path length) at a 20 mm source–detector separation, to over 0.19 at 50 mm separations. NIN sensitivity varied substantially around the head, with occipital pole exhibiting the highest NIRS sensitivity to gray matter, whereas inferior frontal regions had the lowest sensitivity. Increased scalp and skull thickness were strongly associated with decreased sensitivity to brain tissue. Scalp thickness always exhibited a slightly larger effect on sensitivity than skull thickness, but the effect of both varied with SD separation. We quantitatively characterize sensitivity around the head as well as the effects of scalp and skull, which can be used to interpret NIN brain activation studies as well as guide the design, development and optimization of NIRS devices and sensors. © 2013 Elsevier Inc. All rights reserved.

Introduction Near-infrared spectroscopy (NIRS) enables non-invasive monitoring of brain tissue oxygenation (Ferrari et al., 2004; Jobsis, 1977; Obrig and Villringer, 2003)—or near-infrared neuromonitoring (NIN). By definition, non-invasive measurements require recording through the overlying scalp, skull and cerebrospinal fluid (CSF) layers. NIRS studies of brain function have commonly assumed that (a) any observed changes in hemodynamics are restricted to brain tissue, or (b) changes that do occur in the overlying tissue layers are uncorrelated with the changes in brain function and hence can be ignored. Brain function studies over the past three decades have generated numerous important results under these assumptions. However, it has also been recognized that systemic fluctuations in hemodynamics can substantially influence NIN measurements (Gratton and Corballis, 1995; Obrig et al., 2000). More problematic, such physiological “noise” components—including

⁎ Corresponding author at: Neural Systems Group, 149 13th Street, Psychiatry, Rm 2651, Charlestown, MA 02129, USA. Fax: +1 617 726 4078. E-mail address: [email protected] (G.E. Strangman). 1053-8119/$ – see front matter © 2013 Elsevier Inc. All rights reserved. http://dx.doi.org/10.1016/j.neuroimage.2013.04.090

cardiac (Gratton and Corballis, 1995), respiratory (Franceschini et al., 2002), Mayer wave and other low frequency oscillations (Obrig et al., 2000)—are quasiperiodic signals. As a consequence, even if such extracerebral signals are completely uncorrelated with brain activity, their reduction via averaging may require 10s or even 100 s of trials, and hence other methods may be necessary to deal with them (Gratton and Corballis, 1995). Indeed, it has been demonstrated empirically that significant improvements in detecting brain activation are possible when using multi-distance probes to help correct for interference by scalp and skull hemodynamics (Fantini et al., 1994; Gagnon et al., 2011; Liebert et al., 2004; Saager and Berger, 2008; Zhang et al., 2007a, b, 2009). Given that light is absorbed exponentially as it passes through tissue, NIN measurements are inherently most sensitive to tissue nearest the source and detector. A few previous studies have begun to characterize NIRS sensitivity in realistic head models (Custo et al., 2006; Fukui et al., 2003; Hoshi et al., 2005; Mansouri et al., 2010; Strangman et al., 2003). While these studies revealed spatial sensitivity profiles within the head, including maximal sensitivity of NIN measurements in scalp and skull, all of these focused on only a single head region. We have recently characterized both the spatial and depth sensitivity profiles in a canonical

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head model [Strangman—submitted]. Our findings were broadly consistent with previous studies – again showing sensitivity peaks near the source and detector and maximal sensitivity remaining in scalp and skull tissue layers – while also providing additional quantitative detail regarding the depth sensitivity and variability across the nineteen locations of the International 10–20 System. However, the literature still lacks a thorough examination of the relationship between the thickness of scalp and skull tissue layers and NIN sensitivity in realistic head models. Only a small handful of investigations have directly addressed the issue of overlying-tissue layers. A study in piglets (Kurth et al., 1993) suggested minimal contribution of scalp and skull to NIN measurements. However, the combined overlying layers in this study were only 3 mm thick in total, whereas the mean scalp plus skull thickness in an adult human is typically 10–18 mm. An in vitro study in calf brains found that the thickest skulls (13–14 mm) did not provide sufficiently strong NIRS signals for measuring cerebral oxygenation changes with their system, but thinner overlying layers were manageable (Pringle et al., 1998). A dynamic phantom study examined 6, 10 and 20 mm thick overlying tissue layers, simulating the scalp and skull morphology of a human infant, child and adult (Kurth and Thayer, 1999). In this work, sensitivity of NIN measurements was indeed compromised in adult humans, and errors in quantitative accuracy when measuring absorption changes can be greater than 30%. Okada and colleagues conducted several of the most direct studies addressing the issue of overlying scalp and skull tissue layers (Okada, 2000; Okada and Delpy, 2003b; Okada et al., 1995). In one, Monte Carlo simulation results were compared to measurements on a two-layer cylindrical phantom (2 mm outer layer on a 30 mm diameter phantom). At typical optode spacings for NIN measurements, even a 2 mm overlying layer affected the measurement of underlying tissue optical properties (Okada et al., 1995). In somewhat more realistic phantoms (including a 2 mm outer layer plus a 1–2 mm relatively clear CSF layer), a “light piping” effect was demonstrated from the CSF layer at depth in a cylindrical model (Okada, 2000). More recently, the effect of varying skull thickness from 4 to 10 mm was examined, given a fixed 3 mm thick scalp in a 5-layer, flat, semi-infinite slab model (Okada and Delpy, 2003b). In this model, sensitivity to brain tissue decreased as skull thickness increased, with an 80% reduction in NIRS signal intensity when the skull thickness expanded from 4 to 10 mm. They also examined the effect of a CSF layer ranging from 0.5 to 5.0 mm, noting a nearly 50% decrease in signal intensity with thicker (but nevertheless clear) CSF layers. A recent study by Hoshi and colleagues combined time resolved spectroscopy in three different locations on three individuals, with Monte Carlo simulations in a four-layer slab geometry (Hoshi et al., 2005). Results suggested that the primary layer of concern was scalp, and their three samples provided 3–13% NIRS sensitivity to brain tissue. None of these simulation studies, however, were conducted in realistic (e.g., MRI-based) head phantoms, which exhibit considerably higher tortuosity of CSF, gray and white matter layers than any of the models used. Such tortuosity would be expected to significantly reduce effects related to light piping. The evidence is thus considerable that overlying tissue layers such as scalp and skull adversely affect the detection of optical changes in deeper tissues. However, because the simulation studies were conducted in tissue models at considerable variance with an actual adult human head, and experimental studies were conducted in non-human mammals, questions remain regarding (1) the sensitivity to brain activity (changes in optical properties in gray matter) as a function of position on the head in realistic human head models, (2) the extent to which scalp and skull thicknesses affect NIN sensitivity, and (3) whether regional scalp and skull thicknesses interact when influencing NIN sensitivity across the adult human head. In this study, we utilized a comprehensive set of 3555 Monte Carlo simulations to address these questions.

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Materials and methods Brain tissue model We began with the well-known and characterized 1x1x1 mm Colin27 template brain (Holmes et al., 1998). This template was segmented into five tissue types – scalp, skull, cerebrospinal fluid (CSF), gray matter and white matter – by combining SPM8 intracranial segmentation and FSL's scalp and skull segmentation procedures. The SPM8 segmentation process (Ashburner and Friston, 2005) generated three tissue type probability images: gray matter, white matter and cerebrospinal fluid (CSF). Each probability map was then slightly smoothed (0.75 mm FWHM Gaussian kernel) and intracranial voxels were classified as gray matter, white matter or CSF. A voxel was classified as gray matter if it had the highest probability of being gray matter and this probability was greater than 20%. White matter was treated similarly. An intracranial voxel was then classified as CSF if it had a higher probability than both gray and white matter. Holes were filled with the modal nearest-neighbor tissue type (less than 0.02% of all voxels). The original Colin27 template was also passed through FSL's brain extraction tool (Smith, 2002) to generate three masks: scalp, skull, and intracranial tissue. The scalp and skull masks were merged with the above CSF, gray and white matter segmented volume to generate a whole head model with 5 tissue types: scalp, skull, CSF, gray matter, and white matter. Upon measurement, the mean scalp thickness for Colin27 was found to be 11.4 ± 3.0 mm (for MNIz > −20 mm), which is substantially at odds with reported values (Babiloni et al., 1997; Hori et al., 1972; Oldendorf and Iisaka, 1969; Todd and Kuenzel, 1924). This could arise due to various factors related to the MRI acquisition and multi-scan averaging, to which we return in the discussion. We thus eroded the scalp layer by three steps using Freesurfer's mri_binarize tool, resulting in a mean scalp thickness of 6.9 ± 3.6 mm. Example slices from the resulting segmentation appear in Fig. 1A. Optical properties were assigned to these five tissue types as per Table 1. These values represent the mean of published optical properties, in log units, across four typically used NIRS wavelengths: 690, 750, 780 and 830 nm (Bevilacqua et al., 1999; Okada et al., 1997a; Torricelli et al., 2001). For all tissue types, the tissue anisotropy parameter (g) was set to 0.01 – representing predominantly forwardscattered light – and the tissue index of refraction (n) was set to 1. In addition, when applying FSL's brain extraction tool (Smith, 2002) to the template brain, we generated three tessellated surfaces: outer scalp, outer skull, and inner skull. The three generated surfaces are illustrated in partial cutaway in Fig. 1B. Scalp and skull thickness measurement The three surfaces generated by FSL (scalp, outer skull, and inner skull) were each composed of 2562 vertices, 5120 faces, and provided point-to-point correspondence from scalp surface through to inner skull. The thickness of scalp and skull at each mesh point was estimated by computing the Euclidean distance between corresponding point pairs. Toward the inferior edge of the brain, scalp thicknesses in particular became quite large, as most tissues in the face (muscles, cartilage, eyes, etc.) were categorized as scalp tissue. For analyses involving scalp and skull tissues, we therefore excluded any points on the mesh below MNIz = −20 mm, resulting in a total of 1551 mesh points. (Follow up analyses using different cutoffs between −10 mm and −30 mm did not qualitatively change the results reported herein.) Monte Carlo simulation points Some 5000 points were initially spaced 5 mm apart on a 95 mm radius sphere, centered at the center voxel of the Colin27 volume. Sphere points were then moved radially toward or away from this center voxel until they reached the surface of the segmented Colin27 scalp. The points

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list was then pruned to remove points distant from underlying brain tissue, resulting in 3555 points spaced 3–6 mm apart and covering all scalp regions overlying brain tissue. These points constituted the source locations and directions for photon injection for the Monte Carlo simulations.

Monte Carlo simulations We employed a three dimensional Monte Carlo method to simulate light propagation in brain tissue by adopting the tMCimg code, as described in detail by Boas et al. (2002) and based on the general approach described by Wang et al. (1995). One hundred million (10 8) input photons were initially assigned a unit weight, and were traced one by one as they propagated through our 5-layer Colin27 tissue model. At each step, the weight was incrementally decreased by a factor of exp(−μaL) due to absorption, where μa is the absorption coefficient of the tissue and L is the length traveled by the photon. A scattering angle is then calculated using the probability distribution given by the Henyey-Greenstein phase function, and a new scattering length was determined from an exponential distribution. The photon was moved the new distance in the updated direction defined by the scattering angle. This process continued until the photon exited the medium or traveled longer than 10 ns, since the probability of photon detection in perfused tissue after such a period of time is extremely small. The output of a given Monte Carlo simulation included the photon fluence at each 1x1x1 mm voxel within the head model, which is an accumulation of all photon weights within each voxel in the tissue. This output is also known as the 2-point Green's function and depends on the tissue scattering and absorption coefficients in Table 1. In addition, each MC simulation stored the number of photons exiting within a 3 mm diameter of each detector location and the “history” of each detected photon: the (partial) path length traveled by that photon through each of our five tissue types. This path length history information can be used to investigate changes in tissue absorption coefficients without re-running the time consuming Monte Carlo simulations, provided there is no change in scattering coefficients. Importantly, this can be done without making any assumptions about the nature of the perturbation—that is, there is no need to invoke the Born or Rytov approximations to the diffusion equation (Kak and Slaney, 1988). For detectors in each MC run, we selected a subset of the remaining 3554 MC simulation points, namely those that were at least 20 mm but no more than 75 mm distant from the source location, for storage and computational reasons.

Table 1 Optical properties for scalp, skull, CSF, gray and white matter during Monte Carlo simulations. Tissue type

μa(mm−1)

μs(mm−1)

Gray White CSF Skull Scalp

0.019500 0.016900 0.002500 0.011925 0.017275

1.10 1.35 0.01 0.92 0.72

This same procedure was conducted for each of our 3555 MC simulation points. Sensitivity definitions For a NIRS measurement, we define sensitivity as the change in an optical signal (or "response") caused by a unit perturbation in target tissue optical property (or "contrast”). The response is usually expressed in optical density (OD) units: ΔOD ¼ log

ϕ0 ϕ

ð1Þ

where (ϕ0) is the baseline NIRS signal intensity and ϕ is the perturbed NIRS signal intensity. During functional brain activation, a major contrast is due to changes in tissue absorption caused by altered brain hemodynamics (blood volume and oxygenation changes). In our Monte Carlo simulation, only absorption changes are considered; scattering is assumed to be constant. Since non-invasive NIN involves shining light through scalp, skull and CSF to measure changes in brain tissue, all individual NIN measurements are subject to a partial volume effect. In MRI, the total signal intensity in a voxel is a blend of signals from various tissue types (e.g., gray matter, white matter, cerebrospinal fluid, vessels, and so on), roughly in proportion to the volume of each tissue type contained within that voxel (i.e., the partial volume). For a NIN measurement, the total signal intensity measured at the scalp surface is instead related to the mean distance (i.e., path length) that photons travel from source to detector. This total path length can, in turn, be divided into a set of “partial path lengths” (PPLs): the distance that a given photon traveled through each of the various tissue types (e.g., scalp, skull, CSF, gray and white

Fig. 1. (A) Sections through the segmented Colin27 head (clockwise from upper left: MNIx = +10 mm, MNIy = +5 mm, MNIy = −40 mm, MNIz = +10 mm). Shades from white to dark gray are: scalp, skull, cerebrospinal fluid, white and gray matter, respectively. This voxel-space was utilized for the MC simulations. (B) The three main surfaces generated from Colin27: inner skull (yellow with mesh), outer skull (blue) and outer skin (gray plus mesh). For visualization purposes, the outer skull was cut away at MNIx = −30 mm, while the outer skin surface was cutaway at MNIx = −10 mm. These surfaces were used to compute scalp and skull thicknesses at the vertices shown.

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matter; (Hiraoka et al., 1993b; Mansouri et al., 2010)). Eq. (2), relating the partial path length to optical signal change, was originally derived by Hiraoka et al. (1993b).

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separation-independent relative sensitivity (PPLk/TPL). We will thus present both in our results below. Perturbation method for sensitivity estimation

log ϕϕ0 δμ aXk

¼ PPLk :

ð2Þ

Since we defined NIRS sensitivity as the change in signal (ΔOD) per unit change in optical properties (δμa _ k), the absolute sensitivity of a NIRS measurement to a given tissue type is the mean path length traveled through that tissue type (Eq. (2)), as previously derived (Heiskala et al., 2007; Hiraoka et al., 1993b; Mansouri et al., 2010). Combining Eq. (2) with Eq. (1), it is straightforward to derive Eq. (3) which relates the optical density change to the partial path lengths: ΔOD ¼ log

ϕ0 ϕ

N

¼ ∑k¼1 PPLk δμ aXk :

ð3Þ

PPLk represents the absolute sensitivity to an absorption change in tissue k, and is measured in length units (e.g., millimeters). Note that PPLk depends on many parameters such as source–detector separation, tissue optical properties, and the tissue's heterogeneous structure. Another useful measure is the relative sensitivity of a NIN measurement to a given layer (e.g., gray matter): that is, the proportion of the total NIN signal change that derives from a given layer. To estimate this proportion, we use the definition of mean total path length (TPL) derived for heterogeneous media by Hiraoka et al. (1993b). Mean TPL is defined as the speed of light multiplied by the mean total transit time for photon propagation in heterogeneous medium; it is the average path length photons travel in a heterogeneous medium before reaching a detector. For a heterogeneous medium, such the segmented Colin27 head, the TPL is simply the sum of the partial path lengths through each of the individual tissue types: N

TPL ¼ ∑k¼1 PPLk :

ð4Þ

Given this TPL, we can then define the relative sensitivity as follows: Relative sensitivity ¼ PPLk =TPL:

ð5Þ

This relative sensitivity is unitless (range: 0–1) and estimates the proportion of the total path length traveled in a particular layer (e.g., gray matter). To see why relative sensitivity is useful, consider two different NIRS measurements. First, consider an extreme case where the PPL for gray matter, PPLGM, is 5 mm while the TPL = 10 mm. Assuming fluctuations in the overlying scalp and skull layers (e.g., cardiac and respiratory effects) are of similar amplitude to the functional activation signals, about 50% of the NIRS sensitivity (ΔOD) would arise from gray matter. However, if a different SD pair has the same absolute sensitivity, PPLGM = 5 mm, but a TPL = 100 mm, only about 5% of the sensitivity arises from gray matter. In these two examples, the absolute sensitivity is the same, but the relative sensitivity is very different. Note, as can be seen from Eq. (3), the contrast acquired from a surface measurement is a function of both the sensitivity to each layer, and the absorption changes (contrast) due to hemodynamic variations in each layer. The sensitivity and the absorption change are two independent parameters. Since we cannot know a priori the magnitude of fluctuations in each layer in a given study, this paper focuses only on the sensitivity and, for the relative sensitivity, we need to assume similar contrasts in each of the tissue layers. Given the variety of potential interferences in a non-invasive NIN measurement, the variability of overlying tissue layers in the head, and our investigation of SD separations, it is useful to know both the absolute sensitivity to a particular layer (PPLk) as well as the SD

We utilized a “perturbation method” to directly calculate the left-hand side of Eq. (2) (and hence PPL) by separately determining the intensities ϕ0 and ϕ (the detected measurements at the surface of the head before and after absorption perturbations). The calculation of ϕ0 and ϕ can be done according to Eq. (6), using the information stored in MC path length history file (Boas et al., 2002):

ϕ¼

1 N photons

  ∏ exp −μ a; j Li; j

Nphotons N X regions i¼1

ð6Þ

j¼1

where Nphotons is the number of photons collected, μa,j is the absorption coefficient in tissue type j, and Li,j is the path length of photon i through tissue type j. Thus, we first used the path length history information and Eq. (6) to compute the baseline ϕ0 using the absorption values from Table 1. We then increased the absorption of all gray matter voxels by 1% – from 0.0195 mm −1 to 0.0197 mm −1 – and re-computed Eq. (6) to generate the perturbed signal intensity ϕ due to a 1% increase in gray matter absorption (i.e., a small change in absorption in all gray matter voxels). With the resulting ϕo and ϕ plus the known absorption perturbation to gray matter δμa _ GM we could then directly compute PPLGM for a NIRS measurement via the left hand side of Eq. (2). This process was separately performed for scalp, skull, CSF and white matter, to provide PPL estimates for each photon through all 5 tissue types. The sum of all 5 partial path lengths is the total path length (TPL) for a given photon. We could thus compute the relative sensitivity of a given SD-pair to gray matter by computing PPLGM/ TPL. Again, this is a key measure in this paper and means the proportion of the total path length that passes through gray matter voxels, or the relative sensitivity to gray matter. The above process generates one PPLGM/TPL sensitivity measurement, corresponding to a single SD pair. To obtain brain sensitivity estimates that are less biased by regional morphology or probe orientation than in previous studies (i.e., precisely how much scalp, skull or CSF are sampled by a single NIRS measurement), we computed local averages (cf. Fig. 4A). For each point on the head we first identified all pairs of MC simulation points that were separated by less than 70 mm and whose midpoint lay within 10 mm of the target point (Strangman et al., 2003). Sensitivity was then calculated via the perturbation method above for each such pair. The resulting sensitivities were then averaged within 5 mm bins. For example, the sensitivity at a given point to a 25 mm separation was computed by averaging the sensitivities for all SD pairs that were between 22.5 and 27.5 mm apart and whose midpoint lay within 10 mm of the target point, and so on. This approach provided sensitivity estimates at multiple separations, while being minimally influenced by the exact orientation of a probe placed at that location. Quantification of scalp and skull influence on NIRS measurements Finally, to quantify the influence of scalp and skull thicknesses on NIN measurements, we first directly compared scalp and skull thickness in our head model to assess the range of each measure and their co-variance. We then computed multiple linear regressions for seven source–detector separations (20, 25, 30, 35, 40, 45 and 50 mm). Each regression used local scalp thickness, skull thickness, and a scalp-byskull interaction term as predictors of the sensitivity to our 1% perturbation in optical properties in all (but only) gray matter voxels (i.e., dependent variable = PPLGM/TPL).

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Results Scalp and skull thicknesses Fig. 2 maps the computed scalp and skull thicknesses, point by point, in relation to the underlying cortical anatomy in the Colin27 template. Excluding regions inferior to MNIz = −20 mm (gray planes in Fig. 2), the whole head mean scalp thickness for our scalp-eroded model was 6.9 ± 3.6 mm (mean ± SD; range: 3.6–11.2 mm). The whole head mean skull thickness was 6.1 ± 1.9 mm (range: 2.5–10.5 mm). As apparent in Figs. 2 and 3, the thinnest skull, in the lateral temporal region, also tended to be the area with thickest scalp. Quantitative summaries of the thickness values and variability at each of the International 10–20 System locations appear in Table 2. Fig. 3 plots skull thickness versus scalp thickness for all surface points where MNIz > −20 mm (n = 1551). In general, there appeared to be a nonlinear, slightly U-shaped relationship between the two measures in that it was relatively uncommon for a location to have both a thick scalp and a thick skull. A simple linear regression found scalp thickness to be a significant predictor of skull thickness (F(1,1549) = 218.3, p b 0.0001), with a regression coefficient of −0.32. This implies a 1 mm increase in scalp thickness was associated with a 0.32 mm decrease in skull thickness. However, the R2 was only 0.12, suggesting a non-linear model would likely provide a more appropriate fit. Of primary importance here, however, is that we observed a substantial range in both scalp and skull thicknesses (factors of 3 or more), and there was not exceptionally tight co-variation between the two layers in our template head model.

Global and regional sensitivity for near-infrared neuroimaging Fig. 4 illustrates the computation of mean sensitivity to brain tissue at a single location on the head. First, one Monte Carlo simulation point was chosen for sensitivity calculation (blue dot in Fig. 4A). Then all MC points within a radius of 30 mm from the target were identified (red dots), and the absolute sensitivity (PPLGM) was computed between unique pairs if their midpoint lay within 10 mm of the target point, an example depicted by the circled pair of red dots with a midpoint at the x. This process was repeated for all such pairs surrounding the blue target point. Sensitivity was then computed from the path length history file as the change in NIRS signal resulting from a 1% increase in baseline absorption coefficient in all gray matter voxels (and, separately, a 1% increase from respective baseline absorption coefficients for each of the other tissue types). The computed absolute PPL for each of our template's 5 tissue types is plotted against SD separation in Fig. 4B. The relative sensitivity – defined as the partial path length through a given tissue type k (PPLk), divided by the total path length (the sum of PPLks) – is plotted for 10–20 location C3 in Fig. 4C. For visualization purposes, the sensitivity measures were also averaged over 5 mm bins and plotted as black circles connected by lines. From this figure, the sensitivity to gray matter at location C3 (open red circles) rises from 5% at a SD separation of 20 mm up to approximately 15% at SD separations of 55–65 mm. The absolute and relative sensitivity values for gray matter (e.g., red circles, Figs. 4B and C) were then computed at each of the MNI coordinates of the 19 standard locations in the International 10–20 System (Okamoto et al., 2004). The resulting curves (averaged over 5 mm bins) were combined into a grand average curve in Fig. 5, in which the errorbars represent the variability across the nineteen 10–20 locations. Focusing on the results for gray matter, the whole-head average absolute sensitivity (PPLGM) increases essentially linearly (Fig. 5A), whereas the relative sensitivity (PPLGM/TPL) increases from 6% at a separation of 20 mm up to a sensitivity plateau of 17% at 55–65 mm separations (Fig. 5B). Scalp and skull sensitivity varies greatly over this range, but significantly less variability was observed for gray matter (and even less for white matter).

Fig. 6 plots the estimated NIN sensitivity at each of the 10–20 locations as a function of SD separation. For characterization purposes, the variability plotted is the standard deviation across the differentlyoriented SD pairs centered on that 10–20 location. In general, sensitivity appeared slightly more variable at longer SD separations, as well as along the most inferior portion of the brain (F7, F8, T3, T4, T5 and T6). The standard deviation of the relative sensitivity was nevertheless modest, ranging from 5.0 to 15.7% of the mean sensitivity. The detailed scalp thickness, skull thickness, and brain sensitivity values for each of these locations are quantified in Table 2, also separated according to SD separation. Out of the nineteen 10–20 positions we see the highest sensitivity tended to be in O1/O2, regardless of SD separation. The C3/C4 locations were next highest in absolute sensitivity, whereas F3/F4 were next highest in relative sensitivity. Inferior lateral prefrontal cortex (F7, F8) along with midline regions (Fz, Pz) tended to exhibit the lowest sensitivities, and other regions show intermediate sensitivities. (Note that data at Fz and Pz are missing at the longest SD separations due to insufficient photon data from the relevant MC simulations.) Sensitivity maps for near-infrared neuroimaging To map sensitivity across the entire head, we next calculated the average NIN sensitivities (absolute and relative) for each of the 3555 MC positions, using the technique exhibited in Fig. 4A. Sensitivities were again binned by SD separation, and plotted at the inner skull surface to provide reference to the underlying cortex. The color overlay in Fig. 7 depicts the absolute NIN sensitivity to the gray matter (PPLGM) for a source–detector pair X mm apart and centered at each location (where X = 20, 25, 30, 35 40, 45 or 50 mm), whereas Fig. 8 similarly depicts relative sensitivity to gray matter (PPLGM/TPL). Points were projected onto the inner-skull surface (instead of the scalp surface) for visualization purposes. First, as evident from the figure scale bars, there was more than an order of magnitude difference in NIN sensitivity between 20 mm and 50 mm SD separations in several regions. Second, sensitivity to anterior temporal pole and cerebellum was uniformly weak, presumably due to the thicker overlying tissue layers. Third, there was a substantial range in sensitivity around the head, again spanning an order of magnitude or more difference between regions even given a fixed SD separation. The qualitative pattern of absolute vs. relative sensitivity was quite similar. Higher sensitivity was identified in lateral prefrontal cortex, approximately over the middle frontal gyrus, occipital cortex, and in the vicinity of the occipital-temporo-parietal junction. Lower sensitivities were observed in inferior frontal, temporal and occipital regions, cerebellum, and mid-sagittal regions. The sensitivity ranges for all 2917 MC points superior to MNIz = −20 mm (that is, excluding the particularly low sensitivity values in inferior temporal and cerebellar regions) are listed in Table 3. From these values, sensitivity around the head spanned more than an order of magnitude for SD separations of 30 mm or less. Fig. 9 shows the sensitivity estimates in all views for a 30 mm separation, which exhibited good though imperfect left-right symmetry. (Figures for other separations are included as Supplementary Figs. SD1–4.) Sensitivity in relation to scalp and skull thickness Because an analytical equation relating NIN sensitivity to scalp or skull thickness is difficult to derive, we sought to empirically identify and quantify relationships between the scalp and skull thicknesses and our Monte Carlo estimates of brain sensitivity. First, each of the 1551 individual scalp mesh points superior to MNIz = −20 mm was paired with the nearest neighbor from our 3555 MC simulation points. This endowed each scalp mesh point with a scalp thickness and skull thickness as well as mean sensitivity measures for each investigated SD separation. We then applied a multiple linear regression model to each SD separation to predict sensitivity across these 1551 points using scalp thickness, skull thickness, and the scalp-by-skull interaction

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Fig. 2. Regional scalp and skull thicknesses in the Colin27 template. (A) Scalp thicknesses are represented by spheres, sized and colored according to thickness (measured in mm, with color changes at 0.5 mm steps). All spheres were placed at the corresponding point on the inner skull surface to help visualize thicknesses in relation to underlying cortical anatomy. (B) Skull thicknesses, plotted similarly and on the same scale. The most inferior regions (e.g., below the gray plane, located at MNIz = −20 mm) are artifacts related to the face and neck in the Colin27 template.

as predictors. The regression results are compiled in Table 4 and Table SD1. As an example, at 30 mm separation, the regression prediction equations would be: PPL ¼ 29:87–1:52scalp–1:17skull þ 0:067scalpskull

ð7Þ

PPLGM =TPL ¼ 0:197−0:01scalp−0:009skull þ 0:0005scalpskull ð8Þ

Fig. 3. Skull versus scalp thickness for points where MNIz > −20 mm. There was no easily characterized relationship between these two measures. Dotted lines are drawn at the mean scalp and skull thickness.

where the scalp and skull thicknesses are given in millimeters. Dropping the higher order (interaction) terms for simplicity, rounding and regrouping, we obtain an approximate simplified formulas: PPLGM ¼ 30–1:5scalp þ 1:2skull PPLGM =TPL ¼ 0:2–0:01ðscalp þ skullÞ

ð9Þ ð10Þ

Eq. (9) implies that, on average and given a 30 mm separation, the absolute sensitivity to gray matter is 30 mm minus 1.5 mm per millimeter of scalp minus 1.2 mm per millimeter of skull. Similarly from Eq. (10), the percent of the total path length through gray matter (i.e., sensitivity to gray matter) was approximately 20% minus 1% for each millimeter of scalp and skull. The simplified formulas slightly underestimate the sensitivity, as the interaction term would serve to increase the sensitivity (by 1.7 mm or ~1.3% with a 5 mm scalp plus a 5 mm skull layer). The multiple R 2 for the model fits in Table 4 were 0.35, 0.37, 0.40, 0.40, 0.40, 0.42 and 0.44 for the 20 through 50 mm separations respectively. These models, however, represent prediction of sensitivity assuming average SD separations and hence ignore up to 5 mm variations in SD separation. We therefore conducted a follow-up analysis, predicting individual SD pair sensitivities (>4 million points) from exact SD separations plus the scalp thickness, skull thickness, and interaction predictors. This analysis revealed very similar regression coefficients, and increased the R 2 to 0.84, suggesting that the modest variance accounted for by the models in Table 4 is largely related to the unaccounted for variability in SD separations in the previous analysis. For clarity, regression coefficients and variabilities are plotted in Fig. 10. From Table 4 and SD1 and Fig. 10 several points can be noted. First, it is again clear that with increasing SD separation, the baseline

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Table 2 Estimated scalp and skull thicknesses (in mm) plus NIRS relative sensitivity (PPLGM/TPL) at the nineteen International 10–20 System positions. Location

Fp1 Fp2 Fz F3 F4 F7 F8 C3 C4 Cz P3 P4 Pz O1 O2 T3 T4 T5 T6

Scalp

10.6 (1.1) 10.2 (1.7) 4.8 (0.6) 6.3 (0.6) 5.5 (0.5) 9.4 (1.5) 10.8 (1.8) 3.9 (0.5) 3.1 (0.2) 2.8 (0.3) 6.9 (0.9) 7.0 (1.1) 3.4 (0.3) 3.4 (0.4) 3.0 (0.5) 4.4 (0.2) 4.6 (1.0) 3.6 (0.3) 3.4 (0.2)

Skull

5.1 (2.7) 3.2 (1.0) 3.6 (1.3) 2.5 (0.2) 2.3 (0.2) 4.5 (0.5) 3.9 (0.5) 3.6 (0.5) 4.5 (0.9) 3.5 (0.7) 3.6 (0.2) 2.8 (0.3) 4.2 (0.5) 2.2 (0.5) 2.1 (0.1) 5.2 (1.2) 4.1 (0.5) 2.3 (0.2) 2.3 (0.2)

SD separation (mm) 20

25

30

35

40

45

50

0.074 (0.002) 0.073 (0.002) 0.073 (0.001) 0.111 (0.001) 0.104 (0.001) 0.066 (0.002) 0.049 (0.001) 0.102 (0.001) 0.076 (0.001) 0.092 (0.001) 0.111 (0.001) 0.118 (0.001) 0.072 (0.003) 0.139 (0.001) 0.139 (0.001) 0.096 (0.001) 0.090 (0.001) 0.090 (0.001) 0.080 (0.001)

0.093 (0.002) 0.094 (0.002) 0.086 (0.001) 0.136 (0.001) 0.125 (0.001) 0.085 (0.002) 0.069 (0.001) 0.122 (0.001) 0.095 (0.001) 0.105 (0.001) 0.134 (0.001) 0.134 (0.001) 0.099 (0.002) 0.156 (0.001) 0.156 (0.001) 0.114 (0.001) 0.111 (0.001) 0.112 (0.002) 0.101 (0.002)

0.110 (0.001) 0.110 (0.002) 0.093 (0.000) 0.156 (0.001) 0.142 (0.001) 0.102 (0.002) 0.089 (0.002) 0.136 (0.001) 0.111 (0.001) 0.113 (0.001) 0.147 (0.001) 0.145 (0.001) 0.112 (0.001) 0.167 (0.001) 0.168 (0.001) 0.126 (0.001) 0.127 (0.001) 0.132 (0.001) 0.123 (0.002)

0.124 (0.001) 0.123 (0.001) 0.096 (0.001) 0.169 (0.001) 0.156 (0.001) 0.118 (0.001) 0.102 (0.001) 0.145 (0.001) 0.121 (0.001) 0.117 (0.001) 0.156 (0.001) 0.152 (0.001) 0.122 (0.001) 0.175 (0.001) 0.177 (0.001) 0.135 (0.001) 0.135 (0.001) 0.150 (0.001) 0.142 (0.002)

0.135 (0.002) 0.133 (0.001) 0.097 (0.001) 0.177 (0.001) 0.163 (0.001) 0.131 (0.001) 0.120 (0.002) 0.151 (0.001) 0.128 (0.001) 0.122 (0.001) 0.162 (0.001) 0.157 (0.001) 0.127 (0.001) 0.179 (0.002) 0.185 (0.002) 0.142 (0.001) 0.144 (0.001) 0.162 (0.001) 0.157 (0.001)

0.144 (0.002) 0.140 (0.001) 0.099 (0.001) 0.188 (0.002) 0.174 (0.001) 0.141 (0.002) 0.135 (0.002) 0.156 (0.002) 0.135 (0.001) 0.125 (0.002) 0.162 (0.002) 0.160 (0.002) – – 0.182 (0.002) 0.189 (0.002) 0.145 (0.001) 0.147 (0.002) 0.171 (0.001) 0.173 (0.002)

0.148 (0.004) 0.151 (0.003) 0.094 (0.003) 0.202 (0.003) 0.185 (0.003) 0.156 (0.002) 0.145 (0.002) 0.159 (0.003) 0.145 (0.002) 0.133 (0.004) 0.162 (0.004) 0.161 (0.003) – – 0.179 (0.004) 0.188 (0.003) 0.150 (0.001) 0.146 (0.002) 0.178 (0.002) 0.186 (0.002)

sensitivity to brain (i.e., the intercept values) increased substantially, from PPLGM = 13 to 38 mm, or PPLGM/TPL = 0.128 to 0.195 (i.e., reaching nearly 20% of the total NIN signal at 50 mm separations). Second, at essentially every SD separation, scalp and skull exhibited significant negative coefficients; that is, thicker scalp or skull layers were associated with decreased sensitivity to gray matter. Third, the

magnitude of the scalp and skull coefficients varied nonlinearly with increasing separation, with the peak influence of scalp and skull found at a 30 mm separation. Averaging across separations, each millimeter of extra scalp or skull contributed to a decrease in PPLGM of 0. 8 mm and a decrease in PPLGM/TPL of approximately 0.007 (i.e., gray matter contributed 0.7% less to the TPL per millimeter of overlying

Fig. 4. Example computation of sensitivity to brain tissue for 10–20 location C3. (A) A central point (C3; blue) was designated as a target position, and the ring of detectors from within a 30 mm radius were identified (red). A pair of points in the ring (circled and connected by white line) was selected if their midpoint (white x) lay within 10 mm of the target point (blue). (B) Absolute sensitivity (PPL) at the blue target position (C3), in mm, for each tissue type as a function of SD separation. Individual circles represent individual SD pairs. Black dots represent averages over 5 mm bins. (C) Proportional sensitivity (PPLk/TPL) at C3 for all 5 tissue types.

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than 1%. The change in optical density (ΔOD) detected at the surface of the head was recomputed for 10–20 location C3, using eighteen different absorption coefficient perturbations ranging from a 1% to a 50% increase in gray matter absorption. The results are plotted in Fig. 11, and exhibit highly linear relationships between ΔOD and the magnitude of the optical property perturbation. Linearity was best at shorter SD separations, with the worst case regression across 1–50% generating an R2 of 0.995. A 50% increase in gray matter absorption coefficient generated close to a 50-fold larger signal change than a 1% increase in gray matter absorption coefficient. In other words, , although we specified 1% of perturbation in our simulation, the constant slope at each SD separation means that sensitivity calculation is essentially unaffected by the magnitude of the perturbation, and all our MC results are nearly independent of the exact value used. Discussion

Fig. 5. Average sensitivity over the entire head to a 1% change in optical properties for each of the 5 tissue types. (A) Absolute sensitivity to each tissue type (in millimeters). (B) Relative sensitivity to each tissue type. Error bars represent the standard error across the nineteen 10–20 locations used to generate the average curve.

layer). Fourth, the coefficient for scalp thickness was essentially always larger than the effect of skull thickness. And fifth, there was a significant interaction between scalp and skull predictors at shorter SD separations (35 mm or less). At these shorter separations, a thin scalp or skull layer was associated with a larger effect of the other layer (up to 2.3 times larger at a 20 mm separation). This presumably arises because the vast majority of the sensitivity at shorter SD separations comes from scalp and skull layers, so that when one layer is thinner, the influence of the other layer increases substantially. At separations >35 mm, where the NIN measurement sensitivity is more evenly distributed between scalp and skull layers, scalp and skull thicknesses provided strictly additive influences on both absolute and relative NIN sensitivity. Effects perturbation magnitude on NIRS sensitivity calculations It is well known that the brain is capable of producing a broad range of regional alterations in cerebral hemodynamics. As a final check, we therefore performed a series of computations to estimate the linearity of NIN signals to absorption coefficient changes greater

In this paper, we utilized a set of 3555 Monte Carlo simulations – performed on the well-characterized Colin27 MRI head template (with eroded scalp thickness) – to assess the sensitivity of non-invasive NIN around the head, and to quantify the influence of overlying scalp and skull tissue on NIN sensitivity. Overall sensitivity was very strongly modulated by SD separation, as would be expected from the exponential absorption of light through tissue. Regional sensitivity to the brain was also found to be quite variable. Across the 10–20 head positions, sensitivity typically ranged by a factor of 2 at any given separation. Around the head (superior to MNIz = −20 mm), relative sensitivity differed by a factor of 3.4 at a 50 mm SD separation and grew to a factor of 31.6 given a 20 mm source–detector separation. Reasonable left-right symmetry was observed, with notable departures in lateral prefrontal cortex. Independent of SD separation, sensitivity was (1) relatively high in occipital regions and dorsolateral prefrontal cortex (especially on the left), (2) low in the temporal pole and the cerebellum, and (3) moderately low over midline regions. Both scalp and skull thicknesses clearly influenced brain sensitivity, with scalp being consistently more influential than skull. The effects of the two overlying layers were found to be partly but not entirely independent of one another. When combined with detailed SD separation measures, scalp and skull thicknesses accounted for ~84% of the variance in regional sensitivity across the head, suggesting that these are the major factors contributing to the regional sensitivity. Overall, this work helps provide a clearer and much more quantitative picture of the sensitivity of NIRS measurements to the brain in a realistic head model. Scalp and skull thicknesses Point by point scalp and skull thicknesses in this study were estimated from the MRI of a single individual. The measured mean skull thickness of 6.1 mm was quite consistent with prior work (Law, 1993), including a recent CT study on 3000 individuals, which found a mean skull thickness in various parts of the head to range from 5.37 to 7.56 mm in adult males, and slightly thicker, at least in certain regions, in adult females (Li et al., 2007). Relatively few studies of scalp thickness have been conducted to date. Studies of adult human scalp in cadavers have reported thicknesses in the range of 3.5–7 mm (Hori et al., 1972; Oldendorf and Iisaka, 1969; Todd and Kuenzel, 1924), which is roughly half the 11.4 mm thickness initially estimated for the Colin27 template. In vivo measurements of local scalp resistance produced thicker estimates, from 4.8 to 9.5 mm, but still less than the initial mean thickness we estimated (Babiloni et al., 1997). We note, however, that our scalp estimation included (1) considerably more points around the head than previous work, (2) included points covering parts of the ears and inferior frontal regions where our scalp estimates likely represent overestimates or are atypically thick, and (3) involved calculating Euclidean distances between outer skin

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Fig. 6. Sensitivity to gray matter as a function of 10–20 location and SD separation distance. (A) Absolute sensitivity to gray matter (PPLGM, in mm). (B) Relative sensitivity (PPLGM/TPL). Error bars represent the variability (mean ± std) across differently-oriented SD pairs at each point.

and outer scalp surfaces estimated from a combination of 27 MRI scans instead of direct tissue measurements. The differences in method, the classification of muscle and fat layers as part of the “scalp”, the use of a

template warped to MNI space, and individual variability are all possible explanations of our thicker scalp estimates. Given that scalp thicknesses over ~10 mm are associated with the rarely occurring condition of

Fig. 7. Whole-head maps of absolute NIN sensitivity (PPLGM) to a 1% increase in absorption coefficient restricted to gray matter voxels (representing a small increase in functional activation).

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Fig. 8. Whole-head maps of relative NIN sensitivity (PPLGM/TPL) to a 1% increase in absorption coefficient restricted to gray matter voxels (representing a small increase in functional activation).

lipedematous scalp (Martinez-Moran et al., 2009), we elected to erode the scalp layer to 6.9 ± 3.6 mm prior to conducting the Monte Carlo runs, to achieve better overlap with existing scalp estimates. Regardless of absolute thickness, a primary goal of our study was to quantify the changes in sensitivity to brain tissue resulting from varying scalp and skull thicknesses. In this situation, what is most important is the inclusion of a broad range of thicknesses for each tissue layer. The model we generated, albeit limited in terms of more subtle tissue layering, exhibited approximately 3-fold ranges in thickness, thereby reducing concerns about restricted range analyses. In addition, the thickness ranges exhibited substantial overlap with prior thickness estimates, to limit the need for extrapolation. We also performed a full set (3555) of MC simulations on the original, thicker scalp. Qualitatively, we replicated all results reported herein, with the primary difference being uniformly lower sensitivity to brain tissue in the thicker-scalp model. The regression results provided in Table 4 and Table SD1 can be used to estimate sensitivities in head models with thickness combinations other than those specifically contained in the Colin27 head template. However, caution must of course be exercised when extrapolating beyond the ranges given. Consider an extreme case: our “simplified” sensitivity formula for 30 mm, Eq. (10), implies PPLGM/TPL = 0.2 if scalp and skull thicknesses were both zero. However, the case where scalp = skull = 0 mm implies an on-brain (or, technically, on-CSF) measurement, which would certainly provide more than 20% of its sensitivity from gray matter. This would suggest a strong nonlinearity likely exists in the limit of thin overlying layers. Thus, extrapolation to cases where scalp b 2 mm and/or skull b 3 mm, or where other unusual tissue types exist – such as large CSF voids, vascularized tumors, or ischemic penumbras – should be considered highly speculative.

Table 3 PPLGM/TPL sensitivity ranges over the entire head (MNIz > −20 mm) for each source– detector separation. Separation (mm)

Minimum sensitivity

Maximum sensitivity

Max/min ratio

20 25 30 35 40 45 50

0.004 0.007 0.014 0.023 0.030 0.044 0.060

0.114 0.139 0.162 0.178 0.189 0.197 0.205

31.6 20.4 12.0 7.6 6.2 4.5 3.4

Global and regional sensitivity versus source–detector separation Global sensitivity to brain tissue was found to increase quite linearly over SD separations ranging from 20 to 45 mm. Beyond 45 mm, further separation increases continued to improve absolute sensitivity to brain tissue relatively linearly, but only relative sensitivity exhibited notably diminishing returns. Importantly, our estimates are based on the described perturbation method and hence require minimal assumptions about the analytical form of the photon distribution through tissue. The increasing sensitivity at depth with larger separations was expected based on various prior findings (Fukui et al., 2003; Hiraoka et al., 1993a; Mansouri et al., 2010; Strangman et al., 2003). However, given the variable curvature of the head, the irregular distribution of brain tissue, and the variability of overlying tissue types and thicknesses, the quantitative nature of the sensitivity curve in Fig. 5 could not be intuited. The overall global sensitivity curve suggests three components: (1) a minimal-sensitivity region below 20 mm separations, which we were unable to characterize in any detail; (2) a region where there is a significant and largely linear increase from 20 to 45 mm separations, and (3) an asymptotic region in relative sensitivity at 45+ mm separations. This suggests that, on average and when the instrument and experiment allow, deploying SD separations of 45 mm should generally provide a good trade-off between signal levels and sensitivity to brain tissue. We should note, however, that the use of larger SD separations is of course restricted by the noise floor for any given instrument. Analytical derivation of this limit for any given instrument is not possible for the complex geometry of the head, although techniques similar to those presented here could be utilized to calculate such limits analytically in future work. Importantly, the peak sensitivity varied considerably around the head, as seen in Fig. 6 through Fig. 9 and the supplementary data. Thus, a NIRS probe with fixed SD distances would exhibit substantially different brain sensitivity when moved around the head. These regional differences in sensitivity are maximal at the shortest (20–25 mm) SD separations considered. Achieving more uniform NIRS sensitivity to the brain requires the use of larger SD separations. Because we used just a single head model, it was important to account for regional geometric effects such as local pools of CSF, unusually large portions of white matter within the field of view of the NIRS measurement, and so on. We did this by averaging our sensitivity values over all possible SD pairs surrounding a target point on the head, thus allowing us to generalize our results across probe orientation in this head model or, partially equivalently, generalizing over internal

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Fig. 9. Whole-head NIRS sensitivity map (PPLGM) at a typical source–detector separation of 30 mm. Similar plots for 20, 40 and 50 mm SD separations and for plots relative sensitivities can be found in the Supplementary Figures.

structure across different heads. The variability associated with different probe orientations turned out to be modest (cf. Figs. 4C and 6), so probe orientation was not deemed a major factor in NIN sensitivity. Its most prominent role was played around the inferior edge of the brain.

The modest variability also suggests that “simulation noise”, due to the inherently random Monte Carlo method, was also a minor contributor to our NIN sensitivity estimates, as the scattered circles include noise both due to probe orientation and MC run.

Table 4 Regression results predicting relative sensitivity (PPLGM/TPL) from scalp and skull thickness at different source–detector separations. A similar table for absolute sensitivity (PPLGM) is in Table SD1. SD separation

Parameter

Coef.

[Conf. Int.]

20 mm

(Intercept) Scalp Skull Scalp:skull (Intercept) Scalp Skull Scalp:skull (Intercept) Scalp Skull Scalp:skull (Intercept) Scalp Skull Scalp:skull (Intercept) Scalp Skull Scalp:skull (Intercept) Scalp Skull Scalp:skull (Intercept) Scalp Skull Scalp:skull

0.128 −0.007 −0.008 0.0005 0.165 ‐0.009 −0.009 0.0005 0.197 −0.010 −0.009 0.0005 0.210 −0.009 −0.008 0.0004 0.209 −0.007 −0.006 0.0001 0.203 −0.006 −0.004 0.0000 0.195 −0.004 −0.002 −0.0001

0.117 −0.009 −0.009 0.0003 0.152 −0.011 −0.011 0.0003 0.183 −0.011 −0.011 0.0003 0.197 −0.010 −0.010 0.0001 0.196 −0.009 −0.008 −0.0001 0.190 −0.007 −0.006 −0.0002 0.182 −0.005 −0.004 −0.0004

25 mm

30 mm

35 mm

40 mm

45 mm

50 mm

0.139 −0.006 −0.006 0.0006 0.178 −0.008 −0.007 0.0008 0.211 −0.008 −0.007 0.0007 0.224 −0.008 −0.006 0.0006 0.222 −0.006 −0.004 0.0004 0.216 −0.004 −0.002 0.0002 0.208 −0.003 0.000 0.0001

St.Err

T

p

0.0057 0.0006 0.0009 0.0001 0.0066 0.0007 0.0010 0.0001 0.0070 0.0007 0.0011 0.0001 0.0069 0.0007 0.0011 0.0001 0.0068 0.0007 0.0010 0.0001 0.0068 0.0007 0.0010 0.0001 0.0068 0.0007 0.0010 0.0001

22.4 −12.4 −8.7 5.0 25.0 −13.3 −8.9 5.1 28.1 −13.3 −8.5 4.3 30.3 −12.5 −7.4 3.1 30.9 −10.3 −5.6 1.4 30.1 −8.0 −3.7 −0.1 28.5 −5.5 −2.2 −1.2

b0.0001 b0.0001 b0.0001 b0.0001 b0.0001 b0.0001 b0.0001 b0.0001 b0.0001 b0.0001 b0.0001 b0.0001 b0.0001 b0.0001 b0.0001 0.0017 b0.0001 b0.0001 b0.0001 0.1770 b0.0001 b0.0001 0.0002 0.8976 b0.0001 b0.0001 0.0278 0.2148

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Fig. 10. Regression coefficients (and their standard error) for the influence of scalp and skull on relative NIN sensitivity. A coefficient of −0.01 implies a 1 mm increase in scalp (or skull) thickness leads to a decrease in PPLGM/TPL of 0.01.

Effect of scalp and skull on NIRS brain sensitivity The previous simulation study examining skull thickness in relation to non-invasive NIRS measurements (Okada and Delpy, 2003b) found that increasing the skull thickness from 4 mm to 10 mm (in a 5-layer, flat, semi-infinite slab model) resulted in an 80% loss of NIRS signal strength. More detailed investigations of the influence of scalp or skull thickness on NIN measurement sensitivity in a head model had not been previously reported. We hypothesized that, beyond SD separations, regional variability in scalp thickness and, secondarily, skull thickness would be the primary contributors to regional differences in sensitivity. Both scalp and skull thicknesses were found to be significant and substantial predictors of sensitivity, with scalp thickness having a consistently, if modestly, larger effect. On average, at a typical SD separation of 30 mm (the worst case), each millimeter of extra scalp or skull decreased the absolute NIRS sensitivity by 0.8 mm and the relative NIRS sensitivity to brain tissue (PPLGM/TPL) by roughly 0.01. More specifically, using Eq. (8) and the mean scalp thickness of 6.9 mm and mean skull thickness of 6.1 mm, we estimate the sensitivity to gray matter, PPLGM/TPL = 0.094, or 9.4% of the TPL. Increasing scalp thickness to 7.9 mm results in a sensitivity estimate of 8.7% (again using

Fig. 11. Expected change in signal at 10–20 location C3, based on the MC results, given 1%–50% increases in gray matter absorption coefficients, plotted by SD separation.

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Eq. (8)). For comparison, consider a young child with scalp and skull thicknesses that are, say, 5.7 and 3.1 mm for scalp and skull respectively (Adeloye et al., 1975). Given the difference of 4 mm in overlying tissue as compared to our adult human model, Eq. (8) would predict an approximately 30% higher sensitivity (gray matter comprising 12% of the TPL, instead of 9.4%). Similar computations could be made for other combinations of scalp and skull thicknesses or SD separations. Such estimates can also be applied for particular sensor locations in individuals for whom a structural MRI scan of the head is readily available. Again, caution should be exercised near the edges of our tested range of thicknesses, or extrapolating beyond them, or even applying our results to individuals with dramatically different cerebral morphologies (particularly patients with degenerative disease, major brain injury, tumors or stroke). In such cases, new Monte Carlo simulations may be warranted to provide more accurate sensitivity photon propagation estimates. At every SD separation, scalp exhibited a larger effect than skull. Regression coefficients indicated that scalp and skull thicknesses were generally roughly equally important in determining sensitivity. Considerable variance remained unaccounted for in the separate SD separation regression fits. When fully accounting for SD separations, however, only 16% of the variance in sensitivity remained to be explained. This suggests that there are additional, minor contributors to NIN sensitivity. Based on previous studies, a primary candidate is CSF (Hayashi et al., 2003; Mansouri et al., 2010; Okada and Delpy, 2003a,b; Okada et al., 1997b). While we included CSF in our MRI-based head model, CSF does not reliably create a “layer” in such models and hence it was difficult to characterize and regionally quantify CSF for use in regression analysis. We do note, however, that the combination of low absorption and low scattering, as we modeled CSF in this paper, has previously been shown to generate the largest impact on sensitivity to brain (Mansouri et al., 2010; Okada and Delpy, 2003a,b). Our findings are thus consistent with the study by Custo and colleagues suggesting that while CSF can play a role in realistic brain geometries, it is likely a fairly modest one (Custo et al., 2006). Limitations We did not address the role of hair in our MC simulations. In effect, hair and (perhaps more importantly) hair follicles constitute a separate tissue type with different optical properties and a variable distribution around the head and from individual to individual. Hair would be expected to decrease sensitivities in regions with denser hair, while leaving the most frontal sensitivities unaffected. A thorough evaluation of hair's influence on NIN measurements has yet to be conducted, either experimentally or via simulations. Also, the specific methods used to segment the Colin template may have led to over- or under-estimates of tissue thicknesses or volumes. Proper assessment of this hypothesis requires re-segmentation and re-running all Monte Carlo simulations and follow-on analyses and hence was beyond the scope of this study. Our study also required choosing specific optical absorption and scattering coefficients for each tissue type. We did attempt to select typical values inasmuch as possible, we kept the chosen background optical properties constant for our MC simulations, and also ensured that these values were self-consistent: higher scattering in white matter than gray matter, low scattering and absorption in CSF, higher absorption in scalp versus skull (due to greater vascularization), and so on. Preliminary tests with different optical properties suggest that, while our quantitative results would be altered slightly by different absorption coefficients, the qualitative features of our findings would hold. Finally, as already discussed, we could not adequately quantify the contribution of CSF to brain sensitivity. Based on spatial images of photon flux from numerous prior MC simulations, we would hypothesize that CSF effects are maximized when there is in fact a CSF “shell” or “sheet” parallel to the surface from which reflection NIRS measurements are taken (as most prior simulation studies have used). Such a geometry is ideally suited to light-piping (Okada, 2000), unlike a highly convoluted CSF layer as in our model. Such shells

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are more common and more pronounced in the elderly than in younger individuals (Hasan et al., 2007), and hence may differentially affect sensitivity as a function of age. We would predict that pockets of CSF perpendicular to the measurement surface would have a relatively small effect on sensitivity. However, the precise manner in which the CSF layer may affect sensitivity and interact with scalp and skull thickness in complex head geometries remains to be investigated in detail. Conclusions Our study employed 3555 Monte Carlo simulations in an MRI-based head model (Colin27) to provide a comprehensive set of sensitivity estimates at less than 5 mm intervals for non-invasive NIRS measurements of brain tissue. We specifically sought to quantify the role of scalp and skull layers in making such NIN measurements. Scalp was found to have a consistently greater influence on NIRS' brain sensitivity than skull, but both tissue layers were important and both became less influential as source–detector separations increased. Overall, sensitivity varied sigmoidally across SD separations, providing limited sensitivity at 20 mm separations (and below), and near-maximal sensitivity at or above 45 mm separations. There was considerable variability in sensitivity around the head, differing by up to a factor of 31.6 when using shorter SD separations. The increase in minimum sensitivity to gray matter between 20 and 45 mm SD separations could also exceed a factor of 10. Thus, given NIRS instrumentation that is capable of reliable measurements at larger SD separations, it is possible to largely compensate for lower-sensitivity regions by utilizing a probe with larger source–detector separations. Our quantitative results provide indicators for when and where such probe adjustments likely need to be made, how much probe optimization might be needed in specific regions, and for interpreting NIRS results based on the probe geometry and head location probed. Despite being developed on a single head model, our spatial averaging and regression approach enables generalization of our quantitative sensitivity estimates to in other individuals with typical scalp, skull and CSF distributions. Such information is expected to help both in experimental planning and interpretation for future NIN studies and devices. Supplementary data to this article can be found online at http:// dx.doi.org/10.1016/j.neuroimage.2013.04.090. Acknowledgments This work was supported by the National Space Biomedical Research Institute through NASA NCC 9-58. Conflict of interest The authors report no conflicts of interest. References Adeloye, A., Kattan, K.R., Silverman, F.N., 1975. Thickness of the normal skull in the American Blacks and Whites. Am. J. Phys. Anthropol. 43, 23–30. Ashburner, J., Friston, K.J., 2005. Unified segmentation. NeuroImage 26, 13. Babiloni, F., Babiloni, C., Carducci, F., Del Gaudio, M., Onorati, P., Urbano, A., 1997. A high resolution EEG method based on the correction of the surface Laplacian estimate for the subject's variable scalp thickness. Electroencephalogr. Clin. Neurophysiol. 103, 486–492. Bevilacqua, F., Piguet, D., Marquet, P., Gross, J.D., Tromberg, B.J., Depeursinge, C., 1999. In vivo local determination of tissue optical properties: applications to human brain. Appl. Opt. 38, 4939–4950. Boas, D., Culver, J., Stott, J., Dunn, A., 2002. Three dimensional Monte Carlo code for photon migration through complex heterogeneous media including the adult human head. Opt. Express 10, 159–170. Custo, A., Wells III, W.M., Barnett, A.H., Hillman, E.M., Boas, D.A., 2006. Effective scattering coefficient of the cerebral spinal fluid in adult head models for diffuse optical imaging. Appl. Opt. 45, 4747–4755. Fantini, S., Franceschini, M.A., Fishkin, J.B., Barbieri, B., Gratton, E., 1994. Quantitative determination of the absorption spectra of chromophores in strongly scattering media: a light-emitting-diode based technique. Appl. Opt. 33, 5204–5213.

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