pone.0066319 1..13

Depth Sensitivity and Source-Detector Separations for

Near Infrared Spectroscopy Based on the Colin27 Brain

Template

Gary E. Strangman*, Zhi Li, Quan Zhang

Neural Systems Group, Massachusetts General Hospital/Harvard Medical School, Charlestown, Massachusetts, United States of America

Abstract

Understanding the spatial and depth sensitivity of non-invasive near-infrared spectroscopy (NIRS) measurements to brain

tissue–i.e., near-infrared neuromonitoring (NIN) – is essential for designing experiments as well as interpreting research

findings. However, a thorough characterization of such sensitivity in realistic head models has remained unavailable. In this

study, we conducted 3,555 Monte Carlo (MC) simulations to densely cover the scalp of a well-characterized, adult male

template brain (Colin27). We sought to evaluate: (i) the spatial sensitivity profile of NIRS to brain tissue as a function of

source-detector separation, (ii) the NIRS sensitivity to brain tissue as a function of depth in this realistic and complex head

model, and (iii) the effect of NIRS instrument sensitivity on detecting brain activation. We found that increasing the source-

detector (SD) separation from 20 to 65 mm provides monotonic increases in sensitivity to brain tissue. For every 10 mm

increase in SD separation (up to ,45 mm), sensitivity to gray matter increased an additional 4%. Our analyses also

demonstrate that sensitivity in depth (S) decreases exponentially, with a ‘‘rule-of-thumb’’ formula S = 0.75*0.85

depth

. Thus,

while the depth sensitivity of NIRS is not strictly limited, NIN signals in adult humans are strongly biased towards the

outermost 10–15 mm of intracranial space. These general results, along with the detailed quantitation of sensitivity

estimates around the head, can provide detailed guidance for interpreting the likely sources of NIRS signals, as well as help

NIRS investigators design and plan better NIRS experiments, head probes and instruments.

Citation: Strangman GE, Li Z, Zhang Q (2013) Depth Sensitivity and Source-Detector Separations for Near Infrared Spectroscopy Based on the Colin27 Brain

Template. PLoS ONE 8(8): e66319. doi:10.1371/journal.pone.0066319

Editor: Xi-Nian Zuo, Institute of Psychology, Chinese Academy of Sciences, China

Received March 21, 2013; Accepted April 29, 2013; Published August 1, 2013

Copyright: ß 2013 Strangman et al. This is an open-access article distributed under the terms of the Creative Commons Attribution License, which permits

unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited.

Funding: This work was supported by the National Space Biomedical Research Institute through NASA NCC 9-58. The funder had no role in study design, data

collection and analysis, decision to publish, or preparation of the manuscript.

Competing Interests: The authors have declared that no competing interests exist.

* E-mail: [email protected].harvard.edu

Introduction

Near-infrared spectroscopy (NIRS) and diffuse optical imaging

(DOI) have been successfully used for non-invasive assessment of

brain hemodynamics for over three decades [1,2,3]. Properly

interpreting any type of non-invasive measurement – including

NIRS and DOI – requires detailed knowledge about the

measurement’s spatial sensitivity profile. In general, the question

is what tissues are being probed by a given measurement? A more

specific question commonly asked is, what is the depth penetration

of NIN? Addressing these questions is particularly difficult because

light propagation through scattering media with heterogeneous

structure (such as the head) is inherently complex, and because the

governing mathematical models of this process – the radiative

transport equation and its diffusion approximation – are difficult

to solve analytically for any but the most trivial of tissue geometries

[4,5,6,7]. It is even more difficult to empirically measure light

fluence within tissue, as this would require the placement of

omnidirectional light detectors inside a probed medium.

For simple tissue geometries, such as optically homogeneous

tissues with infinite, semi-infinite or slab boundary conditions,

analytical solutions to the diffusion equation have been developed

[8,9,10,11,12,13]. However, even modestly more complex geom-

etries, and especially the irregular boundaries and undulating

layers found in brain tissue, have no analytical solutions. As a

result, far less is understood about the photon distribution through

the head and, consequently, NIRS sensitivity to brain tissue.

In the absence of direct observation or analytical solutions,

questions about sensitivity and penetration depth in complex

tissues must instead rely on numerical approaches. There are two

general categories: (1) approaches based on finite element (FE) and

finite difference (FD) analysis [14,15], or (2) Monte Carlo

simulations of photon propagation through the tissue in question

[16]. The appeal of FE and FD techniques is that they can handle

arbitrary tissue type boundary conditions yet require considerably

less computation time than Monte Carlo methods [15]. A

shortcoming of FE/FD techniques is that they need to assume

an analytical form for the photon migration through tissue.

Typically (though not always, e.g. [17]), the diffusion approxima-

tion is assumed. While the diffusion approximation is generally

well supported, it is difficult to test in detail the required

assumptions, particularly for complex tissue boundary conditions

such as the undulating layers inside a human head.

The other numerical technique typically employed is Monte

Carlo (MC) simulation [16,18,19,20]. This technique proceeds as

follows: (1) select a three-dimensional tissue geometry and divide it

into voxels of different tissue types, (2) assign scattering and

absorption optical properties to each voxel based on tissue type, (3)

select a point on the surface of this geometry and ‘‘inject’’ a photon

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at that point, (4) propagate that photon through the tissue by

allowing it to probabilistically scatter and be absorbed as it travels,

and (5) repeat steps 3–4 many thousands or millions of times and

accumulate the resulting photon weights (or, fluences) along with

the cumulative distance traveled through each tissue type. The

Monte Carlo approach is unfortunately quite computationally

intensive. However, it provides the most accurate estimate of

photon propagation through irregular boundary conditions and

heterogeneous media such as the human brain. Importantly, it

does not need to assume an analytical form for photon

propagation, and hence is not biased by diffusion or other

approximations [21,22].

A number of groups have used Monte Carlo methods to

investigate NIRS sensitivity in layered tissues. Most such studies,

however, have only considered relatively simple geometries such as

layered slabs [23,24,25,26,27], cylinders [28,29,30], or concentric

spheres [31]. In general, these studies confirm general expectations

based on diffusion theory: (1) depth sensitivity increases as source-

detector separation increases [31,32], (2) overlying tissue layers

interfere with the measurement of deeper layers [30,33,34], (3)

sensitivity to deeper layers decreases with increasing thickness of

overlying tissue layers [24,25], (4) depth sensitivity is affected by

the angle at which incident photons contact the surface [28], and

(5) there is an improvement of NIRS sensitivity to deeper tissue

layers when modeling scattering elements are embedded in

cerebrospinal fluid (CSF) layers [26]. These studies have provided

very useful guides, but the use of simple geometries means that the

results cannot be assumed to apply to brain geometries, at least not

quantitatively.

An important set of studies focused more specifically on the role

that the relatively clear CSF layer may play in NIN measurements

[23,24,25,26,29,35,36,37,38]. For example, at least one study

suggested that CSF could distort the sensitivity profile, both

broadening it and reducing the sensitivity to brain with increasing

CSF thicknesses from 0.5 to 5 mm [25]. The CSF effect also

appears strongly modulated by the precise amount of scattering

within the CSF layer itself [24,26,35,36]. These CSF-related

effects appear to be substantial relative to other tissue distribution

issues [38].

Six studies have examined realistic human brain models based

on structural MRI scans [32,34,35,38,39,40]. All of these studies

employed a handful of Monte Carlo simulations, focusing on a

particular location of the head. NIRS sensitivity to functional

brain activation was concluded to be ‘‘high’’ [34], at least for

source-detector (SD) separations in the 30–35 mm range [32,39].

In an MC study on two separate MRI-based head models of pre-

term infants, using 1 source plus 20 detectors around the head,

differences in tissue distributions were found to affect measured

NIRS signals, but these effects were modest compared to the

effects generated by the relatively clear CSF [38]. Another study

examined whether the CSF effect was sufficient to invalidate the

use of the diffusion approximation for computing photon

propagation through head tissue [40]. Using 1 source and 25

linearly aligned detectors in an MRI-based adult head phantom,

sensitivity to the brain reached approximately 11% of the

sensitivity profile at source-detector (SD) separations of 40 mm.

This sensitivity was slightly reduced in the face of larger scattering

coefficients, but the overall conclusion was that a relatively

scattering CSF layer (m’

~0:3mm

) was unlikely to generate

more than 20% error in sensitivity estimates when using the

diffusion approximation.

Most recently, Mansouri and colleagues combined an MRI-

based head model and a highly resource-intensive MC approach

to assess the sensitivity of NIRS to brain tissue over one location in

the left frontal pole [35]. Using four simulations, and examining

source-detector (SD) separations of 20, 33 and 40 mm, they found

sensitivity to brain tissue ranged from approximately 1% of the

total NIRS sensitivity (99% coming from scalp and skull) at a

20 mm SD separation, to 6–9% of the total NIRS sensitivity at

40 mm. The maximum sensitivity again depended on the amount

of scattering in the CSF layer, with higher scattering

(m’

~1:0mm

) leading to greater brain sensitivity as found by

Custo and colleagues.

The above findings–particularly when coupled to the known

anatomical variability for scalp, skull, CSF, gray and white matter

within and between people and brain regions – suggest that small

numbers of MC runs are likely to be biased by regional details in

tissue types and layer thicknesses. The available literature,

however, leaves a notable gap in terms of a more comprehensive

analysis of photon propagation across realistic head geometries.

First, the current maximum of less than 10 Monte Carlo runs in a

single head model is insufficient for comprehensively and robustly

evaluating NIRS sensitivity to complex tissues such as the brain,

much less providing variability measures of such sensitivity.

Second, there has been limited quantification of NIRS sensitivity

to brain versus non-brain tissue compartments as a function of

source-detector separation, or in relation to instrument sensitivity.

And third, NIRS sensitivity as a function of depth remains

particularly poorly understood for complex head geometries, yet

this is key information when trying to interpret NIN data. Here we

address each of these issues using over 3,555 Monte Carlo

simulations in a detailed, five-layer model of the standard Colin27

human head template.

Materials and Methods

Brain Tissue Model

For a well-characterized starting point, we used the 16161mm

Colin27 template brain [41], as distributed with FSL v4.1 [42]. To

this scan, we applied the default SPM8 segmentation process [43]

which generated three tissue type probability images: gray matter,

white matter and cerebrospinal fluid (CSF). Each probability map

was slightly smoothed (0.75 mm FWHM Gaussian kernel) and

then 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 [44] 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 was found to be 11.463.0 mm (for

MNIz.220 mm; Figure 1A-inset), which is substantially at odds

with reported values [45,46,47,48]. This could arise due to various

factors related to the MRI acquisition and multi-scan averaging.

Hence, we eroded the scalp layer by 3 single-voxel steps using

Freesurfer’s mri_binarize tool, resulting in a mean scalp thickness

of 6.963.6 mm which is more in line with prior findings. We

proceeded with the 5-layer model with the eroded scalp

(Figure 1A).

For the Monte Carlo simulations, optical properties were

assigned to the five tissue types, per Table 1. These values

represent the mean of published optical properties across four

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typically-used NIRS wavelengths: 690, 750, 780 and 830nm

[23,49,50]. For all tissue types, the tissue anisotropy parameter (g)

was set to 0.01–representing predominantly forward-scattered

light – and the tissue index of refraction (n) was set to 1.

Monte Carlo Injection Points

Some 5,000 points were initially spaced 5 mm apart on a

95 mm radius sphere (the approximate radius of the Colin27

head). The sphere was centered within the Colin27 volume, and

the sphere points were moved radially toward or away from this

center voxel until they reached the surface of the Colin27 scalp.

This location list was then pruned to remove all points below the

cerebellum (MNIz,260 mm) as well as points that were both

below the eyes (MINz,235 mm) and anterior to the temporal

pole (MNIy.+35 mm). The resulting 3,555 points were spaced 3–

6 mm apart and covered all scalp regions overlying brain tissue

(Figure 1B). These points constituted the source locations and

directions for photon injection during Monte Carlo simulations.

Monte Carlo Simulations

We employed a three-dimensional Monte Carlo (MC) method

based on the tMCimg code described by Boas et al. [51], with the

general approach being described by Wang [52]. In brief, the

initial position and direction of a photon are defined as coming

from a point source with an initial survival weight W

set to 1. A

scattering length L is probabilistically calculated from an

exponential distribution, and the photon is moved through tissue

by this length. The photon’s weight, is incrementally decreased by

a factor of exp ({m

L) due to absorption, where m

is the

absorption coefficient of the tissue and Lis 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 is determined from an

exponential distribution. The photon is 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 10ns, since the probability of photon detection in perfused

tissue after such a period of time is extremely small. When the

photon reaches a boundary, the probability of an internal

reflection is calculated from Fresnel’s formula. If a reflection

occurs, the photon is reflected back into the medium and

propagation continues with a new distance. Otherwise, the

migration of this photon is terminated and a new photon is

launched. The output of a given Monte Carlo simulation included

the photon fluence within the medium: an accumulation of all

photon weights within each voxel in the tissue, also known as the

2-point Green’s function. In addition, for each detector position

the MC simulation stores in a history file: (1) the number of

photons exiting within a 3 mm diameter of that detector location,

and (2) every photon’s path length traveled through each tissue

type that reached that detector. For each of the 3,555 simulations

in our study, 100 million (i.e., 10

) input photons were injected at

the source location. Individual MC simulations required 4–

5 hours of computation time and 1–2 GB of storage (uncom-

pressed).

Sensitivity Map Computation

Unlike x-rays which typically pass straight through biological

tissue, near-infrared photons scatter significantly as they travel

through tissue. The spatial probability distribution of photons

entering tissue at a source location, scattering through the tissue,

and being emitted at a particular detector location, defines the

spatial sensitivity profile (i.e., the ‘‘probed tissue’’) for that source-

detector (SD) pair. In linear DOI image reconstruction, this spatial

probability distribution is represented by a 3-point Green’s

function (see Eqn 1), which can be computed from two separate

2-point Green’s functions (i.e., 2 separate MC results), as described

below (cf. Figure 2).

The probability of a photon traveling from a point source,

,to

any particular voxel inside the head,

rr, is represented by a single

Figure 1. Anatomy used for Monte Carlo simulations and processing. (A) Sagittal section (MNIx = 29 mm) through the segmented Colin27

head. Shades from white to dark gray are: scalp, skull, cerebrospinal fluid, white and gray matter, respectively. The inset shows the original, pre-

eroded scalp on the same slice. (B) Location and orientation of the 3,555 photon injection points around the Colin27 scalp used for the Monte Carlo

simulations. The injection vectors (yellow) are shown in relation to the scalp profile and underlying cortical surface (rendered brain). The nineteen

standard locations in the International 10–20 System are highlighted in blue. (C) Colorized shells representing the masks used for depth sensitivity

analysis (blue = scalp, green = skull, dark blue to pink = twenty-one ,2.8 mm thick shells).

doi:10.1371/journal.pone.0066319.g001

Table 1. Optical properties for scalp, skull, CSF, gray and

white matter used for all Monte Carlo simulations.

Tissue Type

(

)

(

)

Gray matter 0.019500 1.10

White matter 0.016900 1.35

CSF 0.002500 0.01

Skull 0.011925 0.92

Scalp 0.017275 0.72

doi:10.1371/journal.pone.0066319.t001

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2-point Green’s function (W

in Eqn 1; see also Figure 2A,B). The

probability of a photon traveling from a point source, to any

particular voxel inside the head and then arriving a particular

detector location,

, is represented by a 3-point Green’s function

[53], W (see Figure 2C,D). The 3-point Green’s function is

formally given by:

ðÞ~

rr,

ðÞG

rrðÞd

r ð1Þ

where

and

are the locations of the source and detector,

respectively, and

rr is a position inside the head. W

is the fluence

provided by the MC 2-point file for the source point (e.g.

Figure 2B), and the function G is provided by a separate MC 2-

point file for the detector point. For continuous-wave NIRS

measurements, the 3-point function (e.g., Figure 2D) can be

generated by simply multiplying the 2-point function obtained

from the source location (e.g., Figure 2B) by the 2-point function

from the detector location, voxel by voxel. [For energy conserva-

tion, the data stored in each tMCimg 2-point file is first

normalized according to Eqn. (1) in [51].] Once computed, the

3-point function W represents the sensitivity of the optical

measurement for detecting changes at any point inside the

medium, or a ‘‘spatial sensitivity profile’’, from that SD pair

(Figure 2D) – typically described as roughly banana-shaped. We

will refer to the sensitivity function W the ‘‘3- point sensitivity

function’’.

Spatial Sensitivity Analyses

To estimate NIRS sensitivity to our five different tissue types

within the head (e.g., Figure 1A), a given 3-point sensitivity map

was partitioned and accumulated. The total fluence change to a

perturbation in brain tissue, dw

total

, can be partitioned various

ways based on the 3-point maps. For example, one option is to

partition the total fluence change into two components: brain

fluence and non-brain fluence:

total

~dw

brain

zdw

nonbrain

ð2Þ

If we assume the absorption change in brain tissue sampled by

that SD pair is uniform (and similarly for the non-brain tissue),

these can be represented by dm

brain

and dm

nonbrain

respectively. The

total fluence change can then be written in terms of the 3-point

functions W, partitioned into brain and non-brain components:

total

voxels

brain

 dm

brain

voxels

nonbrain

 dm

nonbrain

ð3Þ

Since sensitivity is defined as the change in optical fluence

divided by change in m

(assuming scattering is constant), the

sensitivity to brain tissue and non-brain tissue can be derived by

taking the partial derivative of the above equation with respect to

brain

and m

nonbrain

, respectively:

total

brain

voxels

brain

ð4Þ

total

nonbrain

voxels

nonbrain

ð5Þ

The sensitivity to one partition (e.g., brain tissue) can therefore

be estimated by summing over all voxels in the 3-point weighting

function that comprise that partition,

brain

. This concept

generalizes from a brain/non-brain partition to any other

partitioning of the head. For example, one could separately sum

Figure 2. Photon propagation through scattering tissue. (A) Representation of a single photon moving through tissue, from the source, to an

arbitrary point inside the medium. Accumulation of photon weights during this process is the basis of a 2-point Green’s function. (B) Example 2-point

Green’s function, with colors representing the intensity of light reaching any given point in the tissue (truncated after a 5 order-of-magnitude

reduction in intensity from peak). (C) Representation of a single photon traveling from the source, to a point in the medium, and on to a detector; the

basis of a 3-point sensitivity function. (D) Example 3-point sensitivity function generated from two MC simulations (one for the source, one for the

detector) spaced 30 mm apart.

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over all gray matter voxels to compute the cumulative sensitivity to

gray matter, or sum over white matter voxels to compute the

sensitivity to white matter. One could also use geometric partition

partitions of the head, such as concentric ‘‘depth’’ shells described

further below.

Regional and global sensitivity analysis. To assess

regional NIRS sensitivity around the head, we performed

sensitivity analyses at the 19 standard points of the International

10–20 System in MNI coordinate space [54]. For each of the 19

locations, we first identified every pair of points from our 3,555

MCs that were separated by less than 60 mm and whose midpoint

lay within 10 mm of the given 10–20 location. We then generated

a 3-point map for each pair identified, and summed the 3-point

weights for each of the five tissue types to quantify the probability

of photons passing through each tissue type. This partitioning and

sensitivity computation was repeated for each pair in the list,

retaining SD separation information. Sensitivity and variability

was quantified by averaging results surrounding a given 10–20

location, in 5 mm bins. For example, to estimate sensitivity to gray

matter given a 30 mm separation, we averaged together the gray

matter partition sums for all SD pairs that were 27.5–32.5 mm

apart and also centered on a point within 10 mm of the 10–20

location of interest. This entire process was repeated for each SD

separation considered. Depending on the separation, anywhere

from 30–100 such SD pairs contributed to the average.

The result for a given 10–20 location was an average curve

representing the sensitivity and variability of a NIRS measurement

to each tissue type as a function of SD separation, centered on the

target location. The entire process was then repeated at each of the

nineteen 10–20 locations to quantify sensitivity and variability as a

function of position on the head. To estimate the mean global

sensitivity to the five tissue types, we averaged the curves from the

19 standard locations of the 10–20 system. In this analysis, we

dropped the error associated with individual SD-pairs surrounding

individual locations to highlight the variability across 10–20

location.

In practice, intensity contours such as those shown in Figure 2

are linearly related to the measurement of signal change. Optical

property changes occurring within the farthest contours from the

source and detector will produce smaller signal changes. Hence, a

more sensitive or lower-noise instrument will be required to detect

signals arising from those regions. The farthest contour to which

an instrument is sensitive, therefore, is characterized by the NIRS

instrument’s noise characteristics, sensitivity and dynamic range.

In our study, the entire sensitivity analysis process was performed

both before and after thresholding the 3-point functions at 5, 4, 3

or 2 orders of magnitude in sensitivity loss from peak (i.e., masking

at the 5th, 4th, 3rd or 2nd contour line in Figure 2). This simulates

instruments with progressively lower sensitivity, higher noise, and/

or a more restricted dynamic range.

Depth sensitivity. To assess NIN depth sensitivity, the

intracranial mask generated by FSL was eroded in three

dimensions 21 times via the mri_binarize tool (FreeSurfer,

v5.1), in two-voxel steps. Erosion in a voxellated space depends

upon the surface curvature, but the mean erosion step was

2.8 mm. Successive mask-pairs were then subtracted to generate

a series of twenty-one ‘‘shells’’, each on average 2.8 mm thick,

beginning at the inner edge of the skull and continuing toward

the center of the brain. These were then combined with the scalp

and skull masks to provide a separate head segmentation with 23

complete, non-overlapping shells (colors in Figure 1C). As with

the regional sensitivity analysis, the same groups of 3-point

sensitivity maps surrounding the nineteen 10–20 locations were

partitioned using each of these 23 shells (i.e., ignoring the 3

intracranial tissue types). Sensitivity weights were summed to

independently quantify cumulative photon fluence within each

layer in depth, irrespective of the five tissue types used in the MC

simulations themselves.

Results

Spatial Sensitivity for Near-Infrared Neuroimaging

A series of 3-point spatial sensitivity functions, W, are shown in

Figure 3 in a sagittal slice covering a wide range of SD separations.

Contour lines appear at each order of magnitude decrease in the

photon sensitivity profile from the peak voxel, and are truncated in

each figure after decaying 5 orders-of-magnitude. This represents

the approximate limits of a sensitive, low noise, and well-optimized

NIRS measurement; less sensitive devices or poorly optimized

dynamic range may only provide information up through the first

three or four contour lines.

Consistent with previous findings, as separations increase from 0

to 55 mm, the NIRS ‘‘banana’’ grows and extends deeper into the

brain. At a separation of 55 mm, the overlay shown intersects with

roughly the outer 17 mm of brain tissue. Careful visual inspection

of these examples also reveals that the relatively non-scattering

CSF layer distorted the normally smooth ovoid shape of the NIRS

banana that is found in a homogeneous medium [25]. Such

distortion is particularly noticeable when the CSF layer is more

than 1–2 millimeters thick and the CSF layer is near the edge of

the sensitivity profile (see the 5 and 10 mm separations in Figure 3).

These examples also suggest there is at least limited sensitivity to

gray matter even at SD separations less than 20 mm – separations

that are typically assumed to provide zero brain sensitivity in an

adult human head.

Sensitivity as a Function of Source-Detector Separation

Figure 4 shows quantitatively the average proportion of

sensitivity to brain tissue (gray+white matter) and non-brain tissue

(scalp+skull+CSF) as a function of SD separation, along with

separate estimates for gray and white matter. The fluence mean

and variability within the indicated tissue type(s) was computed

across the nineteen 10–20 locations and error bars hence represent

an estimate of the variability over these 19 head locations. The

results were plotted as a function of SD separation. Two main

points should be noted. First, there was notable sensitivity to brain

tissue at a separation of 20 mm, representing approximately 6% of

the total sensitivity profile. (Smaller separations are not included

because there were too few source-detector pairs having a

midpoint of measurement within 10 mm of the 10–20 positions

for reliable estimation.) Second, at the largest SD separation

(65 mm), the estimated sensitivity to brain tissue reached

approximately 22% of the total sensitivity profile Thus, even at

these larger-than-typical separations, the NIRS measurement is

substantially more sensitive to the scalp, skull and CSF tissue

compartments than the gray and white matter components.

Figure 5 provides equivalent curves for scalp, skull and CSF

tissues.

The sensitivity to gray matter, of particular interest for NIN

measurements, was largely linear up through 45 mm separations,

at which point diminishing returns were observed for larger

separations. Linear regression across the 20 through 45 mm

separation values for gray matter revealed a slope of 0.0460.003

per centimeter. That is, for every 10 mm increase in SD

separation, sensitivity to gray matter increased an additional 4%

(from 6% at 20 mm, to 16% at 45 mm).

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Figure 3. Photon sensitivity profile at a broad range of source-detector separations. Contours are drawn for each order of magnitude loss

in sensitivity from peak and are truncated after 5 orders of magnitude.

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Figure 4. Mean proportion of total sensitivity to the tissue types indicated as a function of source-detector separation. Errorbars

represent standard errors across all nineteen locations in the International 10–20 System. Separate curves represent pre-thresholding of the sensitivity

(3-point Green’s function) maps at 5, 4, 3, or 2 orders of magnitude (OM) reduction in sensitivity compared to peak, representing progressively less

optimal NIRS measurement systems. (A) Sensitivity to brain tissue = gray plus white matter. (B) Non-brain tissue = CSF plus skull plus scalp. (C) Gray

matter only. (D) White matter only.

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Sensitivity as a Function of Instrument Performance

The entire analysis described above was repeated after masking

the 3-point functions at 5 or (separately) 4, 3 or 2 orders of

magnitude sensitivity loss from peak (separate curves in each panel

in Figure 4 and Figure 5). The results with no masking and

masking at 5 orders of magnitude were indistinguishable and

hence only the latter is plotted for clarity. The analyses at 3 and 4

orders of magnitude, simulating progressively lower performing

NIRS instrumentation, provided qualitatively similar curves,

although absolute sensitivity was reduced (downward shifts) to

both gray and white matter layers as progressively more of the 3-

point function was masked. The sensitivity decrement in gray

matter was just significant (p,0.05) at most separations when

masking after 3 orders of magnitude, and reflected an 8–10%

decrease in sensitivity. The magnitude of this decrement was

roughly equivalent to the decrement associated with a 3 mm

increase in SD separation. Masking after only 2 orders of

magnitude sensitivity change – approximately equivalent to an

instrument with 40 dB dynamic range – exhibited substantial and

significant reductions in sensitivity, up to 50%, in all intracranial

tissue classes (CSF, gray and white matter).

NIRS Depth Sensitivity in the Brain

To estimate the NIRS sensitivity to intracranial tissue as a

function of depth in the Colin27 model we used the intracranial

shells depicted in Figure 1C and the described partitioning

method. Figure 6 plots the average sensitivity to each shell –

starting with scalp, then skull, then each successive ,2.8-mm

intracranial shell – averaged over all 10–20 positions. Note that

the first such shell (0–2.8 mm) typically intersected a substantial

portion of CSF plus a modest amount of gray matter. The next

intracranial shell (,2.8–5.6 mm below the inner skull surface)

typically contained substantially less CSF and considerably more

gray matter. The third intracranial shell (5.6–8.4 mm deep) begins

to have more contact with white matter voxels, and so on towards

the center of the brain (cf. Figure 1C).

In Figure 6, two primary effects are prominent. First, as SD

separation increases, the sensitivity to all layers except scalp also

increases (Figure 6A). For example, at a 20 mm separation, scalp

and skull provided approximately 84% and 15% of the NIRS

measurement sensitivity, whereas at 55 mm SD separations they

provided closer to 35% and 45% of the NIRS sensitivity. The

arbitrarily-selected 1% sensitivity line (y-axis = 10

) was exceeded

for approximately the outermost 11.2 mm of intracranial volume,

starting at a 25 mm SD separation.

The 3-point Greens function (Eqn. 1) is essentially exponential,

and hence we plotted log

(sensitivity) as a function of depth into

the intracranial space (Figure 6B). At any given SD separation,

sensitivity was indeed observed to decrease exponentially with

depth. Non-linear regression analysis was performed on the

sensitivity data (from the nineteen 10–20 positions) using an

exponential formula of the following form:

sensitivity~azb  c

depth

ð6Þ

The regressions revealed significant b and c coefficients at each

separation, with models accounting for 53%–91% of the total

variance (see Table 2). As expected, the sensitivity at the innermost

edge of the skull increased significantly as SD separation increased

(T(11) = 16.2, p,0.0001; slope = ; adjusted R

= 0.96). In

addition, the exponential (decay) coefficient c increased signifi-

cantly with larger SD separations, reflecting a slower loss in

sensitivity with depth at larger SD separations. However, the c

coefficient plateaued at approximately a 40 mm separation

(Figure 7).

While depth sensitivity for a given SD separation can be

estimated directly from the coefficients in Table 2 plus Eqn. (6), we

also computed a ‘‘rule of thumb’’ formula. Averaging over the

coefficients for typically used NIRS separations of 20–40 mm

results in the following equation for the sensitivity in depth (S):

S ~0:075  0:85

depth

ð7Þ

Thus, at a ‘‘typical’’ separation, our MCs estimate a

0.075*0.85

= 0.075, or 7.5% sensitivity at the average inner

surface of the skull. At a depth 5 mm into the intracranial space,

the sensitivity would decrease, to 0.075*0.85

= 0.033 or 3.3%.

Such estimates are coarse, and assume overlying scalp and skull

layers comparable to those in our Colin27 template. However,

Equation (7) can provide a reasonable estimate of NIN sensitivity

as a function of depth. For comparison, quantitative depth

sensitivity measures at each 10–20 location for a typical SD

separation of 30 mm are listed in Table 3.

Discussion

Utilizing 3,555 Monte Carlo simulations, we generated

quantitative estimates of the spatial sensitivity and associated

variability of non-invasive NIRS to brain tissue in the Colin27

Figure 5. Mean proportion of total sensitivity to scalp, skull, and CSF as a function of source-detector separation. Errorbars represent

standard errors across all nineteen locations in the International 10–20 System. Separate curves again represent pre-thresholding of the sensitivity (3-

point Green’s function) maps at 5, 4, 3 or 2 orders of magnitude (OM) reduction in sensitivity compared to peak.

doi:10.1371/journal.pone.0066319.g005

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brain. Sensitivity as a function of source-detector separation was

qualitatively consistent with previous reports [23,24,31,32,36].

Global sensitivity to brain tissue reached 20% (and gray

matter = 17%) of the total sensitivity at a SD separation of 55

mm, with the remaining sensitivity coming from scalp, skull and

CSF. More typical SD separations of 25–35 mm exhibited brain

sensitivities in the range of 8–13%. As expected, sensitivity was

degraded when we simulated under-performing NIRS instrumen-

tation, with a typical sensitivity reduction equivalent to the

decrease expected from a 2.5 mm increase in SD separation.

Performance appeared to drop quickly with more severely

degraded instruments (as dynamic range fell from ,60 dB to

,40 dB). Finally, the sensitivity in depth through the intracranial

space was found to be exponentially decreasing, with detailed

exponential coefficients given in Table 2, and an approximation

for sensitivity-in-depth given by Eqn. (7). NIN signals thus appear

strongly biased to absorption changes occurring in the outer 10–

15 mm of the intracranial space. While these results were based on

the thinned-scalp version of Colin27, we also performed a full set

(3,555) of MC simulations on the original, thicker scalp.

Qualitatively, we replicated all results reported herein, with the

primary difference being uniformly but modestly lower sensitivity

to brain tissue in the thicker-scalp model.

Sensitivity versus SD Separation

While an increase in brain sensitivity was anticipated with larger

SD separations [31,32,35,40], the magnitude and variability of this

relationship around the head, and in a realistic geometry, were not

well characterized. Our MC results suggest that, globally, as much

as 6% of the NIRS sensitivity comes from brain tissue at SD

separations of 20 mm. This probability rose sigmoidally over the

range of separations we investigated, increasing to 20% of the

NIRS sensitivity coming from brain tissue at a 55 mm separation.

This is qualitatively consistent with recent studies that examined

only small regions in different head models [35,39,40].

Our results did quantitatively differ to some degree from this

prior work. For example, our observed sensitivity of ,10% at a

separation of 30–35 mm was slightly higher than that found when

using the Chinese head dataset [55], for which 8% was reported at

the same 30–35 mm separation [39]. However, that study – as

well as the others that considered realistic head models – only

examined very small portions of a different head model, whereas

our mean and variability estimates apply to the entire Colin27

head.

Variability in NIRS sensitivity to brain had not been previously

assessed. In our study, variability in sensitivity was modest within

regions, ranging from 10–18%. Variability was somewhat more

substantial between regions, with standard errors across the 10–20

locations spanning 20% of the mean sensitivity values. The

variability around the head, therefore, appears to be an important

contributor to NIN sensitivity. This variability is presumed to be

related to the different tissue layering found across different head

regions.

Figure 6. Mean NIRS depth sensitivity in the brain plotted in two orthogonal ways, by SD separation. (A) The top two traces represent

scalp (blue) and skull (green) sensitivity. Sensitivity to scalp and skull were equal at a SD separation of 25 mm. On average, 1% or more of the

sensitivity profile was achieved for all of the most superficial 11.2 mm of the intracranial volume at SD separations of 25 mm or greater (circle). (B)

Intracranial sensitivity in depth as a function of source-detector separation (excluding scalp and skull). At all separations, sensitivity decreases

exponentially with depth (i.e., linear curves through ,15 mm depth on this semilog plot).

doi:10.1371/journal.pone.0066319.g006

Figure 7. Fitted exponential decay coefficient, c, from the

sensitivity function in Eqn. (6) as a function of SD separation.

The asymptote at ,40 mm separations means that further increasing

the SD separation provides diminishing returns for NIRS sensitivity to

brain function.

doi:10.1371/journal.pone.0066319.g007

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There was a notable gain in sensitivity with SD separation,

particularly at greater than 25 mm separations. In one prior study,

it was recommended that NIRS researchers avoid SD separations

greater than 30–35 mm [39]. While this does not appear to be

supported by our findings, it is important to note that our estimates

do not consider the achievable signal-to-noise ratio (SNR). If an

instrument cannot detect a reliable signal at 40 or 50 mm, larger

separations will not improve brain sensitivity. A trade-off therefore

needs to be made between greater sensitivity to deeper layers and

the resulting loss in SNR. All NIRS instruments have a limit on the

separation where reliable SNR can be achieved, which is readily

determined by experimentation. We investigated a broad range of

separations, spanning the typical capabilities of current instru-

ments, to help individual investigators determine this trade-off for

specific devices.

Based on our results, therefore, NIRS probes for non-invasive

neuromonitoring in adults should ideally be designed with 30–

35 mm SD separations, or larger, assuming the instrument can

Table 2. Regression results for sensitivity as a function of depth.

SD Model Coef. Std. 95% Conf. Interval N Sensitivity at Depth (mm)

Sep. Param Value Err. T p Low High Adj. R2 0 5 10

5 a 0.0000 0.0001 20.6 0.550 20.0002 0.0001 378

b 0.0058 0.0003 19.3 0.000 0.0052 0.0064 0.526 0.58% 0.19% 0.06%

c 0.8042 0.0185 43.4 0.000 0.7678 0.8406

10 a 20.0001 0.0001 20.7 0.491 20.0004 0.0002 399

b 0.0133 0.0005 25.3 0.000 0.0123 0.0143 0.647 1.32% 0.48% 0.17%

c 0.8176 0.0132 62.1 0.000 0.7917 0.8435

15 a 20.0002 0.0003 20.7 0.458 20.0007 0.0003 399

b 0.0261 0.0009 27.8 0.000 0.0243 0.0280 0.687 2.59% 1.00% 0.38%

c 0.8292 0.0113 73.6 0.000 0.8071 0.8514

20 a 20.0003 0.0004 20.9 0.392 20.0011 0.0004 399

b 0.0431 0.0013 32.7 0.000 0.0405 0.0457 0.753 4.27% 1.74% 0.70%

c 0.8377 0.0091 91.8 0.000 0.8198 0.8557

25 a 20.0005 0.0005 21.0 0.341 20.0015 0.0005 399

b 0.0614 0.0017 36.5 0.000 0.0581 0.0647 0.793 6.09% 2.59% 1.09%

c 0.8448 0.0078 107.8 0.000 0.8294 0.8602

30 a 20.0006 0.0006 21.1 0.276 20.0018 0.0005 399

b 0.0781 0.0019 41.6 0.000 0.0744 0.0818 0.832 7.74% 3.37% 1.44%

c 0.8483 0.0067 125.7 0.000 0.8350 0.8616

35 a 20.0008 0.0006 21.2 0.221 20.0020 0.0005 399

b 0.0913 0.0020 45.8 0.000 0.0873 0.0952 0.857 9.05% 4.01% 1.75%

c 0.8514 0.0060 141.5 0.000 0.8395 0.8632

40 a 20.0009 0.0006 21.3 0.182 20.0021 0.0004 399

b 0.1018 0.0021 49.3 0.000 0.0977 0.1059 0.875 10.09% 4.51% 1.99%

c 0.8528 0.0055 154.1 0.000 0.8419 0.8637

45 a 20.0009 0.0007 21.4 0.165 20.0022 0.0004 399

b 0.1095 0.0021 51.5 0.000 0.1054 0.1137 0.883 10.86% 4.89% 2.17%

c 0.8542 0.0053 162.3 0.000 0.8438 0.8645

50 a 20.0010 0.0007 21.4 0.163 20.0023 0.0004 399

b 0.1157 0.0022 52.7 0.000 0.1114 0.1200 0.889 11.47% 5.20% 2.33%

c 0.8554 0.0051 167.9 0.000 0.8454 0.8655

55 a 20.0010 0.0007 21.5 0.134 20.0024 0.0003 378

b 0.1231 0.0022 54.8 0.000 0.1187 0.1276 0.901 12.21% 5.45% 2.40%

c 0.8528 0.0050 171.2 0.000 0.8430 0.8626

60 a 20.0011 0.0007 21.5 0.132 20.0025 0.0003 378

b 0.1264 0.0023 56.0 0.000 0.1219 0.1308 0.905 12.53% 5.65% 2.52%

c 0.8545 0.0048 176.9 0.000 0.8450 0.8640

65 a 20.0011 0.0007 21.6 0.112 20.0025 0.0003 357

b 0.1321 0.0023 57.6 0.000 0.1275 0.1366 0.914 13.09% 5.81% 2.54%

c 0.8518 0.0048 178.6 0.000 0.8425 0.8612

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provide adequate SNR at those separations. Note that this

recommendation should also be weighed against spatial resolution

when choosing SD separations. As SD separations increase, the

effective resolution of the NIRS measurement decreases. In some

studies, the need for a higher spatial resolution (and hence shorter

SD separations) may outweigh the need for more or deeper

sensitivity (and hence larger SD separations).

For close SD pairs, separations of 20 mm included on average

6% of the photon fluence (sensitivity) attributable to brain tissue.

Thus, the commonly used rule of thumb – namely, that

measurements with 20 mm or smaller separations are minimally

sensitive to the brain in adult humans may need to be revised.

Clearly, brain activation that is both strong and superficial could

still be detected with a 20 mm separation. As mentioned earlier,

this would be even more prominent if superficial layers exhibit

little or no change in optical properties, or such changes are

eliminated or suitably accounted for. Since there is substantial

vascularization of and hemodynamic activity in scalp, skull and

pial vessels, experimental manipulations to eliminate such signals

may be difficult. When seeking to independently measure

Table 3. Estimated relative NIRS sensitivity (proportions) as a function of depth for a SD separation of 30 mm.

Shell Depth Range (mm)

Location N Scalp Skull 0–2.8 2.8–5.6 5.6–8.4 8.4–11.2 11.2–14 14–16.8 16.8–19.6

Fp1 45 0.16 0.70 0.059 0.046 0.0202 0.0078 0.00272 0.00079 0.00020

(0.03) (0.02) (0.009) (0.007) (0.0032) (0.0013) (0.00051) (0.00017) (0.00006)

Fp2 47 0.21 0.64 0.064 0.047 0.0190 0.0069 0.00241 0.00073 0.00019

(0.04) (0.03) (0.011) (0.008) (0.0039) (0.0016) (0.00062) (0.00022) (0.00008)

Fz 66 0.26 0.52 0.047 0.046 0.0406 0.0302 0.02048 0.01339 0.00762

(0.02) (0.02) (0.004) (0.004) (0.0032) (0.0033) (0.00307) (0.00255) (0.00187)

F3 78 0.15 0.64 0.084 0.071 0.0341 0.0145 0.00591 0.00217 0.00071

(0.01) (0.01) (0.010) (0.007) (0.0030) (0.0016) (0.00080) (0.00035) (0.00013)

F4 91 0.17 0.64 0.085 0.066 0.0273 0.0097 0.00341 0.00111 0.00032

(0.01) (0.01) (0.008) (0.006) (0.0024) (0.0010) (0.00046) (0.00019) (0.00007)

F7 76 0.65 0.21 0.055 0.046 0.0218 0.0088 0.00318 0.00111 0.00040

(0.06) (0.03) (0.012) (0.009) (0.0041) (0.0016) (0.00062) (0.00025) (0.00012)

F8 71 0.69 0.20 0.041 0.036 0.0185 0.0077 0.00291 0.00114 0.00048

(0.05) (0.03) (0.008) (0.007) (0.0033) (0.0015) (0.00065) (0.00029) (0.00015)

C3 90 0.34 0.41 0.068 0.069 0.0520 0.0297 0.01501 0.00713 0.00325

(0.02) (0.01) (0.005) (0.005) (0.0044) (0.0029) (0.00169) (0.00087) (0.00043)

C4 83 0.36 0.46 0.052 0.053 0.0389 0.0220 0.01047 0.00467 0.00201

(0.02) (0.01) (0.005) (0.005) (0.0037) (0.0023) (0.00126) (0.00064) (0.00031)

Cz 43 0.41 0.30 0.031 0.034 0.0350 0.0358 0.03275 0.02818 0.02398

(0.02) (0.02) (0.002) (0.002) (0.0016) (0.0014) (0.00168) (0.00159) (0.00132)

P3 66 0.26 0.52 0.087 0.073 0.0359 0.0146 0.00566 0.00210 0.00070

(0.02) (0.01) (0.009) (0.007) (0.0044) (0.0023) (0.00107) (0.00047) (0.00019)

P4 65 0.25 0.49 0.095 0.081 0.0452 0.0209 0.00901 0.00346 0.00118

(0.02) (0.01) (0.007) (0.005) (0.0038) (0.0024) (0.00129) (0.00061) (0.00025)

Pz 38 0.48 0.34 0.037 0.037 0.0337 0.0253 0.01693 0.01081 0.00683

(0.06) (0.03) (0.007) (0.007) (0.0064) (0.0051) (0.00369) (0.00245) (0.00159)

O1 34 0.17 0.56 0.132 0.093 0.0333 0.0103 0.00303 0.00084 0.00021

(0.01) (0.01) (0.007) (0.005) (0.0027) (0.0011) (0.00039) (0.00013) (0.00004)

O2 43 0.19 0.51 0.133 0.096 0.0400 0.0147 0.00528 0.00192 0.00065

(0.01) (0.02) (0.009) (0.005) (0.0032) (0.0020) (0.00111) (0.00056) (0.00024)

T3 80 0.68 0.12 0.083 0.066 0.0304 0.0112 0.00387 0.00127 0.00038

(0.02) (0.01) (0.008) (0.006) (0.0029) (0.0011) (0.00043) (0.00016) (0.00006)

T4 66 0.70 0.13 0.076 0.057 0.0264 0.0103 0.00371 0.00123 0.00037

(0.03) (0.01) (0.009) (0.006) (0.0030) (0.0012) (0.00046) (0.00016) (0.00006)

T5 62 0.35 0.49 0.078 0.052 0.0169 0.0048 0.00134 0.00035 0.00006

(0.03) (0.02) (0.012) (0.008) (0.0030) (0.0010) (0.00034) (0.00013) (0.00004)

T6 63 0.40 0.47 0.074 0.043 0.0131 0.0036 0.00094 0.00021 0.00002

(0.05) (0.03) (0.011) (0.007) (0.0025) (0.0008) (0.00024) (0.00007) (0.00002)

doi:10.1371/journal.pone.0066319.t003

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peripheral tissues like scalp and skull, as when making multi-

distance measurements to correct for superficial layer hemody-

namics [56,57,58,59,60], SD separations shorter than 10 mm

should be strongly considered.

Sensitivity and NIRS Instrument Performance

When comparing the different curves within panels in Figure 4

and Figure 5, the peak sensitivity dropped only about 10% when

assuming a NIRS instrument with a lower dynamic range or

optimization: for gray matter at a separation of 55 mm, the

reduction was from 0.20 to 0.18. This dropped more precipitously

(by up to 50% of the original value) to 0.10 with poor dynamic

range or optimization. This suggests the importance of optimizing

instrument sensitivity and reducing all types of noise and signal

interference when making NIN measurements [57,60,61]. This

appears to be particularly for instruments with inherently modest

dynamic range (,60 dB).

Brain Sensitivity in Depth

Our shell-based depth analysis revealed exponentially decreasing

sensitivity with depth at all SD spacings, with expectedly different

intercepts at each separation. Upon reaching 11.2 mm into the

brain, relative sensitivity greater than 1% was only found with

25 mm or greater separations. Thus, in our Colin27 head model,

substantial separation appears required to achieve even modest

sensitivity past the outer 10 mm of intracranial space. Two

important qualifiers should be noted. First, the sensitivity beyond

10 mm into the intracranial space is strongly limited by the

thickness of the overlying tissue layers, including scalp and skull. In

our model these layers together averaged ,13 mm thick. Other

individuals with thicker or thinner scalp and skull layers would be

expected to have decreased or increased overall sensitivities,

respectively. While these are not controllable parameters, they

should be considered with respect to study design. Second, the

ability to detect absorption changes is also a function of contrast and

noise. A large enough change in optical properties (i.e., absorption

or scattering), a large enough region of change, or a low enough

noise floor (including noise generated from systemic physiological

processes as discussed above), could enable detection of events

occurring substantially deeper than 10 mm. Mathematically, the

detectability of a specific functional event depends on the contrast-

to-noise ratio. Usually one uses CNR = 1 (contrast is equal to the

noise floor) to define the minimum detectable contrast. Hence, we

have the equation contrast~

W  dm

~noise . We discussed

at length the role of

W in this paper. However, dm

(the change

in optical properties) is clearly equally important, such that a

doubling of absorption coefficients would lead to a doubling of the

detected contrast.

In terms of noise, if there was precisely zero change in optical

properties in overlying layers (e.g., scalp and skull), or the changes

in overlying layers can be otherwise accounted for, then any

detected change must have come from deeper layers, regardless of

the relative sensitivity at that depth. The magnitude of optical

contrast or the level of noise suppression required for detection of

brain activity at, say, a 20 mm depth into the intracranial space

remains to be investigated.

Study Limitations

Hair is invisible to MRI, and hence was not considered in this

study. Hair can mechanically interfere with NIN measurements

and also has its own absorption spectrum, providing two separate

reductions in NIRS sensitivity. However, in the absence of motion,

hair is expected to be a substantially less dynamic absorber than

scalp or skull tissue, as it lacks hemodynamic and most other time-

dependent physiologic processes. Thus, while the sensitivity in

regions with hair will generally be lower than in regions without

hair (all else being equal), the reductions are expected to be

essentially fixed for a given hair color and density. To our

knowledge, no quantification of the effect of hair on NIN

measurements has yet been performed. Also, the specific methods

used to segment the Colin template may have led to over- or

under-estimates of tissue thicknesses or volumes. Proper assess-

ment 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. Within the segmented regions, our

MC simulations used average optical properties, largely to reduce

the number of separate MCs that had to be performed. While we

have performed a few MC runs using wavelength-specific optical

properties and only observed subtle differences in sensitivity

profiles, systematic quantification or comparison across wave-

lengths in realistic head geometries remains as future work.

Finally, while our MC simulations covered the Colin27 head

model comprehensively, we only examined a single head model.

Different individuals will exhibit different scalp and skull

thicknesses, CSF distributions, cortical folding patterns, white

matter composition, and so forth. For example, females have been

found to have different skull thickness distributions than males

[62,63], children have overall thinner scalps and skulls than our

model [64], older individuals may have different baseline

scattering properties [65], and individuals vary in terms of the

amount and distribution of CSF [66]. Direct assessments of each

of these parameters on NIN sensitivity remain to be performed.

However, our large set of MC simulations did encompass a

substantial range of scalp, skull and CSF combinations, and our

associated variability estimates provide a guide to the importance

of some of these issues.

Conclusions

This study represents the most comprehensive characterization

conducted to date of NIRS sensitivity to brain tissue, including the

importance of source-detector separations, variability in NIRS

sensitivity around the head, the influence of NIRS instrument

performance, as well as NIN sensitivity in depth. Our results

suggest that increasing the source-detector separation past 20 mm

monotonically increases sensitivity to brain tissue, and hence the

larger the separation the better in terms of brain sensitivity.

However, diminishing returns appear to begin around 40–50 mm

SD separations, and sensitivity must also be balanced against the

SNR that can be achieved with any particular instrument at large

separations, as well as the spatial resolution required. Our MC

simulations further suggest that, while the depth sensitivity of

NIRS is not strictly limited, NIRS sensitivity decreases exponen-

tially with depth into the intracranial space and hence NIN signals

are strongly biased towards the outermost 10–15 mm of the

intracranial volume. The detailed quantitative information pro-

vided here can help investigators better design and plan

experiments, head probes and instruments for making NIRS

measurements, as well as providing guidance when interpreting

NIRS studies in terms of the likely sources of the observed signals.

Acknowledgments

We wish to thank our anonymous reviewers for their assistance in clarifying

and enhancing this work.

NIRS Depth and Spatial Sensitivity

PLOS ONE | www.plosone.org 11 August 2013 | Volume 8 | Issue 8 | e66319

Author Contributions

Conceived and designed the experiments: GS ZL QZ. Performed the

experiments: GS ZL QZ. Analyzed the data: GS ZL QZ. Contributed

reagents/materials/analysis tools: GS ZL QZ. Wrote the paper: GS ZL

QZ.

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