2.1.

Participants and Measurement Protocol

For the study, we enrolled and measured 12 healthy subjects. Two subjects were excluded due to low DCS data quality: low DCS photon counts ($<20\mathrm{kcps}/\mathrm{s}$) and a low coherence factor (Siegert relationship $\beta <0.3$).³⁴ Data from these two subjects were not included in this paper and were not numbered. The remaining 10 subjects included 6 males and 4 females of diverse skin tones, with an age range of 21 to 68 years old (Table S1 in the Supplementary Material). The study protocol was reviewed and approved by the Mass General Brigham Institutional Review Board (IRB No. 2020P002463) in accordance with Ethical Principles and Guidelines for the Protection of Human Subjects (Belmont Report). All subjects signed the informed consent before participating in the study.

The protocol consisted of cold pressor tests (CPTs), paced hyperventilation (HV), and brief repeated breath-holding (BH) tasks. For the CPT, subjects submerged one hand in warm water (30°C to 36°C) for 2 minutes; then they moved the hand into icy cold water (3°C to 5°C) for 1 min; finally, they moved the hand back into the warm water for 2 more min. CPT is known for raising blood pressure,³⁵ and the protocol barred any subject with high blood pressure from performing this task. For the paced HV, after a 1-minute baseline of sale-paced breathing, subjects breathed at a rate of 70 breaths per minute following a metronome cue for a minute and then resumed their self-paced breathing for two more minutes. For the BH task, after a 1-minute baseline, subjects repeated a set of 20 s BH and 40 s normal breathing for four times, ending with an extended recovery period of 1 min.

2.2.

Devices

The wearable NIRS system used in the study is a continuous wave, open-source, low-cost, and wearable wireless cerebral oximeter called FlexNIRS, recently developed in our group.²² It consists of a wearable NIRS headband with an embedded flexible optical probe that communicates with a tablet through Bluetooth low energy (BLE) and is powered by a rechargeable lithium-ion battery (Fig. 1). The probe includes two dual-wavelength LEDs (735 and 850 nm, SMT735D/850D, Marubeni, Japan) and three PIN-photodiodes (VEMD5060X01, Vishay Intertechnology, Inc., United States), forming two short SDsep channels of 0.8 cm and two pairs of symmetrically arranged long SDsep channels of 2.8 and 3.3 cm. This geometry allows for a self-calibrating multi-distance scheme that uses two values at each separation to eliminate the effect of different component efficiencies and therefore provides a robust measurement of cerebral hemoglobin oxygenation without the need for external calibration.^36,37 The use of surface-mount source and detector components in direct contact with the skin minimizes signal attenuation, and the use of a dedicated analog front-end chip that amplifies and digitizes the signals on one integrated circuit results in a device with low NEP ($<70\mathrm{fW}/\surd \mathrm{Hz}$). The optimized custom software allows for a sampling rate of 266.66 Hz for all channels. This was a $>2.5$ times improvement in the sampling rate over the original description of the FlexNIRS device (100 Hz).²² This was achieved through shortening the sampling durations (LED-on time for all was reduced from 366 to $117\mu \mathrm{s}$) and eliminating repeated ambient and short SDsep channels.

Fig. 1

Measurement setup. Right: FlexNIRS for hemoglobin concentration and ${\mathrm{SO}}_2$. A piece of white electrical tape was applied to the short SDsep PD to attenuate the light. Left: SNSPD-based DCS for longer separations (2.0 and 3.0 cm) and Si SPAD-based DCS for the short separation (0.5 cm). Middle: pictures of the FlexNIRS and DCS probes. Bottom: the physiological signals from BIOPAC and Finapres recorded with PowerLab.

The DCS system used in this study operates at 1064 nm using a long coherence length laser (CrystaLaser, United States) and four high photon detection efficiency (88%) SNSPD detectors (Opus One, Quantum Opus, United States)¹⁷ (Fig. 1). To further increase SDsep while maintaining SNR, we used a dual-source illumination scheme, splitting the laser into two 3.5 mm diameter illumination spots, each emitting up to the maximal permissible exposure limit of 103 mW at 1064 nm (ANSI Z136.1). Source and detector fibers were terminated with prisms into a custom optical probe made of flexible 3D-printing material (NinjaTek, United States) and arranged to form SDsep of 2.0 cm (one detector fiber) and 3.0 cm (three detector fibers) (Fig. 1). In addition, to acquire scalp signals, we used a silicon single-photon avalanche diode (Si SPAD) detector at 0.5 cm from the sources. A custom 20-channel field-programmable gate array board documented the arrival time of each photon at 150 MHz resolution, and a custom data acquisition software calculated and displayed the $g_2$ and the blood flow index for each channel in real time.

To avoid possible crosstalk between FlexNIRS and the DCS, we positioned the two probes symmetrically on opposite sides of the forehead with the source placed laterally to maximize the distance between them.

We monitored systemic physiology using a non-invasive continuous arterial blood pressure (ABP) monitor (Finapres Medical Systems, Netherlands; Finapres NOVA) and BIOPAC modules (BIOPAC Systems Inc., United States) for electrocardiography (ECG; ECG100), pulse oximetry peripheral oxygen saturation (${\mathrm{SpO}}_2$; OXY100E), and respiratory rate (SS5LB). All systemic physiological signals were acquired with a 1000 Hz digital data acquisition device (ADInstruments, New Zealand; PowerLab).

2.3.

Data Analysis

FlexNIRS and DCS data were analyzed using standard routines to recover slow varying hemodynamic changes and with cardiac-gated averaging algorithms to extract pulsatile waveforms.

2.4.

Modeling of ${\mathrm{pCBF}}_{\mathrm{i}}$ as a Function of NIRS-PPG

Herein we examine the relationship between ${\mathrm{pCBF}}_{\mathrm{i}}$ and NIRS-PPG when the two are simultaneously measured. The tissue is assumed to be a semi-infinite homogenous medium, and a similar depth sensitivity is assumed for the two methods. The pulsatile light absorbance of NIRS-PPG is proportional to the pulsatile blood volume changes. As a result, its first time derivative represents the changing rate of blood volume, which is the difference between the blood inflow and the blood outflow during a heartbeat and is given as^31–33

DCS ${\mathrm{pCBF}}_{\mathrm{i}}$ represents the total flow through the vasculature, which gives

By combining these equations, we derive ${\mathrm{pCBF}}_{\mathrm{i}\text{-}\text{fit}}$, the estimated ${\mathrm{pCBF}}_{\mathrm{i}}$ based on the linear combination of the NIRS-PPG signal and its derivative, as

Finally, by combining Eqs. (1), (3), and (4), we were able to separate the inflow (${\mathrm{BF}}_{\text{in}}$) and outflow (${\mathrm{BF}}_{\text{out}}$) contributions to the pulsatile flow, given as

2.5.

Critical Closing Pressure, Pulsatility Index, and Cerebrovascular Resistance

We obtained the PI, CrCP, and ${\mathrm{CVR}}_{\mathrm{i}}$ using the ${\mathrm{pCBF}}_{\mathrm{i}}$ and the alternative NIRS-PPG-reconstructed ${\mathrm{pCBF}}_{\mathrm{i}\text{-}\text{fit}}$ with much less cardiac-gated averaging. With the SNSPD-DCS-only ${\mathrm{pCBF}}_{\mathrm{i}}$, due to its higher noise, we used 20 heartbeats; with NIRS-PPG-reconstructed ${\mathrm{pCBF}}_{\mathrm{i}\text{-}\text{fit}}$, we used 4 heartbeats. The signals were aligned with the pulsatile ABP (pABP) obtained from the Finapres using the same cardiac-gated averaging. CrCP was obtained by linearly extrapolating the ${\mathrm{pCBF}}_{\mathrm{i}}$ versus pABP relationship to the pABP-axis intercept. Because of the non-linearities during the systolic phase, only the diastolic run-off phase of the pulse cycle was considered, as done previously.¹¹ In the past, the dicrotic notch (DN) was manually found for each subject; however, now due to the high SNR of the ${\mathrm{pCBF}}_{\mathrm{i}\text{-}\text{fit}}$, we can automatically find the diastolic run-off using a PWA algorithm,²³ which we customized for brain NIRS-PPG. The ${\mathrm{CVR}}_{\mathrm{i}}$ was calculated as the inverse of the slope of the pulsatile pressure-flow relationship, which is given as

The PI, defined as the difference between the systolic and diastolic flow velocity divided by the mean flow velocity as measured by transcranial Doppler (TCD) ultrasound, is used to assess vascular resistance,⁴⁷ intracranial pressure, and cerebral perfusion pressure.⁴⁸ Herein we define PI of DCS as the difference between the systolic and diastolic ${\mathrm{pCBF}}_{\mathrm{i}}$ divided by the mean. The same was calculated for ${\mathrm{pCBF}}_{\mathrm{i}\text{-}\text{fit}}$.

When comparing results between conditions, after excluding outliers (exceeding 1.5 IQR above Q3 or below Q1), we examined normality with the Kolmogorov–Smirnov test ($\alpha =0.05$). If normality was not found, instead of the pairwise t-test, we applied the paired-sample sign test.

3.1.

Pulsatile ${\mathrm{CBF}}_{\mathrm{i}}$ and NIRS-PPG Waveforms

Cardiac-gated averaging of DCS and FlexNIRS signals was performed for each subject and condition. Examples of ${\mathrm{pCBF}}_{\mathrm{i}}$, NIRS-PPG, and d(NIRS-PPG)/dt on a representative subject (No. 5) are shown in Fig. 2(a). The four panels show the pulsatile waveforms during baseline, HV, BH, and cold pressor conditions. We report the pulse waveforms in normalized $z$-scores, which is defined as the number of standard deviations away from the mean (calculated as $z=(x_i-\mu )/\sigma$. $x_i$: data points, $\mu$: mean, and $\sigma$: standard deviation). We observed a strong similarity between ${\mathrm{pCBF}}_{\mathrm{i}}$ and d(NIRS-PPG)/dt, with comparable morphology changes of the main peaks with different conditions. Across all subjects and conditions, the $R^2$ between ${\mathrm{pCBF}}_{\mathrm{i}}$ and d(NIRS-PPG)/dt was $0.89\pm 0.10$.

Fig. 2

(a) Average pulsatile waveforms of a representative subject (No. 5) during the measured conditions. The features for PWA are listed on the baseline panel. (b) ${\mathrm{pCBF}}_{\mathrm{i}}$ and ${\mathrm{pCBF}}_{\mathrm{i}\text{-}\text{fit}}$ comparison and inflow and outflow contribution (in ${\mathrm{BF}}_{\mathrm{i}}$ unit ${\mathrm{cm}}^2/\mathrm{s}$) to the pulsatile flow on the same subject.

The difference between ${\mathrm{pCBF}}_{\mathrm{i}}$ and d(NIRS-PPG)/dt can be accounted for by incorporating the NIRS-PPG waveform contribution. Using Eqs. (4)–(6), we were able to reconstruct ${\mathrm{pCBF}}_{\mathrm{i}}$ as ${\mathrm{pCBF}}_{\mathrm{i}\text{-}\text{fit}}$ using NIRS-PPG and separate inflow and outflow [Fig. 2(b), results for the same representative subject]. We found ${\mathrm{pCBF}}_{\mathrm{i}\text{-}\text{fit}}$ to be nearly identical to ${\mathrm{pCBF}}_{\mathrm{i}}$, with $R^2$ of $0.98\pm 0.01$ across all subjects and conditions [Fig. 3(a)]. The fitting parameters $C_1$ and $C_2$ are reported in Fig. S2 in the Supplementary Material, and the ratio $C_2/C_1$ is shown in Fig. 3(b). The parameters $C_1$ and $C_2$ differ between subjects, but weakly depend on different conditions, except for HV, where $C_1$, $C_2$, and $C_2/C_1$ dropped (for $C_2/C_1$ relative to baseline, $p<0.05$, paired-sample sign test).

Fig. 3

(a) Fit quality $R^2$ and (b) fitting parameters $C_2/C_1$ for the three tasks. Different colors represent different subjects. The asterisks indicate paired-sample sign test significant difference levels. (*: $p<0.05$, **: $p<0.01$, and ***: $p<0.001$)

With the higher SNR of the ${\mathrm{pCBF}}_{\mathrm{i}\text{-}\text{fit}}$, we could identify waveform features automatically. We quantified the systolic peak ($P_1$), secondary systolic peaks ($P_2$, tidal wave), DN and diastolic peak amplitudes, and time delay. As an example, the values of $P_1$, $P_2$, and $P_2/P_1$ across subjects and conditions are reported in Fig. S3 in the Supplementary Material. We found that $P_2/P_1$ dropped during HV (relative to recovery, $p<0.01$, paired-sample sign test) and increased during CPT (relative to baseline, $p<0.01$, paired-sample sign test).

3.2.

Minimal Cardiac-Gated Averaging Noise Characterization

To quantify the improvement in SNR of ${\mathrm{pCBF}}_{\mathrm{i}\text{-}\text{fit}}$ with respect to SNSPD-DCS ${\mathrm{pCBF}}_{\mathrm{i}}$, we evaluated the CV of the pulsatile waveforms during a 60-s baseline. Figure 4(a) shows the average and standard deviation of ${\mathrm{pCBF}}_{\mathrm{i}}$ and ${\mathrm{pCBF}}_{\mathrm{i}\text{-}\text{fit}}$ for each subject. The shapes of the pulsatile waveforms were diverse among subjects, yet the NIRS-PPG fits showed a strong agreement with the DCS-measured ${\mathrm{pCBF}}_{\mathrm{i}}$. ${\mathrm{pCBF}}_{\mathrm{i}\text{-}\text{fit}}$ provided an improvement on the CV, as the CV of ${\mathrm{pCBF}}_{\mathrm{i}\text{-}\text{fit}}$ was consistently lower than the CV of ${\mathrm{pCBF}}_{\mathrm{i}}$, and on average, ${\mathrm{CV}}_{\mathrm{pCBFi}}/{\mathrm{CV}}_{\mathrm{pCBFi}\text{-}\text{fit}}=3.1\pm 1.7$ [Fig. 4(b)]. The paired-sample sign test rejected the null hypothesis with $p<0.01$.

Fig. 4

(a) SNSPD-DCS ${\mathrm{pCBF}}_{\mathrm{i}}$ and NIRS-PPG ${\mathrm{pCBF}}_{\mathrm{i}\text{-}\text{fit}}$ average and standard deviation of pulsatile signals during 60-s baseline. (b) Corresponding CV for the 10 subjects (violin plot).

3.3.

Slow Changes in Cerebral and Systemic Measured Parameters with Tasks

In addition to the NIRS hemoglobin concentration and oxygenation changes and DCS relative changes of the CBF index during the three tasks, we calculated the PI, CrCP, and ${\mathrm{CVR}}_{\mathrm{i}}$ changes with time using ${\mathrm{pCBF}}_{\mathrm{i}}$ (one point every 20 s) and ${\mathrm{pCBF}}_{\mathrm{i}\text{-}\text{fit}}$ (one point every 4 s). Across subjects, for the two methods, baseline CrCP was $32\pm 13\mathrm{mm}\text{-}\mathrm{Hg}$ and $36\pm 14\mathrm{mm}\text{-}\mathrm{Hg}$, respectively, and baseline PI was $1.14\pm 0.35$ and $1.37\pm 0.41$, respectively. In Fig. 5, we show the slow cerebral responses to each task averaged across all subjects along with the systemic physiology responses, including $\mathrm{\Delta }\mathrm{Hb}$, $\mathrm{\Delta }{\mathrm{SO}}_2$, scalp ${\mathrm{rBF}}_{\mathrm{i}}$, ${\mathrm{CBF}}_{\mathrm{i}}$, PI, ${\mathrm{CVR}}_{\mathrm{i}}$, CrCP, mean ABP (MAP), HR, and ${\mathrm{SpO}}_2$. Subject No. 2 was excluded because of poor attachment of the FlexNIRS probe, which caused large light intensity jumps during task transitions. Subject No. 5 was excluded due to technical problems with the Finapres pABP measurement, which prevented us from calculating CrCP and ${\mathrm{CVR}}_{\mathrm{i}}$. For the cold pressor task, subject No. 8 did not perform the task due to high blood pressure.

Fig. 5

Group average of all measured parameters during (a) hyperventilation task ($n=8$, HV period in yellow), (b) BH task ($n=8$, block average of four repetitions, BH period in green), and (c) cold pressor test ($n=7$, CPT period in cyan). r-prefix indicates relative to, and Δ-prefix indicates delta changes; both are with respect to the average of 60-s initial baseline. The standard deviation across subjects is shown in lighter colors. rPI, $\mathrm{\Delta }\mathrm{CrCP}$, and ${\mathrm{rCVR}}_{\mathrm{i}}$ were calculated every 4 s using ${\mathrm{pCBF}}_{\mathrm{i}\text{-}\text{fit}}$ (continuous trace) and every 20 s (circles) using ${\mathrm{pCBF}}_{\mathrm{i}}$. All other parameters were calculated at 1 Hz with a 3 s moving average. For $\mathrm{\Delta }\mathrm{Hb}$ graphs: red $\mathrm{\Delta }\mathrm{HbO}$, blue $\mathrm{\Delta }\mathrm{HbR}$, and black $\mathrm{\Delta }\mathrm{HbT}$. The pulse amplitude of NIRS-PPG and its derivative are shown in Fig. S4 in the Supplementary Material.