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1 November 2009 Multidistance probe arrangement to eliminate artifacts in functional near-infrared spectroscopy
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Functional near-infrared spectroscopy has the potential to easily detect cerebral functional hemodynamics. However, in practical fNIRS measurements, a subject's physical or systemic physiological activities often cause undesirable artifacts. Such activities can be evoked even by task execution. In this case, observed artifacts may correlate strongly with the task sequence, and it is difficult to eliminate them by conventional signal filtering techniques. We present a theoretical analysis and Monte Carlo simulations of layered media in which both scattering and absorption changes occur, and show that a multidistance probe arrangement is effective in removing artifacts and extracting functional hemodynamics. The probe arrangement is determined based on simulation results. Artifacts induced by nonfunctional tasks (body tilting, head nodding, and breath holding) are clearly observed when a conventional method is used; such artifacts are appreciably reduced by the proposed method. Signals evoked by single-sided finger movements are observed at both hemispheres when we use a conventional method. On the other hand, localized signals at the primary motor area are observed by the proposed method. A statistically significant increase in oxygenated hemoglobin and decrease in deoxygenated hemoglobin are simultaneously observed at the contralateral primary motor area



Functional near-infrared spectroscopy (fNIRS) is a functional neuroimaging technique similar to functional magnetic resonance imaging (fMRI) and positron emission tomography (PET). It detects cerebral functional hemodynamic changes, but not the cerebral neural activation itself. fNIRS potentially has some advantages over other techniques: portability, inexpensive equipment, and availability for simultaneous use with other measurement devices including fMRI, PET, electroencephalography (EEG), and magnetoencephalography (MEG). However, undesirable artifacts are often observed in fNIRS measurements. Systemic physiological changes, physical movements, and even posture changes in a subject can generate such artifacts. These artifacts are observed because the detected light is influenced not only by the hemodynamic change in gray matter, but also by scattering and absorption changes in all tissues through which the light propagates. It is not known exactly how scattering and absorption changes occur in each tissue with a subject’s physiological change. Thus, various statistical methods, such as conventional filtering and multivariate data analysis, have been used to remove such artifacts from fNIRS measurements.

Artifacts induced by physiological activity, such as cardiac pulsation, respiration, and a blood pressure change, can be effectively removed by low-pass filtering or a moving average method. These techniques work well in a real-time environment because they are very simple to implement. However, they tend to overflatten the signal. Thus, for example, a fast-rising signal of brain activation may be deleted if they are applied. To solve this problem, Zhang, Brown, and Strangman1, 2 proposed an adaptive filtering technique based on low correlation between artifacts and cerebral functional activity. Saager and Berger3 applied the least square fit technique to this problem and conducted a detailed analysis of its performance. Kohno 4 used a powerful technique, independent component analysis, to separate a statistically independent signal from data contaminated with various artifacts.

These techniques and a conventional block averaging technique are useful for suppressing task-uncorrelated noises. However, if the data are contaminated with an artifact that is strongly correlated with a task sequence, these methods cannot work effectively. For example, Izzetoglu 5 pointed out that a subject’s head movement generates a blood flow change; thus, if the subject moves his head synchronously with a task, an artifact induced by this blood flow change will be observed. Since this kind of artifact is tightly correlated with the task sequence, the block averaging technique cannot remove it.

In general, to remove task-correlated artifacts, we adopt an experimental design including a reference task that is considered to generate the same signal as a target task except for a functional component. The artifacts can be canceled, but the functional component remains when we calculate the difference between the target and reference measurements. Such a design, however, usually requires a longer execution time, and it is very difficult to verify the equivalence of artifact components in target and reference tasks.

Another approach to this problem is multivariate data analysis. This approach is based on the empirical knowledge that the artifact signal is observed globally, and the functional signal is observed locally. Principal component analysis is used to extract the functional signal from multichannel measurement data. This method was reported to be effective.6, 7 However, the use of many optodes, most of which have to be positioned at areas unrelated to the target, is a big problem for practical measurement. In addition, if several activations at different areas occur simultaneously, separation of these signals will be difficult.

We do not know precisely how task-correlated artifacts are generated. Presumably they originate mainly from something other than activity in the cortical layer. Thus, it may be useful for functional detection if we can separate the signal of the cortical layer from that of other layers. Hence, several methods using multidistance probe arrangements for separating NIRS signals in lower layers from other layers have been proposed.

A NIRS algorithm using a multidistance probe arrangement, NIR spatially resolved spectroscopy (NIR-SRS), is known.8, 9 NIR-SRS was originally developed to measure the tissue oxygen index (TOI), and Al-Rawi, Smielewski, and Kirkpatrick reported that an extracarotid artery clamp had little influence on the TOI measured by NIR-SRS.10 This result may suggest that NIR-SRS can remove the interference of extracranial blood flow from brain functional activity signals. However, we cannot theoretically validate its ability to reduce artifacts of a superficial layer, because NIR-SRS is based on the theory of light propagation in a monolayered medium.11

Improved approaches of multidistance probe arrangement based on two-layer models were reported. Choi 12 used an analytical solution of a two-layer model that contains an additional superficial layer on a basal semi-infinite medium. They obtained the hemoglobin oxygenation etc. of extra- and intracranial layers by a theoretical curve fitting to experimental data. Fabbri 13 conducted Monte Carlo simulations of a two-layered tissue model and showed that a multidistance probe arrangement is effective in detecting the absorption change in the lower layer (cortical layer), even when optical changes arise in both lower and upper layers. This is a viable technique for separating the signal at the cortical layer from artifacts, regardless of whether they are task correlated or uncorrelated.

Validity of these algorithms greatly depends on the optical models assumed. It should be examined by theoretical or simulation approaches whether such a simplified model of a few layers provides a sufficient condition to separate cortical signals from others. In addition, only absorption change in tissues has been considered in most algorithms based on the modified Lambert-Beer law. In a recent study, Tomita, Ohtomo, and Suzuki reported that hemodynamic changes could be accompanied by scattering changes caused by blood cell aggregation.14 Since scattering also causes optical attenuation changes, we think that analysis considering both absorption and scattering is important.

In this work, we present a theoretical analysis and Monte Carlo simulations of a five-layered tissue model in which both scattering and absorption changes occur, and show that a multidistance probe arrangement is effective in extracting absorption changes in the gray matter layer. The simulation result is used to determine the appropriate probe arrangement. The proposed method is compared with a conventional method through actual experiments on nonfunctional and functional tasks. Artifacts induced by body tilting, head nodding, and breath holding were clearly observed when a conventional method was used, and were appreciably reduced by the proposed method. Signals evoked by single-sided finger movements were observed globally at both hemispheres when we used a conventional method. On the other hand, localized signals at the primary motor area were observed by the proposed method. A statistically significant increase in oxygenated hemoglobin (HbO) and decrease in deoxygenated hemoglobin (HbR) were simultaneously observed only at each contralateral primary motor area.




Optical Multilayer Model

A typical probe arrangement of fNIRS is illustrated in Fig. 1 (source and detector 1). In this arrangement, light power is detectable only when scattering exists in a medium. Light from a source of power I0,λ propagates in a medium according to the spatial distribution of the scattering and absorption coefficients ( μs,λ and μa,λ ), and reaches a detector at a distance d1 with power Iλ . Here, λ indicates the wavelength of the incident light. The optical attenuation is defined as Ad,λ=ln(IλI0,λ) . Since the input power I0,λ is difficult to measure, the optical attenuation change from a certain standard condition is used in an ordinary fNIRS measurement. When the change in scattering and absorption coefficients ( Δμs,λ and Δμa,λ ) from the standard condition is small, the optical attenuation change ΔAd,λ can be represented as

Eq. 1

Here, |X|sv denotes the value of X at the standard condition. The coefficients |Ad,λμa|sv and |Ad,λμs|sv have the dimension of length.

Fig. 1

Schematic illustration of multidistance probe arrangement on the human head.


If the second term of Eq. 1 is negligible, this equation corresponds to the modified Lambert-Beer law, which is the theoretical basis of a conventional fNIRS algorithm. In this case, the coefficient |Ad,λμa|sv is called the mean optical path length. In general, however, the second term cannot be neglected. For instance, Tomita, Ohtomo, and Suzuki experimentally demonstrated in vitro that the scattering property of a blood volume changes when its flow velocity changes.14 Thus, in this work we set the starting point of our theoretical discussion at Eq. 1.

We use a five-layered optical slab model of an adult head, which consists of layers of scalp (sc), skull (sk), cerebrospinal fluid (csf), gray matter (gm), and white matter (wm). Supposing the temporal change in scattering and absorption to be uniform in each layer, Eq. 1 is transformed to

Eq. 2

where vL denotes the parameter v at the layer L . The summations are accomplished with L{sc,sk,csf,gm,wm} , and ld,λL and md,λL denote

Eq. 3

Instead of the analytical derivation of the coefficients ld,λL and md,λL , we numerically obtained these values by a Monte Carlo simulation. The coefficients are calculated as follows:

Eq. 4

where μo represents all parameters except μaL , and μo represents all parameters except μsL . The bar symbol over a parameter μ (μ¯) denotes the standard condition value. Optical attenuations such as Ad,λ(μ¯aL+μaL,μ¯o) and Ad,λ(μ¯sL+μsL,μ¯o) were obtained by a Monte Carlo simulation, where μaL and μsL were set to satisfy μaLμ¯aL=0.1 and μsLμ¯sL=0.1 , respectively. Parameter values at the standard condition and layer thickness were based on the literature (Okui and Okada15) and are shown in Table 1 . The program tMCimg, provided to the public by the Photon Migration Imaging Laboratory at Massachusetts General Hospital (see, was used in the simulation.

Table 1

Hemodynamic parameters, thickness, and optical properties for each layer of an adult head model.

Tissue typeThickness[mm] μa [mm−1] at 670∕690∕720∕750∕780∕830 [nm]
Scalp3 0.0310.0260.0220.0220.0200.019
Skull7 0.0270.0170.0130.0160.0160.017
CSF2 0.00440.00290.0030.00450.00440.0056
Gray matter4 0.0480.0390.0360.0380.0360.041
White matter34 0.0240.0180.0140.0160.0160.018
Tissue type μs [mm1] at 670690720750780830 [nm]
Scalp 2.532.382.
Skull 2.332.131.921.791.661.47
CSF 0.350.320.
Gray matter 2.692.572.462.392.312.10
White matter 10.4910.039.789.629.258.82

Figure 2 shows a 2-D plot of optical attenuation changes when parameters μaL and μsL increase by 10% from standard values in each layer L . Five source-detector distances (10, 15, 20, 25, and 30mm ) were assumed, and an incident light of wavelength 780nm was used in the simulation. This figure shows the following.

  • Scattering and absorption changes at the scalp and skull layers strongly affect the optical attenuation change. Interestingly, the attenuation change increases (skull layer) and decreases (scalp layer) proportionally if we increase the source-detector distance.

  • The optical attenuation change induced by an absorption change in the csf layer is small, and the attenuation change due to a scattering change is comparable to that due to an absorption change in the gray matter layer. The observed attenuation change in the csf layer is thought to be negligible because that layer contains no blood cell, and thus scattering and absorption changes due to blood flow changes should be very small.

  • The absorption change in the gray matter layer influences the attenuation change considerably. This change increases proportionally with the source-detector distance. Remarkably, the optical attenuation change caused by a scattering change in the gray matter layer is very small.

  • The optical attenuation change induced by absorption and scattering changes in the white matter layer is very small.

Consequently, we assume that both the scattering and absorption terms of the csf and white matter layers and the scattering term of the gray matter layer barely contribute to the optical attenuation change. We omit these terms from Eq. 2.

Eq. 5

Concerning the skull layer, diploic veins are found in an area of cancellous bone between the inner and outer compact bone layers in the skull, and blood is drained in this area. However, we do not exactly know how the blood in the skull layer changes its volume and flow with systemic activity changes. Here, we assume two contrasting conditions of minimally and maximally changing hemodynamics in the skull layer. In a minimal condition, hemodynamic change in the skull layer can be negligible by supposing that blood flow in the skull layer is barely affected by systemic activity changes. In this case, we assume Δμa,λsk=0 and Δμs,λsk=0 , thus, the skull term in Eq. 5 is omitted and the scalp term remains as a single superficial layer term. In contrast, we suppose a maximal condition that hemodynamic change in the skull is very similar to that in the scalp layer. In this case, we assume Δμa,λsk=Δμa,λsc and Δμs,λsk=Δμs,λsc , and scalp and skull terms in Eq. 5 are merged into a single superficial layer term. In either condition, Eq. 5 is simplified,

Eq. 6


Eq. 7


Eq. 8

Here, sp denotes the superficial layer. As a result, the five-layer model was simplified to a two-layer model.

Fig. 2

2-D plot of optical attenuation changes where the parameters μaL and μsL increase by 10% from the standard values in each layer L{sc,sk,csf,gm,wm} . Five source-detector distances (10, 15, 20, 25, and 30mm ) were assumed, and an incident light of wavelength 780nm was used in the simulation.



Artifact Cancellation by Multidistance Probe Arrangement

If we use two detectors at different source-detector distances d1 and d2 (d1> d2) , the changes in optical attenuation are written as follows.

Eq. 9

Here, we introduce the ratios ka,λ and ks,λ as follows.

Eq. 10

If detector distances can be arranged to satisfy ka,λ=ks,λ , we can calculate the absorption change at the gray matter layer Δμa,λgm as follows.

Eq. 11

where kλ=ka,λ=ks,λ .

Figure 3 shows simulated values of ka,λ and ks,λ with various combinations of source-detector distances. In many cases of both the minimal and maximal conditions of the superficial layer, ka,λ and ks,λ had very similar values. However, when d2 was 10mm , the values did not coincide sufficiently.

Fig. 3

2-D plots of ka,λ and ks,λ at various combinations of source-detector distances in two contrasting conditions on the superficial layer. (a) Minimal condition ( ld,λsp=ld,λsc , md,λsp=md,λsc ). (b) Maximal condition ( ld,λsp=ld,λsc+ld,λsk , md,λsp=md,λsc+md,λsk ). A wavelength of 780nm was assumed.


We simulated ΔAd1,λka,λΔAd2,λ for various combinations of detector distances. The absorption coefficient at each activation volume of the gray matter layer along the line connecting a source and a detector is assumed to increase by 10% from its standard value. In fMRI studies on human adult brains, functional activations are often observed at a volume of several tens of mm3 . On the other hand, if we set a smaller activation volume (larger photon numbers); a longer computational time will be required to obtain sufficient quality of the simulation result. From this practical reason, we fixed a 5×5×4mm3 volume as an activation volume in this simulation. The result is shown in Fig. 4, which shows the sensitivity distribution for detecting a local absorption change in the gray matter layer. The sensitivities obtained under the minimal and maximal skull layer conditions are very similar to each other. These tend to become high when d1 is large and d2 is small. Thus, d1 should be large and d2 should be small as much as possible to realize good sensitivity. However, if the source-detector distance is increased, the measurement noise would become large, since fewer photons can reach the detector. In addition, if vasculature and hemodynamic activity in the tissues are not sufficiently homogeneous, a larger distance between two detectors may violate our fundamental assumption that each tissue layer is a uniform slab.

Fig. 4

The detection sensitivity of various combinations of source-detector distances, where the absorption coefficient at each 5×5×4mm3 volume of the gray matter layer along the line connecting a source and a detector is assumed to increase by 10% from its standard value. In each frame, the simulated values of ΔAd1,λka,λ ΔAd2,λ at various positions of the activated volume were drawn by blue and red lines, which correspond with the minimal condition ( ld,λsp=ld,λsc , md,λsp=md,λsc ) and the maximal condition ( ld,λsp=ld,λsc+ld,λsk , md,λsp=md,λsc+md,λsk ) of superficial layer, respectively. Green and two blue vertical lines indicate the positions of the source and two detectors, respectively. A wavelength of 780nm was assumed.


Consequently, an effective probe arrangement should satisfy the following constraints.

  • The source-detector distance combination should realize the condition ka,λ=ks,λ as much as possible.

  • d1 should be large and d2 should be small to realize good sensitivity to local absorption changes in the gray matter layer.

  • To keep the measurement noise small, d1 should not be too large.

  • The difference between d1 and d2 should be small enough to satisfy the assumption of uniform tissue layers.

Considering Figs. 3 and 4, we chose the source-detector distance combination d1=30 and d2=20mm as a compromise meeting these conditions.


Estimation of Partial Path Length Ratio k

To calculate the absorption change in the gray matter layer according to Eq. 11, we need to know kλ . We may be able to use a fixed value for kλ ,16 however, it is better to estimate it before each experiment. We may be able to obtain it as kλ=ΔAd1,λrestΔAd2,λrest ,13 where ΔAd1,λrest and ΔAd2,λrest are optical attenuation changes at the resting state of a subject. Here, it is assumed that the absorption change in gray matter is small at the resting state. However, because the absolute value of ΔAd2,λrest could be very small, possibly zero, the ratio ΔAd1,λrestΔAd2,λrest can be very unstable, even when the measurement noise is small. We proposed another estimation method that is stable and gives more accurate values in noisy conditions. The details of the method are described in Appendix { label needed for app[@id='xA'] } in Sec. 6.

We use a triple wavelength measurement, and kλ is estimated for each wavelength. Monte Carlo simulations under both the minimal and maximal conditions of the superficial layer indicate that the wavelength dependence of ka,λ and ks,λ is weak when d1=30mm and d2=20mm (Fig. 5 ). To statistically stabilize the estimation, we used the average k of three estimated values when using Eq. 11.

Fig. 5

2-D plot of wavelength dependence of ka,λ and ks,λ in two contrasting conditions on the superficial layer. Blue and red colored markers correspond with the minimal condition ( ld,λsp=ld,λsc , md,λsp=md,λsc ) and the maximal condition ( ld,λsp=ld,λsc+ld,λsk , md,λsp=md,λsc+md,λsk ) of superficial layers, respectively. Source-detector distances of d1=30mm and d2=20mm were assumed.



Calculation of Changes in HbO and HbR

Based on measurement of the absorption changes Δμa,λ at several wavelengths, temporal hemoglobin changes ΔHbO and ΔHbR can be calculated as follows:

Eq. 12

where ϵHbO,λ and ϵHbR,λ represent molar absorption coefficients of HbO and HbR, respectively, at the wavelength λ . M+ denotes a pseudoinverse matrix of M . Values of ϵHbO,λ and ϵHbR,λ were based on the literature (Matcher). 17

The proposed fNIRS method using a multidistance probe arrangement estimates the absorption change in the gray matter layer as follows [Eq. 11]:

Eq. 13


On the other hand, since a conventional fNIRS method assumes that tissues are a monolayer slab and no scattering change occurs, the absorption change measured by such a method is given as

Eq. 14

where Δμa,λmean and ld1,λmean are the mean absorption change and mean optical path length, respectively.

Absolute values of mean optical path length ld1,λmean can be obtained by time-resolved spectroscopy. However, it is difficult to experimentally obtain partial path length ld1,λgm and ld2,λgm . In this work, we set ld1,λgmkλld2,λgm=1 and ld1,λmean=1 for all wavelengths. As a result of this simplification, we cannot directly compare the magnitudes of ΔHbO and ΔHbR calculated by two different methods. Moreover, the simplification about wavelength dependence may lead to a distortion of hemodynamic changes (cross talk 18, 19, 20). This distortion, however, is considered to be small, since a Monte Carlo simulation shows that the wavelength dependence of optical path length is not very strong (data not shown).



A healthy adult male volunteer participated in the experiment. This study was approved by the Institutional Review Board of National Institute of Advanced Industrial Science and Technology (Japan), and the participant gave his written informed consent.

For fNIRS measurement, we used a near-infrared oximeter with a multiprobe adapter system (NIRO-200 with C9866, Hamamatsu Photonics KK), which has two sources, each with wavelengths 776, 809, and 850nm , and eight detectors. The sampling frequency was 0.5Hz . Each recorded signal was high-pass filtered off-line at a cut-off frequency of 0.01Hz . Based on the simulation results, we set distances from the source to the detectors at d1=30mm and d2=20mm . Using an originally designed holder, the two sources and eight detectors were fixed on the scalp as shown in Figs. 6e and 6f . The detectors were numbered as shown in Fig. 6c. We implemented the conventional method using detectors 1, 3, 5, and 7 and the proposed method using paired detectors 1–2, 3–4, 5–6, and 7–8.

Fig. 6

(a) Axial and (b) coronal sections of the functional volume image of left-hand finger opposition. (c) and (d) Intersections of solid lines give the projections of activated areas on the scalp surface. Paired detectors are located at the position where their middle point corresponds to the projected point. Markers numbered 1 to 8 indicate the detector positions. Markers S1 and S2 indicate source positions. (e) and (f) Photographs of the probe set on a subject model.


Paired detectors 1–2 and 7–8 were positioned on the activation area of the finger opposition task as follows. To locate the activation area during the task, T1-weighted images and echo planar images were measured using MR equipment (MR Signa 3.0T, GE Yokogawa Medical Systems KK). The subject was instructed to tap his thumb with his index finger at a frequency of 4Hz . The block conditions were alternated using visual cues in this order: left-hand finger stimulation periods (20s) , rest periods (20s) , right-hand finger stimulation periods (20s) , and rest periods (20s) . A complete session consisted of an initial reference rest period (20s) and five trials of the block condition (rest, left finger task, rest, right finger task) without any interruption. T-contrast images of left- and right-hand finger opposition against rest periods were obtained using SPM5 (see The images of left-hand activity versus rest appear as colored pixels in Figs. 6a and 6b. The detector was located directly above the activation area, and the position of the activation area was identified by the overlying T1-weighted functional images. The Cz position of an EEG 10–20 system, which is defined as the midpoint of the medial sagittal surface curve connecting nasion and inion, was also identified using the T1-weighted image. The paired detectors 1–2 and 7–8 were located relative to the Cz position.

Optical attenuation changes at the resting state were measured for 10min to estimate the ratio k of each pair of detectors. Table 2 shows the correlation coefficients of the optical attenuation changes in each pair of detectors during the resting state. These values show that the attenuation changes at the paired detectors are highly correlated with each other. Based on the measured optical attenuation change, the k value for each pair was calculated and is shown in the last column of Table 2.

Table 2

Correlation coefficients of ΔAd,λ between adjacent detectors and k values.

Detector pairCorrelation coefficient k
776nm 809nm 850nm

To verify the effect of the proposed method on the cancellation of artifacts caused by posture change, body motion, and respiration, the subject, sitting in a chair, was instructed to perform three tasks: tilting his upper body forward by about 30deg , nodding his head by about 30deg with a frequency of 0.25Hz , and holding his breath. In each task, the block conditions were alternated through task periods (20s) and rest periods (20s) using auditory cues. A complete session consisted of an initial reference rest period (20s) followed by a block of five task/rest sequences.

The finger opposition task was also performed to verify that the proposed method can detect a brain functional signal. To evaluate the performance of the proposed and the conventional (using a single detector and the modified Lambert-Beer law) methods for detecting brain functional activity in the finger opposition task, we analyzed statistical significance by the following procedure. The total task sequence comprises five trials of rest-task pairs. We averaged ΔHbO and ΔHbR at each task and rest periods (each has a duration of 20s ). We adopted a temporal offset of 6s for each period to take into account transient phases of hemodynamic change. Then we calculated the difference between the rest and task averages of five trials. We finally applied the paired t -test to the resultant five differences.



The conventional and proposed methods are compared for cases of body tilting, head nodding, and breath holding in Fig. 7 . ΔHbO and ΔHbR of five task/rest sequences are block-averaged. In all cases using the conventional method, ΔHbO and ΔHbR significantly changed during the task. The magnitude of these changes was comparable to or larger than that of the finger opposition task (shown in Fig. 8 ). The proposed method effectively reduced the magnitude of the changes.

Fig. 7

Block averages and standard deviations of hemoglobin changes during three tasks: body tilting, head nodding, and breath holding. Red, blue, and green lines show ΔHbO , ΔHbR , and the task period, respectively. For each task, frames on left and right sides correspond to the conventional and proposed methods, respectively. Four frames in each column correspond to detector positions 1, 3, 5, and 7 for the conventional method and 1–2, 3–4, 5–6, and 7–8 for the proposed method.


Fig. 8

Hemoglobin changes during the finger opposition task. Red, blue, and green lines show ΔHbO , and ΔHbR , and the task period, respectively. The two left and two right columns show block-averaged hemoglobin changes and their standard deviations for the conventional and proposed methods, respectively. In each method, the left and right frames correspond to left and right finger oppositions, respectively. Four frames in each column correspond to detector positions 1, 3, 5, and 7 for the conventional method, and 1–2, 3–4, 5–6, and 7–8 for the proposed method.


The observed ΔHbO and ΔHbR for the finger opposition task using the two methods are shown in Fig. 8. In the conventional method, increases in ΔHbO were observed at almost all detectors regardless of the side on which finger opposition was performed. The changes in ΔHbR were smaller than those in ΔHbO . On the other hand, significant simultaneous and opposing changes of ΔHbO and ΔHbR were observed only at the detector positions of 1-2 and 7-8 if we used the proposed method. These changes were observed at the contralateral sides in the finger opposition task. The changes in ΔHbO were almost equal in magnitude to those in ΔHbR .

The differences between the rest and task period averages of five trials are shown in the first (conventional method) and third (proposed method) rows of Fig. 9 . In this figure, averaged differences and their standard errors are given. The results of paired t -tests are shown in the second (conventional method) and fourth (proposed method) rows of Fig. 9. Their numerical values are also given in Table 3 . The figure and table show the following. In the conventional method, the detector positions where ΔHbO changed over a level of statistical significance of p=0.05 were not lateralized during finger opposition. ΔHbR showed statistical significance for right finger opposition; however, it showed no significance for left finger opposition. These results suggest that the conventional method failed to detect a cortical functional activation. On the other hand, in the proposed method, the statistical significance of ΔHbO and ΔHbR were clearly lateralized. Statistical significances of the ΔHbO increase and the ΔHbR decrease were simultaneously observed for only two cases: 1 at the 1-2 detector position when left finger opposition was performed, and 2 at the 7-8 detector position when right finger opposition was performed. These positions correspond to locations directly above the activation area identified by fMRI. These results suggest that the proposed method works better than the conventional method in detecting cortical activation.

Fig. 9

Statistical analysis of cerebral activation during the finger opposition task. Upper and lower subfigures show the analysis results of the conventional and proposed methods, respectively. The upper row of each subfigure indicates the difference between the rest and task averages and its standard error. The lower row of each subfigure indicates t -values of paired t -tests. In each frame, red and blue bars indicate values of HbO and HbR, respectively. The left and right parts of each frame correspond to task condition, left- and right-finger opposition, respectively. Asterisks in some frames of t -value indicate statistical significance over the level of p=0.05 .


Table 3

T -values of the paired t -test for the finger opposition task. Asterisks indicate statistical significance level of p=0.05 .

DetectorConventional methodDetectorProposed method
Left handRight handLeft handRight hand
1 6.528* 2.109 1.5270.8731–2 5.280* 3.844* 1.174 0.277
32.1280.218 3.691* 1.438 3–4 0.144 0.130 0.107 1.034
52.5630.833 5.517* 2.027 5–6 0.337 0.026 3.714* 0.838
7 2.717* 0.128 6.287* 5.630* 7–80.2790.130 9.790* 5.815*



Artifacts caused by physical and systemic physiological activities have been a serious problem in fNIRS measurement. We confirmed the existence of artifacts in conventional fNIRS measurement using three tasks: body tilting, head nodding, and breath holding. Their magnitude was comparable to or larger than that observed as a functional signal during finger opposition.

The instability of the optical contact between probes and scalp may have caused some of these artifacts. However, these kinds of signal changes are also observed even when we use another type of probe (A9782, Hamamatsu Photonics KK), which can be attached very stably on the forehead of a subject (data not shown here). Thus, we think that physical movements and systemic physiological activity changes strongly influence conventional fNIRS measurement and may generate serious artifacts, even if we can realize stable optical contacts. Experimental results showed that such artifacts can be eliminated effectively by the proposed method.

Some researchers have reported that NIRS signals were observed at both the contralateral and ipsilateral hemisphere when a subject performs a one-sided finger opposition.6, 21 We confirmed the existence of such a global change in the conventional fNIRS signal. Franceschini suggested that some systemic response accompanying the finger movement causes such global changes in ΔHbO and ΔHbR .6 This component cannot be easily removed by conventional data analysis, and it certainly interferes with detection of brain function. However, if these hemodynamic changes mainly occur in the scalp or skull layers, the interference can be reduced by the proposed method, and in fact, they were reduced well in our experiment (see Fig. 8).

There are some arguments about the correlation between the fNIRS signal and brain functional activity. Some studies claim that a strong correlation exists between ΔHbR decrease and the blood oxygen level dependent signal of fMRI.22 In the proposed method, the localization of ΔHbR decrease coincides well with the localization of fMRI signals. Therefore, this observation supports a consistent relationship between fNIRS and fMRI measurements.

Many researchers consider that an increase in ΔHbO corresponds to brain activity. In our result using the proposed method, the increase in ΔHbO was observed simultaneously with the decrease in ΔHbR ; consequently, it is localized in the area where the fMRI signal was observed. On the other hand, in the conventional method, a certain global component of the ΔHbO increase at a superficial layer seems to be superposed on the ΔHbO increase in the gray matter. Apparently this component is not directly related to brain activity, because it is well known that the cerebral region associated with motor function is highly localized.23 If we consider such a contaminated signal of ΔHbO increase as a “functional” signal, an artificial correlation of ΔHbO to the task sequence may lead fNIRS into false-positive detection of brain activity.

In our multidistance probe arrangement, the distances between the source and each detector were set to 20 and 30mm . However, some studies use another arrangement in which one detector was positioned close to the source to detect the signal from the scalp exclusively, while the other detector is positioned further away to detect the signal from gray matter. Leung, Elwell, and Delpy calculated the measurement accuracy and optimized distance conditions using various numbers of detectors.24 In the case using two detectors, they showed that a distance combination of 5 and 50mm is optimal to detect attenuation change in brain. Saager and Berger also used this type of arrangement and showed by Monte Carlo simulations that it is possible to remove artifacts uncorrelated with a functional signal.3 Our method is different from their studies in the following three points. First, we intend to remove task-correlated or function-correlated artifacts. Thus, we cannot use the low correlation property between artifacts and functional signals. Second, we intend to remove artifacts caused by both the scattering and absorption changes in superficial layers. If a source-detector distance less than 10mm is selected, ka=ks does not hold sufficiently (see Fig. 3), and it can counteract this type of artifact cancellation. Third, if we use their arrangements, the distance between two detectors becomes greater than 20mm . This can violate the assumption of uniform slab in a two-layer model, because vasculature and hemodynamics at the actual superficial layer may not be sufficiently homogeneous.

We adopted the simplification that only functional hemodynamics occur in the gray matter layer. Under this simplification, detected signals from gray matter directly indicate a functional signal. However, systemic physiological activities can affect hemodynamics in the gray matter layer as well as in the superficial layer. Therefore, we discuss in Appendix { label needed for app[@id='xB'] } in Sec. 7 how systemic hemodynamics in gray matter, if it exists, affects the detection of brain function. In brief, the influence of systemic hemodynamics in gray matter can also be removed by the proposed method; see Appendix { label needed for app[@id='xB'] } in Sec. 7 for details.

In this work, data obtained from one single subject were shown. We implemented similar experiments on several subjects. Also in these cases, we confirmed effective artifact reduction and functional signal localization; however, it may require further validation with more subjects. Through further trials of the proposed method, ΔHbO and ΔHbR changes by cerebral activation of human adults, infants, and pathological cases may be revealed in the future. We expect that these can be adopted as cerebral hemodynamic response functions (HRF) in the statistical approaches based on the general linear model.25, 26 Such a statistical parameter mapping (SPM)-like analysis based on a precise HRF will increase the reliability of fNIRS measurement.


{ label needed for app[@id='xA'] }

Appendix A: Procedure for Estimating the Path Length Ratio

If we have temporal absorption and scattering changes Δμa,λ(t) and Δμs,λ(t) , respectively, only at a superficial layer, the optical attenuation changes observed at detectors d1 and d2 are represented as

Eq. 15


Eq. 16

where t is the sampling index, and nd1,λ(t) and nd2,λ(t) are measurement noises with a zero average. We assume that the averages of ΔAd1,λ(t) and ΔAd2,λ(t) are set to zero beforehand. Let ka,λ=ld1,λld2,λ and ks,λ=md1,λmd2,λ . If we assume ka,λ=ks,λ=kλ , as described in Sec. 2.2, we have

Eq. 17


Eq. 18

where ΔAλ=ld2,λΔμa,λ(t)+md2,λΔμs,λ(t) .

To find kλ , we introduce the following criterion.

Eq. 19


Eq. 20


Eq. 21

where σA,λ2 , σn,12 , and σn,22 are the variances of ΔAλ(t) , nd1,λ(t) , and nd2,λ(t) , respectively. We assumed that ΔAλ(t) , nd1,λ(t) , and nd2,λ(t) are mutually independent in the last derivation of the equation.

We assume that the noise variance of detector d1 ’s output is equal to that of detector d2 ’s output, and we represent it as σ2 . In general, noise variances σn,d12 and σn,d22 in the optical attenuation data differ because the log operation is used to calculate the optical attenuation. If we represent the average outputs of detectors d1 and d2 as Id1 and Id2 , respectively, we obtain the following approximate equations:

Eq. 22


Eq. 23

Then J(k) becomes

Eq. 24


If k=kλ , the first term of Eq. 24 becomes zero. Thus, the criterion J(k) achieves the minimum value when k=kλ if no noise exists (σ=0) . However, since the second term of Eq. 24 works as a bias in the criterion, if noise exists, k that minimizes J(k) tends to be smaller than the correct value. To avoid this difficulty, we propose the following criterion J(k) .

Eq. 25


Eq. 26

The minimum of J(k) is achieved when k=kλ , even if noise exists.

{ label needed for app[@id='xB'] }

Appendix B: Reduction of Systemic Hemodynamics in the Gray Matter Layer

If we assume that systemic physiological activities affect hemodynamics in the gray matter layer as well as in superficial layers, Eq. 9 changes as follows.

Eq. 27

Here, Δμa,sys,λsp and Δμa,sys,λgm indicate absorption changes due to systemic physiological activities at the superficial and gray matter layers, respectively. Δμa,func,λgm indicates absorption changes due to functional activity at the gray matter layer. Δμs,sys,λsp denotes the scattering change in the superficial layer. Absorption changes Δμa,sys,λsp and Δμa,sys,λgm possibly show temporal similarity, because both originate from systemic activities. Thus, we suppose a relationship

Eq. 28

Substituting Eq. 28 into Eq. 27, we obtain

Eq. 29


Here, we introduce ka,λ as

Eq. 30

Since our simulation results show ld,λspld,λgm , we can assume ka,λka,λ unless γ is much larger than 1. Thus, if we use the probe distance combination satisfying kλ=ka,λ=ks,λ , we can approximately say kλ=ks,λka,λ . In this case, Δμa,func,λgm is calculated as

Eq. 31

Consequently, the systemic component in gray matter, if it exists, can be removed by our method. In fact, hemodynamics observed by our method were very flat at channels of cerebral nonfunctional areas (see Fig. 8).


The authors thank the Photon Migration Imaging Laboratory at Massachusetts General Hospital for the Monte Carlo simulation code (available at



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©(2009) Society of Photo-Optical Instrumentation Engineers (SPIE)
Toru Yamada, Shinji Umeyama, and Keiji Matsuda "Multidistance probe arrangement to eliminate artifacts in functional near-infrared spectroscopy," Journal of Biomedical Optics 14(6), 064034 (1 November 2009).
Published: 1 November 2009

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