Letter to the editor: Deriving transfer function analysis metrics from driven methods

Driven and spontaneous methods have been used to quantify the cerebral pressure-flow relationship via transfer function analysis (TFA). Commonly, TFA derived estimates are assessed using band averages within the very-low (0.02-0.07 Hz) and low (0.07-0.20 Hz) frequency during spontaneous oscillations but are quantified at frequencies of interest where blood pressure oscillations are driven (e.g., 0.05 and/or 0.10 Hz). Driven estimates more closely resemble the autoregulatory challenges individuals experience on a daily basis, while also eliciting higher levels of reliability. While driven estimates with point-estimates are not feasible for all clinical populations, these approaches increase the ability to understand pathophysiological changes.

Impaired Dynamic Cerebral Autoregulation in Patients With Cerebral Venous Sinus Thrombosis: Evaluation Using Transcranial Doppler and Silent Reading Stimulation

OBJECTIVE

Cerebral venous sinus thrombosis (CVST) may impair dynamic cerebral autoregulation (dCA) of the middle cerebral artery (MCA). However, most studies have focused on dCA of the MCA; a few studies are based on the posterior cerebral artery (PCA) during silent reading and neurovascular coupling (NVC). This study explored the effects of CVST on dCA of the MCA and PCA during silent reading and NVC.

METHODS

From January 2021 to August 2022, 60 CVST patients and 30 controls were enrolled in this study. Non-invasive continuous beat-to-beat blood pressure, cerebral blood flow velocity and other associated information on the MCA and PCA during silent reading were collected using a transcranial Doppler. NVC assessment was performed by opening and closing the eyes periodically based on voice prompts, and eye-opening visual stimulation was achieved by silently reading Chinese tourism materials. Visual stimulation signals can selectively activate Brodmann's areas 17, 18, and 19 of the occipital when reading silently with open eyes, prompting them to release neurotransmitters and dilate PCA. dCA was determined by transfer function analysis.

RESULTS

In dCA of the PCA during silent reading, the CVST group's very low frequency phase was lower than that of the control group (p = 0.047). In NVC, the difference in the indexes of the cerebrovascular conductance and visually evoked flow response of the CVST group were lower than those of the control group (p = 0.017 and p = 0.019, respectively).

CONCLUSION

Compared with the control group, dCA and NVC of the PCA during silent reading were impaired in CVST patients.

Effects of posture changes on dynamic cerebral autoregulation during early pregnancy in women with obesity and/or sleep apnea

The incidence of syncope during orthostasis increases in early human pregnancy, which may be associated with cerebral blood flow (CBF) dysregulation in the upright posture. In addition, obesity and/or sleep apnea per se may influence CBF regulation due to their detrimental impacts on cerebrovascular function. However, it is unknown whether early pregnant women with obesity and/or sleep apnea could have impaired CBF regulation in the supine position and whether this impairment would be further exacerbated in the upright posture. Dynamic cerebral autoregulation (CA) was evaluated using transfer function analysis in 33 women during early pregnancy (13 with obesity, 8 with sleep apnea, 12 with normal weight) and 15 age-matched nonpregnant women during supine rest. Pregnant women also underwent a graded head-up tilt (30° and 60° for 6 min each). We found that pregnant women with obesity or sleep apnea had a higher transfer function low-frequency gain compared with nonpregnant women in the supine position (P = 0.026 and 0.009, respectively) but not normal-weight pregnant women (P = 0.945). Conversely, the transfer function low-frequency phase in all pregnancy groups decreased during head-up tilt (P = 0.001), but the phase was not different among pregnant groups (P = 0.180). These results suggest that both obesity and sleep apnea may have a detrimental effect on dynamic CA in the supine position during early pregnancy. CBF may be more vulnerable to spontaneous blood pressure fluctuations in early pregnant women during orthostatic stress compared with supine rest due to less efficient dynamic CA, regardless of obesity and/or sleep apnea.

Respiratory training in older women: Unravelling central and peripheral hemodynamic slow oscillatory patterns

We hypothesized that inspiratory muscle training (IMT) increases the respiratory-induced low-frequency oscillations of mean blood pressure (MBP) and middle cerebral artery blood velocity (MCAv), upregulating cerebrovascular function in older women. Firstly, participants were recorded with free-breathing (FB) and then breathed at a slow-paced frequency (0.1 Hz; DB test) supported by sonorous metronome feedback. Blood pressure was recorded using finger photoplethysmography method, ECG, and respiration using a thoracic belt. To obtain the MCAv a transcranial ultrasound Doppler device was used. Spectral analysis of MBP, R-R intervals, and mean MCAv time series was obtained by an autoregressive model. The transfer function analysis (TFA) was employed to calculate the coherence, gain, and phase. After that, older women were enrolled in a randomized controlled protocol, the IMT-group (n = 8; 64 ± 3 years-old) performed IMT at 50 % of maximal inspiratory pressure (MIP), and Sham-group, a placebo training at 5 % MIP (Sham-group; n = 6; 66 ± 3 years-old). Participants breathed against an inspiratory resistance twice a day for 4-weeks. DB test is repeated post IMT and Sham interventions. IMT-group, compared to Sham-group, augmented tidal volume responses to DB (Sham-group 1.03 ± 0.41 vs. IMT-group 1.61 ± 0.56 L; p = 0.04), increased respiratory-induced MBP (Sham-group 26.37 ± 4.46 vs. IMT-group 48.21 ± 3.15 mmHg²; p = 0.04) and MCAv (Sham-group 14.16 ± 31.26 vs. IMT-group 79.90 ± 21.76 cm²s^-2; p = 0.03) slow oscillations, and reduced TFA gain (Sham-group 2.46 ± 1.32 vs. IMT-group 1.78 ± 1.30 cm·s^-1.mmHg^-1; p = 0.01). Our findings suggest that IMT increases the respiratory-induced oscillations in MBP and MCAv signals and reduces TFA gain. It seems compatible with an improved dynamic cerebrovascular regulation following IMT in older women.

Validity of transcranial Doppler ultrasonography-determined dynamic cerebral autoregulation estimated using transfer function analysis

Transcranial Doppler ultrasonography (TCD) is used widely to evaluate dynamic cerebral autoregulation (dCA). However, the validity of TCD-determined dCA remains unknown because TCD is only capable of measuring blood velocity and thus only provides an index as opposed to true blood flow. To test the validity of TCD-determined dCA, in nine healthy subjects, dCA was evaluated by transfer function analysis (TFA) using cerebral blood flow (CBF) or TCD-measured cerebral blood velocity during a perturbation that induces reductions in TCD-determined dCA, lower body negative pressure (LBNP) at two different stages: LBNP - 15 mmHg and - 50 mmHg. Internal carotid artery blood flow (ICA Q) was assessed as an index of CBF using duplex Doppler ultrasound. The TFA low frequency (LF) normalized gain (ngain) calculated using ICA Q increased during LBNP at - 50 mmHg (LBNP50) from rest (P = 0.005) and LBNP at - 15 mmHg (LBNP15) (P = 0.015), indicating an impaired dCA. These responses were the same as those obtained using TCD-measured cerebral blood velocity (from rest and LBNP15; P = 0.001 and P = 0.015). In addition, the ICA Q-determined TFA LF ngain from rest to LBNP50 was significantly correlated with TCD-determined TFA LF ngain (r = 0.460, P = 0.016) despite a low intraclass correlation coefficient. Moreover, in the Bland-Altman analysis, the difference in the TFA LF ngains determined by blood flow and velocity was within the margin of error, indicating that the two measurement methods can be interpreted as equivalent. These findings suggest that TCD-determined dCA can be representative of actual dCA evaluated with CBF.

The Effect of Data Length on the Assessment of Dynamic Cerebral Autoregulation with Transfer Function Analysis in Neurological ICU Patients

Background

Cerebral autoregulation plays an important role in safeguarding adequate cerebral perfusion and reducing the risk of secondary brain injury, which is highly important for patients in the neurological intensive care unit (neuro-ICU). Although the consensus white paper suggests that a minimum of 5 min of data are needed for assessing dynamic cerebral autoregulation with transfer function analysis (TFA), it remains unknown if the length of these data is valid for patients in the neuro-ICU, of whom are notably different than the general populations. We aimed to investigate the effect of data length using transcranial Doppler ultrasound combined with invasive blood pressure measurement for the assessment of dynamic cerebral autoregulation in patients in the neuro-ICU.

Methods

Twenty patients with various clinical conditions (severe acute encephalitis, ischemic stroke, subarachnoid hemorrhage, brain injury, cerebrovascular intervention operation, cerebral hemorrhage, intracranial space-occupying lesion, and toxic encephalopathy) were recruited for this study. Continuous invasive blood pressure, with a pressure catheter placed at the radial artery, and bilateral continuous cerebral blood flow velocity with transcranial Doppler ultrasound were simultaneously recorded for a length of 10 min for each patient. TFA was applied to derive phase shift, gain, and coherence function at all frequency bands from the first 2, 3, 4, 5, 6, 7, 8, 9, and 10 min of the 10-min recordings in each patient on both hemispheres. The variability in the autoregulatory parameters in each hemisphere was investigated by repeated measures analysis of variance.

Results

Forty-one recordings (82 hemispheres) were included in the study. According to the critical values of coherence provided by the Cerebral Autoregulation Research Network white paper, acceptable rates for the data were 100% with a length ≥ 7 min. The final analysis included 68 hemispheres. The effects of data length on trends in phase shift in the very low frequency (VLF) band (F_{1.801,120.669} = 6.321, P = 0.003), in the LF band (F_1.274,85.343 = 4.290, P = 0.032), and in the HF band (F_1.391,93.189 = 3.868, P = 0.039) were significant for 3–7 min, for 4–7 min, and for 5–8 min, respectively. Effects were also significant on the gain in the VLF band (F_{1.927,129.134} = 3.215, P = 0.045) for 2–8 min and on the coherence function in all frequency bands (VLF F_{2.846,190.671} = 90.247, P < 0.001, LF F_{2.515,168.492} = 55.770, P < 0.001, HF F_{2.411, 161.542} = 33.833, P < 0.001) for 2–10 min.

Conclusions

Considering the acceptable rates for the data and the variation in the TFA variables (phase shift and gain), we recommend recording data for a minimum length of 7 min for TFA in patients in the neuro-ICU.

Perioperative Dynamics of Intracranial B-waves of Blood Flow Velocity in the Basal Cerebral Arteries in Patients with Brain Arteriovenous Malformation

Intracranial B-waves (8-30 mHz) of blood flow velocity (BFV) in the cerebral arteries are observed in various pathologies of the brain. Changes in B-waves of BFV in pathological arteriovenous shunting and "steal" syndrome remain poorly understood. The aim of this study was to evaluate the dynamics of the B-wave amplitude of BFV (BWA) in patients with an arteriovenous malformation (AVM) in the brain. In 38 such patients, cerebral autoregulation (CA) was assessed using a cuff test and transfer function analysis of the mean blood pressure (BP) and BFV in the basal cerebral arteries within the range of Mayer waves (80-120 mHz). BWA was calculated with spectral analysis. Reliable CA impairment was denoted on the AVM side as compared with the contralateral side prior to intervention. BWA was greater on the AVM side (4.5 ± 2.7 cm/s) than on the contralateral side (2.2 ± 1.4 cm/s, p < 0.05). After embolization, there was a reliable improvement (p < 0.05) in CA and a decrease in BWA on the AVM side (2.7 ± 1.8 cm/s). Thus, a considerable increase in BWA on the AVM side that is not induced by BP fluctuations may indicate additional compensation for blood flow under conditions of reduced perfusion pressure. This assumption is supported by a reduction in BWA after AVM embolization.

Dynamic cerebral autoregulation after confinement in an isolated environment for 14 days

BACKGROUND

To develop human space exploration, it is necessary to study the effects of an isolated and confined environment, as well as a microgravity environment, on cerebral circulation. However, no studies on cerebral circulation in an isolated and confined environment have been reported. Therefore, we investigated the effects of a 14-day period of confinement in an isolated environment on dynamic cerebral autoregulation.

METHODS

We participated in an isolation and confinement experiment conducted by the Japan Aerospace Exploration Agency in 2016. Eight healthy males were isolated and confined in a facility for 14 days. Data were collected on the days immediately before and after confinement. Arterial blood pressure waveforms were obtained using a finger blood pressure monitor, and cerebral blood flow velocity waveforms in the middle cerebral artery were obtained using transcranial Doppler ultrasonography for 6 min during quiet rest in a supine position. Dynamic cerebral autoregulation was evaluated by transfer function analysis between spontaneous variability of beat-to-beat mean arterial blood pressure and mean cerebral blood flow velocity.

RESULTS

Transfer function gain in the low- and high-frequency ranges increased significantly (0.54 ± 0.07 to 0.69 ± 0.09 cm/s/mmHg and 0.80 ± 0.05 to 0.92 ± 0.09 cm/s/mmHg, respectively) after the confinement.

CONCLUSION

The increases observed in transfer function gain may be interpreted as indicating less suppressive capability against transmission from arterial blood pressure oscillation to cerebral blood flow velocity fluctuation. These results suggest that confinement in an isolated environment for 14 days may impair dynamic cerebral autoregulation.

TRIAL REGISTRATION

UMIN000020703 , Registered 2016/01/22.

How many squat-stand manoeuvres to assess dynamic cerebral autoregulation?

Purpose

Squat–stand manoeuvres (SSMs) have been used to induce blood pressure (BP) changes for the reliable assessment of dynamic cerebral autoregulation. However, they are physically demanding and thus multiple manoeuvres can be challenging for older subjects. This study aimed to determine the minimum number of SSMs required to obtain satisfactory coherence, thus minimising the subjects’ workload.

Method

20 subjects performed SSMs at a frequency of 0.05 Hz. End-tidal CO₂, cerebral blood flow velocity, heart rate, continuous BP and the depth of the squat were measured. 11 subjects returned for a repeat visit. The time points at which subjects had performed 3, 6, 9, 12 and 15 SSMs were determined. Transfer function analysis was performed on files altered to the required length to obtain estimates of coherence and the autoregulation index (ARI).

Results

After three SSMs, coherence (0.05 Hz) was 0.93 ± 0.05, and peaked at 0.95 ± 0.02 after 12 manoeuvres. ARI decreased consecutively with more manoeuvres. ARI was comparable across the two visits (p = 0.92), but coherence was significantly enhanced during the second visit (p < 0.01). The intra-subject coefficients of variation (CoV) for ARI remained comparable as the number of manoeuvres varied.

Conclusions

This analysis can aid those designing SSM protocols, especially where participants are unable to tolerate a standard 5-min protocol or when a shorter protocol is needed to accommodate additional tests. We emphasise that fewer manoeuvres should only be used in exceptional circumstances, and where possible a full set of manoeuvres should be performed. Furthermore, these results need replicating at 0.10 Hz to ensure their applicability to different protocols.

MRI-based cerebrovascular reactivity using transfer function analysis reveals temporal group differences between patients with sickle cell disease and healthy controls

OBJECTIVES

Cerebrovascular reactivity (CVR) measures the ability of cerebral blood vessels to change their diameter and, hence, their capacity to regulate regional blood flow in the brain. High resolution quantitative maps of CVR can be produced using blood-oxygen level-dependent (BOLD) magnetic resonance imaging (MRI) in combination with a carbon dioxide stimulus, and these maps have become a useful tool in the clinical evaluation of cerebrovascular disorders. However, conventional CVR analysis does not fully characterize the BOLD response to a stimulus as certain regions of the brain are slower to react to the stimulus than others, especially in disease. Transfer function analysis (TFA) is an alternative technique that can account for dynamic temporal relations between signals and has recently been adapted for CVR computation. We investigated the application of TFA in data on children with sickle cell disease (SCD) and healthy controls, and compared them to results derived from conventional CVR analysis.

MATERIALS AND METHODS

Data from 62 pediatric patients with SCD and 34 age-matched healthy controls were processed using conventional CVR analysis and TFA. BOLD data were acquired on a 3 Tesla MRI scanner while a carbon dioxide stimulus was quantified by sampling the end-tidal partial pressures of each exhaled breath. In addition, T1 weighted structural imaging was performed to identify grey and white matter regions for analysis. The TFA method generated maps representing both the relative magnitude change of the BOLD signal in response to the stimulus (Gain), as well as the BOLD signal speed of response (Phase) for each subject. These were compared to CVR maps calculated from conventional analysis. The effect of applying TFA on data from SCD patients versus controls was also examined.

RESULTS

The Gain measures derived from TFA were significantly higher than CVR values based on conventional analysis in both SCD patients and healthy controls, but the difference was greater in the SCD data. Moreover, while these differences were uniform across the grey and white matter regions of controls, they were greater in white matter than grey matter in the SCD group. Phase was also shown to be significantly correlated with the amount that TFA increases CVR estimates in both the grey and white matter.

CONCLUSIONS

We demonstrated that conventional CVR analysis underestimates vessel reactivity and this effect is more prominent in patients with SCD. By using TFA, the resulting Gain and Phase measures more accurately characterize the BOLD response as it accounts for the temporal dynamics responsible for the CVR underestimation. We suggest that the additional information offered through TFA can provide insight into the mechanisms underlying CVR compromise in cerebrovascular diseases.

Evaluation of jaw and neck muscle activities while chewing using EMG-EMG transfer function and EMG-EMG coherence function analyses in healthy subjects

This study aims to quantitatively clarify the physiological features in rhythmically coordinated jaw and neck muscle EMG activities while chewing gum using EMG-EMG transfer function and EMG-EMG coherence function analyses in 20 healthy subjects. The chewing side masseter muscle EMG signal was used as the reference signal, while the other jaw (non-chewing side masseter muscle, bilateral anterior temporal muscles, and bilateral anterior digastric muscles) and neck muscle (bilateral sternocleidomastoid muscles) EMG signals were used as the examined signals in EMG-EMG transfer function and EMG-EMG coherence function analyses. Chewing-related jaw and neck muscle activities were aggregated in the first peak of the power spectrum in rhythmic chewing. The gain in the peak frequency represented the power relationships between jaw and neck muscle activities during rhythmic chewing. The phase in the peak frequency represented the temporal relationships between the jaw and neck muscle activities, while the non-chewing side neck muscle presented a broad range of distributions across jaw closing and opening phases. Coherence in the peak frequency represented the synergistic features in bilateral jaw closing muscles and chewing side neck muscle activities. The coherence and phase in non-chewing side neck muscle activities exhibited a significant negative correlation. From above, the bilateral coordination between the jaw and neck muscle activities is estimated while chewing when the non-chewing side neck muscle is synchronously activated with the jaw closing muscles, while the unilateral coordination is estimated when the non-chewing side neck muscle is irregularly activated in the jaw opening phase. Thus, the occurrence of bilateral or unilateral coordinated features in the jaw and neck muscle activities may correspond to the phase characteristics in the non-chewing side neck muscle activities during rhythmical chewing. Considering these novel findings in healthy subjects, EMG-EMG transfer function and EMG-EMG coherence function analyses may also be useful to diagnose the pathologically in-coordinated features in jaw and neck muscle activities in temporomandibular disorders and whiplash-associated disorders during critical chewing performance.

How measurement artifacts affect cerebral autoregulation outcomes: A technical note on transfer function analysis

Cerebral autoregulation (CA) is the mechanism that aims to maintain adequate cerebral perfusion during changes in blood pressure (BP). Transfer function analysis (TFA), the most reported method in literature to quantify CA, shows large between-study variability in outcomes. The aim of this study is to investigate the role of measurement artifacts in this variation. Specifically, the role of distortion in the BP and/or CBFV measurementon TFA outcomes was investigated. The influence of three types of artifacts on TFA outcomes was studied: loss of signal, motion artifacts, and baseline drifts. TFA metrics of signals without the simulated artifacts were compared with those of signals with artifacts. TFA outcomes scattered highly when more than 10% of BP signal or over 8% of the CBFV signal was lost, or when measurements contained one or more artifacts resulting from head movement. Furthermore, baseline drift affected interpretation of TFA outcomes when the power in the BP signal was 5 times the power in the LF band. In conclusion, loss of signal in BP and loss in CBFV, affects interpretation of TFA outcomes. Therefore, it is vital to validate signal quality to the defined standards before interpreting TFA outcomes.

The dynamics of cerebrovascular reactivity shown with transfer function analysis

Cerebrovascular reactivity (CVR) is often defined as the increase in cerebral blood flow (CBF) produced by an increase in carbon dioxide (CO2) and may be used clinically to assess the health of the cerebrovasculature. When CBF is estimated using blood oxygen level dependent (BOLD) magnetic resonance imaging, CVR values for each voxel can be displayed using a color scale mapped onto the corresponding anatomical scan. While these CVR maps therefore show the distribution of cerebrovascular reactivity, they only provide an estimate of the magnitude of the cerebrovascular response, and do not indicate the time course of the response; whether rapid or slow. Here we describe transfer function analysis (TFA) of the BOLD response to CO2 that provides not only the magnitude of the response (gain) but also the phase and coherence. The phase can be interpreted as indicating the speed of response and so can distinguish areas where the response is slowed. The coherence measures the fidelity with which the response follows the stimulus. The examples of gain, phase and coherence maps obtained from TFA of previously recorded test data from patients and healthy individuals demonstrate that these maps may enhance assessment of cerebrovascular pathophysiology by providing insight into the dynamics of cerebral blood flow control and distribution.

Sustained mild hypergravity reduces spontaneous cardiac baroreflex sensitivity

Head-to-foot gravitational force >1G (+Gz hypergravity) augments venous pooling in the lower body and reduces central blood volume during exposure, compared with 1Gz. Central hypovolemia has been reported to reduce spontaneous cardiac baroreflex sensitivity. However, no investigations have examined spontaneous cardiac baroreflex sensitivity during exposure to sustained mild +Gz hypergravity. We therefore hypothesized that mild +Gz hypergravity would reduce spontaneous cardiac baroreflex sensitivity, compared with 1Gz. To test this hypothesis, we examined spontaneous cardiac baroreflex sensitivity in 16 healthy men during exposure to mild +Gz hypergravity using a short-arm centrifuge. Beat-to-beat arterial blood pressure (tonometry) and R-R interval (electrocardiography) were obtained during 1Gz and 1.5Gz exposures. Spontaneous cardiac baroreflex sensitivity was assessed by sequence slope and transfer function gain. Stroke volume was calculated from the arterial pressure waveform using a three-element model. All indices of spontaneous cardiac baroreflex sensitivity decreased significantly (up slope: 18.6±2.3→12.7±1.6ms/mmHg, P<0.001; down slope: 19.0±2.5→13.2±1.3ms/mmHg, P=0.002; transfer function gain in low frequency: 14.4±2.2→10.1±1.1ms/mmHg, P=0.004; transfer function gain in high frequency: 22.2±7.5→12.4±3.5ms/mmHg, P<0.001). Stroke volume decreased significantly (88±5→80±6ml, P=0.025). Moreover, although systolic arterial pressure variability increased, R-R interval variability did not increase. These results suggest that even mild +Gz hypergravity reduces spontaneous cardiac baroreflex sensitivity, increasing the risk of cardiovascular disturbance during the exposure.

Between-centre variability in transfer function analysis, a widely used method for linear quantification of the dynamic pressure-flow relation: the CARNet study

Transfer function analysis (TFA) is a frequently used method to assess dynamic cerebral autoregulation (CA) using spontaneous oscillations in blood pressure (BP) and cerebral blood flow velocity (CBFV). However, controversies and variations exist in how research groups utilise TFA, causing high variability in interpretation. The objective of this study was to evaluate between-centre variability in TFA outcome metrics. 15 centres analysed the same 70 BP and CBFV datasets from healthy subjects (n=50 rest; n=20 during hypercapnia); 10 additional datasets were computer-generated. Each centre used their in-house TFA methods; however, certain parameters were specified to reduce a priori between-centre variability. Hypercapnia was used to assess discriminatory performance and synthetic data to evaluate effects of parameter settings. Results were analysed using the Mann-Whitney test and logistic regression. A large non-homogeneous variation was found in TFA outcome metrics between the centres. Logistic regression demonstrated that 11 centres were able to distinguish between normal and impaired CA with an AUC>0.85. Further analysis identified TFA settings that are associated with large variation in outcome measures. These results indicate the need for standardisation of TFA settings in order to reduce between-centre variability and to allow accurate comparison between studies. Suggestions on optimal signal processing methods are proposed.

Dynamic model for the tissue concentration and oxygen saturation of hemoglobin in relation to blood volume, flow velocity, and oxygen consumption: Implications for functional neuroimaging and coherent hemodynamics spectroscopy (CHS)

This article presents a dynamic model that quantifies the temporal evolution of the concentration and oxygen saturation of hemoglobin in tissue, as determined by time-varying hemodynamic and metabolic parameters: blood volume, flow velocity, and oxygen consumption. This multi-compartment model determines separate contributions from arterioles, capillaries, and venules that comprise the tissue microvasculature, and treats them as a complete network, without making assumptions on the details of the architecture and morphology of the microvascular bed. A key parameter in the model is the effective blood transit time through the capillaries and its associated probability of oxygen release from hemoglobin to tissue, as described by a rate constant for oxygen diffusion. The solution of the model in the time domain predicts the signals measured by hemodynamic-based neuroimaging techniques such as functional near-infrared spectroscopy (fNIRS) and functional magnetic resonance imaging (fMRI) in response to brain activation. In the frequency domain, the model yields an analytical solution based on a phasor representation that provides a framework for quantitative spectroscopy of coherent hemodynamic oscillations. I term this novel technique coherent hemodynamics spectroscopy (CHS), and this article describes how it can be used for the assessment of cerebral autoregulation and the study of hemodynamic oscillations resulting from a variety of periodic physiological challenges, brain activation protocols, or physical maneuvers.