The association between BOLD-based cerebrovascular reactivity (CVR) and end-tidal CO₂ in healthy subjects

Abstract

Cerebrovascular reactivity (CVR) mapping using CO₂-inhalation can provide important insight into vascular health. At present, blood-oxygenation-level-dependent (BOLD) MRI acquisition is the most commonly used CVR method due to its high sensitivity, high spatial resolution, and relatively straightforward processing. However, large variations in CVR across subjects and across different sessions of the same subject are often observed, which can cloud the ability of this promising measure in detecting diseases or monitoring treatment responses. The present work aims to identify the physiological components underlying the observed variability in CVR data. When studying the association between CVR value and the subject’s CO₂ levels in a total of N = 253 healthy participants, we found that CVR was lower in individuals with a higher basal end-tidal CO₂, EtCO₂ (slope = −0.0036 ± 0.0008%/mmHg², p < 0.001), or with a greater EtCO₂ change (ΔEtCO₂) with hypercapnic condition (slope = −0.0072 ± 0.0018%/mmHg², p < 0.001). In a within-subject setting, when studying the CVR difference between two repeated scans (with repositioning) in relation to the corresponding differences in basal EtCO₂ and ΔEtCO₂ (n = 11), it was found that CVR values were lower if the basal EtCO₂ or ΔEtCO₂ during that particular scan session was greater. The present work suggests that basal physiological state and the level of hypercapnic stimulus intensity should be considered in application studies of CVR in order to reduce inter-subject and intra-subject variations in the data. Potential approaches to use these findings to reduce noise and augment sensitivity are proposed.

1. Introduction

With a growing need for biomarkers in large-vessel and small-vessel brain diseases, there has been a surging interest in mapping cerebrovascular reactivity (CVR) in recent years. CVR refers to the ability of cerebral vessels to dilate or constrict in response to vasoactive challenges such as hypercapnia or injection of acetazolamide. It is a marker of vascular reserve and is complementary to basal measures of brain hemodynamics such as cerebral blood flow (CBF), cerebral blood volume (CBV) and oxygen extraction fraction (OEF) (Chen, 2018; Liu et al., 2019). Non-invasive measurements of CVR have found clinical applications in a broad spectrum of brain diseases including arterial stenosis (De Vis et al., 2015; Liu et al., 2017; Mandell et al., 2008), stroke (Geranmayeh et al., 2015; Taneja et al., 2019), brain tumors (Fierstra et al., 2016), traumatic brain injury (Chan et al., 2015), dementia (Yezhuvath et al., 2012), multiple sclerosis (Marshall et al., 2014), and normal aging (Lu et al., 2011; McKetton et al., 2018; Peng et al., 2018). Additionally, CVR has also been used for the calibration of fMRI signal and estimation of cerebral metabolic rate of oxygen consumption (CMRO₂) (Bright et al., 2017; Davis et al., 1998; Gauthier and Hoge, 2013; Hoge et al., 1999; Liu et al., 2013; Murphy et al., 2011).

The most commonly used approach to measure CVR is to employ hypercapnic challenge inside the MRI scanner while continuously collecting end-tidal CO₂ (EtCO₂) and Blood-Oxygenation-Level-Dependent (BOLD) images (Bright et al., 2011; Fierstra et al., 2013; Liu et al., 2019; Yezhuvath et al., 2009). A regression analysis between EtCO₂ and BOLD signal time-courses will then yield a CVR index in the units of %/mmHg CO₂. While the data collection and analysis methods of CVR MRI are straightforward due to the robustness of both the EtCO₂ and BOLD signals, there have been observations of substantial variations in CVR values across normal subjects (Bright et al., 2011; Halani et al., 2015; Lu et al., 2011; Murphy et al., 2011), sometimes even across different sessions of the same subjects (Bright and Murphy, 2013; Peng et al., 2018). To date, the physiological mechanisms of these variations have not been elucidated.

A better understanding of normal variations in CVR is of importance in both clinical and basic science applications of this promising technique. First, variations in CVR data increase “noise level” when comparing normal to abnormal populations and reduce the statistical power to detect pathology-related differences. They may also preclude personalized determination of abnormalities. Second, a better understanding of CVR variations will allow more informed interpretation of CVR results. One can ascertain whether the observed CVR change is truly due to vascular reserve alterations or due to differences in its physiological modulators. Finally, identification of physiological modulators of CVR will help improve the reliability of fMRI calibration and normalization, as fMRI and its calibration scans are typically performed under different experimental settings (e.g. with and without mask, mouthpiece, etc.).

Given that the BOLD MRI signal is a complex function of CBF (Bhogal et al., 2014; Sobczyk et al., 2014) and that CBF itself may be a non-linear function of EtCO₂ (Tancredi and Hoge, 2013), we hypothesize that BOLD-based CVR measure is dependent on both basal EtCO₂ (bEtCO₂) and its change due to hypercapnia (ΔEtCO₂) in healthy subjects. The goal of the present study is, therefore, to investigate the effects of bEtCO₂ and ΔEtCO₂ on CVR, in both between-subjects and within-subject settings. To study the between-subject effect, we examined the association between CVR and the above-mentioned physiological factors using data from 4 CVR studies that we had performed, with an aggregated sample size of 253 healthy subjects. To study the within-subject effect, we examined CVR values from repeated CVR scans and investigate if their differences are dependent on differences in bEtCO₂ and ΔEtCO₂. Finally, numerical simulations were also performed using a BOLD biophysical model to verify the experimental findings.

2. Materials and methods

The present work consists of two major components. One is to study the inter-subject relationship between CVR and EtCO₂; the other is on their intra-subject relationship.

2.1. Inter-subject variations in CVR and their dependence on end-tidal CO₂

2.1.1. Experiment

The datasets used for this study consist of data from 4 independent studies totaling 253 adults ranging from 20 to 88 years old (Table 1). All study procedures were approved by the Institutional Review Board of the Johns Hopkins University or The University of Texas at Dallas. The participants gave informed written consent before being enrolled.

Table 1.

Summary of demographic and imaging parameters of the four studies performed in this work.

	Study 1	Study 2	Study 3	Study 4
N	11	10	25	207
Age, yo (SD)	24.1 (3.2)	28 (6.8)	68.8 (6.0)	50.9 (19.9)
Gender
Male	7	3	8	82
Female	4	7	17	125
EtCO2
Basal EtCO2, mmHg (SD)	37.9 (4.0)	36.6 (4.2)	36.0 (3.8)	38.5 (4.3)
ΔEtCO2, mmHg (SD)	9.3 (1.8)	8.1 (1.1)	9.3 (1.8)	9.1 (2.0)
Image parameter
Repetition Time, ms	1500	1500	1500	2000
Echo Time, ms	21	21	21	25
Flip Angle	90°	90°	90°	80°
Field of View, mm2	205 × 205	205 × 205	220 × 220	220 × 220
Slice Number	36	36	36	43
Slice-thickness, mm	3.5	3.5	3.8	3.5
Gap, mm	0	0	0	0
In-plane resolution, mm2	3.2 × 3.2	3.2 × 3.2	3.4 × 3.4	3.4 × 3.4
Scan Duration, min	7	5	7	7

All CVR experiments were conducted on Philips 3T MRI (Achieva). Studies 1, 2, and 3 were performed on a scanner at Johns Hopkins University, while Study 4 was performed on a scanner at University of Texas. Gas delivery during the experiments used an identical apparatus and was based on an inspired 5% CO₂ challenge as described in previous studies (Lu et al., 2014). Briefly, subjects were fitted with a nose clip, and breathed approximately 1 min of 5% CO₂ gas mixture (21% O₂, 74% N₂) and 1 min of room-air in an interleaved fashion through a mouthpiece (Fig. 1a). The CO₂ gas mixture was contained in Douglas bags and delivered through a two-way non-rebreathing valve (Hans Rudolph, 2600 series, Shawnee, KS). A research assistant was inside the magnet room throughout the experiment to switch the valve and monitor the subjects. The EtCO₂ was recorded throughout the experiment using a capnograph device, an example of which is shown in Fig. 1b.

Fig. 1.

Illustration of Cerebrovascular Reactivity (CVR) measurement and data. (a) Schematic illustration of gas delivery and recording inside the MRI. (b) Representation data of EtCO₂ and whole-brain BOLD signal time course. (c) CVR map averaged over the entire cohort (N = 253).

In addition to the BOLD CVR scan, each subject in each study also received a T1-weighted scan for anatomic reference. The T1-weighted scan used the following imaging parameters which were identical in all four studies: magnetization-prepared rapid gradient-echo sequence (MPRAGE), TR = 8.1 ms, TE = 3.7 ms, shot interval = 2100 ms, FA 12°, FOV = 204 × 256 mm², 160 slices with 1 × 1 × 1 mm³ voxels.

Table 1 summarizes participant demographic information and imaging parameters of the four studies, which were performed under different projects. None of these projects have published data related to the CO₂ effect that is of interest in this work. Study 2 used two CO₂ inhalation blocks with a scan duration of 5 min, while the other studies used three CO₂ blocks with a 7-min scan duration. We also want to note that the TEs used for these CVR studies were slightly shorter than typical fMRI experiments. This was to reduce the signal contrast between parenchymal and cerebrospinal fluid (CSF) spins and minimize the sensitivity of the sequence to changes in cerebral blood volume (CBV) (Ravi et al., 2016; Thomas et al., 2013).

2.1.2. Data processing

Image analysis was conducted using the software Statistical Parametric Mapping (SPM, University College London, UK) and in-house MATLAB (MathWorks, Natick, MA) scripts. The BOLD CVR data first underwent standard pre-processing steps including slice timing correction, realignment, skull stripping, normalization to Montreal Neurologic Institute (MNI) standard brain space via MPRAGE image, and spatial smoothing using a Gaussian filter with a full-width half-maximum of 4 mm (Hou et al., 2019).

The data were further processed to compute CVR maps (Liu et al., 2019). Briefly, the EtCO₂ time course was temporally aligned with the global BOLD time series to account for the time it takes for CO₂ to travel from the lung (where the EtCO₂ was recorded) to the brain (where the BOLD signal was recorded). Next, a multi-linear regression was performed using

$$\text{BOLD}(\text{t})={\beta }_0+{\beta }_1\cdot {\text{EtCO}}_{2,\text{aligned}}(\text{t})+{\beta }_2\cdot \text{t}$$ (1)

where BOLD(t) is the BOLD MRI signal time course, t is time, and β₀, β₁, β₂ are coefficients to be estimated. Note that the term β₂ · t was added to account for potential drifting of the signal.

CVR can then be computed as

$$\text{CVR}=\frac{{\beta }_1}{{\beta }_0+{\text{bEtCO}}_2\cdot {\beta }_1}$$ (2)

We note that CVR was not calculated as $\frac{{\beta }_1}{{\beta }_0}$, but instead contains the bEtCO₂ · β₁ term, so that the measured CVR is in reference to basal EtCO₂ state under room air, rather than in reference to a non-physiological state of EtCO₂ of 0 mmHg. However, it should be pointed out that, for practical purposes, the bEtCO₂ · β₁ term is much smaller than β₀ (−0.7 ± 0.2% in our data). Thus, researchers can also use $\frac{{\beta }_1}{{\beta }_0}$ to compute CVR value with minimal differences. Considering the typical EtCO₂ time course in our study (e.g. Fig. 1b) and certain fluctuations, we defined bEtCO₂ as the average of the lowest 25% of the EtCO₂ time course. Similarly, the EtCO₂ during hypercapnia was defined as the average of the highest 25% of the EtCO₂ time course. ΔEtCO₂ was then calculated as their difference. Supplementary Fig. S1 illustrates boundary lines of the top and bottom 25% on the EtCO₂ time course of the 4 studies.

To obtain region-of-interest (ROI) CVR values, the T1-MPRAGE image was segmented to obtain a masked image without scalp. This image was further analyzed with BET of FSL to remove residual extracranial tissue (Smith, 2002). The final mask was applied to the CVR data to obtain whole-brain CVR value. For lobar CVR, lobar masks defined on Pickatlas (Lancaster et al., 2000; Maldjian et al., 2003) were applied on the CVR data to obtain values in frontal, temporal, parietal, and occipital lobes as well as subcortical areas.

2.1.3. Statistical analysis

A mixed-effect linear model (Chen et al., 2013) was used to study the dependence of CVR on bEtCO₂ and ΔEtCO₂ using data from all 4 studies. The whole-brain CVR was the dependent variable. The bEtCO₂ and ΔEtCO₂ were used as fixed-effect independent variables. The study index was used as a random-effect variable. Age was a covariate (Lu et al., 2011). Cohen f² effect size was calculated from the mixed-effect linear model using established methods (Selya et al., 2012).

To determine if the dependence of CVR on bEtCO₂ and/or ΔEtCO₂ is age-specific, we also examined the interaction terms between age and the EtCO₂ measures. Moreover, to examine whether the relationships between CVR and bEtCO₂ (or ΔEtCO₂) are different across major brain lobes, we performed additional analyses by including lobes and their interactions with EtCO₂ as independent variables.

For all statistical analyses, a p-value of 0.05 or less is considered significant. We performed multiple comparison (Bonferroni) corrections for the lobal data. All analyses were conducted with SPSS v23 (IBM, Armonk, NY).

2.2. Intra-subject variations in CVR and their dependence on end-tidal CO₂

In order to study intra-subject variability, in a subset of subjects (n = 11, those in Study 1 as described in Table 1), the CVR scans were repeated after repositioning. The gap between the two scans was approximately 30 min. This generated two CVR data sets from the same participant.

To examine within-subject EtCO₂ effects, within-subject differences in CVR [denoted δ(CVR)], bEtCO₂ [δ(bEtCO₂)], and ΔEtCO₂ [δ(ΔEtCO₂)] were computed between the two sessions. Linear regression analysis was then performed in which δ(CVR) was the dependent variable and δ(bEtCO₂) and δ(ΔEtCO₂) were the independent variables. The intercept of the linear function was set to be zero as the differences in CVR are expected to be zero when bEtCO₂ and ΔEtCO₂ are zeros.

2.3. Numerical simulations

To confirm the experimental findings, numerical simulations were performed to verify the relationship between CVR and EtCO₂. The calibrated BOLD model relates CBF and CMRO₂ to the BOLD signal using the following equation (Davis et al., 1998; Hoge et al., 1999):

$$\begin{gathered} \text{BOLD}\propto \text{Exp}(-\text{TE}\cdot {\text{R}}_2^{*}{|}_{\text{dHb}}) \\ =\text{Exp}(-\text{A}\cdot \text{TE}\cdot \text{CBV}\cdot {\text{dHb}}^{\beta }) \\ =\text{Exp}\left[-{\text{A}}^{\prime }\cdot \text{TE}\cdot {\text{CBF}}^{\alpha }\cdot {\left(\frac{{\text{CMRO}}_2}{\text{CBF}}\right)}^{\beta }\right] \end{gathered}$$ (3)

In Eq. [3], the exponent α describes the coupling relationship between CBF and CBV (Grubb et al., 1974), i.e. CBV∝CBF^α. β is a power-law relationship between venous blood oxygenation and transverse relaxation rate (Ogawa et al., 1992). dHb reflects the oxygen extraction fraction and is related to CMRO₂/CBF. In essence, the bracket term indicates that the BOLD signal is modulated by both cerebral blood flow and cerebral metabolic rate (Gauthier and Fan, 2019; Griffeth and Buxton, 2011). If an iso-metabolic assumption is used (but see (Peng et al., 2017; Xu et al., 2011) or non-iso-metabolic reports), the CMRO₂ term would reduce to constant. The BOLD signal is, therefore, a simple function of CBF.

$$\text{BOLD}\propto \text{Exp}(-\text{K}\cdot {\text{CBF}}^{\alpha -\beta })$$ (4)

where K is $\text{A}\prime \cdot \text{TE}\cdot {\text{CMRO}}_2^{\beta }$. In this study, we used four different combinations of α and β values based on widely accepted studies (Bulte et al., 2012; Davis et al., 1998; Griffeth and Buxton, 2011; Merola et al., 2016). For K, we tested a range of values from 2.25 to 4.25 at an interval of 0.5, which yielded BOLD signals in the typical range of CVR experiments.

Furthermore, based on the reported equation (Eq. [5]) between EtCO₂ and CBF (Jiang et al., 2019), the BOLD signal can be simulated for each EtCO₂ level.

$$\text{CBF}=0.88\cdot {\text{EtCO}}_2+7.65$$ (5)

CVR, which is defined as BOLD signal change between two EtCO₂ levels divided by the EtCO₂ change, at any bEtCO₂ or ΔEtCO₂ values can then be evaluated.

3. Results

3.1. Relationship between CVR and EtCO₂ levels between subjects

Fig. 1c shows the group-averaged CVR map (N = 253). The maps of standard deviation and coefficient-of-variation (COV) are shown in Supplementary Fig. S2. Fig. 2 shows histograms of whole-brain CVR, bEtCO₂ and ΔEtCO₂ values in the entire cohort. The fittings of the CO₂ histograms to a Gaussian function are also shown. The CVR has a mean value of 0.190%/mmHg with an intersubject variation (in standard deviation across subjects) of 0.048%/mmHg. The bEtCO₂ values had a mean value of 38.1 mmHg and an intersubject variation of 4.3 mmHg. For ΔEtCO₂, the mean and intersubject variations were 9.1 mmHg and 1.9 mmHg, respectively. The basal EtCO₂ revealed an age-related decrease (slope = −0.0285 ± 0.0135 mmHg/year, p = 0.036), while ΔEtCO₂ showed an increase with age (slope = 0.0155 ± 0.0058 mmHg/year, p = 0.008). Supplementary Fig. S3 shows scatter plots of CVR, bEtCO₂, and ΔEtCO₂, as a function of age.

Fig. 2.

The distributions of (a) whole-brain CVR, (b) basal EtCO₂, and (c) ΔEtCO₂ in the entire cohort (N = 253). The Gaussian fittings of the histograms are also shown.

Linear mixed model analysis that combined data from all studies revealed that whole-brain CVR was significantly correlated with bEtCO₂ (slope = −0.0036 ± 0.0008%/mmHg², mean ± SE, p < 0.001) and ΔEtCO₂ (slope = −0.0072 ± 0.0018%/mmHg², p <0.001) (Fig. 3). Their effect size was 0.05 and 0.04, respectively. We also observed an age-related decline in whole-brain CVR (−0.0012 ± 0.0001%/mmHg/year, p < 0.001), similar to those reported in previous literature (Fluck et al., 2014; Lu et al., 2011; McKetton et al., 2018). No interaction effects were observed between age and bEtCO₂ (p = 0.20) or between age and ΔEtCO₂ (p = 0.96). The random effect size, i.e. CVR differences across studies, was estimated to be 0.026%/mmHg. As a confirmation, we performed linear regression analyses separately for each of the four studies conducted. The results are summarized in Fig. 3. All four studies showed that bEtCO₂ and ΔEtCO₂ were inversely associated with whole-brain CVR across subjects, although not all results reached statistical significance.

Fig. 3.

Summary of the dependence of CVR on (a) basal EtCO₂ and (b) ΔEtCO₂ when considering each study separately and when combining all data.

We also assessed whether the effect of EtCO₂ on CVR could be observed in all major brain lobes and whether there were lobe differences in the coefficients. It was found that CVR was significantly associated with bEtCO₂ (corrected p < 0.01, combining all studies) and ΔEtCO₂ (corrected p < 0.05, combining all studies) in all lobes examined including frontal, occipital, parietal, temporal, and subcortical gray matter. Fig. 4 plots the coefficients in each lobe when using data from all four studies, with the coefficients from individual studies displayed in Supplementary Fig. S4. The additional comparison indicated that CVR in the occipital lobe had the greatest dependence on bEtCO₂ (p < 0.001) and ΔEtCO₂ (p < 0.001) among all major brain lobes.

Fig. 4.

The slope of the CVR dependence on CO₂ in major brain lobes. (a) Slope between CVR and basal EtCO₂. (b) Slope between CVR and ΔEtCO₂.

3.2. Relationship between CVR and EtCO₂ levels within a subject

Within-subject variations in CO₂ levels, calculated as standard deviations of the values between two repeated CVR scans, were 0.72 ± 0.59 mmHg (mean ± SD) and 0.68 ± 0.62 mmHg for bEtCO₂ and ΔEtCO₂, respectively. These variation values were lower than those between subjects (3.52 mmHg and 1.78 mmHg for bEtCO₂ and ΔEtCO₂, respectively, in the same cohort). There was no significant difference in CVR values between the two repetitions. Linear regression analysis revealed that differences in whole-brain CVR between two repeated scans were inversely associated with both δ(bEtCO₂) (slope = −0.0171 ± 0.0031%/mmHg², p < 0.001) and δ(ΔEtCO₂) (slope = −0.0098 ± 0.0031%/mmHg², p = 0.012) differences. Their effect size was 3.36 and 1.08, respectively. Fig. 5 shows the partial correlation (after factoring out the other regressor) between differences in CVR and differences in CO₂ levels. We also applied similar analyses to lobar CVR. It was found that within-subject differences in CVR are correlated with δ(bEtCO₂) and δ(ΔEtCO₂) in all major brain lobes. The slopes of these relationships were not different across lobes (p > 0.05), as evaluated by adding the lobe-by-EtCO₂ interaction terms to the regression model.

Fig. 5.

Scatter plot between CVR and EtCO₂ variations in a within-subject setting. The x-axis shows the differences in EtCO₂ between two sessions. The y-axis shows the differences in CVR between two sessions. (a) shows the basal EtCO₂ effect. (b) shows the ΔEtCO₂ effect. Because the CVR difference is dependent on both basal EtCO₂ and ΔEtCO₂ differences, we factored out the other regressor and re-referenced to its zero value before plotting the scatter plot.

3.3. Numerical simulation results

The assumed relationship between CBF and EtCO₂ (Jiang et al., 2019) is shown in Fig. 6a. Based on this formula between CBF and BOLD described in Eq. [3], we simulated the correspondence between BOLD and EtCO₂ (Fig. 6b), for a range of coefficient K values.

Fig. 6.

Numerical simulation results. (a) Assumed relationship between EtCO₂ and CBF that is used in the simulation. (b) Absolute BOLD signal as a function of EtCO₂. The BOLD signal here indicates the MR signal intensity obtained from the EPI-based T2*-weighted pulse sequence. (c) CVR as a function of basal EtCO₂. (d) CVR as a function of ΔEtCO₂. α = 0.14, β = 0.91 (Griffeth and Buxton, 2011).

A non-linear relationship between them can be clearly seen. We then calculated CVR as a function of bEtCO₂ for a fixed amount of ΔEtCO₂ (=9 mmHg) and the results are shown in Fig. 6c. An inverse relationship between CVR and bEtCO₂ can be seen, in agreement with the experimental results. Similarly, Fig. 6d shows simulation results in which CVR was plotted as a function of ΔEtCO₂ when fixing the bEtCO₂ (=38 mmHg). An inverse relationship is observed. To ensure that the simulation results are not dependent on the choice of model parameters, α and β, we repeated the numerical simulations with several other different combinations of α and β (Bulte et al., 2012; Davis et al., 1998; Griffeth and Buxton, 2011; Merola et al., 2016). The results were generally consistent with those shown in Fig. 6. Supplementary Fig. S5 shows simulation results when using several other sets of α and β values.

4. Discussion

The present work examined the influence of basal EtCO₂ and hypercapnia-induced EtCO₂ change on the measured CVR values in both between-subject and within-subject settings. We found that, in both settings, higher basal EtCO₂ and greater EtCO₂ change in CVR experiments are associated with lower CVR values. The present work suggests that both basal physiological state and the level of hypercapnic stimulus intensity should be considered in application studies of CVR, to reduce inter-subject and intra-subject variations in the data.

The observed dependence of CVR on EtCO₂ can be attributed to the BOLD signal mechanism. The BOLD signal difference is associated with changes in venous oxygenation between the basal state and the hypercapnic state. The larger the venous oxygenation change, the greater the BOLD signal difference (i.e. CVR). However, the venous oxygenation level can only go as high as 100%, thus this value will reach a plateau at high EtCO₂. That is, in the high EtCO₂ range, each unit of EtCO₂ increase will result in a small BOLD signal change. This “plateau” phenomenon is well-known in the fMRI field from both between-subject (Lu et al., 2008) and within-subject (Cohen et al., 2002; Xu et al., 2011) point-of-view. The present study extends this relationship of BOLD-versus-basal physiology to CVR results. Our numerical simulations provided an additional, more quantitative illustration of this notion. Although the figure shown (Fig. 6) was based on one set of α and β values, we have conducted additional simulations using other values and all results showed an inverse dependence of CVR on bEtCO₂ and ΔEtCO₂ (Supplementary Fig. S5). Another possible mechanism for the dependence of CVR on EtCO₂ could be related to the non-linear relationship between EtCO₂ and CBF itself. As basal CO₂ level is raised and a blood vessel dilates accordingly, the vascular reserve is diminished. Thus, the further hypercapnic challenge will elicit smaller vasodilation. This may be another explanation underlying the inverse relationship between CVR and CO₂. We also want to point out that the CVR measure reported in this study was calculated as BOLD signal change per mmHg change in EtCO₂. Thus, the actual CO₂ change induced by hypercapnic breathing has been considered in the CVR quantification.

As CVR MRI receives increasing attention in recent years, the impact of experimental condition on the CVR measurement has been becoming a topic of great interest. Using a ramp CO₂ paradigm, Bhogal et al. (2014) showed that the relationship between BOLD signal and EtCO₂ was, in fact, non-linear and that the actual CVR values measured were dependent on the range of EtCO₂ values studied in the experiment. van Niftrik et al. (2018) showed that, when comparing two groups of healthy subjects in whom one group was measured at their natural level of CO₂ while the other group was studied under raised CO₂ level, the elevated-CO₂ group revealed a lower CVR value compared to the natural-level group. While these findings are not directly comparable to our study, the general observation that a higher basal CO₂ corresponds to a lower CVR is consistent with the data in the present study. Bright et al. (2011), Halani et al. (2015) and De Vis et al. (2018) have studied the effect of basal state on CVR measurement in an intra-subject setting, again by elevating the subject’s basal CO₂ level. The results were not coherent, with some studies showing an absence of effect of basal CO₂ on CVR while others suggesting a trend of reduction in selected brain regions. We note that all of the subjects in the present study were studied under their natural basal states. Owing to the large sample size afforded in this analysis, we were able to show a definitive (p < 0.001) inverse correlation between CVR and basal EtCO₂. This relationship was observed throughout the brain. Furthermore, we showed that there was an inverse correlation between CVR and ΔEtCO₂, a parameter that has received less attention in the previous literatures.

The findings from the present study have several implications for basic science and clinical applications of CVR MRI. First, it should be recognized that much of the “noise” in CVR data is physiological, rather than thermal noise, such as the CO₂-level related variations described in the present study. These noise sources, once understood, can be corrected or reduced. For example, for the EtCO₂ and ΔEtCO₂ related variations, one can use the slopes reported in this study (i.e. 0.0036%/mmHg² for bEtCO₂ and 0.0072%/mmHg² for ΔEtCO₂) to correct the CVR values before subjecting them to statistical analysis of patients-versus-controls or before-versus-after treatment. An alternative approach to account for the CO₂ effect is to include bEtCO₂ and ΔEtCO₂ in the regression model as covariates. Both methods can be used if one does not expect a systematic difference in CO₂ levels between the patient and control groups. On the other hand, for clinical studies in which CO₂ levels may be altered by disease, e.g. sleep apnea or chronic obstructive pulmonary disease (COPD), the slope-correction method is recommended to avoid variable co-linearity in the regression model. Given the observed influence of EtCO₂ and ΔEtCO₂ on CVR, another approach to minimize these effects is to use CO₂ clamping technique so that every participant has the same basal CO₂ and CO₂ change (Fisher, 2016; Slessarev et al., 2007). However, one issue is that each individual presumably has their own “operating” CO₂ level in their daily life. In fact, the present study and others have shown that the “operating” CO₂ level varies with age, and other factors (Cantin et al., 2011; Dhokalia et al., 1998). Thus, experimental alternation of their basal CO₂ level may cause profound changes in their brain and respiratory physiology. These changes and the associated compensatory responses may result in a CVR value that is dramatically different from their natural breathing state. This is relevant to the choice of CVR experimental apparatus that has stimulated some discussions in the field. One type of stimulus apparatus, generally referred to as fixed inspired CO₂ system (Bulte et al., 2009; Driver et al., 2016; Lajoie et al., 2016; Lu et al., 2014), delivers a fixed concentration of CO₂ to the subject and, because different subjects have different ventilation rate/volume as well as in their responses to CO₂ gas, the actual EtCO₂ and its change during CVR experiments are different across subjects. Another type of system uses a feedback loop to control the EtCO₂ of the subject so that every subject has the same basal EtCO₂ (e.g. 40 mmHg) and EtCO₂ change (e.g. 10 mmHg) during the experiment (Fisher, 2016; Slessarev et al., 2007). The benefits and limitations of each system have been under some debate. The present work shows that clamping or modulating the subject’s EtCO₂ to a level different from their natural state will result in a difference in the measured value. However, it remains to be determined whether these modulated CVR values would reveal less or more variations within a supposedly homogeneous group of participants. This question should be investigated in future studies. Finally, one can consider using CBF-based techniques such as arterial-spin-labeling (ASL) for CVR measurement. However, ASL-CVR has its own challenges such as low signal-to-noise ratio (SNR) (Halani et al., 2015; Ho et al., 2011), sensitivity to bolus-arrival-time change during hypercapnia (Ho et al., 2011; Su et al., 2017), and potential changes in labeling efficiency when arterial flow velocity is increased (Aslan et al., 2010).

Our lobar analysis revealed that there were some differences in the slope of the relationship between CVR and EtCO₂ and that the occipital lobe had the greatest slope values. Interestingly, previous studies have shown that the occipital lobe also had the highest CVR values among all major brain lobes (Yezhuvath et al., 2009; Zhou et al., 2015). Given that the occipital lobe was adjacent to large venous sinuses, we also performed additional analysis to erode the ROI mask to remove the sinus voxels, and found that the CVR-vs-CO₂ slope was minimally affected by the erosion.

In this study, the basal and hypercapnic CO₂ levels were defined as the bottom and top 25% of the EtCO₂ time course. We have also tried several other approaches to define these values, including using 15% and 5% of the time course, using the peak values, and using the average of the first 20 time points as baseline while using the average of the values during the time window corresponding to the CO₂ breathing block as hypercapnic EtCO₂. The findings on the relationship between CVR and basal EtCO₂/ΔEtCO₂ were the same. Supplementary Table S1 shows coefficients and p-values of these additional analyses.

In the within-subject variation study, there was a difference in basal EtCO₂ between the two scans. Basal EtCO₂ during session two appeared to be lower than that during session one (p = 0.008). We therefore further investigated the nature of this decrease. Supplemental Fig. S6 shows the group-averaged EtCO₂ time courses of the two sessions. It can be seen that the basal EtCO₂ of the two sessions started at approximately the same levels, but session 2 seems to show a gradual decrease over blocks. This may be due to fatigue of the participants in the latter session. Further investigation is needed to confirm and understand this effect.

Several limitations of the current study should be acknowledged. First, the four studies conducted in this work used slightly different imaging parameters such as TE, voxel size, CO₂ block number, and scan time. Since BOLD percentage signal change, thereby CVR, is known to be affected by TE (Lu and van Zijl, 2005), there may be systematic heterogeneities in the data. However, we should note that our linear regression was based on a mixed-effect model where the study index was used as a random-effect variable, thus data from each study were treated as independent groups. Second, although the group results were significant, there were discrepancies in their results for individual studies. Furthermore, the effect sizes of EtCO₂ and ΔEtCO₂ (0.05 and 0.04, respectively) in the between-subject data are still relatively small, thus their practical utility is unclear. The within-subject effect sizes (3.36 and 1.08) are greater, thus may be useful in comparison of CVR before and after intervention or follow-up. Third, while we have high confidence in the presence of an inverse relationship between CVR and EtCO₂ (p < 0.001), the slope value (i.e. bEtCO₂ slope = −0.0036 ± 0.0008 %/mmHg², ΔEtCO₂ slope = −0.0072 ± 0.0018 %/mmHg²) still contains certain degree of uncertainties (about 25% of the estimated values). Thus, more data are needed to determine the exact values of the slope variables as well as their dependence on population, e.g. through a meta-analysis. Similarly, it should be kept in mind that these slope values are for 3 T and may not be valid for other field strengths such as 1.5T or 7T. Finally, the present study has only examined CVR data from healthy controls. The extent to which the relationship between CVR and EtCO₂ can be observed in diseased populations requires further investigation. Relevant to this point, Study 3 only showed a trend of EtCO₂ effects on CVR and one possible reason is that participants in Study 3 were all elderly subjects and many of them have commonly vascular risks such as hypertension, hypercholesterolemia, etc.

5. Conclusions

CVR, as typically quantified by BOLD MRI signal change per unit change in EtCO₂, was found to be dependent on the physiological state of the individual. Specifically, CVR was lower in individuals with a higher basal EtCO₂ and/or with a greater EtCO₂ change upon hypercapnia. Similarly, within the same individual, the measured CVR value was lower if their basal EtCO₂ or ΔEtCO₂ during that particular scan session were greater. These observations have important implications in understanding physiological noise in CVR data and in applying CVR MRI to clinical studies. Potential approaches to use these findings to reduce noise and augment sensitivity have been proposed.