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- SPIE
- ISSN
- 2329-423X
- eISSN
- 2329-4248
- DOI
- 10.1117/1.NPh.4.4.041407
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Abstract
Graph theoretical approach to functional connectivity in prefrontal cortex via fNIRS Zahra Einalou Keivan Maghooli Seyaed Kamaledin Setarehdan Ata Akin Zahra Einalou, Keivan Maghooli, Seyaed Kamaledin Setarehdan, Ata Akin, “Graph theoretical approach to functional connectivity in prefrontal cortex via fNIRS,” Neurophoton. 4(4), 041407 (2017), doi: 10.1117/1.NPh.4.4.041407. Neurophotonics 4(4), 041407 (Oct–Dec 2017) Graph theoretical approach to functional connectivity in prefrontal cortex via fNIRS a b, c d Zahra Einalou, Keivan Maghooli, * Seyaed Kamaledin Setarehdan, and Ata Akin Department of Biomedical Engineering, North Tehran Branch, Islamic Azad University, Tehran, Iran Department of Biomedical Engineering, Science and Research Branch, Islamic Azad University, Tehran, Iran University of Tehran, Control and Intelligent Processing Center of Excellence, School of Electrical and Computer Engineering, College of Engineering, Tehran, Iran Acibadem University, Department of Medical Engineering, Istanbul, Turkey Abstract. Functional near-infrared spectroscopy (fNIRS) has been proposed as an affordable, fast, and robust alternative to many neuroimaging modalities yet it still has long way to go to be adapted in the clinic. One request from the clinicians has been the delivery of a simple and straightforward metric (a so-called biomarker) from the vast amount of data a multichannel fNIRS system provides. We propose a simple-straightforward signal processing algorithm derived from fNIRS-HbO data collected during a modified version of the color-word match- ing Stroop task that consists of three different conditions. The algorithm starts with a wavelet-transform-based preprocessing, then uses partial correlation analysis to compute the functional connectivity matrices at each condition and then computes the global efficiency values. To this end, a continuous wave 16 channels fNIRS device (ARGES Cerebro, Hemosoft Inc., Turkey) was used to measure the changes in HbO concentrations from 12 healthy volunteers. We have considered 10% of strongest connections in each network. A strong Stroop interference effect was found between the incongruent against neutral condition (p ¼ 0.01) while a similar sig- nificance was observed for the global efficiency values decreased from neutral to congruent to incongruent con- ditions [F ð2;33Þ¼ 3.46, p ¼ 0.043]. The findings bring us closer to delivering a biomarker derived from fNIRS data that can be reliably and easily adopted by the clinicians. © 2017 Society of Photo-Optical Instrumentation Engineers (SPIE) [DOI: 10.1117/1.NPh.4.4.041407] Keywords: weighted connectivity graph; global efficiency; Stroop task; wavelet-based partial correlation. Paper 17050SSR received Apr. 6, 2017; accepted for publication Jul. 19, 2017; published online Aug. 21, 2017. subjects make large movements, or in studies for monitoring 1 Introduction cortical activation in response to noxious stimuli in infants, Functional near-infrared spectroscopy (fNIRS) has been pro- 14 15 16 adults, patients, and assessment of human response to pain. posed as a noninvasive, rapid, and affordable alternative of func- Currently, there are two trends followed by the “fNIRSan” tional neuroimaging modality to fMRI and positron emission (members of the fNIRS community) in their efforts to gain tomography (PET). Although this technique was introduced acceptance of their system by the clinicians: (1) increase spatial and developed in the last three decades, few scientists recently and temporal resolution to provide a full brain scanner; hence be have allocated their efforts on this issue. For establishing clinical a competitor and an attractive alternative to fMRI and (2) opti- applications, the major parts of their attempts have focused on mize the number of channels and provide a metric (a biomarker) the amendments of sensitivity and specificity of this method. In that correlates well with the neurovascular coupling physiology Refs. 1–3, a relatively complete discussion can be found on during cognitive activity. The first trend requires the develop- fNIRS advantages and limitations. Despite its many years of ment of an expansive and bulky system that is neither versatile introduction to the community, it has only one significant clini- nor mobile whereas the second trend aims to develop a system cal application: transcranial oximetry as a monitor for perfusion that is mobile, flexible, inexpensive yet crude and may lack the of the brain. This approach has been readily commercialized necessary accuracy of its competitor. However, the second trend and several FDA-approved instruments are already placed in also bestows the highest hope of providing a clinically relevant the operation room. Acceptance of the fNIRS system to neuro- marker. The researchers try to align themselves with one of these psychology and neuropsychiatry has not been all that welcome. camps in their efforts to push this system into the clinic. We have Although fNIRS offers many advantages over traditional neuro- chosen to be allies with the second camp and propose a metric imaging techniques, it still suffers from several physical and that can be used effectively in evaluating the cognitive state of technical issues that lead to hesitations by clinicians and the individual with respect to his/her physiological finding 5,6 researchers in their adaptation of this technique. Despite a derived from fNIRS measurements. lower resolution due to diffusive behavior of light propagation The best way to find a clinical marker is to extract meaning- in tissue, fNIRS is attractive because of its noninvasiveness, ful information from the recorded fNIRS data. To reach this 6–11 comfort, and cost-effectiveness. Allowing the tolerance to goal, many researchers have adapted innovative signal process- head motion fNIRS has been used in experiments in which ing algorithms to extract features that can be readily used as 7,17–23 these markers. In fact, after the success of functional *Address all correspondence to: Keivan Maghooli, E-mail: k_maghooli@srbiau. ac.ir 2329-423X/2017/$25.00 © 2017 SPIE Neurophotonics 041407-1 Oct–Dec 2017 Vol. 4(4) Einalou et al.: Graph theoretical approach to functional connectivity in prefrontal cortex via fNIRS connectivity studies using fMRI, similar studies using fNIRS 7,24–31 have emerged recently. Recent studies have shown obvi- ously that human brain connectome networks can be constructed 32 33 using fMRI, diffusion tensor imaging, electroencephalogra- 34 35,36 phy (EEG), and magnetoencephalography (MEG) data, and even further be investigated by graph theoretical approaches. In this study, we aimed to investigate the efficiency of the graphs formed in the prefrontal cortex (PFC) during a modified 30,38 version of the color-word matching Stroop task. Connectiv- ity patterns obtained from the partial correlations (PC) of the hemodynamic responses acquired from 16 different regions of the PFC to various stimuli are expected to be different from chan- 19,39,40 nel to channel and this is related with the cognitive load. A Fig. 1 Stroop task protocol: the subjects responded to each stimulus continuous wave 16 channels near-infrared spectroscopy device in a 4-s interval. (ARGES Cerebro, Hemosoft Inc., Turkey) was used to measure the changes in HbO concentrations from 12 healthy volunteers. Subjects were informed to perform the task as quickly and An important aspect of our research is the exploration of the correctly as possible. The words stayed on the screen until the potential of fNIRS to be used as a functional neuroimaging response was given with a maximum time of 3 s. The screen was modality in an expectation to deliver a clinical marker. The sec- blank between the trials. The experiment consisted of neutral ond important contribution of our research is the introduction of a (N), congruent (C), and incongruent (IC) trials. In the neutral simple and straightforward signal-processing algorithm: a wave- condition (N), the upper word consisted of four X’s (XXXX) let-based partial correlation (WPC) analysis that allowed us to in ink color. In the congruent condition (C), ink colors of the focus on the functional connectivity in a well-defined frequency upper word and the word itself were the same, whereas in the interval (0.0035 to 0.08 Hz) while eliminating the use of high incongruent condition (IC), they were different. The trials were order digital filters and preprocessing techniques that end up presented in a semiblocked manner (see Fig. 1 for the details). warping the data dramatically. Use of wavelet transform-based Each block consisted of six trials. The interstimulus interval elimination of nonneural sources of noise, such as cardio respi- within the block was 4.5 s and the blocks were placed 20 s apart ratory effects, has been quite successful in fNIRS signal-process- in time. The trial type within a block was homogeneous (but the 30,41–43 ing applications. Moreover, WPC analysis helps to remove arrangements of false and correct trials were altering). There the effect of indirect paths; since by applying this method while were five blocks of each type. The experiments were performed the WPC between two channels is correlated, an underlying cor- in a silent, lightly dimmed room. Words were presented via an relation common to all other 14 regions can be regressed out. LCD screen that was 0.5 m away from the subjects. The task Hence the main aim of this study is to explore the feasibility of protocol was approved by the Ethics Review Board of Bogazici fNIRS to monitor the neural correlates of the cognitive activity in 7,19,45,46 University. PFC during a Stroop test by using wavelet analysis and graph theory. The choice of a wavelet-based filtering can in fact be more justified for real-time analysis since wavelets are excellent 2.2 Data Acquisition choices for real-time applications. Usually real-time neurofeed- The fNIRS device is capable of transmitting near-infrared light back systems require several seconds of data recording before at two wavelengths (730 and 850 nm), which are known to be proving feedback. Hence a collection of initial 10 to 20 s of able to penetrate through the scalp and probe the cerebral cortex. data for real-time feedback would be ideal and then every new Employing 4 LEDs and 10 detectors, the device can sample 16 second the previous 20 s would be analyzed to provide the feed- different channels in the brain simultaneously (see Fig. 2 for the back. Correlation and GE calculations are very fast algorithms details of the probe ). LEDs and detectors were placed in a flex- that can be computed in the millisecond range by any DSP chip. ible printed circuit board that was specially designed to fit the curvature of the forehead. The source–detector separation is 2 Materials and Methods fixed at 2.5 cm, which is optimized for penetration depth (∼1.5 cm from the surface to allow sampling from the cortex ) 2.1 Subjects and Protocol 7,8,49–53 and a wider sampling area of the PFC. Sampling fre- quency of the device was 1.7 Hz. Calculation of concentration Data were collected from 12 healthy volunteers (7 females and 5 changes of oxy-Hb and deoxy-Hb in blood is based on a modi- males) from the university community (right-handed, mean age 7,8,20,54 fied version of the Beer–-Lambert law. 26.17 4.30, range 20 to 31) at the Neuro-Optical Imaging Laboratory, Bogazici University Istanbul, Turkey. Control sub- jects had no history of psychiatric or neurological disorders. 2.3 Signal Processing Algorithm Subjects were asked to perform color-word matching Stroop 38,44 tasks whose trials are the Turkish versions of Zysset et al. The signal processing algorithm proposed is summarized Subjects were presented with two words, one written above the in Fig. 3. other. The top one was written in ink color whereas the bottom As can be seen, this is a consolidation of techniques proposed one was in white. Subjects were asked to judge whether the in the literature by many others. The wavelet transform has word written below correctly denotes the color of the upper been proposed to remove artifacts and irrelevant physiological 30,36,41,42,55–57 word or not. If color and word match, then subjects were to signals. The choice of the details and approxima- press on the left mouse button with their forefinger, and if not, tion coefficients was based on the spectral analysis of fNIRS 7,19,20,28,58–60 on the right mouse button with their middle finger. signals. Neurophotonics 041407-2 Oct–Dec 2017 Vol. 4(4) Einalou et al.: Graph theoretical approach to functional connectivity in prefrontal cortex via fNIRS band of the hemodynamic response falls in the approximation at level 3 (CA3: 0.0035 to 0.110 Hz) with respect to the sam- pling frequency of the fNIRS instrument. The coefficients at very low and higher frequency values were nulled and then a new fNIRS-HBO signal was reconstructed for each detector. 2.3.2 Partial correlation PC is a useful statistical tool for determining the relationship between two variables after removing the effects of other varia- 62,63 bles. The goal of PC analysis is to figure out the hidden rela- tion between two channels, while the interactions of other channels on them have been eliminated. In our study, 16 channels were used to investigate the functional connectivity (D ¼ 16). Suppose that x ¼ðx Þ are the time signals related to each i¼1;:::;D of the 16 channels of the fNIRS signal. The PC coefficient between the two channels i and j is defined by Π ,which is i;j a calculation of the conditional correlation between channels i and j irrespective of the effect of D-2 remaining channels (R∕fði; jÞg). EQ-TARGET;temp:intralink-;e001;326;535Π ¼ corr½x ;x jx .(1) i;j i j R\fi;jg Fig. 2 Details of the fNIRS probe and its approximate placement on the forehead. It has been shown that the PC matrix can be obtained by calcu- 38,39 lating the covariance matrix (Σ)from D channels. Thus, for D ¼ 16, the number of PC coefficients will be equal to DðD − 1Þ∕2 ¼ 120, which is obtained from the PC matrix. Matrix Π can be easily calculated through the reverse of covari- −1 ance matrix (ϒ ¼½ϒ ¼ Σ ). The reverse covariance matrix of i;j 47,62–83 X is called precision matrix or concentration matrix. Thus, ij EQ-TARGET;temp:intralink-;e002;326;426Π ¼ −pffiffiffiffiffiffiffiffiffiffiffiffiffi ; (2) i;j ϒ ϒ ii jj where i and j are the two separate channels and Π ¼ 1.The ii value range of PC is between þ1 and −1. PC values were com- puted for each frequency band in three types of stimuli. Since PC analysis helps to remove the effect of indirect paths, by applying this method, the PC between two channels is correlated with the 62,63 activity at all other 14 regions regressed out. By applying this method, we investigated connectivity graphs based on PCs Fig. 3 Signal processing steps used in generation of the global effi- between the inverse wavelet transformed (reconstructed) data that ciency metric. DC, direct current (baseline signal value); IWT, inverse correspond to the specific frequency band of interest. wavelet transform; BPF, band pass filter; FC, functional connectivity. 2.3.3 Weighted connectivity graph 2.3.1 Wavelet transform-based preprocessing Graph-based network analysis represents the state-of-the-art The discrete wavelet transform (DWT) uses filter banks to per- methodology in brain connectivity. We considered the channels form the wavelet analysis. The DWT decomposes the signal as a set of vertices V and the PC coefficients assigned weights on into wavelet coefficients that can represent the signal in various the set of edges E, leading to an undirected complete weighted 21,56,64 frequency bands. The choice of wavelet function plays an graph G ¼ðV; EÞ. We investigated the connectivity important role in the quality of the analysis of fNIRS signals. graphs of the PCs computed between wavelet coefficients at the Similarity of the mother wavelet to the hemodynamic response third level (corresponding to 0.0035 to 0.110 Hz frequency function improves the detectability of the estimation accuracy range) of each channel. The graphs were computed for each stimulus type. of the signal. Hence, the decomposition was done by the Daubechies 5 (Db5) as the mother wavelet because of its high 42,61 similarity to hemodynamic response. The wavelet domain 2.3.4 Global efficiency and cost of a graph is advantageous to focus in a defined frequency interval to Efficiency can be evaluated for a wide range of networks, emphasize the functional association between brain regions sub- including weighted graphs. The formal definition is as follows: tended by cognitive activity. Neuronal activity-related hemo- dynamic response observed in fNIRS-HBO data are shown X 1 1 22,28,45,46 EQ-TARGET;temp:intralink-;e003;326;100GE ¼ ; (3) to occupy the frequency range of (0.003 to 0.08 Hz). NðN − 1Þ L ij i≠j∈G According to the wavelet decomposition tree, the frequency Neurophotonics 041407-3 Oct–Dec 2017 Vol. 4(4) Einalou et al.: Graph theoretical approach to functional connectivity in prefrontal cortex via fNIRS where N is the number of nodes in the network, L is the short- 0.01). Analysis of variance (ANOVA) was used to test the stat- ij est path length between nodes i and j. Maximal possible istical significance among GE values from different stimulus global efficiency (GE) occurs when all edges are present in the types (i.e., GE ; GE ; and GE ). Figure 4(b) shows signifi- N C IC network. We used Latora and Marchiori’s efficiency measure, cance at six different threshold values. The purple triangles indi- since it allows us to work with weighted connectivity graphs. In cate that there are significant differences between the GE of this case, the GE is computed as three types of stimuli (p < 0.05). We investigated the topologi- cal properties of the brain functional network as a function of 1 1 69 70 GE and K, following the studies by Stam et al. and Liao et al. EQ-TARGET;temp:intralink-;e004;63;686GE ¼ ; (4) NðN − 1Þ d ij The choice of a threshold value will have a major effect i≠j∈G on the topological properties of the resulting networks. This allowed us to compare the topological properties among the where d is “defined as the smallest sum of the physical distan- ij three types of stimuli in a manner that is relatively independent ces throughout all the possible paths in the graph from i to j.” of the network size. The threshold is selected to ensure that brain This has an interpretation, as stronger connection weights intui- networks have a lower GE compared to random networks with tively correspond to shorter lengths. Equation (4) generates val- ues of GE in the range of [0;∞]. This value can be normalized to relatively the same degree of connectivity distribution. Ten per- [0; 1] by dividing it into randomly generated networks with the cent of the strongest connections in each network (highest val- same number of nodes. This analysis provides an insight to the ues of wavelet PC) is considered, which corresponded to the robustness of the network and its closeness to small network degree of connectivity threshold [see Fig. 4(b)]. GE values were 32,55,66 properties. We generated 100 degree matched random net- computed for each stimulus condition. Path length is inversely works to compute the ratios of global efficiency (GE∕GE ) related to the GE of a network for the transfer of information random between the real brain functional networks and 100 degree among nodes by multiple parallel paths, and that GE is easier matched random networks to assess small-worldliness of brain to estimate than path length when studying sparse networks. functional networks. Typically, GE of a small world network (GESW) approximates to the GE of a random network (GESW∕GE ∼ 1). random We, then, investigated the topological properties of the brain functional network as a function of GE and K . The total num- cost ber of edges in a graph divided by the maximum possible num- ber edges N ðN − 1Þ∕2 EQ-TARGET;temp:intralink-;e005;63;430K ¼ K (5) cost i NðN − 1Þ i∈G is called the cost of the network, which measures how expensive it is to build the network. The degree of each node, K , i ¼ 1;2;:::; 16, is defined as the number of nodes in the sub- graph G . A subgraph G is defined as the graph including the i i nodes that are the direct neighbors of the i’th node. K is the cost (a) average of the degrees of all the nodes in the graph, which is a measure for the sparsity of a network. 1.2 GE/GE Neutral random GE/GE Congruent random 2.3.5 Behavioral results GE/GE Incongruent random 1.15 To achieve the behavioral results, we analyzed the reaction times (RTs) from data of 12 subjects. In order to compare each pair of 1.1 stimuli, we apply a two-tailed paired t-test for RTs. The inter- ference effect for the RTs between IC and N conditions 1.05 (p ¼ 0.01) and facilitation effect for the RTs of N against C con- ditions are significantly different (p ¼ 0.03). However, there is no significant difference between RT of IC and C (p ¼ 0.8). 0.95 0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.5 3 Results Threshold (b) 3.1 Global Efficiency Results We averaged across all 100 generated random networks to Fig. 4 (a) The dependence among global efficiency values for three ¯ types of stimuli [neutral (N), congruent (C), and incongruent (IC)] and obtain a mean GE for each degree K and threshold T. random percentage of strongest connections in the network (K ). The solid cost Over a wide range of cost (0.005 < K < 0.04), results are con- lines correspond to real network, and the dashed lines correspond to 55,68 sistent with previous functional brain network studies. random networks. (b) The ratios of global efficiency (GE∕GE ) random Figure 4(a) shows GE values for N, C, and IC in a real network between the real brain functional networks and 100 degree matched (average of 12 subjects) and random networks for each K cost. random networks to assess small-worldliness of brain functional net- We investigated the small-world that corresponded to the works. The purple triangles indicate that there are significant differences among the GE of three types of stimuli (p < 0.05). degree of connectivity threshold 0.01 < T < 0.99 (with steps of Neurophotonics 041407-4 Oct–Dec 2017 Vol. 4(4) GE/GE random Einalou et al.: Graph theoretical approach to functional connectivity in prefrontal cortex via fNIRS of detection and diagnosis if not taken care of. Lindauer et al. have proven that the underlying cerebrovascular dynamics are greatly affected by the metabolism, pharmacological interven- tions, and even diseases and hence hinder the accurate estima- tion of the neuronal response. In recent years, several investigators decided to tackle this problem either by proposing 18,20,72–74 optical probe geometries or advanced signal processing 19,22,29,42,62,63 techniques. While a remedy to this interference problem might be adding optodes with short separation, it comes at a cost of increased device complexity and expense. Signal processing tools have shown to reliably improve this desensitization to superficial fluctuations with a common physiological background. Tak and Ye have provided an excel- lent review on the capabilities of such alternatives. The nature of this interference is the basic underlying physiology and it can be assumed to be present with a varying degree of contamination Fig. 5 Mean of GE and RT for three types of conditions. Data are in each and every time series of fNIRS data. One alternative to shown as mean standard error (SE). N, neutral task; C, congruent eliminate this contamination and achieve nuisance-free fNIRS task; IC, incongruent task. Black asterisk indicates p < 0.05. data representing the neural activity is the use of PC analy- 24,62 sis. The method we used in this study based on PC elimi- nates this deceiving correlation by considering the similar trends GE decreased as the stimulus type became more difficult underlying other optode data and eliminating them. This [Fð2;33Þ¼ 3.46, p ¼ 0.043] as seen in Fig. 5 (GE > approach also provides a means to bypass any unnecessary pre- GE > GE ). Although the two-way ANOVA provided a sig- C IC processing of the data. Among many denoising algorithms, we nificance, this significance is clearly between the GE and GE IC N decided to use the wavelet transform-based approach since the but not between GE and GE as expected. Normally, the IC C effectiveness of this technique has been shown in many cases Stroop findings focus on the interference effect (null hypothesis where there might be spike-like or stepwise motion artifacts is that the mean value of GE is the same as the mean value IC in the signal. Such artifacts will not be removed by any bandpass of GE ). infinitive impulse response filtering technique and in fact lead to a more fatal distortion in the signal as the smearing of that spike 3.2 GE versus Behavioral Results onto the adjacent time points. Yet another advantage of wavelet- based denoising is its use of very short duration filters causing We investigated the relationship between the RTs and GE values minimal phase distortion possibly minimizing an error in calcu- in the N, C, and IC matrices. We computed the change in RTs for lation of the correlation coefficient. ICA can be considered as an different stimulus types and also the change in the GE of the N, alternative yet the assumption in ICA-based approaches is that C, and IC. Behavioral results and GE analysis according to the the sources are already independent of each other. The noise stimulus type are shown simultaneously in Fig. 5. The most might be independent but the systemic physiological back- sought after finding in a color-word matching Stroop task is the ground signal is not. Hence, it is nearly impossible to find contrast of the incongruent condition against the neutral con- ICA sources that are band limited yet uncorrelated with the dition. We show that both in RTs and GE values there is a noise. So the natural choice was a wavelet-based approach. strong interference effect between the incongruent and neutral Graph theoretical metrics have been applied to many neuro- conditions. 21,36,37,67 imaging data especially from fMRI. Studies by Supekar All in all, we believe that the decreasing GE throughout a et al. have shown that functional connectivity computed by task might possess clinical significance. the correlation approach provides clinically significant value 4 Discussion specifically in Alzheimer’s patients. Studies by Skidmore et al. have shown functional connectivity computed by wavelet This study proposes a simple and straightforward algorithmic correlation analysis in individuals with idiopathic Parkinson’s method to quantify the functional connectivity of the brain using disease. A graph theoretical metric, GE, was used in discrimi- graph theoretical techniques applied to fNIRS-HBO signals. nating the functional connectivity patterns observed in these We also propose to integrate the well-studied wavelet-based fil- patients. We used the same metric to investigate further in tering and PC analyses as preprocessing tools before graph effi- healthy people how this metric is influenced among various cog- ciency is computed. Graph theory gives us a language for nitive loads. In contrast to these fMRI studies, we performed an networks. It allows us to define networks exactly and to quantify analysis to prove that fNIRS can reliably be applied to obtain network properties at many different levels. This quantification these metrics. Recently, Niu et al. used the graph theoretical net- is likely to improve further since new graph measures are work analysis approach to examine the topological organization described regularly. of the human whole-brain functional network constructed using Mesquita et al. performed an fNIRS study during resting 27,31,54 resting-state fNIRS data. Studies by Liu et al. have shown state and then applied correlation analysis to determine the func- that functional connectivity computed again by the PC approach tional connectivity among brain regions. They used the corre- provides clinically significant values specifically in schizophre- lation analysis between two optodes. This approach is prone to nia patients. Previous fNIRS studies have shown that patients incorrect correlations since both data might contain similar trends due to interference from systemic fluctuations. Tachtsidis with schizophrenia have impaired activity in the PFC. Taniguchi et al. have shown how these fluctuations can alter the accuracy et al. measured reduced brain activity in PFC of schizophrenia Neurophotonics 041407-5 Oct–Dec 2017 Vol. 4(4) Einalou et al.: Graph theoretical approach to functional connectivity in prefrontal cortex via fNIRS patients compared to healthy controls during the Stroop task. sampling. Hence, we might be observing a piece of a network GE has an intuitive interpretation, as higher connection weights and the cognitive demand could be distributed over other parts of the brain. That could also explain a decrease in GE as the intuitively correspond to shorter lengths. cognitive load increases. In contrast to studies emphasizing whole-brain network, we found that data from a specific region (i.e., PFC) can be used to generate a global connectivity metric during cognitive tasks. 4.1 Limitation of the Study As Eq. (4) dictates, GE is “the average inverse shortest path length” that may significantly contribute to an integration in We reiterate the rationale behind our choice of this source– larger and sparser networks. GE values are inversely related detector separation. This has been a long debate and many to link weights, as large weights typically represent strong asso- authors have favored the use of source–detector separations as ciations, so might GE decrease as the cognitive activity becomes close as 2.5 cm. In fact one of the pioneers of fNIRS, the late Dr. more demanding. GE results are consistent with the hypothesis Britton Chance himself has used rectangular probe geometry that information transfer among the regions of PFC will increase with an SD separation of 2.5 cm in most of his studies. We with the increasing cognitive load. Path length provides a mea- would like to bring to your attention to a paragraph from his one sure of the network’s capacity for serial information transfer of the most cited articles. The major intracerebral contribution among nodes, whereas global efficiency is a measure of the net- probably comes from the gray matter. This has been confirmed work’s capacity for parallel information transfer among nodes in two studies performing PET and NIRS simultaneously that via multiple series of edges. Since the evidence is strong that the have shown the best correlation between NIRS and PET param- 11,79 brain is already massively parallel processing, it seems prefer- eters in the outer 1 cm of the brain tissue. Interestingly, it able to adopt comprehensive measures of the efficiency of the seems that even at interoptode distances as short as 2 to 2.5 cm 55 76 brain’s functional network topology. Among various graph gray matter is part of the sample volume. This is consistent theory metrics, we focused on the GE as a marker of the engage- with work assessing changes in local brain activity successfully ment of the PFC with respect to cognitive load since on a global with interoptode distances of 2.5 cm. Other authors have scale, GE quantifies the exchange of information across the reported measurements at even smaller interoptode distances. whole network where information is concurrently exchanged Our group has also shown through Monte Carlo simulations run on a realistic head model that we can actually probe the gray while local efficiency quantifies a network’s resistance to failure matter. We agree that the probed gray matter area will increase on a small scale. That is, the local efficiency of a node character- when the source–detector separation is enlarged to 3 cm, albeit izes how well information is exchanged by its neighbors when it at the cost of reduction in SNR. Even at an SD separation of 2.5 is removed. Since PFC is usually considered to have been one we are losing ∼1∕10 of the photons. Hence, this choice large network, it would seem only reasonable to treat it as one becomes an optimization issue. Even though only about 2% network and so we focused on a metric that would provide the 82,83 to 3% of the signal we collect comes from the gray matter, connectivity of the whole network. Intrinsic functional net- the dynamical changes observed and extracted with proper sig- works of the human brain have been generated by EEG, fMRI, nal processing techniques correlate significantly with the task. or MEG modalities and they all demonstrate a converging and Hence as engineers we are faced with the dilemma ensuring a highly conserved topological organization over different scales, 21,33,55,57,65,66,70 deeper penetration depth via a larger SD separation at the such as small-world and modular structures. More expense of complexity and cost of equipment and bulkiness of importantly, some of these features exhibit specific changes the probe, or choosing an optimized distance at the expense of associated with normal development, aging, and various patho- lesser probing of the gray matter but a higher SNR and far less logical attacks, which indicates the potential value of these inexpensive and complex instrumentation. approaches in capturing and monitoring the brain organization 1,3,4,25–31,60,75 under different mental states. Our findings on the decrease of GE as the cognitive demand increases might 5 Conclusion sound counterintuitive since a major hypothesis of network In this study, a modified version of the color-word matching theory is that an adaptive network should reorganize itself to Stroop task was employed during fNIRS data collection. The minimize its cost and increase efficiency under increasing load. aim was to elucidate the adaptation of brain connectivity pat- Considering the increase in RT to represent an increase in cog- terns in the PFC during the task. The data were preprocessed by nitive load, we see a consecutive decrease in the GE values. WPC and local efficiency values were assessed among the 16 There might be several explanations for this finding: (1) a flaw different regions. The findings show promise when interference with the signal processing methodology and (2) a lack in observ- between incongruent and neutral conditions is considered. The ing only a piece of a larger network. The PC algorithm we simple yet straightforward signal processing approach proposed employed uses the remaining 14 channels data as regressors for may lead to new findings in the assessment of connectivity computing the correlation between the two channels. It is quite changes for diagnostic and prognostic purposes. The choice possible that this approach might be leading to an over regres- of this specific signal processing algorithm was motivated sion (removing too much of the dependence) from the channels from the literature findings where a convergence was observed leading to a smaller correlation value. Hence the functional con- to a wavelet-based elimination of irrelevant physiological back- nectivity matrix calculated after this operation might leave only ground activity and some instrumentation noise. The choice the very close channels as strongly correlated. This will even- of PC to compute the functional connectivity matrix was moti- tually lead to a lower GE value. Second, PFC is a part of a larger vated by the need to eliminate a common background systemic brain network, albeit its fundamental role in decision-making. physiological activity that can be observed in each recording. fNIRS has access only to this region and it might be quite pos- The study is limited in its choice of the graph theoretical metrics sible that as the cognitive demand increases many other parts to only global efficiency. Although many metrics could have of the brain might be employed that are not visible to fNIRS been employed, we believe that global efficiency actually is the Neurophotonics 041407-6 Oct–Dec 2017 Vol. 4(4) Einalou et al.: Graph theoretical approach to functional connectivity in prefrontal cortex via fNIRS 23. M. L. Schroeter et al., “Towards a standard analysis for functional near- major metric since it is derived from other metrics of graph infrared imaging,” NeuroImage 21(1), 283–290 (2004). theory. 24. Z. 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He was a postdoctoral research fellow in the University of small-world network analysis,” PLoS One 8(1), e53199 (2013). Strathclyde in Glasgow, United Kingdom. In 2001, he joined the 68. M.-E. Lynall et al., “Functional connectivity and brain networks in School of Electrical and Computer Engineering, College of Engineer- schizophrenia,” J. Neurosci. 30(28), 9477–9487 (2010). ing, University of Tehran, Iran, where he is currently a professor of 69. C. J. Stam et al., “Graph theoretical analysis of magnetoencephalo- biomedical engineering. His main research interests are medical ultra- graphic functional connectivity in Alzheimer’s disease,” Brain 132(1), sound and medical applications of the near-infrared spectroscopy. 213–224 (2009). 70. W. Liao et al., “Altered functional connectivity and small-world in Ata Akin received his PhD in biomedical engineering from Drexel mesial temporal lobe epilepsy,” PLoS One 5(1), e8525 (2010). University in 1998, his MS degree in biomedical engineering, and his 71. I. Tachtsidis et al. “False positives in functional near infrared topogra- BS degree in electronics and telecommunication engineering both phy.” in Oxygen Transport to Tissue XXX, pp. 307–314, Springer from Istanbul Technical University in 1995 and 1993, respectively. (2009). Currently, he works at the Department of Medical Engineering at 72. L. Gagnon et al., “Further improvement in reducing superficial con- Acıbadem University and serves as the dean of Faculty of Engineer- ing. His research interests are in the fields of functional neuroimaging tamination in NIRS using double short separation measurements,” and systems biology. NeuroImage 85, 127–135 (2014). Neurophotonics 041407-8 Oct–Dec 2017 Vol. 4(4)
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Neurophotonics – SPIE
Published: Oct 1, 2017