Cerebral autoregulation in the microvasculature measured with near-infrared spectroscopy

Abstract

Cerebral autoregulation (CA) is the mechanism that allows the brain to maintain a stable blood flow despite changes in blood pressure. Dynamic CA can be quantified based on continuous measurements of systemic mean arterial pressure (MAP) and global cerebral blood flow. Here, we show that dynamic CA can be quantified also from local measurements that are sensitive to the microvasculature. We used near-infrared spectroscopy (NIRS) to measure temporal changes in oxy- and deoxy-hemoglobin concentrations in the prefrontal cortex of 11 human subjects. A novel hemodynamic model translates those changes into changes of cerebral blood volume and blood flow. The interplay between them is described by transfer function analysis, specifically by a high-pass filter whose cutoff frequency describes the autoregulation efficiency. We have used pneumatic thigh cuffs to induce MAP perturbation by a fast release during rest and during hyperventilation, which is known to enhance autoregulation. Based on our model, we found that the autoregulation cutoff frequency increased during hyperventilation in comparison to normal breathing in 10 out of 11 subjects, indicating a greater autoregulation efficiency. We have shown that autoregulation can reliably be measured noninvasively in the microvasculature, opening up the possibility of localized CA monitoring with NIRS.

Introduction

Cerebral autoregulation is the mechanism that maintains cerebral blood supply, hence cerebral blood flow (CBF), approximately constant despite changes in mean arterial blood pressure (MAP) or, more precisely, despite changes in cerebral perfusion pressure (CPP; defined as the difference between MAP and intracranial pressure). This mechanism is valid for a certain range of CPP, namely 50 to 150 mm Hg.^{1, 2, 3} Within that range, changes in CPP lead to vasomotor adjustments in cerebrovascular resistance (CVR) thus allowing CBF to remain relatively constant. Lassen¹ constructed, based on measurements reported in the literature, a so-called autoregulation curve, which shows a CBF plateau in the aforementioned CPP range, essentially showing that CBF remains constant. Assessing the boundaries of this plateau and whether the autoregulation mechanism is intact or impaired is critical, since impaired autoregulation can lead to cerebral ischemia or brain damage because of abnormal perfusion. Therefore, determining the effectiveness of cerebral autoregulation is relevant for a variety of patient populations.

In general, the assessment of autoregulation can be classified into two categories. The first category considers only steady-state or static relationships between CBF and MAP, without taking time courses of changes in MAP and CBF into account. This can be achieved by infusion of drugs, which do not have an effect on the cerebral vasculature or metabolism but change MAP.^{4, 5, 6} Measurements of CBF are performed during baseline as well as during the altered MAP state. This yields two values of CBF and their difference in relation to the MAP change is indicative of autoregulation. A recent review on static autoregulation⁷ questioned the validity of the autoregulation curve introduced by Lassen by showing that the slope of CBF as a function of MAP is dependent on whether MAP increases or decreases, invalidating the plateau of the autoregulation curve. In general, the accuracy of measuring autoregulation based on two points, on the autoregulation curve is questionable, with the measurements being several minutes apart from each other, since CBF depends on a number of factors, such as partial pressure of carbon dioxide (pCO₂), cerebral metabolism, and hematocrit, which all can change while MAP reaches a new steady state,^{3, 7} whereas the change in MAP alone is what drives autoregulation.

The second category of autoregulation assessment is based on measuring dynamic changes of CBF in response to dynamic changes in MAP, hence this is referred to as dynamic cerebral autoregulation. Regardless of the exact measurement setup, the underlying idea is that after a step change in MAP, CBF will first react to such MAP change and will then return to its original value within a finite amount of time, where this amount of time is a measure of autoregulation efficiency. The faster CBF returns to its baseline value, the better is the autoregulation mechanism. This delayed CBF adaptation was first observed in animals.⁸ Aaslid et al⁹ introduced a thigh cuff–based method of inducing fast MAP changes, which is the most frequently used method to induce rapid MAP perturbations. For this, pneumatic cuffs are placed around the subjects' thighs and are inflated 20 to 40 mm Hg above systolic pressure for at least 2 minutes. The release of the thigh-cuff pressure results in MAP dropping by ~10 to 20 mm Hg. Since Aaslid et al have shown that MAP and CBF return to baseline within ~15 seconds after thigh-cuff release, changes in cerebral metabolism and hematocrit can be neglected over this time scale.^{3, 9} Furthermore, the method is quick and can therefore be repeated multiple times on the same subject for monitoring applications. However, since the time window in which the autoregulation mechanism can be studied is ~15 seconds, only a limited number of measurement techniques exist, which can capture these fast transients in CBF. Transcranial Doppler (TCD) is such an imaging technique with a sufficient temporal resolution; it measures CBF velocity (CBFV) in the middle cerebral artery (MCA). Under the assumption that the diameter of the MCA does not change, CBFV can be taken to be a reliable representation of global CBF. Together with continuous blood pressure measurements, the dynamics of MAP changes and CBF changes can be assessed with an adequate temporal resolution for dynamic (CA) assessment.

Such measurements of dynamic changes in CBF in response to sudden changes in MAP, where the time of CBF recovery is indicative of autoregulation, have already been used in numerous disease models,¹⁰ where it has been found that cerebral autoregulation is altered or impaired in patients with a variety of conditions such as autonomic failure,¹¹ diabetes,¹² Parkinson's disease,¹³ and stroke.¹⁴

Using the CBF recovery time, different methods exist to assess and quantify autoregulation. One such method defines autoregulation by the rate of regulation, which is given by the temporal slope of CVR recovery, where CVR=CPP/CBF, after the sudden perturbation in the thigh-cuff release method.^{9, 15} A steeper slope of CVR as a function of time indicates a better autoregulation mechanism. Another method to quantify autoregulation from the CBF recovery after the cuff release is based on an autoregulation index, which is introduced in a second-order differential equation that relates dynamic changes in MAP and CBF.¹⁵

Another way of measuring dynamic CA, instead of inducing rapid MAP changes, is based on studying CBF responses to slow oscillations in MAP. Such oscillations can be induced at a specific frequency by a number of protocols including paced breathing,^{16, 17} head-up tilting,¹⁸ and periodic thigh-cuff inflation,¹⁹ with oscillations typically being induced around 0.1 Hz. The measurement of dynamic CA can then be performed by transfer function analysis where beat-to-beat MAP measurements are used as input and CBF measurements as output.^{3, 11, 20, 21, 22} Transfer function analysis is based on analysis of the coherence, gain, and phase differences between MAP and CBF as a function of frequency. Similar to the rapid change in MAP with thigh cuffs, the phase differences, related to the time delay, between MAP and CBF found with transfer function analysis, has been found to be a good indicator of autoregulation efficiency.

Although TCD together with MAP measurements have been used in numerous patient populations for autoregulation assessment (see the comprehensive review by Panerai¹⁰), TCD has its limitations. In particular, TCD measures CBFV in the MCA, and cannot measure microvascular, localized changes in CBF. Taking advantage of the fact that CBF changes are sensed by near-infrared spectroscopy (NIRS) in all vascular compartments with special sensitivity to the microvasculature, we introduce a novel imaging platform, which is sensitive to localized, microvascular CBF changes, and we show that dynamic CA can be measured and quantified in the microvasculature. Specifically, NIRS measures cerebral changes in oxy- [O(t)], deoxy- [D(t)], and total- [T(t)] hemoglobin concentrations noninvasively and continuously on the cerebral cortex. Since O(t) and D(t) are sensitive to microvascular changes in CBF, specifically to capillary blood flow, as well as cerebral blood volume (CBV) changes, we show that NIRS data, together with a novel hemodynamic model, yields quantitative measurements of dynamic CA.

We use the thigh-cuff method of Aaslid et al⁹ and measure the hemodynamic response to the rapid change in MAP after the cuff pressure is released. We analyze the data with our hemodynamic model, which translates O(t) and D(t) into temporal traces of CBV and CBF. Based on literature, it is known that the autoregulation mechanism can be described as a high-pass filter for which MAP is an input and CBF in an output.^{11, 17} We adopt this idea of describing dynamic autoregulation with a high pass filter, but we use local microvascular CBV (measured by T(t) and hypothesized to be directly linked to the local arterial blood pressure) as input, and local microvascular blood flow (measured by NIRS and our hemodynamic model) as output. The cutoff frequency of the high-pass filter, which is inversely related to the CBF recovery time discussed above, quantifies the effectiveness of autoregulation.²³

Changes in PaCO₂ have been shown to influence CA.^{9, 24, 25} The mechanism is hypothesized to be linked with the effect of PaCO₂ on cerebrovascular reactivity (enhancement during hypocapnia and suppression during hypercapnia),⁹ which in turn is associated with the vascular dilation during hypercapnia and vascular constriction during hypocapnia.²⁴ Hypocapnia reduces CBF, while also reducing the response time of CBF after a step change in MAP.^{2, 9} This reduced response time is an indicator of improved CA. Since hypocapnia can be induced by performing hyperventilation,⁹ we have measured healthy volunteers during normal breathing and hyperventilation to induce a predictable change (increase during hyperventilation) in cerebral autoregulation. We show that local NIRS measurements, which are mostly sensitive to the cerebral microvasculature, together with hemodynamic perturbations induced by a fast thigh-cuff release, can measure these different levels of autoregulation effectiveness in the cerebral microvasculature.

Materials and methods

Data Acquisition

Eleven healthy subjects (five males and six females, age range: 21 to 50 years) without any history of neurologic disorders or cardiovascular disease participated in the study, with the experimental protocol approved by the Tufts University Institutional Review Board. Written informed consent was obtained from all participants before the study and the experiments were performed in accordance with the Declaration of Helsinki. Figure 1 shows the data acquisition setup and analysis flow. NIRS data were collected with a commercial frequency-domain tissue spectrometer (OxiplexTS, ISS, Champaign, IL, USA), operating at wavelengths 690 and 830 nm. Optical probes were placed on the subject's forehead and secured by a headband to hold them in place. MAP was recorded with a beat-to-beat finger plethysmography system (NIBP100D, BIOPAC Systems, Goleta, CA, USA). Two pneumatic cuffs were placed around both thighs and connected to an automated cuff inflation device (E-20 Rapid Cuff Inflation System, D. E. Hokanson, Bellevue, WA, USA). The protocol consisted of 2 minutes of baseline measurements, after which the cuffs were inflated at 200 mm Hg for 2 minutes, as seen in Figure 2. The rapid deflation of the cuffs results in a drop in MAP, which induces changes in cerebral O, D, and T. Two minutes after cuff deflation, the cuffs were inflated again for 2 minutes. The subjects were asked to perform hyperventilation for 2.5 minutes, starting at the second cuff inflation. Hyperventilation was performed at 20 breaths per minute, with the subjects being guided by a metronome. Breathing depth was not controlled, but subjects were instructed to breathe as deeply as possible. Breathing was measured with a respiration belt around the subjects' chest to validate that the subjects performed hyperventilation at the set frequency.

Figure 1.

Experimental setup and data flow. The NIRS sensor was placed on the forehead, the MAP monitor on the right arm and fingers, and the thigh cuffs around both legs. A respiration belt was used to monitor respiration. The measured signals were fed into the hemodynamic model and the six unknown model parameters were calculated based on fitting the model to the data. CBV₀, static blood volume; MAP, mean arterial blood pressure; NIRS, near-infrared spectroscopy.

Figure 2.

Typical example of a measurement time series (data from subject 5). The top panel shows the cuff pressure. The center panel shows low-pass filtered (cutoff at 0.15 Hz) time traces of O(t) and D(t). The bottom panel shows the time traces of T(t) and mean arterial blood pressure (MAP). The insets show the time period right after the two cuff releases, which have been used for analysis with the hemodynamic model.

After removing slow temporal drifts from the NIRS data, optical intensity changes were translated into relative changes of O, D, and T by applying the modified Beer-Lambert law to data from the largest source-detector distance (35 mm). Based on phantom calibration and data at multiple source-detector distances (20 to 35 mm), the instrument also provided absolute measurements of the baseline concentrations of oxy-hemoglobin (O₀), deoxy-hemoglobin (D₀), and total hemoglobin (T₀=O₀+D₀). MAP time traces were obtained by band pass filtering (between 0.02 Hz and 0.15 Hz) the beat-to-beat blood pressure output with a linear-phase band-pass filter (function ‘firpmord' in MATLAB, MathWorks, Natick, MA, USA). Hemoglobin traces were also filtered between these frequencies to remove contributions from the cardiac pulsation and respiration. Only the data collected in the 10 seconds after the thigh-cuff release were used for further analysis with the hemodynamic model, since this is the time frame in which the autoregulation response is taking place.

Hemodynamic Model

The dynamic multicompartment hemodynamic model introduced by Fantini²³ describes the effects of perturbations in CBF, CBV, and cerebral metabolic rate of oxygen (CMRO₂) onto O, D, and T. By denoting with lower case letters the relative and normalized changes in CBV, CBF, and CMRO₂ concerning baseline (cbv(t)=ΔCBV(t)/CBV₀, cbf(t)=ΔCBF(t)/CBF₀, and cmro₂(t)=ΔCMRO₂(t)/CMRO₂|₀), the time-dependent expressions for the absolute tissue concentrations of O(t), D(t), and T(t) (with units of micromoles per unit tissue volume) are given by:²⁶

where ctHb is the hemoglobin concentration in blood, expressed in units of micromoles per unit blood volume, F^(c) is the Fåhraeus factor (ratio of capillary-to-large vessel hematocrit), * denotes the convolution operator, and the superscripts indicate the arterial (a), capillary (c), and venous (v) compartment values of hemoglobin saturation (S), static blood volume (CBV₀), and relative blood volume changes (cbv). The mean capillary and venous saturations are given by and where α is the rate constant of oxygen diffusion and t^(c) is the mean capillary transit time, and 〉 denotes a spatial average over the capillary bed.²⁷ The static blood volume is defined as .²⁶ We have set the capillary volume perturbation cbv^(c)(t)=0 since cerebral capillary recruitment and dilation has been found to be negligible.^{28, 29, 30, 31, 32, 33} The impulse response functions associated with the blood transit time in the capillary bed and in the venous compartment are given by resistor-capacitor and Gaussian low-pass filters, respectively:²³

where H(t) is the Heaviside unit step function (H(t)=0 for t<0; H(t)=1 for t⩾0). Since we are considering cases in which cmro₂(t) contributions are negligible, we set cmro₂=0. Total blood volume changes can be written as a weighted average of arterial and venous volume changes:

with T₀=ctHb CBV₀.

The cerebral autoregulation process can be described as a high-pass filter that regulates CBF dynamics in response to MAP changes.^{11, 17, 22, 34} In the case of sinusoidal oscillations, this description implies that MAP oscillations at high frequencies do not result in regulated blood flow (i.e., CBF oscillates in phase with MAP), whereas MAP oscillations at low frequencies result in a regulated blood flow (i.e., CBF does not oscillate and stays constant). The reference frequency to quantify ‘high' and ‘low' frequencies in the previous sentence is the cutoff frequency for autoregulation at which CBF oscillations feature an amplitude that is (or 0.707) times their amplitude at the high-frequency limit and a phase lead of π/4 concerning the driving MAP oscillations. Even though this transfer function analysis description of cerebral autoregulation is common,^{3, 11, 20, 21, 22} we are aware of only a few studies that are explicitly based on a high-pass filter analysis involving the concept of autoregulation cutoff frequency.^{11, 17, 35} In this work, we focus on the assessment of autoregulation cutoff frequencies as a measure of the effectiveness of cerebral autoregulation: namely, the higher the cutoff frequency, the better the suppression of CBF oscillations at any frequency, and the better the autoregulation.

In our NIRS approach, which implements the novel technique of Coherent Hemodynamics Spectroscopy (CHS),²³ we aim to express cerebral autoregulation in terms of optically measured hemodynamic quantities that pertain to the microvasculature within a localized tissue region. This differs from the more standard approach based on systemic measurements of MAP and on measurements of the blood flow velocity in the MCA. The dynamics of CBF, described by cbf(t) in Equations (1) and (2), are representative of relative changes in the local CBF.²⁶ The blood volume oscillations described by cbv(t) in Equation (6) provide a local measurement of vascular expansion and contraction, and are closely related to the MAP. In fact, it was reported that oscillations in cbv (measured with NIRS) and MAP are essentially synchronous, with a nonsignificant phase difference at a frequency of 0.1 Hz.^{16, 18} For these reasons, we opted to express the local cerebral autoregulation at the level of microcirculation in terms of focal NIRS measurements of cbf(t) and cbv(t) according to the following relationship.²³

where k is the inverse of the modified Grubb's exponent, is the resistor-capacitor high-pass impulse response function with cutoff frequency that describes the effect of autoregulation, and * denotes a temporal convolution. The resistor-capacitor high-pass impulse response function is given by:

where (with ) and δ is the Dirac delta.

Since MAP was measured continuously, access to arterial blood volume changes was possible by assuming a proportional dependence of arterial blood volume on MAP, so that . T(t) is determined by a weighted average of venous and arterial blood volume changes, and by the baseline hemoglobin concentration T₀. The baseline arterial blood volume fraction could be estimated from oscillatory T(t) at the heart rate by assuming that only arterial blood contributes to a volume change because of the cardiac pulsation. By filtering the measured relative total hemoglobin time traces as well as MAP around the cardiac pulsation, Equation (6) reduces to:

where hr indicates the filtered data around the cardiac pulsation (heart rate). After assuming the arterial saturation to be S^(a)=0.98, and calculating from Equation (9), the remaining unknown parameters of the model are (the normalized capillary baseline blood volume contribution), and α.

The six unknown parameters could be fitted for using a fitting algorithm in MATLAB (function lsqcurvefit) with a trust region reflective algorithm. The fitting procedure considers as input values the measured absolute hemoglobin concentration time traces (O(t), D(t)), MAP(t), as well as , and finds the optimal set of the six unknown parameters by minimizing a cost function (X²). The stopping criterion for the fit was estimated based on the variances of the measured data. We have used 96 different sets of initial guesses for the six unknown parameters, which were evenly spread throughout the range of upper and lower bounds of the parameters. For each initial guess, the solutions of the six parameters were stored for further analysis.

Statistical Analysis

All statistical analyses were performed in MATLAB. A group-level-based, nonparametric one-tailed signed-rank test was performed for determining statistically significant differences between normal breathing and hyperventilation for all the six model output parameters.

Results

Figure 2 shows a typical measurement time series. The top panel shows the cuff pressure, which was set to 200 mmHg during normal breathing and hyperventilation. The center panel shows low-pass filtered (below 0.15 Hz) time traces of O(t) and D(t), where O(t) decreases significantly after the cuff pressure is released whereas D(t) increases. The bottom panel shows the time traces of T(t) and MAP. T(t) follows MAP closely, with a small time delay as indicated in the insets. No time delay was seen between T(t) and MAP at the cardiac pulsation frequency, which allowed for calculating the arterial baseline contribution to the total blood volume () based on Equation (9). The group averaged (over the 11 subjects) arterial blood volume fraction was found to be , during both normal breathing and hyperventilation, and it was time independent, showing the robustness of the method.

A representative case of the model fit to the data over the 10 seconds immediately after the thigh-cuff release is seen in Figure 3. The top panel shows the measured hemoglobin traces (symbols) and the model fit (continuous lines). For clarity purposes of the figure only, the data have been referenced to baseline hemoglobin values, with ΔO(t)=O(t)−O₀ and ΔD(t)=D(t)−D₀. The fit shown is the mean of the 96 independent fits. Black symbols and lines refer to normal breathing, and gray symbols and lines refer to hyperventilation. The center panel shows percentage changes in MAP after the cuff release. For both normal breathing and hyperventilation, MAP stays low for the 10 seconds considered for the data analysis. The bottom panel shows the measured cbv(t) (dashed lines) and the estimated cbf(t) on the basis of Equation (7) (solid lines). The estimated cbf(t) traces shown are based on the mean of those cbf(t) traces obtained for the 96 initial guesses. Since autoregulation increases during hyperventilation, cbf(t) was expected to recover faster during hyperventilation than during normal breathing. This behavior was found in the data as seen in Figure 3 (bottom panel) and was quantified by the cutoff frequency of autoregulation defined by Equation 8.

Figure 3.

Typical time traces after thigh-cuff release (data from subject 3). Symbols in the top panel show measured hemoglobin concentrations, solid lines show the model fit. Black indicates normal breathing and gray indicates hyperventilation. The center panel reports measured mean arterial blood pressure (MAP) traces, showing the typical drop in MAP after thigh-cuff release. The bottom panel shows measured cerebral blood volume, cbv(t) (dashed lines), and cerebral blood flow, cbf(t) (solid lines), calculated based on the autoregulation description in Equation (7). The cbf traces during hyperventilation (enhanced autoregulation) show a faster recovery to baseline in comparison to normal breathing.

Figure 4A shows the autoregulation cutoff frequency of all 11 subjects, where the black bars indicate the cutoff frequency during normal breathing and gray bars during hyperventilation. The error bars are the s.d. of the 96 solutions of the fit. Figure 4B reports the difference of the autoregulation cutoff frequencies measured during hyperventilation and normal breathing, respectively, and shows an increase in cutoff frequency during hyperventilation in 10 out of 11 subjects. To evaluate the reproducibility of our measurements, we retested 4 of the 11 subjects, who were able to come back for additional measurements (subjects 1, 2, 9, and 11). Figure 4C shows the results of the repeated measurements. In these subjects, we reproduced the previously observed changes in induced by hyperventilation (increase in subjects 1, 2, and 11; decrease in subject 9). The repeated measurements on these subjects have been performed on different days, with the optical probe placed at slightly different locations on the subject's forehead. The varying location of the imaging probe may account for the within-subject variability of and also suggests how these local measurements may be extended to imaging and mapping of cerebral autoregulation over extended areas of the cerebral cortex. However, the repeated measurements on these four subjects indicate that the method is robust for measuring local changes in autoregulation within individual subjects, and not just at a group level.

Figure 4.

(A) Autoregulation cutoff frequency measured in all the 11 subjects, where black bars indicate normal breathing and gray bars indicate hyperventilation. The numbers on the horizontal axis enumerate the subjects. Error bars are the s.d. of the results obtained with the fitting routine for 96 initial guesses of the set of parameters. (B) Difference in cutoff frequencies between hyperventilation and normal breathing. (C) Autoregulation cutoff frequency in repeated measurements on subjects 1, 2, 9, and 11 (same notation as in A).

Table 1 summarizes the group averages of all the six model parameters during the two conditions. Values are given as the mean and standard error of the measurements across all subjects. The transit time in the capillaries was found to be 1.1 seconds, which falls into the reported range of 0.3 to 1.7 seconds, as measured on rats with fluorescence videography.^{36, 37} The transit time in the veins was found to be ~5.6 seconds, which corresponds to a venule length of 5.6 mm, assuming a typical speed of blood flow in venules of 1 mm/s. Although this length is outside the range of venule lengths of 1 to 3 mm measured on human brain tissue samples with confocal laser microscopy,³⁸ it must be noted that NIRS is sensitive to a macroscopic tissue volume (of several cubic centimeters), so that the measured venule length corresponds to the overall length of draining venules within the probed volume rather than any individual venule segments.

Table 1. Output parameters of the model fit.

	Capillary transit time t(c) (seconds)	Venous transit time t(v) (seconds)	Autoregulation cutoff frequency	Inverse of modified Grubb's exponent (k)	Capillary blood volume ratio	Rate constant of oxygen diffusion α (per second)
Normal breathing	1.1±0.1	5.6±0.7	0.017±0.002	2.6±0.3	0.54±0.03	0.56±0.02
Hyperventilation	1.1±0.1	5.7±0.8	0.034±0.005	3.0±0.2	0.45±0.04	0.55±0.02

The inverse of the Grubb's exponent, which we have used to describe the magnitude of cbf changes, was found to be k~2.8, which is also well within the reported range of 2 to 5, as measured on rats and humans with magnetic resonance imaging as well as NIRS.^{39, 40, 41, 42} The capillary compartment contribution to the total baseline blood volume, , was found to be ~0.5, which also corresponds well to reported values 0.3 to 0.65 in the human brain cortex.³⁸ The rate constant of oxygen diffusion was found to be α~0.56 per second, where the rate constant can be estimated by α=D/d², where D is the diffusion coefficient of oxygen in tissue and d is the intercapillary distance. For the oxygen diffusion coefficient D, literature values of 1.7 × 10⁻⁵ to 2 × 10⁻⁵ cm²/s have been reported for brain tissue.^{43, 44} Values of ~40 to 60 μm have been reported for the intercapillary distance d in the rat brain and human gray matter.^{45, 46} These reported measured ranges for D and d lead to a range of possible oxygen diffusion rate constants (α) of 0.4 to 1.2 per second.

The autoregulation cutoff frequency was found to be during normal breathing, and 0.034±005 Hz during hyperventilation. This increase was found to be significant (p=0.006) based on a one-tailed signed-rank test. None of the other parameters changed significantly during hyperventilation. As we mentioned above, we are aware of very few published studies that referred to an autoregulation cutoff frequency. Blaber et al¹¹ stated the use of an autoregulation cutoff frequency of 0.15 Hz on the basis of a previous study that found a broad range of phase differences (70°±30°) between CBFV and MAP¹⁷ at 0.1 Hz. However, this cutoff frequency used by Blaber et al does not correspond to the definition of a high-pass filter cutoff frequency. Rather, Blaber et al used the term to describe the frequency range (0 to 0.15 Hz), in which autoregulation is effective. A more explicit measurement of autoregulation cutoff frequency of 0.03 Hz has been reported by Fraser et al³⁵ on the basis of a Butterworth high-pass filter analysis of phase differences (at multiple frequencies) between arterial blood pressure and intracranial pressure in a neonatal swine model. Because of the broad range of phase differences considered and the different quantities used (MAP, MCA blood flow velocity, and intracranial pressure), the above reference values may not serve as much more than order of magnitude references to our results. However, a more significant reference to our results is the study of the effect of hypocapnia (achieved here with hyperventilation) on autoregulation, as measured by Aaslid et al⁹ by recording the response of CBFV to a step change in arterial blood pressure (step response). By considering the resistor-capacitor high-pass filter considered by us, the relationship between the time to recovery to half of the baseline CBF value (t_0.5) is related to the cutoff frequency introduced by us as follows: . The values for t_0.5 reported by Aaslid et al⁹ during normocapnia (3.4 seconds) and hypercapnia (1.9 seconds) can be translated into cutoff frequencies, as defined by us, of ~0.03 Hz (normocapnia) and ~0.06 Hz (hypercapnia), respectively. These results are in qualitative agreement with our results, and also in good quantitative agreement (considering, again, that different quantities were measured in our study and in the study by Aaslid et al⁹).

Discussion

We have shown that the cerebral autoregulation enhancement induced by hyperventilation can be measured locally in the microvasculature by NIRS together with the dynamic hemodynamic model we recently introduced. By describing dynamic autoregulation in terms of a high-pass filter between cbv(t) and cbf(t), we have found an increase in autoregulation cutoff frequency, which corresponds to a faster response of cbf to cbv during hyperventilation compared with normal breathing. Autoregulation is defined as the mechanism that maintains constant cbf(t) despite changes in MAP, where the recovery time of cbf(t) is indicative of autoregulation. The majority of studies on autoregulation have used the dynamics of blood flow as measured with TCD in the MCA in relation to MAP. Here, we have introduced a novel way of measuring autoregulation, which is based on local cbv(t), rather than systemic MAP, and microvascular cbf(t). This proposed approach has a twofold appeal: first, it is based on a local measurement of vascular dilation/constriction that is hypothesized to be closely linked to local blood pressure perturbations; second, it relies on measurements with the same technology that is sensitive to local changes in CBF, thus realizing a self-contained and spatially congruent technology for local autoregulation assessment. Although the delay between cbv(t) and MAP(t) is small (<2 seconds as seen in Figure 2), our method inherently takes contributions of venous volume change, cbv^(v)(t), into account. Since the arterial and venous blood volume changes exhibit different dynamic behaviors,^{47, 48} there is a possibility that the dynamics of local cbf(t), as reflected in the autoregulation cutoff frequency, might be dependent on the relative amount of venous and arterial blood present in the tissue sampled. The amount of venous blood relative to arterial blood depends on the tissue imaged and hence the location of the optical sensor. This could therefore explain, at least in part, the intersubject (Figure 4A) and the intrasubject (Figure 4C) variability observed in was found with subjects performing hyperventilation, showing the robustness of the method for monitoring purposes. The issue of the inclusion of venous contributions to cbv(t), possibly through optimal weight factors in Equation (6), is an open area of research in our effort to further develop and refine the methods introduced in this work.

In the frequency-domain version of Equation (7), the impulse response function of Equation (8) is replaced by a complex transfer function that specifies the phase difference between oscillations of CBF and CBV at a given frequency.²⁶ By carrying out this transfer function analysis, and by using the frequency-domain versions of Equations (1) and (2) together with the model parameters obtained and reported in Table 1, we have found a phase difference of −276° between D and O oscillations at a frequency of 0.1 Hz. These numbers agree well with literature values, where O and D oscillations associated with paced breathing at 0.1 Hz were reported to be −260°⁴⁹ and −200°¹⁶ in healthy volunteers. The phase difference between oscillations of CBF and CBV at 0.1 Hz, considering the average autoregulation cutoff frequencies of 0.017 Hz (normal breathing) and 0.034 Hz (hyperventilation) were found to be 10° and 20°, respectively. This phase difference is lower than the reported 60° between MAP and CBF oscillations measured in the MCA.¹⁶ Again, this discrepancy may be explained by the fact that in Equation (7) we are considering local microvascular blood volume changes rather than systemic MAP changes. However, the measured increase in autoregulation during hyperventilation has proven to be robust. Furthermore, the magnitude of the reported CBF change corresponds well to literature values. Although, in response to the fast release of the thigh-cuff pressure, MAP typically drops by 10% to 20%⁹ and the MCA blood flow velocity (measured by TCD) also drops by ~20%, we have found that local cbv changes (measured by NIRS) are much smaller (<2%), yielding microvascular cbf changes in the order of ~4%.

Besides the autoregulation cutoff frequency, the other model parameters did not show a significant difference between normal breathing and hyperventilation. A constant transit time in the capillary compartment, t^(c), translates into unaltered mean capillary and venous saturations. The group averaged capillary saturation was and the venous saturation was S^(v)~53%. Constant arterial, capillary, and venous blood volume ratios result in a constant tissue saturation, which was measured to be StO₂ ~67%. Although the hemodynamic model allows for the assessment of capillary and venous saturations noninvasively, it shall be pointed out that the capillary transit time is coupled with the rate constant of oxygen diffusion, α, through the product αt^(c) in the expressions for S^(c) and S^(v), whereas t^(c) appears independently of α in the capillary and venous impulse response functions (see Equations (4) and (5)). This is the basis for our separate determination of t^(c) and α reported in Table 1.

Within the measured tissue volume accessed with NIRS on the prefrontal cortex, we have found that the capillary compartment contributes ~50% of the total baseline volume (Table 1). Since we have estimated the arterial contribution to be only ~4%, the venous contribution results in ~46% of the overall measured hemoglobin signals. Although our estimated arterial contribution is much lower than reported values of ~30%,⁵⁰ it shall be pointed out that we have considered only the pulsatile signal of the cardiac pulsation, which is dominant in large arteries. Consequently, we may have underestimated the contributions of arterioles, which have a weaker pulsatile signature, to the arterial blood volume. In addition, we have assumed a proportional relationship between arterial blood volume and MAP (see Equation (9)). A power law between arterial blood volume and MAP may be a better approximation and would result in a greater estimated arterial blood volume. Preliminary results based on a power law relationship (data not shown) indeed yield a greater arterial blood volume, but the autoregulation cutoff frequency is largely unaffected.

The model fit was performed on measured absolute concentrations of hemoglobin, which we obtained with frequency-domain NIRS. We have also evaluated the model fit if only relative changes, as measured with continuous-wave NIRS systems, are available. In this case, the value of baseline hemoglobin concentration has to be assumed rather than measured. We have found (data not shown) that while some of the model parameters, in particular t^(c), depend on the specific value assumed for the baseline hemoglobin concentration, the autoregulation cutoff frequency is independent of such assumption. Therefore, the method proposed here for measurements of local cerebral autoregulation is robust and can be used even if only relative changes in hemoglobin concentrations are measured.

Because NIRS is sensitive to superficial layers, as well as brain tissue, we investigated whether superficial layer contamination would possibly alter the results. For this, we repeated the experiments on three additional subjects, where the optical probe was equipped with an additional small source–detector separation (0.75 cm), which yields data that is only sensitive to superficial extracerebral tissue (scalp, skull, etc.). Results indicate that the superficial layers (shortest source-detector distance) do not exhibit the same dynamics as deeper layers. Specifically, we found that after the cuff pressure release, deoxy-hemoglobin and oxy-hemoglobin concentration responses are approximately synchronous and both decreasing at the short source–detector distance (not sensitive to brain tissue), whereas they are asynchronous and in opposite directions (Figure 3) at the long source–detector distance (sensitive to brain tissue). This indicates that superficial tissue layers are dominated by blood volume changes, whereas blood flow changes also contribute to the signals originating at deeper cerebral tissue. The significant differences between the temporal dynamics of the measured signals at a short source–detector distance (exclusively sensitive to superficial extracerebral tissue) and at a long source–detector distance (sensitive to both extracerebral and cerebral tissue) gives us confidence about the negligible contribution of superficial tissues to our dynamic measurements of autoregulation. However, this is an important question that we are still exploring in our further development of this technique.

Conclusion

Maintaining an adequate blood perfusion is of paramount importance for brain health. Cerebral autoregulation plays a critical role and is known to be impaired in a number of pathologic conditions such as stroke, subarachnoid hemorrhage, and bacterial meningitis. There are clinical situations, for example cardiopulmonary bypass and general anesthesia, where monitoring cerebral autoregulation could help prevent brain damage and guide adjustments to the procedure. There are also brain development areas of study, such as the mechanisms that lead to the establishment of cerebral autoregulation in newborn babies, which can benefit from autoregulation monitoring techniques. We have presented a novel, noninvasive approach (Coherent Hemodynamics Spectroscopy) to the assessment of local cerebral autoregulation through optical measurements that are mostly sensitive to the microvasculature. For the presented approach, systemic MAP changes have to be induced to affect the blood volume and blood flow in the cerebral microvasculature. Here, we have used a 2-minute arterial thigh-cuff occlusion and sudden release to achieve rapid MAP changes. The induced drop in MAP is typically in the order of 10% to 20% of its baseline value, which is about two times greater than spontaneous MAP fluctuations. Although this cuff method has been used in vulnerable patients, such as traumatic brain injury patients,^{51, 52} and has been shown to be safe, other methods to induce MAP changes can also be used.

Our results pave the way for a variety of applications in which the noninvasive assessment and monitoring of cerebral autoregulation is important. Furthermore, the local sensitivity of the proposed measurements lends itself to imaging applications, allowing for mapping cerebral autoregulation effectiveness over extended brain areas.

The authors declare no conflict of interest.