Can Alterations in Cerebrovascular CO2 Reactivity Be Identified Using Transfer Function Analysis without the Requirement for Carbon Dioxide Inhalation?

The present study aimed to examine the validity of a novel method to assess cerebrovascular carbon dioxide (CO2) reactivity (CVR) that does not require a CO2 inhalation challenge, e.g., for use in patients with respiratory disease or the elderly, etc. In twenty-one healthy participants, CVR responses to orthostatic stress (50° head-up tilt, HUT) were assessed using two methods: (1) the traditional CO2 inhalation method, and (2) transfer function analysis (TFA) between middle cerebral artery blood velocity (MCA V) and predicted arterial partial pressure of CO2 (PaCO2) during spontaneous respiration. During HUT, MCA V steady-state (i.e., magnitude) and MCA V onset (i.e., time constant) responses to CO2 inhalation were decreased (p < 0.001) and increased (p = 0.001), respectively, indicative of attenuated CVR. In contrast, TFA gain in the very low-frequency range (VLF, 0.005–0.024 Hz) was unchanged, while the TFA phase in the VLF approached zero during HUT (−0.38 ± 0.59 vs. 0.31 ± 0.78 radians, supine vs. HUT; p = 0.003), indicative of a shorter time (i.e., improved) response of CVR. These findings indicate that CVR metrics determined by TFA without a CO2 inhalation do not track HUT-evoked reductions in CVR identified using CO2 inhalation, suggesting that enhanced cerebral blood flow response to a change in CO2 using CO2 inhalation is necessary to assess CVR adequately.


Introduction
An increase in the partial pressure of arterial carbon dioxide (PaCO 2 ) leads to a dilatation of the cerebral blood vessels. This mechanism of cerebral blood flow (CBF) regulation is termed cerebrovascular CO 2 reactivity (CVR) and functions alongside the central respiratory chemoreflex to help maintain brain pH homeostasis [1][2][3]. Increases in PaCO 2 lower brain pH, which modulates enzyme and ion channel activity [4], meaning that CVR is important for maintaining brain function [1]. Accordingly, the assessment of CVR is used worldwide to directly evaluate brain vascular health [5]. For example, an impaired CVR is related to mild cognitive impairment [6] and Alzheimer's disease [7], and has been identified in cardiovascular, cerebrovascular, and neurological disorders [8][9][10][11]. These previous findings suggest that CVR measurements have clinical utility in the prediction of brain disease.
Several methodologies have been established to identify CVR in humans using timedomain analysis [2,[12][13][14][15][16][17][18] and frequency-domain analyses (e.g., transfer function analysis (TFA), autoregressive moving average analysis, or support vector machines) [3,[19][20][21][22][23]. In these methodologies, a CO 2 inhalation challenge has been used to accurately determine CVR via an increase in the response range of CBF because fluctuations in CO 2 are relatively small during spontaneous respiration without CO 2 inhalation. However, CO 2 inhalation may cause acute stress that produces intense behavioral and physiological responses in humans [24], such as transient elevations of blood pressure (i.e., the fight-orflight response) [23,25]. Acute stress can have a vasoconstrictive effect on the peripheral vasculature [26], with the potential to indirectly modify CVR. In addition, CO 2 inhalation can cause anxiety, which has been reported to enhance CVR [27]. CO 2 inhalation also causes hyperventilation via the respiratory chemoreflex [2], which modifies the CBF response to a change in CO 2 [28]. Therefore, it is possible that these physiological responses induced by CO 2 inhalation modify CVR independent from hypercapnia-induced direct cerebral vasodilation. Moreover, CO 2 inhalation for identifying CVR has both financial and time implications [29]. Given these issues, a method for accurately determining CVR without the need for CO 2 inhalation would be advantageous, such as for patients with respiratory disease or the elderly, etc. The use of TFA to quantify the relationship between spontaneously occurring fluctuations in CBF and the partial pressure of end-tidal CO 2 (P ET CO 2 ), akin to the assessment of dynamic cerebral autoregulation [30], may provide an easy (no intervention) and stress-free method for determining CVR.
Given this background, the aim of the present study was to examine the validity of the method (TFA) under spontaneous respiration without CO 2 inhalation for assessing CVR. In our recent study [31], we observed that orthostatic stress (50 • head-up tilt, HUT) attenuated CVR determined by traditional methods (i.e., magnitude response or time response, τ). In the present study, the change in CVR during 50 • HUT from supine was assessed using the TFA between middle cerebral artery blood velocity (MCA V) and predicted PaCO 2 during spontaneous respiration (at the operating point) to compare with CVR indices determined using the traditional methods with a CO 2 inhalation challenge. We hypothesized that the CVR determined by TFA without CO 2 inhalation attenuated during HUT if this new method is valid to determine CVR.

Ethics
The experimental protocol was approved by the Institutional Review Board at Toyo University (Approval Number: 2019-045) and each participant provided written informed consent before participation. The study was undertaken in accordance with the principles of the Declaration of Helsinki.

Participants
Twenty-one healthy adults participated in this study (13 men and 8 women; age, 23 ± 3 years; stature, 166.8 ± 9.6 cm; body mass, 59.4 ± 12.4 kg, mean ± standard deviation). All participants were non-smokers, free of any cerebrovascular and/or cardiovascular diseases, and were not taking any over-the-counter and/or prescribed medications. Before the experiment, participants were required to abstain from caffeinated beverages, strenuous exercise, and alcohol for 24 h [32]. Furthermore, the participants were instructed to consume a light meal at least 4 h before the start of the experiment.

Study Design
All measurements were performed on the same day for each participant. CVR was determined in two body positions: supine and 50 • head-up tilt (HUT). The order of the supine and 50 • HUT conditions was randomized for each participant. After instrumentation, participants were placed on the tilt table. It takes a few minutes for fluid shifts to reach equilibrium following a change in body position [33], and positional changes also alter pulmonary ventilation [34], taking~7-8 min to reach steady-state subsequent to chemoreflex activation [35]. Therefore, each condition began with a 20 min rest, following which 5 min of baseline data were obtained while participants spontaneously breathed room air. After the baseline recording was completed, participants were switched to inspiring a gas mixture from a Douglas bag containing 5% CO 2 and 21% O 2 , balanced with N 2 . The hypercapnia induced by a rapid change in the F I CO 2 lasted for 12 min to ensure a steady-state equilibration was achieved. After the first condition, the body position was changed (supine to 50 • HUT or 50 • HUT to supine), and once again participants rested for at least 20 min while inspiring room air. The baseline and hypercapnia protocol were repeated. Room temperature was set at 24-25 • C.

Measurements
Heart rate (HR) was measured using a lead II electrocardiogram (bedside monitor, BMS-3400; Nihon Kohden, Tokyo, Japan). Beat-to-beat arterial blood pressure (ABP) was monitored continuously using a finger photoplethysmography (Finometer Pro; Finapres Medical Systems, Amsterdam, The Netherlands) with a cuff placed on the middle finger of the left hand, which was supported at the level of the right atrium in the mid-axillary line. Mean MCA V (MCA V mean ), an index of CBF, was measured through the right temporal window using a transcranial Doppler ultrasonography (TCD) system (DWL Doppler Box-X; Compumedics, Singen, Germany). The TCD probe was fixed in position using a dedicated headband (Elastic Headband T; Compumedics) to maintain a constant insonation angle throughout the experiment. For the characterization of respiratory responses to hypercapnia (CO 2 inhalation), participants breathed through a leak-free face mask attached to a flowmeter and two-way valve. The valve mechanism allowed participants to inspire room air or a gas mixture from a 300 L Douglas bag. Respiratory rate (RR), pulmonary ventilation (V E ), tidal volume (V t ), and P ET CO 2 were measured breath-by-breath using an automated gas analyzer (AE-310S, Minato Medical Science, Osaka, Japan).

Data Analysis
All data were sampled continuously at 1 kHz using an analog-to-digital converter (Power Lab 16 s; AD Instruments, Sydney, Australia) and stored on a laboratory computer for offline analysis. Mean arterial pressure (MAP) and MCA V mean were obtained from each waveform. The predicted PaCO 2 was derived from P ET CO 2 using the following equation [13]: predicted PaCO 2 = 2.367 + 0.884 × P ET CO 2 . Importantly, a previous study demonstrated that the relationship between P ET CO 2 and PaCO 2 was unchanged by changes in central blood volume [36]. During supine and 50 • HUT, all variables were averaged over 120 s immediately before and at the end of CO 2 inhalation for steady-state measurements.
Steady-state change in CO 2 -determined CVR (the magnitude response of CVR): CVR was expressed as the absolute change in MCA V mean per absolute change in PaCO 2 (cm/s/mmHg) using a linear model: MCA V mean = A + B×predicted PaCO 2 , where the CVR is given by the slope B [12,13].
Step-change in CO 2 -determined CVR (time constant, the time response of CVR): Dynamic responses of MCA V mean were evaluated using a one-compartment nonlinear least-squares optimization method [16,17,37]. Before analysis, MCA V mean data was resampled at 10 Hz. The onset response of MCA V mean to the CO 2 inhalation protocol was then fitted to the single-exponential regression equation consisting of the response time latency [CO 2 -response delay (t0)], baseline value, gain term (G), and time constant (τ): where t is time, and MCA V mean 0 is a baseline value. Time 0 reflects the start of CO 2 inhalation ( Figure 1A). The "τ" is used to determine the time response of CVR, and a prolonged τ means a worse/attenuated time response of CVR.
TFA-determined CVR (TFA gain and phase): TFA analysis between predicted PaCO 2 and MCA V mean was performed to evaluate the dynamic CBF response to spontaneously occurring changes in CO 2 during supine and 50 • HUT. The 5 min breath-by-breath (predicted PaCO 2 ) (mmHg) and beat-to-beat (MCA V mean ) (cm/s) data without (5 min steady-state data) CO 2 inhalation were resampled at 4 Hz for spectral analysis [30]. The time series were first detrended with third-order polynomial fitting and then subdivided into 512-point segments with 50% overlap for spectral estimation. For each segment, the linear trend was subtracted and a Hanning window was applied. Following that, frequency-domain transformations were computed with a fast Fourier transformation algorithm. The transfer function H(f) between the two signals was calculated as H(f) = Sxy(f)/Sxx(f), where Sxx(f) is the auto spectrum of changes in predicted PaCO 2 and Sxy(f) is the cross-spectrum between predicted PaCO 2 and MCA V mean . The transfer function magnitude |H(f)| and phase spectrum |Φ(f)| were obtained from the real part HR(f) and imaginary part HI(f) of the complex function. Moreover, the transfer function H(f) was normalized to the mean values of input (x) and output (y) variables as H (f) = [Sxy(f)x]/[Sxx(f)y], and the normalized gain was calculated as 20 log H (f) to provide values in decibels. The TFA coherence, phase, and normalized gain were calculated in the very low (VLF; 0.005-0.024 Hz), low (LF; 0.024-0.15 Hz), and high frequency (HF; 0.15-0.30 Hz) ranges, respectively. This frequency range was determined by previous studies [3,38,39]. Additionally, the dynamic effects of nonlinearities and CO 2 are more prominent in the VLF range [38,39] and TFA gain between predicted PaCO 2 and MCA V mean as an index of dynamic CVR gradually decreased with an increase in frequency over a cut-off frequency (0.024 Hz) [3]. Ogoh et al. [3] have for the first time assessed dynamic CVR in all frequency ranges using a binary white noise sequence (0-7% inspired CO 2 fraction) from the P ET CO 2 to mean MCA V or minute ventilation, respectively. The authors demonstrated that the dynamic characteristics of the relationship between CO 2 inhalation-induced binary white noise of P ET CO 2 and MCA V were maintained below a cut-off frequency of 0.024 Hz but gradually decreased with an increase in frequency over 0.024 Hz. In the present study, therefore, we focused on the TFA parameters within the VLF range below 0.024 Hz to examine the dynamic CVR during spontaneous respiration.

Statistical Analysis
Data from our pilot study (n = 6) were used to perform a prospective power analysis. The critical sample size was estimated to be 19 participants to detect differences in τ assessed by MCA V mean between supine and 50 • HUT conditions, with an assumed type 1 error of 0.05 and statistical power of 80%. Thus, the sample size of the present study was sufficient to achieve the desired statistical assurance. A linear mixed-effects model with fixed-effects of "Condition (supine vs. 50 • HUT)" and/or "Time (with vs. without CO 2 inhalation)" was used to compare steady-state data. Before the analysis for step-change in CO 2 -and TFA-determined CVR during supine and 50 • HUT without (baseline) or with CO 2 inhalation, the Shapiro-Wilk's test was applied to verify the normal distribution for each variable. A normal distribution was confirmed in all CVR indices (W ≥ 0.911, p ≥ 0.057). To compare normally distributed outcomes between supine and 50 • HUT, and between without and with CO 2 inhalation, we incorporated paired samples t-tests. The Wilcoxon matched-pairs signed-ranks test was employed where appropriate as a non-parametric equivalent. All data were analyzed using SPSS (IBM SPSS Statistics Version 27.0) and expressed as mean ± standard deviation (SD). Statistical significance was set at p < 0.05.

Time Domain Analysis Determined CVR
The magnitude response of CVR, determined from the MCA V mean response to a steady-state change in CO 2 , decreased from supine to 50 • HUT (p < 0.001, Figure 1). The time constant (τ) determined from the MCA V mean onset response to step-change in CO 2 increased from supine (27.5 ± 28.9 s) to 50 • HUT (55.4 ± 31.5 s, p = 0.001, Table 2 and Figure 2), indicating that the time response of CVR was attenuated by orthostatic stress. Both these results showed that CVR was attenuated during HUT.

TFA-Determined CVR without CO 2 Inhalation
TFA phase, gain, and coherence between predicted PaCO 2 and MCA V mean without CO 2 inhalation are provided in Figure 3 and Table 3. As shown in Figure 3, coherence was higher than 0.5 in the VLF range, but above 0.024 Hz coherence gradually decreased and was <0.3 in the LF and HF ranges. These findings indicate that TFA in the VLF range rather than other frequency range is useable as an index of CVR. TFA gain in all frequency ranges was unchanged during 50 • HUT compared with the supine condition without CO 2 inhalation, indicating the magnitude of CVR unchanged during HUT, and it was not matched with the magnitude response of CVR determined from the step-change in CO 2 . The VLF TFA phase approached zero during HUT compared with supine (supine: −0.38 ± 0.59 and 50 • HUT: 0.31 ± 0.78 radians, p = 0.003, Table 3 and Figure 3) during spontaneous respiration without CO 2 inhalation. This finding of VLF TFA phase indicates that the time response of CVR was increased (not attenuated) during HUT, and it was not matched with the time response of CVR determined from the step-change in CO 2 . Furthermore, LF and HF TFA phases without CO 2 inhalation were not different between supine and 50 • HUT conditions (LF: p = 0.064 and HF: p = 0.705, Table 3).

Discussion
In the present study, we assessed whether CVR can be reliably determined using TFA between the predicted PaCO 2 and MCA V mean without the requirement for CO 2 inhalation (i.e., during spontaneous respiration), that may be advantageous for patients with respiratory disease or the elderly, etc. As expected, we observed that CVR, determined with the traditional method, using a CO 2 inhalation challenge was impaired during 50 • HUT. However, TFA gain and phase did not represent a similar trend to these traditional CVR indexes during 50 • HUT. These findings suggest that TFA (gain and phase) without CO 2 inhalation under spontaneous respiration does not adequately assess CVR.
As in previous studies [31,39], the magnitude response and time response of CVR (τ) determined by CO 2 inhalation, the traditional index of CVR, were attenuated during 50 • HUT (p < 0.001, Figure 1 and p = 0.001, Figure 2, respectively). The physiological mechanism explaining the orthostatic stress-induced attenuation in CVR remains unknown, but it has been speculated that the attenuated CVR may reflect a progressively reduced cerebrovascular reserve to compensate for the increasingly unstable systemic circulation during orthostatic stress, which could ultimately lead to cerebral hypoperfusion and syncope [31,39]. In addition, orthostatic stress could influence the cerebrovasculature, including ventilation-perfusion matching that is distributed across the zones of the lung during these posture changes and affects PaCO 2 . In the present study, we examined whether TFA-determined CVR was changed during 50 • HUT in a similar way to the traditional CVR index to examine the validity of the TFA data without CO 2 inhalation as an index of CVR. However, TFA gain (all frequencies) without CO 2 inhalation was not different between the supine and 50 • HUT conditions (Table 3). This finding suggests that TFA gain without CO 2 inhalation does not represent the magnitude response of CVR (i.e., attenuated) as a traditional CVR index. On the other hand, the value of the VLF TFA phase as a dynamic time response was increased but approached zero from supine during 50 • HUT to reach a positive value without CO 2 inhalation (p = 0.003, Table 3), indicating that orthostatic stress shortened (i.e., improved) the time response of dynamic CVR. This finding also suggests that the TFA phase did not accurately assess the time response of CVR (τ) calculated from the MCA V mean onset response to step-change in CO 2 (i.e., attenuated) as a traditional CVR index. Collectively, these findings suggest that the TFA phase and gain without CO 2 inhalation may not be adequate to assess changes in CVR as the traditional index during HUT.
The main findings of our study are supported by a previous study [40] using blood oxygen level-dependent (BOLD) MRI. This previous study [40] reported that larger CO 2 stimuli provide a more sensitive means of identifying reductions in the vasodilatory reserve. This suggests that without a sufficiently large stimulus, such as CO 2 inhalation, the CBF response to CO 2 may be underestimated. BOLD imaging has the benefit that it gives semiquantitative information on CVR, and it provides high spatial resolution, which allows the identification of smaller regions of impaired reactivity. However, the BOLD signal itself provides an indirect rather than a direct measure of cerebral perfusion, as provided by newer MRI techniques such as arterial spin labeling. In addition, MRI measurement is expensive and many previous studies used CBF velocity measured by the Doppler method to assess CVR [2,3,[12][13][14]16,[21][22][23]28]. Importantly, the relative change in BOLD signal is lower than that of CBF velocity determined by the Doppler method [41,42]; therefore, it is possible that under hypercapnic stimulus, the relationship between BOLD signal change and CBF may differ in different individuals [41]. Thus, further investigation may be needed to examine whether small CO 2 exposures can identify CVR using the Doppler method and TFA technique to minimize the potentially confounding effects of CO 2 inhalation.
Previous studies [3,38,43] provided important information regarding the use of frequency domain analysis for assessing CVR. Panerai et al. [43] demonstrated use of a cross-correlation function that spontaneous breath-to-breath changes in P ET CO 2 , as well as arterial blood pressure, can contribute significantly to the observed CBF velocity variability. In addition, Mitsis et al. [38] demonstrated use of a multiple input model that arterial pressure fluctuations explain most of the high-frequency blood flow velocity variations (above 0.04 Hz), while P ET CO 2 fluctuations, as well as nonlinear interactions between arterial pressure and CO 2 , have a considerable effect in the lower frequencies (below 0.04 Hz). These findings indicate that the CBF response to a change in CO 2 is slower than that of a response to a change in arterial pressure. However, the independent contribution of change in P ET CO 2 on cerebrovasculature in the dynamic analysis below 0.04 Hz is unclear because this previous study used a multiple input model. More recently, Ogoh et al. [3] demonstrated the dynamic characteristics of the relationship between CO 2 inhalationinduced binary white noise of P ET CO 2 , and MCA V gradually decreased with an increase in frequency over a cut-off frequency (0.024 Hz). This finding suggests that the reflection of the dynamic relationship between P ET CO 2 and MCA V to TFA data reduces in the range of frequency above 0.024 Hz. Indeed, the coherence was highest in the VLF range and gradually decreased above 0.024 Hz ( Figure 3). Thus, the relationship between spontaneous changes in predicted PaCO 2 and MCA V is statistically stronger in the range of frequency below 0.024 Hz compared with the range from 0.024 to 0.04 Hz. However, in the present study, TFA coherence in the VLF range was close to 0.5, which is an acceptable level of TFA, but slightly below it (supine, 0.47 ± 0.22; HUT 0.50 ± 0.18, Table 2). In addition, the TFA phase and gain in the VLF range without CO 2 inhalation below 0.024 Hz did not represent a similar change to the CVR determined by the onset of MCA V response to a step-change in CO 2 . These findings suggest that TFA data may not be adequate to assess CVR, especially without CO 2 inhalation under spontaneous respiration. Importantly, Ogoh et al. [3] used CO 2 inhalation to determine the dynamic characteristics of the relationship between binary white noise of P ET CO 2 (0-5%) and MCA V. Taken together, CO 2 inhalation, which enhanced MCA V response to changes in P ET CO 2 , appears necessary to assess CVR, even using TFA.
Potential limitations of the present study warrant careful consideration. First, a change in the diameter of the target vessels (MCA) could modify blood velocity measured using transcranial Doppler independently of flow. MCA diameter is changed during severe CO 2 inhalation [44,45]. However, the MCA diameter appears to remain relatively constant in humans during moderate variations in blood pressure and CO 2 [46] and during orthostatic stress [47]. Second, TFA coherence is low, and thus the validity of the TFA method may not be sufficient to identify CVR under spontaneous respiration (at the operating point). Although CO 2 inhalation did not increase TFA coherence, further studies using techniques to increase TFA coherence (e.g., controlling respiration rate [28]) may be needed to increase the validity of the findings of the present study. Third, the present study examined only one physiological stressor (orthostatic stress) in healthy subjects. Thus, further work is required to verify that the relationships reported between the different methods to assess CVR hold true during other physiological perturbations, or in patients with respiratory disease. In addition, our assessment of TFA was performed using a relatively small sample size, which may increase the probability of a type I error. However, retrospective power calculations indicated that the sample size required to detect a difference in LF TFA gain between supine and HUT conditions would be~100 participants, tentatively arguing against sample size inflation. Finally, we did not identify the menstrual phases in the female subjects. In female subjects, sex hormones change across the menstrual cycle. However, we assessed the validity of TFA analysis between P ET CO 2 and MCA V under spontaneous respiration as an index of CVR, and the different two methods were applied to each subject in the same menstrual phase. Thus, the changes in sex hormones across the menstrual cycle did not affect the current results.

Perspectives and Significance
The traditional methods for determining CVR employ a CO 2 inhalation challenge to increase the CBF response range to accurately identify CVR, but the changes produced in PaCO 2 are much larger than the spontaneous changes in PaCO 2 that occur in everyday life. Along with increasing ventilation via a central chemoreflex [1,3,28], CO 2 inhalation causes activation of sympathetic nerve activity [48,49]. Moreover, CO 2 inhalation can cause acute stress [26] and anxiety [27], which affect cerebral vasculature. An important consideration when using CO 2 inhalation to assess CVR is that it may affect ventilation via a central chemoreflex [1,3,28], and the resultant change in ventilation can modify PaCO 2 , and thus CBF, via the closed-loop feedback system [1,2]. Thus, the time and magnitude responses of CVR may not respond uniformly in all experimental circumstances and populations (e.g., patients and the elderly). For example, the central respiratory chemoreflex, which is a ventilatory response to CO 2 inhalation, is attenuated in patients with respiratory disease, e.g., chronic obstructive pulmonary disease (COPD) [50][51][52][53], raising the possibility that attenuation of the respiratory chemoreflex overestimates CVR. Thus, some previous studies [54][55][56] demonstrated that CVR attenuated in patients with COPD. However, further investigation is needed to identify how the respiratory response contributes to CVR clinically, especially in patients with respiratory disease. Under these backgrounds, it is possible that CO 2 inhalation modifies the CBF regulatory system, as well as cerebral vasculature, and, consequently, it may alter the CBF response to change in PaCO 2 per se. Therefore, determining CVR without CO 2 inhalation may be better to assess CVR accurately, especially in patients with respiratory disease. Unfortunately, the findings of the present study indicate that the TFA phase and gain cannot be used to assess CVR during spontaneous respiration without CO 2 inhalation. As such, we may need to establish other methods which do not affect respiratory function, such as spontaneous respiration with low concentration CO 2 inhalation, to accurately identify CVR.

Conclusions
The present study, for the first time, identified CVR during spontaneous respiration without CO 2 inhalation using TFA and assessed whether these TFA data without CO 2 inhalation are representative of CVR identified using the time domain CO 2 challenge method (the magnitude and time responses of CVR). These findings indicate that CVR metrics determined by TFA without a CO 2 inhalation do not track HUT-evoked reductions in CVR identified using CO 2 inhalation, suggesting that CO 2 inhalation which enhances CBF response to changes in CO 2 is necessary to assess CVR adequately. Future research is needed to investigate whether low-concentration CO 2 inhalation can be used to identify cerebral CO 2 reactivity in those for whom pronounced hypercapnia is unsuitable. Informed Consent Statement: Informed consent was obtained from all subjects involved in the study.

Data Availability Statement:
The data presented in this study are available upon request, due to ethical restrictions.