Coherent Spontaneous Hemodynamics in the Human Brain

Goal: This work investigates the presence of cerebral hemodynamics (namely Oxy (O) and Deoxy (D) hemoglobin concentrations) that are coherent with spontaneous oscillations in Arterial Blood Pressure (ABP) in 78 healthy subjects during a driving simulation task. Methods: Spatially resolved O and D were measured on the prefrontal cortex with multi-channel near-infrared spectroscopy (NIRS). Wavelet coherence and phasor analysis were performed between O and ABP, and between D and ABP to evaluate the amplitude ratio, phase difference, and duration of significant coherence. Results: In the low-frequency range, oscillations at 0.1 Hz featured significant coherence for the longest time fraction (∼10%–30%). At this frequency, the amplitude ratio and phase difference showed a greater variance across subjects than over cortical locations, and no significant difference between driving tasks and baseline. Conclusions: Measuring low-frequency cerebral hemodynamics that are coherent with systemic ABP holds promise for non-invasive assessment of cerebral perfusion and autoregulation at the cerebral microvascular level.

Transfer Function Analysis (TFA) has been used in TCD to investigate the frequency dependence of gain and phase for coherent oscillations of Cerebral Blood Flow Velocity (CBFV) and ABP [9], but this technique is limited in that it cannot measure micro-vasculature and localized changes in cerebral blood flow. A number of systematic studies on detection of LFOs by NIRS on human subjects have been reported [6], [10], [11], mainly focusing on 0.1 Hz. Over a range of frequencies, the highest coherence between cerebral hemodynamics and ABP lies around 0.1 Hz [6], [12] but have been limited in the number of subjects investigated. Spontaneous oscillations have lower coherence than induced oscillations [13], but are relevant when inducing oscillations is not feasible. The motivation behind this work is to look at the amplitude ratio, phase shift and coherence in hemodynamic parameters of spontaneous oscillations in a relatively large data set.
Here we report a study on 78 healthy human subjects involved in a simple driving task with a series of braking events with the goal to evaluate the use of spontaneous coherent hemodynamics. The time of coherent oscillations during 3-minute periods were evaluated over a large range of subjects to assess the extent to which spontaneous oscillations feature significant coherence. Transfer function analysis was done to evaluate the relative amplitude and phase between cerebral hemodynamics and ABP, at 0.1 Hz, to evaluate variance within and across subjects. Lastly, the baseline driving condition and periods with braking events were compared to evaluate the impact of brain activation on coherent spontaneous cerebral hemodynamics.  Board (IRB) approved study (protocol number: 1802002, approval date: 02/14/2018). Continuous Wave (CW) NIRS and ABP measurements were performed while the subject was in a medium fidelity partial-cab driving simulator (RTI, Ann Arbor, MI), which has been previously described [14]. CW-NIRS measurements were acquired with a NIRScout system (NIRx Medical Technology, Berlin, Germany) sampled at 7.81 Hz. The instrumental configuration consisted of 8 light-emitting diode (LED) sources (wavelengths: 760 and 850 nm) and 7 Photo-Diode (PD) detectors, which resulted in 20 Single-Distance (SD) measurement channels at a source-detector spacing of 30 mm on the pre-frontal cortex ( Fig. 1(a)). A beat-to-beat finger plethysmography system (NIBP100D, BIOPAC Systems, Goleta, CA) used to measure non-invasive ABP [15] using changes in blood volume in the artery was placed on the subjects' left fingers and upper arm, and data were sampled at 20 Hz. Fig. 1(b) depicts the driving simulator set up with the ABP and CW-NIRS instruments connected to the subject.

A. Study Protocol and Data Acquisition
The experimental protocol consisted of a baseline period with uneventful, constant-speed driving for approximately 3 minutes on a 2-lane highway. Participants than engaged in a total of 10 events, which were ordered randomly for each subject and session. Six events were labeled as real braking (where the participant needed to brake to avoid a collision with a leading car that was braking in front of them) and four fake braking (where the leading car appeared but did not brake). An example experimental protocol can be seen in Fig. 2(a), where the black line indicates where the leadings cars brake lights turned on and the shaded region when the car was in front of the participants car.

B. Near-InfraRed Spectroscopy and Arterial Blood Pressure Data Processing
Methods described here were applied to each subject, experiment, and SD channel independently. NIRS intensity measurements for both wavelengths and the ABP signal were synchronized and interpolated to 20 Hz. NIRS measurements were evaluated for artifacts due to non-physiological changes by linear piecewise detrending which identified sections in which the variance of the signal is above the 75th and below the 25th percentiles and used these as breakpoints in the detrend. The ΔO and ΔD were calculated using the modified Beer Lambert Law [16] with a wavelength dependent Differential Pathlength Factor (DPF) [16], [17]. NIRS channels recording non-physiological variation over 1 µM were disregarded [18], as data with this high non-physiological noise would mask those of systematic oscillations. Example time traces of ΔO and ΔD can be seen in Fig. 2(b) and of ABP in Fig. 2(c), where the solid line shows the signal low-passed to 0.2 Hz for visualization and the shaded region is the original signal that reflects systolic-diastolic variations.

C. Transfer Function and Coherence Analysis
Transfer function and coherence analysis between the hemodynamic signals (ΔO and ΔD) and ABP were performed using previously described methods [16], [19], [20]. Data were then sectioned into a total of six 3-minute non over lapping blocks, where the first 3-minute block (minutes 0 to 3) is referred to as the baseline. Each block was than processed independently.
Time-frequency maps of the wavelet coherence between ΔO and ABP, and ΔD and ABP were calculated using a modified version of MATLAB's wcoherence function that removes smoothing in frequency. A coherence threshold generated using random surrogate data (alpha level = 0.05) [21], [22] was applied so that only pixels in time and frequency that have a statistically significant coherence were evaluated. Multiple comparisons were not accounted for. A logical AND was taken between the ΔD-ABP and ΔO-ABP maps to create a significant coherence map used for ΔD and ΔO. TFA between time signals of ΔO and ABP, ΔD and ABP, and ΔD and ΔO for each block was performed using the continuous wavelet transform with a complex Morlet mother wavelet to find the phasor ratio maps of O/ABP, D/ABP, and D/O in time and frequency [16], [19], [20]. This resulted in the amplitude ratio and the phase difference between the two parameters across time and frequency.

D. Coherence Requirements and Spontaneous Oscillation Frequencies
Coherent spontaneous oscillations within the range of 0.01-1.5 Hz were considered. A series of central frequencies and their bandwidths (as determined by the half power bandwidth of a sinusoidal wave at that central frequency [19]) were found. Maps of significant coherence for O and ABP, D and ABP, and the logical AND were further filtered to require that in each frequency band of interest, significant coherence lasted longer than one period of the central frequency and significant coherence at the central frequency. Filtered maps were applied to the phasor ratio maps so that only pixels in time and frequency with statistically significant coherence that passed the requirements were considered in further analysis. The logical map between ΔD-ABP and ΔO-ABP was applied to the phasor ratio map of D/O. An average phasor ratio was computed for O/ABP, D/ABP, and D/O over each frequency band, resulting in one value for each block (6), channel (20), subject (78), and session (2) across frequencies.

A. Availability of Coherent Hemodynamics
The fraction of time, during baseline, for which the coherence requirements were fulfilled (statistically significant coherence for at least 1 period of the central frequency) across frequency are shown in Fig. 3(a) for O/ABP, D/ABP and for the logical AND between O/ABP and D/ABP. The values for each channel, subject, and experiment were treated as independent data points. Fig. 3(b) depicts the number of subjects that had significant data in 10 or more NIRS channels. The highest fraction of time with coherence occurred at ∼1 Hz, which is indicative of the heart rate. At this frequency, O/ABP has the highest fraction of coherence as arterial pulsation results in hemodynamic oscillations that are mostly associated with oxyhemoglobin (oxygen saturation of arterial blood is close to 100%). Large arterial oscillations can be seen in Fig. 2(b), while ΔD has a smaller contribution.
In the range of physiologically relevant frequencies for assessing cerebral health (∼0.01-0.1 Hz) [8], [23]  for the respective data types. At all frequencies, O/ABP showed the largest fraction followed by D/ABP. The logical condition is the lowest on average which shows that D is not always coherent with ABP when O is coherent with ABP. This indicates that both hemodynamic parameters are not always concurrently driven by ABP. Fig. 4 shows the average phasor ratios at 0.1 Hz over channels and sessions for each subject (Fig. 4(a), (b), and (c)), and over subjects and sessions for each channel (Fig. 4(d), (e), and (f)). Averaging over the channels and sessions gives insight into the variability across subjects. The lowest spread in phase was seen in O/ABP (Fig. 4(a)), while D/ABP varied by ∼120 degrees, with varying amplitude ratios across subjects. For D/ABP and D/O, as the phase difference approached 0 the amplitude decreased. Averaging over subjects and sessions for each channel gives insight onto the spatial variability over the probed brain region. Neither O/ABP, D/ABP or D/O (Fig. 4(d), (e), and (f)) show significant differences among the channels.

B. Average Baseline Phasor Ratios
The average over channels, subjects, and session for O/ABP, D/ABP, and D/O is shown in Fig. 5(a), (b), and (c), allowing for an examination of the range amongst the population. The phase standard deviation was ∼30 degrees for O/ABP, ∼60 degrees for D/ABP, and ∼70 degrees for D/O. For the amplitude ratio, |D/ABP| had the lowest standard deviation of 0.03 µM/mmHg, while it was 0.06 µM/mmHg for |O/ABP|. Fig. 6 reports the average phasor ratios across all subjects, sessions, and channels for the 6 blocks. Braking events occurred randomly for every subject/session, and due to their approximate timing during the experiment it was assumed that at least one event occurred during each block. The average phasor ratios for O/ABP, D/ABP, and D/O for each block (denoted by a different color) is shown in Fig. 6. All phasor ratios lie within the standard deviations and are overlapping, which shows no difference between all 6 blocks. Table I reports the average amplitude ratio and phase difference with the standard deviation for each block, where block 1 is the baseline. O/ABP showed the smallest deviation between the blocks and overall variability.

IV. DISCUSSION
An in-depth analysis was performed to evaluate the amount of time with coherent hemodynamics at frequencies between 0.01 and 1.5 Hz. The heart rate showed the highest amount, which has previously been reported [6], and is expected due to arterial pulsation contributions to ΔO measurements. The lower fraction of time from ΔD can be explained by the small ΔD signal (and thus small signal-to-noise) originating from the arteries due to high oxygen saturation of arterial blood.
For LFOs, ∼0.1 Hz showed the highest fraction of time with coherence for O/ABP, D/ABP, and the logical AND between O/ABP and D/ABP (Fig. 3(a)). A peak at ∼0.1 Hz has previously been shown [6], [12]. This frequency is associated with Mayer waves, which are linked with spontaneous oscillations in ABP and oscillations in sympathetic nerve activity [8]. These systemic oscillations drive cerebral hemodynamics and account for the high coherence observed. Previous studies considered a low number of subjects (3 and 13, respectively [6], [12]), while the results presented in Fig. 3 allows for examination of variability across the 78 subjects, 2 sessions and 20 channels. This study shows the promise of using spontaneous oscillations for Coherent Hemodynamics Spectroscopy (CHS) given that in 3-minutes, on average, ∼30% of time features coherent cerebral hemodynamics at 0.1 Hz in as many as half of the NIRS channels used in this study.
Spontaneous and induced oscillations at 0.1 Hz have been used in combination with NIRS [6], [11], [16] to study the relationship between hemodynamics and ABP. In this study, D/O had an average amplitude ratio (∼0.18) and phase difference (∼−212 degrees) that aligns with reported results on 5 subjects with repeated induced oscillation measurements at 0.1 Hz and 30 mm source-detector separation [24]. The mean phase difference for all phasor ratios aligned with reported results on healthy human subjects [10], [25].
The phase difference between O and ABP had the lowest standard deviation in all blocks (Table I). Higher variability in D/ABP and D/O can be explained by their sensitivity to changes in blood flow, a higher sensitivity to blood volume changes in superficial tissue, and a lower signal-to-noise associated with measurements of ΔD. Assuming a constant O/ABP a relative increase in blood volume contributions versus blood flow contributions to the optical measurements would shift D/ABP towards O/ABP and cause a decrease in its amplitude [20]. This was seen for D/ABP over subjects ( Fig. 4(b)) and could explain the larger variability as the contribution of blood volume to the optical signal differed for each subject.
Spatial averages (Fig. 4(d), (e), and (f)) showed no qualitative significant differences between channels suggesting spatially uniform cerebral hemodynamics associated with systemic changes in ABP [26], [27]. Variability among the subjects ( Fig. 4(a), (b), and (c)) was larger than across the channels and indicates that subjects may be separable from each other resulting from individual cerebrovascular or anatomical features.
Comparison between baseline and other blocks that involved a braking task showed no qualitative significant difference (Fig. 6). This implies that there were no detectable changes in the relative dynamics of cerebral hemodynamics and ABP during the driving events. Previous work showed an increase in the wavelet coefficient amplitude between straight driving and driving mixed with tasks in the frequency range of 0.0095-0.021 Hz on the pre-frontal cortex [28] but not at the frequency band including 0.1 Hz for ΔO which aligns with presented results.

V. CONCLUSION
Cerebral hemodynamics coherent with systemic ABP provide indications on the health of cerebral perfusion and autoregulation [10], [19], [29]. Measurements of cerebral hemodynamics (specifically, O and D) with NIRS are non-invasive and reflect blood volume, blood flow, and rate of oxygen delivery to tissue at the microcirculation level [9], [10]. This work has shown that NIRS can measure spontaneous cerebral hemodynamic oscillations in the autoregulation frequency range of 0.1 Hz that show a significant coherence and meet strict requirements with ABP for about 10%-30% of the measurement time. This result means that spontaneous coherent hemodynamics can be measured with NIRS to evaluate cerebral perfusion health and efficiency of cerebral autoregulation, at least when measurements can be performed over a time of at least a few minutes and physiological conditions remain stable during this period. Another implication of this work is that CHS [30], [31] may be based on spontaneous rather than induced ABP and cerebral hemodynamic oscillations, provided that proper care is taken in identifying significant levels of coherence which is needed to ensure changes in ABP are the driving forces for the hemodynamic changes. The possibility of relying on spontaneous hemodynamics rather than induced hemodynamics has important practical implications as subjects would not be required to undergo physiological maneuvers or perturbations. Finally, the finding of a lack of significant effects of braking tasks on the relative amplitude and phase of coherent cerebral hemodynamics and ABP may be specific to this measurement protocol. Future work will involve functional brain activation with a variety of motor, visual, or cognitive workloads for a more thorough characterization of coherent cerebral hemodynamics during brain activation.