2.1.

Instrument

We used a frequency-domain near-infrared spectrophotometer (Omnia ISS Inc.), which was previously described.¹² The light of 16 laser diodes (8/wavelength) at 830 and 758 nm, respectively, is intensity modulated at 110,000 kHz. The laser diodes are time multiplexed, i.e., only one laser diode is on at a given time, and their light is focused by a gradient index lens into glass fibers of a 400-μm diameter, which guide the light to the tissue. The light is detected by two glass fibers of 3-mm diameter and conducted back to the instrument, where it is collected in two photomultiplier tube detectors. The high voltage and consequently, the amplification of the photomultipliers, is modulated at a frequency of 110,005 kHz frequency. This heterodyning demodulates the high frequency and the resulting frequency of 5 kHz is recorded and by time locked fast Fourier transform (FFT), the mean intensity (dc), modulation amplitude (ac), and phase (Φ) of the detected light are determined.

The geometry of the sensor consists of two partly overlapping circles at a radius of 3 cm. In each circle center, a detector is placed and the source pairs (both wavelengths per pair) are arranged along the circular arc equidistantly to the corresponding detector (Fig. 1). This arrangement provides 10 bi-wavelength source detector channels. The laser diodes were sequentially multiplexed at 100 Hz to permit discrimination between different channels and wavelengths at each detector. The sample rate for an entire map was 6.25 Hz.

Fig. 1

The light sources are arranged in two circles of 3 cm radius around the two detector fibers. Thus, an area of 5.7 × 10.8 cm is investigated with a spatial resolution of 10 pixels.

2.2.

Measurement Protocol

The sensor was placed on the subject's head above the motor cortex (C3 or C4 position,¹³ depending on the subject's handiness) contralateral to the exercising hand. All subjects except one were right-handed.

After 5 min of baseline, the subjects performed two different palm-squeezing tasks at a palm-squeezing frequency of approximately 1.4 Hz. Each task consisted of alternating stimulation and rest periods, which were repeated 10 times. During the first task, the subject was palm-squeezing for 21 s and resting for 20 s (total duration 430 s), and during the second task was palm-squeezing for 10 s and resting for 17 s (total duration 297 s). Two different timings were chosen to examine their potential effect on VFC, since they may affect the vascular functional response. The specific values of the timing were chosen because they showed clear functional activation in a previous study.¹⁰

The protocol was approved by the Institutional Review Board of the University of Illinois at Urbana–Champaign (No. 94125), where the study was carried out.

2.3.

Data Analysis

The optical raw data (dc) was converted to O₂Hb, HHb, and tHb by using the differential pathlength factor (DPF)-method:¹⁴ In the first step, the natural logarithm of the dc values was taken. Then, the mean value of the complete measurement was subtracted to receive I. I was divided by the sources detector distance r and the respective DPF_{758 nm} = 6.32 and DPF_{830 nm} = 5.64. These DPF values are based on their own measurements. O₂Hb and HHb were calculated according to the following equation:

The O₂Hb, HHb, and tHb data were low-pass filtered (cut-off 0.1 Hz) to remove arterial pulsations and effects of breathing, and to focus on spontaneous low-frequency fluctuations.¹⁵ The filter was a digital symmetric window low pass filter, specifically designed not to introduce any phase shifts. Data were visually inspected for movement artifacts, which were manually removed.

2.3.2.

Time lag and coherence between locations

Time lags between two traces of a specific phase plane plot were determined numerically. One trace was shifted with respect to the other in consecutive steps of 0.16 s from a total shift of −10 to +10 s. For each step of time shift the mean deviation (MD) of the data points from the 45º and 135º line (i.e., the mean thickness of the pattern with respect to that line) in the particular phase plane plot was calculated. If two traces are in phase, which is the case for O₂Hb plots (Fig. 2) and HHb plots (Fig. 3), their MD will have a minimum ideally at the 45º line. If the two traces are in antiphase, which was found for O₂Hb versus HHb plots (Fig. 4), the minimum will ideally occur at the 135º line. The step of time shift with the minimum deviation represents the time lag.

Fig. 2

Maps of phase plane plots depicting the changes in O₂Hb during baseline recording, Task 1 and 2 from a 60 yr old subject. The arrangement of the phase plane plots represents the location on the head as shown in Fig. 1. The O₂Hb of the leftmost figure was used as a reference for all x-axis values and therefore, represents a straight line. Independent of the task, it can clearly be seen that the phase plane plots close to the reference are approximately straight lines and therefore in good correlation and almost in phase with the reference. The broadening of the figures to an ellipse represents a phase shift. Toward the right-side, four figures appear round and more chaotic, which shows that the correlation to the reference is lost. The light gray (red) part of the traces in the figure represents the O₂Hb level during the palm squeezing task, and the dark gray (blue) the traces during rest. Thus, it can be seen that there is a distinct polarity of the palm squeezing task and the rest periods especially for the left-side with the good correlation. A separation of the two shades of gray (colors) in the vertical direction indicates an activation at the specific location, while a separation in the horizontal direction indicates an activation at the reference location. Thus, in task 2 a distinct activation occurs across the whole map, which is in contrast to task 1. Each plot is 8 standard deviations (±4) high and wide.

Fig. 3

Maps of phase plane plots of the concentration changes in HHb, which are from the same subject as in Fig. 2 and have an analogous format. The HHb pattern is different from the O₂Hb pattern and shows coherences for the three leftmost phase plane plots.

Fig. 4

Maps of phase plane plots of the concentration changes in tHb, which are from the same subject as in Fig. 2 and have an analogous format. These maps are similar to the ones displayed in Fig. 2, because O₂Hb constitutes a major part of the tHb.

2.3.7.

Statistics

The correlation between patterns or parameters was tested using Pearson's correlation coefficient for linear relations and the Spearman's rho for nonlinear correlations as indicated (statistical software: SPSS 11.0). The patterns of O₂Hb versus HHb (Fig. 7) were compared by calculating the correlation coefficient between two conditions (i.e., baseline versus task 1 or baseline versus task 2) for all subjects at a specific location.

Fig. 7

The O₂Hb on the y-axis was plotted versus the HHb on the x-axis. Between O₂Hb and HHb, a negative correlation is revealed, which is strong in this 22 yr old subject compared to older subjects.

5.1.

Correlation of Resting State and Task Related VFC

Maps of changes in O₂Hb, tHb, and HHb in the brain obtained by frequency-domain near-infrared spectrophotometry were analyzed by phase plane plots and cross correlation. These are two model-based methods, which require a seed pixel as a reference. There is a variety of other methods for VFC; their advantages and limitations are described in recent reviews.^{18, 19}

For resting state oscillations, previous publications⁸ used the conventional FFT, which is not accurate when the frequency of the observed signal is not constant, which is true for resting state oscillations, and when the signal has a low frequency and contains only a few periods, which is true for the functional tasks. Thus, in our study, the amplitude of the resting state oscillation was not significantly different from the one due to functional activation, while Ref. 8 suggests that the amplitude due to activation is approximately twice as high as the one of resting state oscillations. This may be an artifact, because the frequency of resting state oscillations is not constant, which leads to a broadening of the peak in the FFT and consequently falsely low amplitude. The same is true for the cross correlation function, whose secondary peaks are diminished, when the frequency is not constant. Therefore, we chose phase plane plots that are not influenced by a changing periodicity, and are therefore excellent tools to analyze the patterns of functional maps. In addition, phase plane plots are user-friendly, because, after a short period of acquaintance, they present the important information and quality of the data in a comprehensible way.

Other studies using NIRS used appropriate seed-based correlation analysis and cluster analysis to analyze resting state connectivity in the sensorimotor and auditory cortex region and found robust maps of connectivity, which were in line with previous fMRI findings and thus were considered as a validation of the validity of NIRS.²⁰

Another advantage of the phase plane plots is that they display the whole evolution of the signal rather than averaged measurement. This enables one to detect movement artifacts and irregularities at once, while they can be hidden in block averaged data or cross correlation functions.

Furthermore, the separate coloring of the stimulation and rest periods, which can clearly be seen in Figs. 2, 3, 4 makes activation visible.

A time lag leads to a broadening of the phase plane plots. For small delays, the plots become ellipsoid, while for delays of a period of π/2 the plots become circular. These can easily be distinguished from chaotic plots (e.g., Fig. 2, task 2, locations 5, 6, and 8), which represent poor correlation.

Concerning the size of the regions of coherence, e.g., for tHb the mean r ²± standard deviation of 0.62±0.27 means that there was in average 62% of agreement between the seed pixel and other pixels. A value of r ² = 1.0 indicated that all pixels correlated perfectly with the seed pixel, while a value of r ² = 0.0 indicated that the changes in tHb were completely uncorrelated between the seed pixel and the other pixels. Considering that the region of connectivity is limited, it is expected, and indeed the case, that a proportion of the pixels is not or little correlated with the seed pixel. The mean r ² = 0.62 indicates that there are considerable regions of high correlation. A high r ² ≥ 0.8 (r ² ≥ 0.6) was found in 22 (46), 3 (10), and 33% (63%) of the pixels for O₂Hb, HHb, and tHb, respectively. Except for HHb, this indicates that considerable regions of high coherence were found.

These regions were very similar during baseline compared to task periods. Not even the amplitude was significantly affected by the condition. This similarity between resting state and task related patterns is remarkable (Figs. 2, 3, 4). However, in the same figures, it is also quite obvious that these regions were not congruent with the regions of functional activity.

Resting state oscillations have been extensively analyzed using the BOLD signal of fMRI (see review in Ref. 9) and also in studies by NIRS, e.g., in the motor cortex region²⁰ or larger regions of the brain.²¹ Since task related changes in neuronal metabolism are small (<5%), when compared to resting state metabolism,⁹ it is not surprising that there is quite a degree of similarity between VFC during resting state and functional task, which is what we find. This resting state VFC may be more important than the task related VFC. Since the BOLD signal is limited to the HHb only, our data delivers the complete hemodynamic change by providing O₂Hb and tHb, in addition to HHb.

What is the origin of this resting state VFC? It could either be due to structural connectivity, i.e., the structure of the blood vessels, or it is a functional connectivity component reflected by the similarity between brain activity during resting state and motor stimulation. So far in reviews,^{4, 9} the favored hypothesis that functional activity is the origin and supportive direct and indirect evidence for a neural basis of resting state slow oscillations is cited. Surprisingly, the possibility that the structure of the tree of blood vessels may contribute to this VFC is little considered. The fact that regions of a high degree of connectivity also show small time lags may indicate that the role of this structural connectivity based on the vasculature and not neurons, may be underestimated.

5.2.

Functionally Related and Unrelated Connectivity

The FRC was higher than the FUC, which indicates that there is a significant relation between the functional hemodynamic changes and the resting state slow oscillations. This can be interpreted, according to Ref. 10, as hemodynamic oscillations that are present with considerably variable frequencies during resting state. Motor stimulation leads to a synchronization of these resting state oscillations with the stimulation events. The degree of synchronization depends on the frequency of the stimulation and HHb is more significantly affected than O₂Hb. This is an effect well-known in nonlinear systems (frequency pulling). This means that functional cerebral hemodynamics can also be considered as a nonlinear synchronization phenomenon.

The coherence patterns and the connectivity were considerably lower for HHb. This may be due to physiological differences, i.e., HHb is more affected by oxygen consumption than O₂Hb and may imply that HHb is a better indicator for activation than O₂Hb. However, O₂Hb is generally considered to be the most reliable indicator for functional brain activity in the NIRS literature,⁶ because it has a higher amplitude and contains the same information. Thus, in Fig. 7, it is obvious that O₂Hb displays the inverted pattern of the HHb. Since the amplitude of the HHb signal is smaller than for the O₂Hb signal, the HHb signal is more affected by noise. This is likely to derogate the detection of the connectivity in our data presented in Table 1.

Our results are in contrast to Refs. 11 and 17, who found a much higher FRC and much lower FUC than in our data, but without measuring O₂Hb or tHb. There are several possible reasons for this discrepancy. Since NIRS quantifies concentration changes, we are able to set threshold values for changes in HHb of <−0.1 μm/l, which is comparable between subjects. Thus, Refs. 11 and 17 relied on a correlation coefficient >0.35 when comparing the BOLD-signal to a square wave function, which represented the task.

Compared to Refs. 11 and 17, we investigated only one cerebral hemisphere, a smaller area of cerebral tissue around the motor cortex, and specifically superficial layers of cerebral tissue. Our instrument had a lower spatial resolution. These factors may explain the higher percentage for the FUC.

In addition, the connectivity widely depends on the thresholds set for the correlation coefficients and for the concentration changes. Generally, higher threshold values lead to smaller areas of detected activity and a higher FRC and lower FUC. This indicates that indeed during baseline, areas of the motor cortex remain connected. The largest difference between FRC and FUC of approximately 65% was found in O₂Hb for a functional change >0.4 μm/l and r ² > 0.75.

5.3.

The Effect of Age

The coherence in the O₂Hb versus HHb plots was less distinct in older subjects compared to younger subjects. This new finding may be either an interesting physiological feature or be due to a smaller amplitude of the signal in older subjects, i.e., a matter of signal-to-noise ratio. What is the origin of the higher amplitude in younger subjects?

Reference 22 found an age dependence of the DPF, which is used to calculate O₂Hb, HHb, and tHb. When this age-dependence was taken into account, the age dependent effect in our data was more pronounced and the significance increased approximately threefold. Thus, changes in optical properties with age are not an explanation.

To test whether the effect may be related to anatomical differences depending on the age, e.g., a different thickness of the skin, skull, and distance to the brain, which would affect the path of light, we measured the thickness of these layers using MRI. No significant correlation between the anatomical features and the amplitude of the O₂Hb and HHb oscillations was found.

There is a cognitive decline with age.²³ Older people also use different areas of the brain than younger people,²⁴ which may imply that the functional networks change. Thus, different levels of brain activity with age may very well explain the difference.

In addition, the cerebral blood vessels decline as well. The stiffness of arteries increases.²⁵ This reduced elasticity may be a vascular explanation for the reduced amplitude with age.

It has to be kept in mind that this study was not designed to detect an age-related effect, and such effect was not expected before conducting the study. The effect was discovered when analyzing the data. Consequently, the subjects are not evenly distributed between the different ages, and there are only two subjects older than 35 years of age. However, even if these subjects are removed from the data, a highly significant age-related effect persists. To corroborate these results, it will be necessary to reproduce the effect in a group of subjects with evenly distributed ages.

5.4.

Limitations of the Study

The current set-up with only two detector locations, which was chosen according to instrumental factors, may lead to crosstalk. If there is an optical change directly below the detector, this will appear like a change in the whole area around the detector. This type of artifact would lead to identical signals in all channels of one detector, which in addition should have no time lag. In practice, these two conditions were never fulfilled and we can thus exclude this artifact.

In order to achieve a higher signal-to-noise ratio, it may be more effective to use stimulation and rest periods that are not constant. This may reduce noise, because constant periods can be subject to resonance effects, frequency pulling, and are more likely to coincide with physiological frequencies. Variable periods are used to study evoked potentials by EEG.

It has been shown that the resting state VFC depends on the frequency band chosen.²¹ Due to its potentially high time resolution, NIRS is an excellent tool to study these properties. The current study focused on frequencies between 0.014 to 0.1 Hz and the two specific frequencies elicited by the functional activation tasks in our study. No frequency specific connectivity was found.

The effect of systemic parameters such as changes in blood pressure was not assessed in this study. Changes in systemic blood pressure may contribute to cerebral hemodynamics both during resting state,²⁶ as well as during the stimulation task,²⁷ which could lead to an overestimation of VFC. Since our results show localized patterns of VFC, such a systemic effect, which has to be generalized, is unlikely to have played a decisive role. However, in future studies systemic parameters should be taken into consideration.