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Independent component analysis of broadband near-infrared spectroscopy data acquired on adult human head

The goal of this study was to investigate the ability of independent component analysis in the time-spectral domain to isolate physiological sources of functional near infrared spectroscopy signals. We apply independent component analysis to the broadband fNIRS data acquired on the human forehead at 650 different wavelengths between 700 nm and 950 nm. To induce cerebral oxygenation changes we use the breath holding paradigm. We found one major independent component during baseline and two major components during exercise. Each independent component corresponds to one oxy-hemoglobin and one deoxy-hemoglobin time courses. The corresponding characteristic spectra of changes in optical absorption suggested that one component represented vasodilation of cerebral arterioles while the delayed component represented the washout of deoxyhemoglobin either in cerebral capillaries and venules or in extra cerebral tissue. We found that both broadband and isolated wavelength data can produce similar independent components.


Introduction
Functional near infrared spectroscopy (fNIRS) aims at non-invasively measuring the effects of the brain tissue on near-infrared light propagating through the intact human head [1,2]. Various fNIRS systems use continuous-wave (CW), frequency-domain and time-resolved sources of light [1]. Although the time-resolved and frequency-domain systems have capabilities of separating absorption and scattering properties of tissues, they are more expensive and have lower signal-to-noise ratio. Therefore, CW fNIRS is considered to be most practical. CW systems use either broadband [3,4] or selected wavelength light sources [5]. While both types of sources have their advantages, a number of recent studies demonstrated benefits of broadband systems [3,4]. A drawback of all types of fNIRS systems is that the light integrates signals from all types of small blood vessels: arterioles, capillaries and venules [1,2]. Also, besides the brain the light travels through all extracerebral head tissues, whose vasomotion biases functional signals. Therefore the separation of functional signals from contamination by systemic and local physiological fluctuations is an important research topic. This problem was approached by using various signal processing methods, including blind signal separation techniques [5][6][7][8]. In particular, principal component and independent component analyses (PCA and ICA, respectively) were applied separately either to the oxy-or deoxyhemoglobin time series reconstructed from the bi-wavelength NIRS data acquired on the human head during repetitive hyper-or hypocapnia episodes [5] with the goal to filter out "surface effects". The ICA criterion for the "surface effects" was the value of the coefficient of spatial uniformity (CSU) calculated using elements of the spatial mixing matrix [7]. In [5] the independent components with higher CSU were excluded and remaining components were recombined into the filtered oxy-and deoxyhemoglobin traces. ICA was also used in NIRS for the motion artifact removal [7][8][9], and to study the functional cerebral connectivity of the resting state [10].
Previously fNIRS ICA was performed only in the time-spatial domain on data acquired either at multiple source-detector separations or at different locations [6][7][8][9][10]. The goal of our present study was to investigate fNIRS independent components not in the time-spatial but in the time-spectral domain. In particular we wanted to understand relationships between the spectral independent components and the changes in the oxy-and deoxyhemoglobin concentrations. We show that the rows of the time-spectral ICA mixing matrix allow for a physiological interpretation in terms of the oxy-and deoxyhemoglobin concentrations. We apply a well-established Matlab version of ICA FastICA [11] to the broadband NIRS data acquired at one location on the human forehead at a single source-detector separation but at 650 different wavelengths between 700 nm and 950 nm. To induce cerebral oxygenation changes the breath holding (BH) paradigm was used because it generated blood carbon dioxide (CO 2 ) [12]. Vasodilation induced by CO 2 caused increased cerebral blood flow which resulted in changes in cerebral blood volume and oxygenation [13]. Although the individual wavelength signals were quite diverse and noisy, we found very few independent components whose origin can be interpreted based on their characteristic spectral signatures and time courses.

Participants and experimental paradigm
Optical data was obtained from 7 healthy adult participants (1 male, 6 females), all of whom were right-handed. All participants gave informed consent before participation and the experiment has been performed according to Ryerson University 2008-003-01 Research Ethics protocol. Participants were audibly cued to perform a breath hold at the end of expiration with voluntary resumption of breathing after holding for about 15-20 seconds. The exercise was repeated six times with 40-second rest intervals. Breath holding was used in many studies (for example [3,14]) to induce hypercapnia, which typically resulted in increased concentrations of oxyhemoglobin 2 ( ) HbO and decreased concentrations of deoxyhemoglobin ( ) HHb . All data set including the baseline were acquired during 6 minutes.

Data acquisition
Near-infrared light was generated by a stabilized fan-cooled AvaLight-HAL Tungsten Halogen Light Source (Avantes Inc., Broomfield, CO) with an adjustable focusing connector to maximize light coupling with the source fiber. The source fiber bundle was made of 30 Thorlabs broadband silica 400 m µ core diameter fibers. On the probe the source fibers were arranged circularly around the location of the detector bundle at a radius of 25 mm (Fig. 1). Such geometry allowed for reducing the effects of the scalp's large blood vessels occasionally located near a light source. Light was collected using a 3-mm diameter fiber optic bundle (Sunoptic Technologies, FL). The detector bundle was connected to a QEB65000 cooled spectrometer (Ocean Optics, Dunedin, FL), which had 1044 wavelength channels in a spectral range between 650 and 1100 nm. The spectrometer output was digitized using the Spectral Suite software (Ocean Optics, Dunedin, FL). The optical probe was positioned on the left side of the forehead near the hairline to avoid sinuses. Spectra were acquired at the sampling rate of one spectrum per second resulting in 360 time points per data set. This sampling rate was selected to ensure that the instrumental noise did not affect physiological data.

Data processing: independent component analysis and general linear modeling
For 630 signals at different near-infrared wavelengths between 700 nm and 950 nm the absorbance A(λ,t) was calculated as where Dark was the dark signal, reference was the signal measured directly through air (without tissue), and λ was the optical wavelength. Each instantaneous spectrum was smoothed using the Matlab smooth function at 15 points. No temporal smoothing was performed. The 630 x 360 matrix of 630 detrended time series of absorbance changes ( , ) A t λ ∆ was fed into the FastICA algorithm [8], which used fpica Matlab function to separate the input into the N independent components (ICs): where ( ) T t was the 360 x N matrix of statistically independent temporal components (ICs) [ two components always covered more than 90% of non-zero eigenvalues of the covariance matrix, and at the same conditions the norm of ( , ) R t λ was much smaller than the norm of ( , ) A t λ ∆ at each time moment. If the number of ICs N was set greater than two, the output of FastICA showed one or two non-noisy ICs (such as red traces in Fig. 1 (a,c) whose spectra spanned much greater ranges of values than the spectra of other ICs. ICs whose time courses appeared noisy in Figs. 1(a) and 1(c) also had noisy spectra (blue, green and black curves in Fig. 1(b) and blue and green curves in Fig. 1(d)). Therefore we focused on the analysis of only two components spanning the greatest ranges of ( ) i S λ values. In this approximation and for each moment of time Eq. (2) reduced to where 1 ( ) T t and 2 ( ) T t were the instantaneous values of the temporal independent components, and 1 ( ) S λ and 2 ( ) S λ were the corresponding time-independent amplitude spectra. One should note that according to Eq. (3) the signs of 1,2 ( ) T t and 1,2 ( ) S λ were arbitrary up to their simultaneous conjoined inversion. In order to homogenize the cross-subject analysis we fixated the signs of 1 ( ) S λ and 2 ( ) S λ as they appear in Fig. 1(d). This also fixated the signs of 1 ( ) T t and 2 ( ) T t . We assumed that, apart from the noise, the dynamic of ( , ) A t λ ∆ was only due to changes in the concentrations of oxy-hemoglobin 2 ( ) HbO and deoxy-hemoglobin ( ) HHb , and that it follows the modified Lambert-Beers law [1]: where X C was the concentration and ( ) X ε λ was the extinction coefficient of the chromophore X. The values of chromophore concentrations were taken from [16] and [17]. The concentrations of 2 HbO , HHb , and water were assumed 55 M µ (micromolars), 20 M µ , and 85%, respectively in accordance with values known from [18] for water and from [1,19] for hemoglobin. In order to analyze the contributions of 2 HbO and HHb changes to each IC, and in accordance with Eqs. (3) and (4)  IC (identified based on the shape of its spectrum 1 S ). The shape of 1 S (the spectrum of 1 IC ) was topologically similar for all subjects but in some cases quantitatively changed considerably between rest and exercise. 2 IC appeared only during exercises. The topological differences between 1 S and 2 S were shown in Fig. 2(d) (red and black curves, respectively). More examples of both component spectra were shown in Fig. 3. Different subjects were indicated by different colors. One can see that the main differences between 1 S and 2 S were the shape of the spectrum near 760 nm (a much more pronounced spectral feature in 2 S than in 1 S near the HHb absorption peak wavelength) and the range of values on the y axis. While the values of 1 S were all positive, the values of 2 S were either all negative or negative at shorter wavelengths and positive at longer wavelengths. We note that although the signs of 1,2 ( ) S λ were arbitrary up to their conjoined inversion with 1,2 ( ) T t , one can see from Fig. 3 that the inversions of signs could not convert spectra of one type into another type. Therefore, we used the topological differences between the shapes of 1 ( ) Encircled is the IC2 spectral feature near the peak wavelength of the deoxy-hemoglobin absorption.  differences between 1 ( ) S λ and 2 ( ) S λ were revealed by the results of GLM fitting shown in Table 1. From Table 1 one can see that the main difference between two components was in the relative magnitude of the oxy-hemoglobin changes, represented by 2 HBO Ψ compared to that of the deoxy-hemoglobin, represented by HHb Ψ .

Results
Since 2 1 HBO Ψ was much greater than 1 HHb Ψ , the contribution of the deoxy-hemoglobin changes to 1 IC was much smaller than the contribution of the oxy-hemoglobin changes. For 2 IC on average both oxy-and deoxy-hemoglobin changes were approximately equal by magnitude and, on average, opposite by sign. Figure 4 shows examples of the time courses of 1 IC and 2 IC for three subjects during the repetitive BH exercises. In all panels of Fig. 3  In order to investigate whether 1 ( ) T t and 2 ( ) T t could be obtained using a small number of wavelengths, we created five signals by averaging ten adjacent wavelength signals around each of 760 nm, 800 nm, 830 nm, 860 nm, and 900 nm wavelengths. Then 1 ( ) T t and 2 ( ) T t were obtained by applying FastICA to the pairs of signals, one at 760 nm and another either at 800 nm, or at 830 nm, or at 860 nm, or 900 nm. The comparisons of the time courses of ICs obtained using the full spectrum and a pair of wavelengths (760 nm and 900 nm) were presented in Fig. 5. One can see that the time courses obtained using the full and reduced spectra were similar and the main difference was a much noisier 2 ( ) T t obtained using two wavelengths. Figure 6 compares ICs obtained using the full spectrum and pairs of wavelengths in terms of STDs of the differences between the corresponding temporal ICs. We note that the values of standard deviations in Fig. 6 should be also compared with the standard deviations of 1 ( ) T t and 2 ( ) T t , which were both equal to one due to the normalization. From Fig. 6 one can conclude that (a) for all pairs of wavelengths the differences in 2 ( ) T t from the    Fig. 7. Standard deviations of IC time courses computed using the full spectrum relative to those obtained using two wavelengths: one at 760 nm and another at a wavelength shown. full spectrum were much larger than for 1 ( ) T t , (b) for 1 ( ) T t the difference was minimal at 860 nm, and (c) for 2 ( ) T t the difference was minimal at 830 nm. Also from Fig. 6 one can see that the wavelength of 830 nm allowed for about 15-20% improvement compared to 800 nm and