Cerebral Autoregulation in the Microvasculature Measured with Near-Infrared Spectroscopy

ORIGINAL ARTICLE Cerebral autoregulation in the microvasculature measured with near-infrared spectroscopy

Jana M Kainerstorfer, Angelo Sassaroli, Kristen T Tgavalekos and Sergio Fantini

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.

Journal of Cerebral Blood Flow & Metabolism (2015) 35, 959–966; doi:10.1038/jcbfm.2015.5; published online 11 February 2015 Keywords: brain imaging; cerebral blood ﬂow measurement; cerebral hemodynamics; near-infrared spectroscopy; optical imaging

INTRODUCTION questioned the validity of the autoregulation curve introduced Cerebral autoregulation is the mechanism that maintains cerebral by Lassen by showing that the slope of CBF as a function of MAP is blood supply, hence cerebral blood flow (CBF), approximately dependent on whether MAP increases or decreases, invalidating constant despite changes in mean arterial blood pressure (MAP) the plateau of the autoregulation curve. In general, the accuracy of or, more precisely, despite changes in cerebral perfusion pressure measuring autoregulation based on two points, on the auto- (CPP; defined as the difference between MAP and intracranial regulation curve is questionable, with the measurements being pressure). This mechanism is valid for a certain range of CPP, several minutes apart from each other, since CBF depends on a namely 50 to 150 mm Hg.1–3 Within that range, changes in CPP number of factors, such as partial pressure of carbon dioxide (pCO2), cerebral metabolism, and hematocrit, which all can lead to vasomotor adjustments in cerebrovascular resistance (CVR) 3,7 1 change while MAP reaches a new steady state, whereas the thus allowing CBF to remain relatively constant. Lassen con- change in MAP alone is what drives autoregulation. structed, based on measurements reported in the literature, a so- The second category of autoregulation assessment is based on called autoregulation curve, which shows a CBF plateau in the measuring dynamic changes of CBF in response to dynamic aforementioned CPP range, essentially showing that CBF remains changes in MAP, hence this is referred to as dynamic cerebral constant. Assessing the boundaries of this plateau and whether autoregulation. Regardless of the exact measurement setup, the the autoregulation mechanism is intact or impaired is critical, underlying idea is that after a step change in MAP, CBF will first since impaired autoregulation can lead to cerebral ischemia or react to such MAP change and will then return to its original value brain damage because of abnormal perfusion. Therefore, deter- within a finite amount of time, where this amount of time is a mining the effectiveness of cerebral autoregulation is relevant for measure of autoregulation efficiency. The faster CBF returns to its a variety of patient populations. baseline value, the better is the autoregulation mechanism. This In general, the assessment of autoregulation can be classified delayed CBF adaptation was first observed in animals.8 Aaslid into two categories. The first category considers only steady-state et al9 introduced a thigh cuff–based method of inducing fast MAP or static relationships between CBF and MAP, without taking time changes, which is the most frequently used method to induce courses of changes in MAP and CBF into account. This can be rapid MAP perturbations. For this, pneumatic cuffs are placed achieved by infusion of drugs, which do not have an effect on the ’ fl – around the subjects thighs and are in ated 20 to 40 mm Hg cerebral vasculature or metabolism but change MAP.4 6 Measure- above systolic pressure for at least 2 minutes. The release of the ments of CBF are performed during baseline as well as during the thigh-cuff pressure results in MAP dropping by ~ 10 to 20 mm Hg. altered MAP state. This yields two values of CBF and their Since Aaslid et al have shown that MAP and CBF return to baseline difference in relation to the MAP change is indicative of within ~ 15 seconds after thigh-cuff release, changes in cerebral autoregulation. A recent review on static autoregulation7 metabolism and hematocrit can be neglected over this time

Department of Biomedical Engineering, Tufts University, Medford, Massachusetts, USA. Correspondence: Dr JM Kainerstorfer, Department of Biomedical Engineering, Tufts University, 4 Colby Street, Medford, MA 02155, USA. E-mail: [email protected] This research was supported by the National Institutes of Health (Grant no. R01-CA154774) and by the National Science Foundation (Award no. IIS-1065154). Received 16 September 2014; revised 17 December 2014; accepted 6 January 2015; published online 11 February 2015 Microvascular autoregulation with NIRS JM Kainerstorfer et al 960 scale.3,9 Furthermore, the method is quick and can therefore be and CBF. Based on literature, it is known that the autoregulation repeated multiple times on the same subject for monitoring mechanism can be described as a high-pass filter for which MAP is applications. However, since the time window in which the an input and CBF in an output.11,17 We adopt this idea of autoregulation mechanism can be studied is ~ 15 seconds, only a describing dynamic autoregulation with a high pass filter, but we limited number of measurement techniques exist, which can use local microvascular CBV (measured by T(t) and hypothesized capture these fast transients in CBF. Transcranial Doppler (TCD) is to be directly linked to the local arterial blood pressure) as input, such an imaging technique with a sufficient temporal resolution; it and local microvascular blood flow (measured by NIRS and our measures CBF velocity (CBFV) in the middle cerebral artery (MCA). hemodynamic model) as output. The cutoff frequency of the high- Under the assumption that the diameter of the MCA does not pass filter, which is inversely related to the CBF recovery time change, CBFV can be taken to be a reliable representation of discussed above, quantifies the effectiveness of autoregulation.23 9,24,25 global CBF. Together with continuous blood pressure measure- Changes in PaCO2 have been shown to influence CA. The ments, the dynamics of MAP changes and CBF changes can be mechanism is hypothesized to be linked with the effect of PaCO2 assessed with an adequate temporal resolution for dynamic (CA) on cerebrovascular reactivity (enhancement during hypocapnia assessment. and suppression during hypercapnia),9 which in turn is associated Such measurements of dynamic changes in CBF in response to with the vascular dilation during hypercapnia and vascular sudden changes in MAP, where the time of CBF recovery is constriction during hypocapnia.24 Hypocapnia reduces CBF, while indicative of autoregulation, have already been used in numerous also reducing the response time of CBF after a step change in 10 disease models, where it has been found that cerebral MAP.2,9 This reduced response time is an indicator of improved autoregulation is altered or impaired in patients with a variety of CA. Since hypocapnia can be induced by performing 11 12 conditions such as autonomic failure, diabetes, Parkinson’s hyperventilation,9 we have measured healthy volunteers during 13 14 disease, and stroke. normal breathing and hyperventilation to induce a predictable Using the CBF recovery time, different methods exist to assess change (increase during hyperventilation) in cerebral autoregula- fi and quantify autoregulation. One such method de nes autoregulation. We show that local NIRS measurements, which are mostly tion by the rate of regulation, which is given by the temporal slope sensitive to the cerebral microvasculature, together with hemo- of CVR recovery, where CVR = CPP/CBF, after the sudden perturba- 9,15 dynamic perturbations induced by a fast thigh-cuff release, can tion in the thigh-cuff release method. A steeper slope of CVR as a measure these different levels of autoregulation effectiveness in function of time indicates a better autoregulation mechanism. the cerebral microvasculature. 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 MATERIALS AND METHODS 15 dynamic changes in MAP and CBF. Data Acquisition Another way of measuring dynamic CA, instead of inducing Eleven healthy subjects (five males and six females, age range: 21 to 50 rapid MAP changes, is based on studying CBF responses to slow years) without any history of neurologic disorders or cardiovascular fi oscillations in MAP. Such oscillations can be induced at a speci c disease participated in the study, with the experimental protocol approved frequency by a number of protocols including paced bre- by the Tufts University Institutional Review Board. Written informed 16,17 18 19 athing, head-up tilting, and periodic thigh-cuff inflation, consent was obtained from all participants before the study and the with oscillations typically being induced around 0.1 Hz. The experiments were performed in accordance with the Declaration of measurement of dynamic CA can then be performed by transfer Helsinki. Figure 1 shows the data acquisition setup and analysis flow. NIRS function analysis where beat-to-beat MAP measurements are used data were collected with a commercial frequency-domain tissue spectro- as input and CBF measurements as output.3,11,20–22 Transfer meter (OxiplexTS, ISS, Champaign, IL, USA), operating at wavelengths 690 ’ function analysis is based on analysis of the coherence, gain, and and 830 nm. Optical probes were placed on the subject s forehead and phase differences between MAP and CBF as a function of secured by a headband to hold them in place. MAP was recorded with a beat-to-beat finger plethysmography system (NIBP100D, BIOPAC Systems, frequency. Similar to the rapid change in MAP with thigh cuffs, Goleta, CA, USA). Two pneumatic cuffs were placed around both thighs the phase differences, related to the time delay, between MAP and and connected to an automated cuff inflation device (E-20 Rapid Cuff CBF found with transfer function analysis, has been found to be a Inflation System, D. E. Hokanson, Bellevue, WA, USA). The protocol good indicator of autoregulation efficiency. consisted of 2 minutes of baseline measurements, after which the cuffs Although TCD together with MAP measurements have been were inflated at 200 mm Hg for 2 minutes, as seen in Figure 2. The rapid used in numerous patient populations for autoregulation assess- deflation of the cuffs results in a drop in MAP, which induces changes in ment (see the comprehensive review by Panerai10), TCD has its cerebral O, D, and T. Two minutes after cuff deflation, the cuffs were limitations. In particular, TCD measures CBFV in the MCA, and inflated again for 2 minutes. The subjects were asked to perform fl cannot measure microvascular, localized changes in CBF. Taking hyperventilation for 2.5 minutes, starting at the second cuff in ation. advantage of the fact that CBF changes are sensed by near- Hyperventilation was performed at 20 breaths per minute, with the subjects being guided by a metronome. Breathing depth was not infrared spectroscopy (NIRS) in all vascular compartments with controlled, but subjects were instructed to breathe as deeply as possible. special sensitivity to the microvasculature, we introduce a novel Breathing was measured with a respiration belt around the subjects’ chest imaging platform, which is sensitive to localized, microvascular to validate that the subjects performed hyperventilation at the set CBF changes, and we show that dynamic CA can be measured and frequency. quantified in the microvasculature. Specifically, NIRS measures After removing slow temporal drifts from the NIRS data, optical intensity cerebral changes in oxy- [O(t)], deoxy- [D(t)], and total- [T(t)] changes were translated into relative changes of O, D, and T by applying hemoglobin concentrations noninvasively and continuously on the modified Beer-Lambert law to data from the largest source-detector the cerebral cortex. Since O(t) and D(t) are sensitive to distance (35 mm). Based on phantom calibration and data at multiple microvascular changes in CBF, specifically to capillary blood flow, source-detector distances (20 to 35 mm), the instrument also provided as well as cerebral blood volume (CBV) changes, we show that absolute measurements of the baseline concentrations of oxy-hemoglobin NIRS data, together with a novel hemodynamic model, yields (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) quantitative measurements of dynamic CA. fi 9 the beat-to-beat blood pressure output with a linear-phase band-pass lter We use the thigh-cuff method of Aaslid et al and measure the (function ‘firpmord’ in MATLAB, MathWorks, Natick, MA, USA). Hemoglobin hemodynamic response to the rapid change in MAP after the cuff traces were also filtered between these frequencies to remove contribu- pressure is released. We analyze the data with our hemodynamic tions from the cardiac pulsation and respiration. Only the data collected in model, which translates O(t) and D(t) into temporal traces of CBV the 10 seconds after the thigh-cuff release were used for further analysis

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.

hDE ð Þ¼ - ðaÞ ðaÞ þ ðaÞðÞ þ - ðcÞ ðcÞ ðcÞ with the hemodynamic model, since this is the time frame in which the D t ctHb 1 S CBV0 1 cbv t 1 S F CBV0 i h autoregulation response is taking place. hiðcÞ þ - ðvÞ ðvÞ þ ðvÞð Þ - S ðcÞ ðvÞ ðcÞ ðcÞ ðcÞ 1 S CBV0 1 cbv t ctHb ð Þ S - S F CBV h ðtÞ S v 0 RC - LP i Hemodynamic Model þ ðaÞ - ðvÞ ðvÞ ðvÞ ð Þ ½ð Þ - ð Þ ; ð Þ S S CBV0 hG - LP t cbf t cmro2 t 2 The dynamic multicompartment hemodynamic model introduced by Fantini23 describes the effects of perturbations in CBF, CBV, and cerebral TðtÞ¼ctHb CBV0½1 þ cbvðtÞ ; ð3Þ 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 CMRO where ctHb is the hemoglobin concentration in blood, expressed in units 2 (c) concerning baseline (cbv(t)=ΔCBV(t)/CBV0, cbf(t)=ΔCBF(t)/CBF0, and of micromoles per unit blood volume, F is the Fåhraeus factor (ratio of capillary-to-large vessel hematocrit), * denotes the convolution operator, 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 and the superscripts indicate the arterial (a), capillary (c), and venous (v) micromoles per unit tissue volume) are given by:26 compartment values of hemoglobin saturation (S), static blood volume (CBV ), and relative blood volume changes (cbv). The mean capillary and hiDE 0 ð Þ ð Þ¼ ðaÞ ðaÞ þ ðaÞð Þ þ ðcÞ ðcÞ ðcÞ þ ðvÞ ðvÞ þ ðvÞð Þ ðcÞ ¼ ðaÞ - - αt c = α ðcÞ ðvÞ ¼ O t ctHb S CBV0 1 cbv t S F CBV0 S CBV0 1 cbv t venous saturations are given by S S 1 e t and S ð Þ hiðaÞ - αt c α (c) ðcÞ S e where is the rate constant of oxygen diffusion and t is the þ hiS ðcÞ ðÞv ðcÞ ðcÞ ðcÞ ðaÞ ðvÞ ðvÞ ðvÞ ctHb ð Þ S - S F CBV h ðtÞþ S - S CBV h ðtÞ 〉 S v 0 RC - LP 0 G - LP mean capillary transit time, and 〈 denotes a spatial average over the capillary bed.27 The static blood volume is deﬁned as ðaÞ ð Þ ðcÞ ðvÞ 26 ½cbfðtÞ - cmro2ðtÞ ; ð1Þ ¼ þ c þ CBV0 CBV0 F CBV0 CBV0 . We have set the capillary volume

© 2015 ISCBFM Journal of Cerebral Blood Flow & Metabolism (2015), 959 – 966 Microvascular autoregulation with NIRS JM Kainerstorfer et al 962 perturbation cbv(c)(t) = 0 since cerebral capillary recruitment and dilation hemoglobin time traces as well as MAP around the cardiac pulsation, has been found to be negligible.28–33 The impulse response functions Equation (6) reduces to: ½ ðcÞ ð Þ associated with the blood transit time in the capillary bed hRC - LP t and Δ ð Þ ðaÞ ðaÞΔ ð Þ ð Þ T t CBV ðaÞ CBV MAP t in the venous compartment ½h v ðtÞ are given by resistor-capacitor 9 ¼ 0 cbv ðtÞ9 ¼ 0 9 ð9Þ G - LP T hr CBV hr CBV MAP hr and Gaussian low-pass filters, respectively:23 0 0 0 0 where hr indicates the filtered data around the cardiac pulsation (heart ðcÞ ð Þ¼ ð Þ e - et=tðcÞ ; ð Þ (a) h - t H t ð Þe 4 rate). After assuming the arterial saturation to be S = 0.98, and calculating RC LP c ð Þ t CBV a 0 from Equation (9), the remaining unknown parameters of the model CBV0 ð Þ 1 ðÞc ðÞv 2 ðÞc ðÞv 2 ðÞ ð Þ ð Þ ð Þ ðcÞ v ð Þ¼ - π½t - 0:5ðÞt þt =½0:6ðÞt þt ; ð Þ are t c ; t v ; f AR , k; F c CBV =CBV (the normalized capillary baseline hG - LP t ðÞ ðÞ e 5 c 0 0 0:6 t c þ t v blood volume contribution), and α. fi fi where H(t) is the Heaviside unit step function (H(t) = 0 for to0; H(t) = 1 for The six unknown parameters could be tted for using a tting algorithm fi fl t ⩾ 0). Since we are considering cases in which cmro (t) contributions are in MATLAB (function lsqcurve t) with a trust region re ective algorithm. 2 The fitting procedure considers as input values the measured absolute negligible, we set cmro2 = 0. Total blood volume changes can be written as ð Þ CBV a a weighted average of arterial and venous volume changes: hemoglobin concentration time traces (O(t), D(t)), MAP(t), as well as 0 , CBV0 ðÞ ðÞ and finds the optimal set of the six unknown parameters by minimizing a ΔTtðÞ CBV a CBV v cbvðtÞ¼ ¼ 0 cbvðÞa ðtÞþ 0 cbvðÞv ðÞt ; ð6Þ cost function (Χ2). The stopping criterion for the fit was estimated based on T 0 CBV0 CBV0 the variances of the measured data. We have used 96 different sets of

with T0 = ctHb CBV0. initial guesses for the six unknown parameters, which were evenly spread The cerebral autoregulation process can be described as a high-pass throughout the range of upper and lower bounds of the parameters. For filter that regulates CBF dynamics in response to MAP changes.11,17,22,34 In each initial guess, the solutions of the six parameters were stored for the case of sinusoidal oscillations, this description implies that MAP further analysis. oscillations at high frequencies do not result in regulated blood flow (i.e., CBF oscillates in phase with MAP), whereas MAP oscillations at low Statistical Analysis frequencies result in a regulated blood flow (i.e., CBF does not oscillate and stays constant). The reference frequency to quantify ‘high’ and ‘low’ All statistical analyses were performed in MATLAB. A group-level-based, nonparametric one-tailed signed-rank test was performed for determining frequencies in the previous sentence is the cutoff frequency for fi ð Þ statistically signi cant differences between normal breathing and hyper- autoregulation f AR at which CBF oscillations feature an amplitude pffiffiffi c ventilation for all the six model output parameters. that is 1= 2 (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 autoregula- RESULTS 3,11,20–22 tion is common, we are aware of only a few studies that are Figure 2 shows a typical measurement time series. The top panel explicitly based on a high-pass filter analysis involving the concept of 11,17,35 shows the cuff pressure, which was set to 200 mmHg during autoregulation cutoff frequency. In this work, we focus on the normal breathing and hyperventilation. The center panel shows assessment of autoregulation cutoff frequencies as a measure of the low-pass filtered (below 0.15 Hz) time traces of O(t) and D(t), effectiveness of cerebral autoregulation: namely, the higher the cutoff fi frequency, the better the suppression of CBF oscillations at any frequency, where O(t) decreases signi cantly after the cuff pressure is and the better the autoregulation. released whereas D(t) increases. The bottom panel shows the In our NIRS approach, which implements the novel technique of time traces of T(t) and MAP. T(t) follows MAP closely, with a small Coherent Hemodynamics Spectroscopy (CHS),23 we aim to express cerebral time delay as indicated in the insets. No time delay was seen autoregulation in terms of optically measured hemodynamic quantities between T(t) and MAP at the cardiac pulsation frequency, which that pertain to the microvasculature within a localized tissue region. This allowed for calculating the arterial baseline contribution to the ð Þ differs from the more standard approach based on systemic measure- total blood volume (CBV a =CBV ) based on Equation (9). The fl 0 0 ments of MAP and on measurements of the blood ow velocity in the group averaged (over the 11 subjects) arterial blood volume MCA. The dynamics of CBF, described by cbf(t) in Equations (1) and (2), are ðaÞ= ¼ : 7 : % representative of relative changes in the local CBF.26 The blood volume fraction was found to be CBV0 CBV0 3 9 0 5 , during both oscillations described by cbv(t) in Equation (6) provide a local measure- normal breathing and hyperventilation, and it was time indepen- ment of vascular expansion and contraction, and are closely related to the dent, showing the robustness of the method. MAP. In fact, it was reported that oscillations in cbv (measured with NIRS) A representative case of the model fit to the data over the and MAP are essentially synchronous, with a nonsignificant phase 10 seconds immediately after the thigh-cuff release is seen in difference at a frequency of 0.1 Hz.16,18 For these reasons, we opted to Figure 3. The top panel shows the measured hemoglobin traces express the local cerebral autoregulation at the level of microcirculation in (symbols) and the model fit (continuous lines). For clarity purposes terms of focal NIRS measurements of cbf(t) and cbv(t) according to the of the figure only, the data have been referenced to baseline following relationship.23 hemoglobin values, with ΔO(t)=O(t) − O0 and ΔD(t)=D(t) − D0. The ð Þ¼ ðARÞ ð Þ ð Þ; ð Þ fit shown is the mean of the 96 independent fits. Black symbols cbf t khRC - HP t cbv t 7 ð Þ and lines refer to normal breathing, and gray symbols and lines where k is the inverse of the modified Grubb’s exponent, h AR ðtÞ is the RC - HP refer to hyperventilation. The center panel shows percentage resistor-capacitor high-pass impulse response function with cutoff ðARÞ changes in MAP after the cuff release. For both normal breathing frequency f c that describes the effect of autoregulation, and * denotes a temporal convolution. The resistor-capacitor high-pass impulse response and hyperventilation, MAP stays low for the 10 seconds consid- function is given by: ered for the data analysis. The bottom panel shows the measured cbv(t) (dashed lines) and the estimated cbf(t) on the basis of ðÞAR 1 - t h ðtÞ¼ - e τ þ δðÞt ; ð8Þ Equation (7) (solid lines). The estimated cbf(t) traces shown are RC - HP τ based on the mean of those cbf(t) traces obtained for the 96 initial τ ¼ =oðARÞ oðARÞ ¼ π ðARÞ δ where 1 c (with c 2 f c ) and is the Dirac delta. guesses. Since autoregulation increases during hyperventilation, Since MAP was measured continuously, access to arterial blood volume cbf(t) was expected to recover faster during hyperventilation than changes was possible by assuming a proportional dependence of arterial ð Þ Δ ðÞ during normal breathing. This behavior was found in the data as blood volume on MAP, so that cbv a ðtÞ¼ MAP t . T(t) is determined by a MAP0 fi weighted average of venous and arterial blood volume changes, and by seen in Figure 3 (bottom panel) and was quanti ed by the cutoff frequency of autoregulation defined by Equation 8. the baseline hemoglobin concentration T0. The baseline arterial blood volume fraction could be estimated from oscillatory T(t) at the heart rate by Figure 4A shows the autoregulation cutoff frequency of all 11 assuming that only arterial blood contributes to a volume change because subjects, where the black bars indicate the cutoff frequency of the cardiac pulsation. By filtering the measured relative total during normal breathing and gray bars during hyperventilation.

Journal of Cerebral Blood Flow & Metabolism (2015), 959 – 966 © 2015 ISCBFM Microvascular autoregulation with NIRS JM Kainerstorfer et al 963 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. 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.39–42 The capillary compartment contribution to the total ð Þ FðcÞCBV c baseline blood volume, 0 , was found to be ~ 0.5, which also CBV0 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 Figure 3. Typical time traces after thigh-cuff release (data from (α) of 0.4 to 1.2 per second. ðARÞ ¼ subject 3). Symbols in the top panel show measured hemoglobin The autoregulation cutoff frequency was found to be f c concentrations, solid lines show the model fit. Black indicates 0:0177002Hz during normal breathing, and 0.034 ± 005 Hz normal breathing and gray indicates hyperventilation. The center during hyperventilation. This increase was found to be significant panel reports measured mean arterial blood pressure (MAP) traces, (p = 0.006) based on a one-tailed signed-rank test. None of the showing the typical drop in MAP after thigh-cuff release. The fi bottom panel shows measured cerebral blood volume, cbv(t) other parameters changed signi cantly during hyperventilation. (dashed lines), and cerebral blood flow, cbf(t) (solid lines), calculated As we mentioned above, we are aware of very few published based on the autoregulation description in Equation (7). The cbf studies that referred to an autoregulation cutoff frequency. Blaber traces during hyperventilation (enhanced autoregulation) show a et al11 stated the use of an autoregulation cutoff frequency of faster recovery to baseline in comparison to normal breathing. 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 The error bars are the s.d. of the 96 solutions of the fit. Figure 4B frequency. Rather, Blaber et al used the term to describe the reports the difference of the autoregulation cutoff frequencies frequency range (0 to 0.15 Hz), in which autoregulation is effective. measured during hyperventilation and normal breathing, respec- A more explicit measurement of autoregulation cutoff frequency 35 tively, and shows an increase in cutoff frequency during hyper- of 0.03 Hz has been reported by Fraser et al on the basis of a ventilation in 10 out of 11 subjects. To evaluate the reproducibility Butterworth high-pass filter analysis of phase differences (at of our measurements, we retested 4 of the 11 subjects, who were multiple frequencies) between arterial blood pressure and able to come back for additional measurements (subjects 1, 2, 9, intracranial pressure in a neonatal swine model. Because of the and 11). Figure 4C shows the results of the repeated measure- broad range of phase differences considered and the different ments. In these subjects, we reproduced the previously observed quantities used (MAP, MCA blood flow velocity, and intracranial ðÞAR changes in f c induced by hyperventilation (increase in subjects pressure), the above reference values may not serve as much 1, 2, and 11; decrease in subject 9). The repeated measurements more than order of magnitude references to our results. However, on these subjects have been performed on different days, with the a more significant reference to our results is the study of the effect ’ optical probe placed at slightly different locations on the subject s of hypocapnia (achieved here with hyperventilation) on auto- forehead. The varying location of the imaging probe may account 9 ðÞAR regulation, as measured by Aaslid et al by recording the response for the within-subject variability of f c and also suggests how of CBFV to a step change in arterial blood pressure (step these local measurements may be extended to imaging and response). By considering the resistor-capacitor high-pass filter mapping of cerebral autoregulation over extended areas of the considered by us, the relationship between the time to recovery to cerebral cortex. However, the repeated measurements on these half of the baseline CBF value (t0.5) is related to the cutoff four subjects indicate that the method is robust for measuring ðARÞ ffi : = frequency introduced by us as follows: f c 0 11 t0:5. The values local changes in autoregulation within individual subjects, and not 9 just at a group level. for t0.5 reported by Aaslid et al during normocapnia (3.4 seconds) Table 1 summarizes the group averages of all the six model and hypercapnia (1.9 seconds) can be translated into cutoff parameters during the two conditions. Values are given as the mean frequencies, as defined by us, of ~ 0.03 Hz (normocapnia) and and standard error of the measurements across all subjects. The ~ 0.06 Hz (hypercapnia), respectively. These results are in qualita- transit time in the capillaries was found to be 1.1 seconds, which tive agreement with our results, and also in good quantitative falls into the reported range of 0.3 to 1.7 seconds, as measured on agreement (considering, again, that different quantities were rats with fluorescence videography.36,37 The transit time in the veins measured in our study and in the study by Aaslid et al9).

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. Output parameters of the model ﬁt

Capillary transit Venous transit Autoregulation cutoff Inverse of Capillary blood Rate constant of oxygen (c) (v) ðARÞ ð Þ time t (seconds) time t (seconds) frequency f ðHzÞ modiﬁed Grubb's FðcÞCBV c diffusion α (per second) c volume ratio 0 exponent (k) CBV0

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

DISCUSSION the dynamics of local cbf(t), as reflected in the autoregulation We have shown that the cerebral autoregulation enhancement cutoff frequency, might be dependent on the relative amount of induced by hyperventilation can be measured locally in the venous and arterial blood present in the tissue sampled. The microvasculature by NIRS together with the dynamic hemody- amount of venous blood relative to arterial blood depends on the namic model we recently introduced. By describing dynamic tissue imaged and hence the location of the optical sensor. autoregulation in terms of a high-pass filter between cbv(t) and This could therefore explain, at least in part, the intersubject cbf(t), we have found an increase in autoregulation cutoff (Figure 4A) and the intrasubject (Figure 4C) variability observed in ðÞAR ðÞAR frequency, which corresponds to a faster response of cbf to cbv f c . Nevertheless, a reliable increase in f c was found with during hyperventilation compared with normal breathing. Auto- subjects performing hyperventilation, showing the robustness of regulation is defined as the mechanism that maintains constant the method for monitoring purposes. The issue of the inclusion of cbf(t) despite changes in MAP, where the recovery time of cbf(t)is venous contributions to cbv(t), possibly through optimal weight indicative of autoregulation. The majority of studies on auto- factors in Equation (6), is an open area of research in our effort to regulation have used the dynamics of blood flow as measured further develop and refine the methods introduced in this work. with TCD in the MCA in relation to MAP. Here, we have introduced In the frequency-domain version of Equation (7), the impulse a novel way of measuring autoregulation, which is based on local response function of Equation (8) is replaced by a complex cbv(t), rather than systemic MAP, and microvascular cbf(t). This transfer function that specifies the phase difference between proposed approach has a twofold appeal: first, it is based on a oscillations of CBF and CBV at a given frequency.26 By carrying out local measurement of vascular dilation/constriction that is this transfer function analysis, and by using the frequency-domain hypothesized to be closely linked to local blood pressure versions of Equations (1) and (2) together with the model perturbations; second, it relies on measurements with the same parameters obtained and reported in Table 1, we have found a technology that is sensitive to local changes in CBF, thus realizing phase difference of − 276° between D and O oscillations at a a self-contained and spatially congruent technology for local frequency of 0.1 Hz. These numbers agree well with literature autoregulation assessment. Although the delay between cbv(t) values, where O and D oscillations associated with paced and MAP(t) is small (o2 seconds as seen in Figure 2), our method breathing at 0.1 Hz were reported to be − 260°49 and − 200°16 in inherently takes contributions of venous volume change, cbv(v)(t), healthy volunteers. The phase difference between oscillations of into account. Since the arterial and venous blood volume changes CBF and CBV at 0.1 Hz, considering the average autoregulation exhibit different dynamic behaviors,47,48 there is a possibility that cutoff frequencies of 0.017 Hz (normal breathing) and 0.034 Hz

Journal of Cerebral Blood Flow & Metabolism (2015), 959 – 966 © 2015 ISCBFM Microvascular autoregulation with NIRS JM Kainerstorfer et al 965 (hyperventilation) were found to be 10° and 20°, respectively. This extracerebral tissue (scalp, skull, etc.). Results indicate that the phase difference is lower than the reported 60° between MAP and superficial layers (shortest source-detector distance) do not exhibit CBF oscillations measured in the MCA.16 Again, this discrepancy the same dynamics as deeper layers. Specifically, we found that may be explained by the fact that in Equation (7) we are after the cuff pressure release, deoxy-hemoglobin and oxy- considering local microvascular blood volume changes rather than hemoglobin concentration responses are approximately synchro- systemic MAP changes. However, the measured increase in nous and both decreasing at the short source–detector distance autoregulation during hyperventilation has proven to be robust. (not sensitive to brain tissue), whereas they are asynchronous and Furthermore, the magnitude of the reported CBF change in opposite directions (Figure 3) at the long source–detector corresponds well to literature values. Although, in response to distance (sensitive to brain tissue). This indicates that superficial the fast release of the thigh-cuff pressure, MAP typically drops by tissue layers are dominated by blood volume changes, whereas 9 10% to 20% and the MCA blood flow velocity (measured by TCD) blood flow changes also contribute to the signals originating at also drops by ~ 20%, we have found that local cbv changes deeper cerebral tissue. The significant differences between the (measured by NIRS) are much smaller (o2%), yielding micro- temporal dynamics of the measured signals at a short source– vascular cbf changes in the order of ~ 4%. detector distance (exclusively sensitive to superficial extracerebral Besides the autoregulation cutoff frequency, the other model tissue) and at a long source–detector distance (sensitive to both fi parameters did not show a signi cant difference between normal extracerebral and cerebral tissue) gives us confidence about the breathing and hyperventilation. A constant transit time in the fi (c) negligible contribution of super cial tissues to our dynamic capillary compartment, t , translates into unaltered mean measurements of autoregulation. However, this is an important capillary and venous saturations. The group averaged capillary question that we are still exploring in our further development of ðcÞ % saturation was S 73 and the venous saturation was this technique. 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 CONCLUSION the assessment of capillary and venous saturations noninvasively, Maintaining an adequate blood perfusion is of paramount it shall be pointed out that the capillary transit time is coupled α importance for brain health. Cerebral autoregulation plays a critical with the rate constant of oxygen diffusion, , through the product role and is known to be impaired in a number of pathologic αt(c) in the expressions for S(c) and S(v), whereas t(c) appears α conditions such as stroke, subarachnoid hemorrhage, and bacterial independently of in the capillary and venous impulse response meningitis. There are clinical situations, for example cardiopulmon- functions (see Equations (4) and (5)). This is the basis for our ary bypass and general anesthesia, where monitoring cerebral separate determination of t(c) and α reported in Table 1. autoregulation could help prevent brain damage and guide Within the measured tissue volume accessed with NIRS on the adjustments to the procedure. There are also brain development prefrontal cortex, we have found that the capillary compartment areas of study, such as the mechanisms that lead to the establish- contributes ~ 50% of the total baseline volume (Table 1). Since we ment of cerebral autoregulation in newborn babies, which can have estimated the arterial contribution to be only ~ 4%, the benefit from autoregulation monitoring techniques. We have venous contribution results in ~ 46% of the overall measured hemoglobin signals. Although our estimated arterial contribution presented a novel, noninvasive approach (Coherent Hemodynamics is much lower than reported values of ~ 30%,50 it shall be pointed Spectroscopy) to the assessment of local cerebral autoregulation out that we have considered only the pulsatile signal of the through optical measurements that are mostly sensitive to the cardiac pulsation, which is dominant in large arteries. Conse- microvasculature. For the presented approach, systemic MAP quently, we may have underestimated the contributions of changes have to be induced to affect the blood volume and blood fl arterioles, which have a weaker pulsatile signature, to the arterial ow in the cerebral microvasculature. Here, we have used a 2- blood volume. In addition, we have assumed a proportional minute arterial thigh-cuff occlusion and sudden release to achieve relationship between arterial blood volume and MAP (see rapid MAP changes. The induced drop in MAP is typically in the Equation (9)). A power law between arterial blood volume and order of 10% to 20% of its baseline value, which is about two times fl MAP may be a better approximation and would result in a greater greater than spontaneous MAP uctuations. Although this cuff estimated arterial blood volume. Preliminary results based on a method has been used in vulnerable patients, such as traumatic 51,52 power law relationship (data not shown) indeed yield a greater brain injury patients, and has been shown to be safe, other arterial blood volume, but the autoregulation cutoff frequency is methods to induce MAP changes can also be used. largely unaffected. Our results pave the way for a variety of applications in which The model fit was performed on measured absolute concentra- the noninvasive assessment and monitoring of cerebral auto- tions of hemoglobin, which we obtained with frequency-domain regulation is important. Furthermore, the local sensitivity of the NIRS. We have also evaluated the model fit if only relative proposed measurements lends itself to imaging applications, changes, as measured with continuous-wave NIRS systems, are allowing for mapping cerebral autoregulation effectiveness over available. In this case, the value of baseline hemoglobin extended brain areas. concentration has to be assumed rather than measured. We have found (data not shown) that while some of the model parameters, DISCLOSURE/CONFLICT OF INTEREST in particular t(c), depend on the specific value assumed for the baseline hemoglobin concentration, the autoregulation cutoff The authors declare no conflict of interest. frequency is independent of such assumption. Therefore, the method proposed here for measurements of local cerebral REFERENCES autoregulation is robust and can be used even if only relative changes in hemoglobin concentrations are measured. 1 Lassen NA. Cerebral blood flow and oxygen consumption in man. Physiol Rev 39 – Because NIRS is sensitive to superficial layers, as well as brain 1959; :183 238. fi 2 Paulson OB, Strandgaard S, Edvinsson L. Cerebral autoregulation. Cerebrovasc tissue, we investigated whether super cial layer contamination Brain Metab Rev 1990; 2: 161–192. would possibly alter the results. For this, we repeated the 3 Panerai RB. Assessment of cerebral pressure autoregulation in humans—a review experiments on three additional subjects, where the optical probe of measurement methods. Physiol Meas 1998; 19:305–338. was equipped with an additional small source–detector separation 4 Lassen NA. Control of cerebral circulation in health and disease. Circ Res 1974; 34: (0.75 cm), which yields data that is only sensitive to superficial 749–760.

© 2015 ISCBFM Journal of Cerebral Blood Flow & Metabolism (2015), 959 – 966 Microvascular autoregulation with NIRS JM Kainerstorfer et al 966 5 Tietjen CS, Hurn PD, Ulatowski JA, Kirsch JR. Treatment modalities for hyperten- 30 Kuschinsky W, Paulson OB. Capillary circulation in the brain. Cerebrovasc Brain sive patients with intracranial pathology: options and risks. Crit Care Med 1996; 24: Metab Rev 1992; 4:261–286. 311–322. 31 Villringer A. The intravascular susceptibility effect and the underlying physiology 6 Paulson OB, Waldemar G, Andersen AR, Barry DI, Pedersen EV, Schmidt JF et al. of fMRI. Neuroimage 2012; 62:995–999. Role of angiotensin in autoregulation of cerebral blood flow. Circulation 1988; 77: 32 Villringer A, Them A, Lindauer U, Einhaupl K, Dirnagl U. Capillary perfusion I55–158. of the rat brain cortex. An in vivo confocal microscopy study. Circ Res 1994; 75: 7 Numan T, Bain AR, Hoiland RL, Smirl JD, Lewis NC, Ainslie PN. Static autoregulation 55–62. in humans: a review and reanalysis. Med Eng Phys 2014; 36: 1487–1495. 33 Zoccoli G, Lucchi ML, Andreoli E, Bach V, Cianci T, Lenzi P et al. Brain capillary 8 Early CB, Dewey RC, Pieper HP, Hunt WE. Dynamic pressure-flow relationships of perfusion during sleep. J Cereb Blood Flow Metab 1996; 16: 1312–1318. brain blood flow in the monkey. J Neurosurg 1974; 41: 590–596. 34 Haubrich C, Kruska W, Diehl RR, Moller-Hartmann W, Klotzsch C. Dynamic auto- 9 Aaslid R, Lindegaard KF, Sorteberg W, Nornes H. Cerebral autoregulation regulation testing in patients with middle cerebral artery stenosis. Stroke 2003; 34: dynamics in humans. Stroke 1989; 20:45–52. 1881–1885. 10 Panerai RB. Transcranial Doppler for evaluation of cerebral autoregulation. Clin 35 Fraser CD 3rd, Brady KM, Rhee CJ, Easley RB, Kibler K, Smielewski P et al. The Auton Res 2009; 19:197–211. frequency response of cerebral autoregulation. J Appl Physiol 2013; 115:52–56. 11 Blaber AP, Bondar RL, Stein F, Dunphy PT, Moradshahi P, Kassam MS et al. Transfer 36 Jespersen SN, Ostergaard L. The roles of cerebral blood flow, capillary transit time function analysis of cerebral autoregulation dynamics in autonomic failure heterogeneity, and oxygen tension in brain oxygenation and metabolism. J Cereb patients. Stroke 1997; 28: 1686–1692. Blood Flow Metab 2012; 32: 264–277. 12 Mankovsky BN, Piolot R, Mankovsky OL, Ziegler D. Impairment of cerebral auto- 37 Stefanovic B, Hutchinson E, Yakovleva V, Schram V, Russell JT, Belluscio L et al. regulation in diabetic patients with cardiovascular autonomic neuropathy and Functional reactivity of cerebral capillaries. J Cereb Blood Flow Metab 2008; 28: 20 – orthostatic hypotension. Diabet Med 2003; : 119 126. 961–972. 13 Vokatch N, Grotzsch H, Mermillod B, Burkhard PR, Sztajzel R. Is cerebral auto- 38 Cassot F, Lauwers F, Fouard C, Prohaska S, Lauwers-Cances V. A novel three- regulation impaired in Parkinson's disease? A transcranial Doppler study. J Neurol dimensional computer-assisted method for a quantitative study of microvascular 254 – Sci 2007; :49 53. networks of the human cerebral cortex. Microcirculation 2006; 13:1–18. 14 Eames PJ, Blake MJ, Dawson SL, Panerai RB, Potter JF. Dynamic cerebral auto- 39 Grubb RL Jr., Raichle ME, Eichling JO, Ter-Pogossian MM. The effects of changes in regulation and beat to beat blood pressure control are impaired in acute PaCO on cerebral blood volume, blood flow, and vascular mean transit time. 72 – 2 ischaemic stroke. J Neurol Neurosurg Psychiatry 2002; : 467 472. Stroke 1974; 5: 630–639. 15 Tiecks FP, Lam AM, Aaslid R, Newell DW. Comparison of static and dynamic 40 Kida I, Rothman DL, Hyder F. Dynamics of changes in blood flow, volume, and 26 – cerebral autoregulation measurements. Stroke 1995; : 1014 1019. oxygenation: implications for dynamic functional magnetic resonance imaging 16 Reinhard M, Wehrle-Wieland E, Grabiak D, Roth M, Guschlbauer B, Timmer J et al. calibration. J Cereb Blood Flow Metab 2007; 27:690–696. Oscillatory cerebral hemodynamics—the macro- vs. microvascular level. J Neurol 41 Leung TS, Tachtsidis I, Tisdall MM, Pritchard C, Smith M, Elwell CE. Estimating a Sci 2006; 250:103–109. modified Grubb's exponent in healthy human brains with near infrared spec- 17 Diehl RR, Linden D, Lucke D, Berlit P. Phase relationship between cerebral blood troscopy and transcranial Doppler. Physiol Meas 2009; 30:1–12. flow velocity and blood-pressure. A clinical test of autoregulation. Stroke 1995; 26: 42 Mandeville JB, Marota JJ, Ayata C, Moskowitz MA, Weisskoff RM, Rosen BR. MRI 1801–1804. measurement of the temporal evolution of relative CMRO(2) during rat forepaw 18 Cheng R, Shang Y, Hayes D Jr., Saha SP, Yu G. Noninvasive optical evaluation of stimulation. Magn Reson Med 1999; 42: 944–951. spontaneous low frequency oscillations in cerebral hemodynamics. Neuroimage 43 Kasischke KA, Lambert EM, Panepento B, Sun A, Gelbard HA, Burgess RW et al. 2012; 62: 1445–1454. Two-photon NADH imaging exposes boundaries of oxygen diffusion in cortical 19 Aaslid R, Blaha M, Sviri G, Douville CM, Newell DW. Asymmetric dynamic cerebral vascular supply regions. J Cereb Blood Flow Metab 2011; 31:68–81. autoregulatory response to cyclic stimuli. Stroke 2007; 38: 1465–1469. 44 Masamoto K, Kershaw J, Ureshi M, Takizawa N, Kobayashi H, Tanishita K et al. 20 Panerai RB. Nonstationarity of dynamic cerebral autoregulation. Med Eng Phys Apparent diffusion time of oxygen from blood to tissue in rat cerebral cortex: 2014; 36: 576–584. implication for tissue oxygen dynamics during brain functions. J Appl Physiol 2007; 21 Panerai RB, Rennie JM, Kelsall AW, Evans DH. Frequency-domain analysis of cer- 103:1352–1358. ebral autoregulation from spontaneous fluctuations in arterial blood pressure. 45 Masamoto K, Kurachi T, Takizawa N, Kobayashi H, Tanishita K. Successive depth Med Biol Eng Comput 1998; 36:315–322. 22 Zhang R, Zuckerman JH, Giller CA, Levine BD. Transfer function analysis of variations in microvascular distribution of rat somatosensory cortex. Brain Res 995 – dynamic cerebral autoregulation in humans. Am J Physiol 1998; 274: H233–H241. 2004; :66 75. fl 23 Fantini S. Dynamic model for the tissue concentration and oxygen saturation of 46 Pardridge WM. Drug transport in brain via the cerebrospinal uid. Fluids Barriers 8 – hemoglobin in relation to blood volume, flow velocity, and oxygen consumption: CNS 2011; :1 4. fi implications for functional neuroimaging and coherent hemodynamics 47 Kim T, Kim SG. Temporal dynamics and spatial speci city of arterial and venous fi spectroscopy (CHS). Neuroimage 2014; 85:202–221. blood volume changes during visual stimulation: implication for BOLD quanti - 31 – 24 Blaha M, Aaslid R, Douville CM, Correra R, Newell DW. Cerebral blood flow and cation. J Cereb Blood Flow Metab 2011; : 1211 1222. dynamic cerebral autoregulation during ethanol intoxication and hypercapnia. J 48 Lee SP, Duong TQ, Yang G, Iadecola C, Kim SG. Relative changes of cerebral fl Clin Neurosci 2003; 10: 195–198. arterial and venous blood volumes during increased cerebral blood ow: impli- 45 – 25 Panerai RB, Deverson ST, Mahony P, Hayes P, Evans DH. Effect of CO2 on dynamic cations for BOLD fMRI. Magn Reson Med 2001; : 791 800. cerebral autoregulation measurement. Physiol Meas 1999; 20: 265–275. 49 Obrig H, Neufang M, Wenzel R, Kohl M, Steinbrink J, Einhaupl K et al. Spontaneous 26 Fantini S. A new hemodynamic model shows that temporal perturbations of low frequency oscillations of cerebral hemodynamics and metabolism in cerebral blood flow and metabolic rate of oxygen cannot be measured indivi- human adults. Neuroimage 2000; 12:623–639. dually using functional near-infrared spectroscopy. Physiol Meas 2014; 35:N1–N9. 50 Ito H, Kanno I, Iida H, Hatazawa J, Shimosegawa E, Tamura H et al. Arterial fraction 27 Fantini S. A haemodynamic model for the physiological interpretation of in vivo of cerebral blood volume in humans measured by positron emission tomography. measurements of the concentration and oxygen saturation of haemoglobin. Phys Ann Nucl Med 2001; 15:111–116. Med Biol 2002; 47: N249–N257. 51 Christ M, Noack F, Schroeder T, Hagmueller A, Koch R, May SA et al. Continuous 28 Chen JL, Wei L, Acuff V, Bereczki D, Hans FJ, Otsuka T et al. Slightly altered cerebral autoregulation monitoring by improved cross-correlation analysis: permeability-surface area products imply some cerebral capillary recruitment comparison with the cuff deflation test. Intensive Care Med 2007; 33: 246–254. during hypercapnia. Microvasc Res 1994; 48:190–211. 52 Sviri GE, Aaslid R, Douville CM, Moore A, Newell DW. Time course for auto- 29 Gobel U, Klein B, Schrock H, Kuschinsky W. Lack of capillary recruitment in the brains regulation recovery following severe traumatic brain injury. J Neurosurg 2009; of awake rats during hypercapnia. J Cereb Blood Flow Metab 1989; 9:491–499. 111:695–700.