Measurement of CMRO 2 and its relationship with CBF in hypoxia with an extended calibrated BOLD method

Abstract

Cerebral blood flow (CBF) and cerebral metabolic rate of oxygen (CMRO₂) are physiological parameters that not only reflect brain health and disease but also jointly contribute to blood oxygen level-dependent (BOLD) signals. Nevertheless, unsolved issues remain concerning the CBF–CMRO₂ relationship in the working brain under various oxygen conditions. In particular, the CMRO₂ responses to functional tasks in hypoxia are less studied. We extended the calibrated BOLD model to incorporate CMRO₂ measurements in hypoxia. The extended model, which was cross-validated with a multicompartment BOLD model, considers the influences of the reduced arterial saturation level and increased baseline cerebral blood volume (CBV) and deoxyhemoglobin concentration on the changes of BOLD signals in hypoxia. By implementing a pulse sequence to simultaneously acquire the CBV-, CBF- and BOLD-weighted signals, we investigated the effects of mild hypoxia on the CBF and CMRO₂ responses to graded visual stimuli. Compared with normoxia, mild hypoxia caused significant alterations in both the amplitude and the trend of the CMRO₂ responses but did not impact the corresponding CBF responses. Our observations suggested that the flow-metabolism coupling strategies in the brain during mild hypoxia were different from those during normoxia.

Introduction

Cerebral blood flow (CBF) and cerebral metabolic rate of oxygen (CMRO₂) are essential physiological parameters in the brain. Variations in the CBF and CMRO₂ collectively determine blood oxygenation, the physiological foundation of blood oxygen level-dependent (BOLD) functional magnetic resonance imaging (fMRI).^1–3 The exact relationship between focal changes in the CBF and CMRO₂ in the working brain has been of great research interest in the field of neuroimaging.

Investigations on the CBF–CMRO₂ relationship date back to the 1890s, when focal CBF was first suggested to vary with the local metabolic demand during functional activities. ⁴ The increased oxygen demand of oxidative metabolism was considered the driving force behind increases in CBF during functional tasks. In the 1980s, Fox et al.^5,6 reported that the increase in CBF was 6–10 times greater than the increase in CMRO₂ in the areas of functional activation, suggesting that CBF was regulated by factors other than oxygen demand. Thereafter, a substantial amount of research was conducted to find divergent CBF–CMRO₂ relationships under various conditions. Factors such as age; ⁷ the type, ⁸ frequency ⁹ and duration ¹⁰ of a stimulus; blood CO₂ level; ¹¹ and caffeine exposure ¹² have been shown to affect the CBF–CMRO₂ relationship. However, previous studies have rarely discussed the influence of oxygen availability on the CBF–CMRO₂ relationship. The brain is particularly sensitive to changes in oxygen level and is prone to irreversible damage due to long-term hypoxia, which, unfortunately, is often experienced at high altitudes or in the context of brain disorders. The effects of hypoxia on stimulus-induced CBF changes alone have been well studied, and CBF responses have been reported to be unaffected by mild hypoxia.^13,14 Nevertheless, the effects of hypoxia on the CBF–CMRO₂ relationship are under studied.

Under normoxic conditions, relative changes in CMRO₂ are mostly measured using a robust calibrated BOLD model (hereinafter refers to as the “Davis model”) first proposed by Davis et al. ¹⁵ The Davis model assumes that arterial blood is fully oxygenated and that the BOLD signal is related to changes in the volume and deoxyhemoglobin concentration in venous blood. ¹⁵ A scaling factor, M, is used to calibrate the change in the BOLD signal against its baseline state. ¹⁵ M is usually obtained via gas-related physiological challenges. In hypoxia, however, not only both arterial and venous blood contributes to the BOLD signal, and furthermore, the hypoxic M factor cannot be easily obtained through physiological calibrations. Thus, the Davis model is not valid in hypoxia.

The specific aim of this study is twofold. First, an extended calibrated BOLD model (hereinafter refers to as the “extended model”) incorporating CMRO₂ measurements in hypoxia was developed. This extended model calculated an effective deoxyhemoglobin concentration that properly weighted deoxyhemoglobin from both arterial and venous blood and scaled the hypoxic M factor in relation to the normoxic M factor. The extended model was cross-validated with a multicompartment BOLD model proposed by Griffeth and Buxton (hereinafter refers to as the “G-B model”). ¹⁶ Second, the effects of mild hypoxia on CMRO₂ and its relationship with CBF during brain stimulation were investigated. In this work, mild hypoxia was induced by having subjects breathe a gas mixture composed of 12%O₂ and 88%N₂. An MRI pulse sequence was implemented with simultaneous acquisition to measure the cerebral blood volume (CBV)-, CBF- and BOLD-weighted signals ¹⁷ during graded visual stimulations at 1, 4 and 8 Hz. A hypercapnia challenge task was conducted individually to determine the normoxic M factor. In addition, the effects of mild hypoxia on the task-evoked CBF and CMRO₂ responses were evaluated and compared with those under normoxic conditions.

Theory

In the following context, we define $\text{δBOLD}=\text{BOLD}/{\text{BOLD}}_0-1$ , where $\text{BOLD}$ and ${\text{BOLD}}_0$ represent the BOLD signals measured during a stimulus and in the resting state, respectively. The definitions of $\text{δCBV}$ , $\text{δCBF}$ and ${\text{δCMRO}}_2$ are similar to that of $\text{δBOLD}$ .

The extended calibrated BOLD model

Boxerman et al. ¹⁸ demonstrated that the change in the effective transverse relaxation rate, ${\text{ΔR}}_2^{\text{*}}$ , can be expressed as follows

$${\text{ΔR}}_2^{\text{*}}=\text{A}\left(\text{CBV}{\left(1-\text{Y}\right)}^{\text{β}}-{\text{CBV}}_0{\left(1-{\text{Y}}_0\right)}^{\text{β}}\right)$$

(1)where the subscript 0 denotes the resting state, $\text{A}$ is a constant that depends on the field strength and sample-specific properties, which was assumed to stay constant from normoxia to mild hypoxia. $\text{β}$ is a constant characterizing the relationship between ${\text{ΔR}}_2^{\text{*}}$ and the magnetic susceptibility difference between blood and tissue. $\text{β}$ is dependent on the vessel size: $\text{β}=2$ for small capillaries, and $\text{β}=1$ for larger vessels. ¹⁹ In normoxia, $\text{β}=1.5$ was simulated with 2% capillary and 2% venule volume fractions. ¹⁵ In mild hypoxia, the average vessel size is likely to have a small increase due to the incorporation of arterioles (∼1% volume fraction), ¹⁶ which may lead to a slight decrease in $\text{β}$ . However, fluctuations in $\text{β}$ in the range of 1–1.8 have been shown to have little effects on the results. ¹⁵ Thus, we assumed $\text{β}=1.5$ for both normoxic and hypoxic conditions, but also explored the effects of variations in $\text{β}$ on the hypoxic results. In normoxia, deoxyhemoglobin in the arterial blood is ignored, and thus $\text{Y}$ normally represents the oxygen saturation in the venous blood. However, since hypoxia results in increased deoxyhemoglobin concentration in the arterial vasculature, $\text{Y}$ in this context denotes an effective oxygen saturation in the blood that considers the appropriate weighting of contributions from both arterial and venous oxygenation. Similarly, CBV normally represents venous cerebral blood volume in the Davis model, ¹⁵ but in this context, CBV denotes the total cerebral blood volume, which includes both arterial and venous blood.

Assuming a small ${\text{ΔR}}_2^{\text{*}}$ in fMRI experiments, Davis et al. ¹⁵ further suggested the following

$$\text{δBOLD}\sim -{\text{TEΔR}}_2^{\text{*}}$$

(2)where TE is the time of echo. Therefore, combining equations (1) and (2) yields

$$\begin{array}{c}\text{δBOLD}=︸\underset{\text{M}}{\text{TE}\cdot \text{A}\cdot {\text{CBV}}_0\cdot {\left(1-{\text{Y}}_0\right)}^{\text{β}}}\\ \left[1-\left(\text{δCBV}+1\right){(\frac{\left(1-\text{Y}\right)}{\left(1-{\text{Y}}_0\right)})}^{\text{β}}\right]\end{array}$$

(3)

Using a two-compartment model for the vasculature, which assumes that the capillary blood is correspondingly distributed into the arterial and venous blood, $\text{Y}$ is estimated via^20–22

$$\text{Y}={\text{αY}}_{\text{a}}+(1-\text{α}){\text{Y}}_{\text{v}}$$

(4)where the subscripts $\text{a}$ and $\text{v}$ denote arterial and venous, respectively, and $\text{α}$ represents the arterial volume fraction. Measurements using various techniques agree that $\text{α}$ ranges from 0.2 to 0.3 in healthy humans.^23–26 Studies have shown that $\text{α}$ changes in hypoxia, ²² but $\text{Y}$ calculated with a fixed $\text{α}$ is highly correlated with that calculated with a dynamic $\text{α}$ .^21,22,27 A fixed $\text{α}$ was selected for this study, although the influence of $\text{α}$ variations on the hypoxic results was also analyzed.

The Fick principle depicts the relationship among CMRO₂, CBF and the arterial and venous oxygen content ( ${\text{C}}_{\text{a}}{\text{O}}_2$ and ${\text{C}}_{\text{v}}{\text{O}}_2$ ) as follows

$${\text{CMRO}}_2=\text{CBF}\left({\text{C}}_{\text{a}}{\text{O}}_2-{\text{C}}_{\text{v}}{\text{O}}_2\right)$$

(5)

The blood oxygen content is the sum of the oxygen bound to hemoglobin and the oxygen dissolved in plasma, as follows ²⁸

$${\text{C}}_{\text{i}}{\text{O}}_2=\left(\text{φ}\cdot \left[\text{Hb}\right]\cdot {\text{Y}}_{\text{i}}\right)+\left({\text{P}}_{\text{i}}{\text{O}}_2\cdot \text{ε}\right),\text{i}=\text{a}\text{or}\text{v}$$

(6)where $\text{φ}=1.34{\text{\hspace{0.17em}ml O}}_2/\text{g\hspace{0.17em}Hb}$ represents the oxygen-carrying capacity of hemoglobin; $\left[\text{Hb}\right]=15\text{\hspace{0.17em}g\hspace{0.17em}Hb}/100\text{\hspace{0.17em}ml}$ blood represents the concentration of hemoglobin in blood; ${\text{P}}_{\text{i}}{\text{O}}_2$ represents the arterial $\left({\text{P}}_{\text{a}}{\text{O}}_2\right)$ or venous $\left({\text{P}}_{\text{v}}{\text{O}}_2\right)$ partial pressure; and $\text{ε}=0.003{\text{\hspace{0.17em}ml\hspace{0.17em}O}}_2/\left(100\text{\hspace{0.17em}ml blood}\cdot \text{mmHg}\right)$ represents the solubility of oxygen in blood. As the second term in equation (6) is far less (<1%) than the first term, ²⁸ it can be omitted from the estimation of blood oxygen content. Thus, equation (5) can be rewritten as follows

$${\text{CMRO}}_2\sim \text{φ}\cdot [\text{Hb}]\cdot \text{CBF}({\text{Y}}_{\text{a}}-{\text{Y}}_{\text{v}})$$

(7)

Allowing two physiological conditions in one experiment, ${\text{Y}}_{\text{v}}$ can be derived from equation (7)

$${\text{Y}}_{\text{v}}=\left({\text{Y}}_{\text{v},0}-{\text{Y}}_{\text{a},0}\right)\left(\frac{{\text{δCMRO}}_2+1}{\text{δCBF}+1}\right)+{\text{Y}}_{\text{a}}$$

(8)

Combining equations (3), (4) and (8), the extended model becomes

$$\text{δBOLD}=\text{M}[1-\left(\text{δCBV}+1\right){\left(\frac{\left(1-\text{α}\right)\left({\text{Y}}_{\text{a},0}-{\text{Y}}_{\text{v},0}\right)\left(\frac{{\text{δCMRO}}_2+1}{\text{δCBF}+1}\right)+\left(1-{\text{Y}}_{\text{a}}\right)}{1-{\text{αY}}_{\text{a},0}-(1-\text{α}){\text{Y}}_{\text{v},0}}\right)}^{\text{β}}]$$

(9)where

$$\text{M}=\text{TE}\cdot \text{A}\cdot {\text{CBV}}_0\cdot {\left(1-{\text{Y}}_0\right)}^{\text{β}}$$

(10)

Note that no assumption has been made regarding blood oxygen saturation during the deduction of this extended model. Therefore, equations (9) and (10) can be applied to normoxia, hypoxia and other conditions of oxygen availability.

Estimating δCMRO₂ under normoxic conditions

In normoxic environments, arterial blood is assumed to be fully oxygenated. Substituting ${\text{Y}}_{\text{a}}={\text{Y}}_{\text{a},0}=1$ , equation (9) becomes

$$\text{δBOLD}=\text{M}\left[1-\left(\text{δCBV}+1\right){\left(\frac{{\text{δCMRO}}_2+1}{\text{δCBF}+1}\right)}^{\text{β}}\right]$$

(11)which is a modified form of the Davis model.^9,29 Thus, M can be obtained by calibrating the physiological challenges in the setting of hypercapnia, ¹⁵ hyperoxia ²⁸ or exposure to a combination of the two gas mixtures, ³⁰ assuming that the CMRO₂ is not different under these conditions compared with that in breathing air (i.e. ${\text{δCMRO}}_2=0$ ). After M is determined, δCMRO₂ can be solved for using equation (11) by measuring δCBV, δCBF and δBOLD during an fMRI experiment in normal air.

Estimating δCMRO₂ under hypoxic conditions

In hypoxic environments, the Davis model is not valid due to reduced oxygen saturation in the arterial blood. Moreover, the M value under hypoxic conditions, denotes M^hypo, cannot be easily acquired from physiological calibrations because breathing hypoxic and breathing other (e.g. normoxic, hypercapnic, or hypoxic+hypercapnic) gas mixtures yield uncorrelated CMRO₂ values. ³¹ However, M^hypo is related to M according to equations (4) and (10)

$${\text{M}}^{\text{hypo}}=\text{M}\left(\frac{{\text{CBV}}_0^{\text{hypo}}}{{\text{CBV}}_0^{\text{norm}}}\right){\left(\frac{1-{\text{αY}}_{\text{a},0}^{\text{hypo}}-\left(1-\text{α}\right){\text{Y}}_{\text{v},0}^{\text{hypo}}}{1-{\text{αY}}_{\text{a},0}^{\text{norm}}-\left(1-\text{α}\right){\text{Y}}_{\text{v},0}^{\text{norm}}}\right)}^{\text{β}}$$

(12)where the superscripts hypo and norm represent hypoxic and normoxic conditions, respectively. ${\text{Y}}_{\text{a},0}^{\text{norm}}\approx 1$ . ${\text{Y}}_{\text{a},0}^{\text{hypo}}$ can be estimated with a pulse oximeter on the index finger, ³² which stays stable (i.e. ${\text{Y}}_{\text{a},0}^{\text{hypo}}={\text{Y}}_{\text{a}}^{\text{hypo}}$ ) during functional activation. The values of the terms $\frac{{\text{CBV}}_0^{\text{hypo}}}{{\text{CBV}}_0^{\text{norm}}}$ , ${\text{Y}}_{\text{v},0}^{\text{norm}}$ and ${\text{Y}}_{\text{v},0}^{\text{hypo}}$ can be acquired by various MRI approaches and were adopted from the literature in this study, as shown in Table 1. The effects of physiological variations in these variables were analyzed and discussed. After M^hypo is determined, δCMRO₂ can be solved for via equation (9) by measuring δCBV, δCBF and δBOLD during an fMRI experiment in a hypoxic environment.

Table 1.

Variables used in the extended model.

Variable	Standard value (range tested)	Description
α	0.3 (0.2–0.5)	Arterial volume fraction in the two-compartment vasculature 26
β	1.5 (1.3–1.6)	Constant characterizing the ${\text{ΔR}}_2^{\text{*}}$ dependence on blood oxygenation9,15
$\frac{{\text{CBV}}_0^{\text{hypo}}}{{\text{CBV}}_0^{\text{norm}}}$	1.04 (1.0–1.1)	Ratio of hypoxic resting CBV over normoxic resting CBV38,65,66
${\text{Y}}_{\text{v},0}^{\text{norm}}$	0.65 (0.6–0.7)	Resting venous oxygen saturation during normoxia67,82
${\text{Y}}_{\text{v},0}^{\text{hypo}}$	0.55 (0.5–0.6)	Resting venous oxygen saturation during hypoxia 82

Material and methods

Subjects

Fourty-eight healthy subjects (22 females, average age $(\text{mean}\hspace{0.17em}\pm \hspace{0.17em}\text{SD})=24.5\pm 2.7$ years) were included in this study. All subjects had normal or corrected to normal vision. The subjects’ intake of alcohol and caffeine was restricted for at least 24 h before MRI scanning. The study was approved by the Institutional Review Board of Peking University, in accordance with the Helsinki Declaration of 1975 (and as revised in 1983). Written informed consent was obtained from each subject.

Gas supply

For the entire scanning session, breathing gases were supplied to all subjects at a constant flow rate of 15L/min via a laboratory-built gas supply system. Three types of gas mixtures were separately stored in three high-pressure gas tanks: (1) medical air, consisting of 21%O₂ and 79%N₂; (2) a mildly hypoxic gas mixture, consisting of 12%O₂ and 88%N₂; and (3) a hypercapnic gas mixture, consisting of 5%CO₂, 21%O₂ and 74%N₂. The hypercapnic gas mixture was used to calibrate M as described in the “Theory” section. The three gas tanks, equipped with pressure regulators and flowmeters, were connected to a nonrebreather facial mask by a four-way valve and provided gas to the subjects one at a time.

Experimental procedures

All subjects sequentially performed two runs of the visual task and a hypercapnia challenge task. The arterial oxygen saturation (%SpO₂) of each subject was monitored by a digital pulse oximeter (Model 7500FO, Nonin, Plymouth, USA) throughout the experiments.

The visual task was a block-design paradigm of a 12 s dummy period followed by seven 60 s sessions alternating between resting and activation states. Visual stimuli displayed on a desktop monitor were reflected by a mirror placed directly in front of the subjects’ eyes. The subjects were shown a white crosshair located at the center of a black background during the resting states and a black-and-white radial checkerboard pattern flickering at 1, 4 or 8 Hz for each activation state. The orders of the flicker frequencies were randomized (i.e. [1, 4, 8] for one possibility, [4, 8, 1] for a second possibility, [8, 1, 4] for another possibility, and so on), and all six sequential possibilities were counterbalanced across the subjects. The subjects were instructed to focus on the center of the screen throughout the 432 s task duration.

Medical air was provided during the first run of the visual task. The mildly hypoxic gas mixture was switched on upon the completion of the first run and remained on until the end of the second run. The two runs were separated by a 5–7 min rest, allowing the %SpO₂ of the subjects to decrease and stabilize. As soon as the second run of the visual task was completed, medical air was switched back on, and another 5–7 min rest was included for the %SpO₂ to recover so that the hypercapnia challenge task could start. During the halts, the subjects were briefly questioned about any signs of shortness of breath, discomfort or concentration difficulty; they could answer these questions with simple hand gestures indicating yes or no while keeping their heads still.

During the hypercapnia challenge, the subjects were instructed to remain awake while supplied with medical air for the first 132 s (including a 12 s dummy period) and with the hypercapnic gas mixture for an additional 180 s.

MRI scanning protocol

The data were collected on a 3.0T MRI system (Discovery MR750, GE Healthcare, Milwaukee, USA) equipped with an 8-channel head coil. A single oblique slice passing through the anterior and posterior commissures and extending to the primary visual cortex (V1) was imaged. A sequence that simultaneously acquired vascular space occupancy (VASO), arterial spin labeling (ASL) and BOLD signals ¹⁷ was implemented to measure functional changes. The acquisition parameters were as follows: $\text{FOV}=260\times 260{\text{\hspace{0.17em}mm}}^2$ , matrix $\text{size}=64\times 64$ , slice $\text{thickness}=6\text{\hspace{0.17em}mm}$ , $\text{TE}=9.4\text{ms}/11.6\text{ms}/28.1\text{ms}$ for VASO/ASL/BOLD signals, inversion $\text{slab}=102\text{\hspace{0.17em}mm}$ , and $\text{TR}=2000\text{\hspace{0.17em}ms}$ . The blood nulling time (TI₁) for the VASO signal was individually determined with an inversion recovery sequence by searching for the lowest signal intensity in the sagittal sinus. ²⁹ In three subjects, we measured TI₁ in both normoxia and mild hypoxia and found no significant difference between the two oxygen conditions. Thus, TI₁ measured in normoxia ( $708.7\text{ ms\hspace{0.17em}}\pm 19.2\text{ ms}\left(\text{mean}\hspace{0.17em}\pm \hspace{0.17em}\text{SD}\right)$ ) was used to acquire VASO images. ${\text{TI}}_2=1200\text{ ms}$ was used to acquire the ASL images. In addition, a T₁-weighted fluid-attenuated inversion recovery sequence was implemented to acquire anatomical details, with acquisition parameters as follows: $\text{FOV}=260\times 260{\text{\hspace{0.17em}mm}}^2$ , matrix $\text{size}=256\times 256$ , slice $\text{thickness}=6\text{\hspace{0.17em}mm}$ , and $\text{TR}/\text{TE}/\text{TI}=1750\text{ ms}/23.2\text{ ms}/633\text{\hspace{0.17em}ms}$ .

Data analysis

Images acquired during the dummy periods were discarded, and the remaining images were processed with customized MATLAB scripts (MATLAB 2016, MathWorks, Natick, USA). The VASO/ASL/BOLD images were obtained by surround average/subtraction/average of the adjacent label and control images ³³ acquired during the first/second/third echo of the simultaneous acquisition sequence, respectively. Linear detrending was performed on the data from the visual task. Spatial smoothing ( $\text{FWHM}=8\text{\hspace{0.17em}mm}$ ) was applied to the data from all tasks.

A general linear model was utilized to identify functionally activated voxels, where $p<0.05$ was considered statistically significant. The region of interest (ROI) was defined as the voxels activated in common in all three modalities under both normoxic and mildly hypoxic conditions. The mean time series of the VASO, ASL and BOLD signals were extracted from the ROI and normalized to the corresponding baseline values (the averages of the data during the first minute of the time series). After excluding the data from the first 8 s of each activation session to account for the hemodynamic response effect, δVASO, δCBF and δBOLD values were obtained by averaging the data during the activation sessions in VASO, ASL and BOLD time series, respectively. δCBV was calculated from δVASO using the following equation ²⁹

$$\text{δCBV}=-\left(\frac{{\text{C}}_{\text{par}}}{{\text{C}}_{\text{blood}}{\text{CBV}}_0^{\text{j}}}\right)\text{δVASO}$$

(13)where the superscript $\text{j}=\text{norm or hypo}$ ; ${\text{CBV}}_0^{\text{norm}}=0.055\text{\hspace{0.17em}ml blood}/\text{ml}$ parenchyma was selected for the normoxic resting CBV;²⁹ ${\text{CBV}}_0^{\text{hypo}}$ was calculated according to $\frac{{\text{CBV}}_0^{\text{hypo}}}{{\text{CBV}}_0^{\text{norm}}}$ shown in Table 1; and ${\text{C}}_{\text{par}}=0.89$ and ${\text{C}}_{\text{blood}}=0.87\text{\hspace{0.17em}ml\hspace{0.17em}water}/\text{ml}$ parenchyma (blood) represent the water content in the parenchyma and blood, respectively. Then, δCBV, δCBF and δBOLD were used to calculate the δCMRO₂ caused by visual stimulations using the following two models.

The extended model

In the extended model, M for the normoxic condition was individually determined with equation (11) by replacing δCMRO₂ with 0 and the δCBV, δCBF and δBOLD measured during the hypercapnia challenge task. Then, ${\text{M}}^{\text{hypo}}$ for the hypoxic condition was individually estimated using equation (12). After M and ${\text{M}}^{\text{hypo}}$ were determined, the visual task-induced δCMRO₂ was evaluated using equations (9) and (11) for the normoxic and mildly hypoxic conditions, respectively.

In addition to the standard values, the effects of physiological variations (reported in Table 1) on the mildly hypoxic δCMRO₂ estimated using the extended model were evaluated.

The G-B model

We adopted the G-B model using variables with their standard values originally provided ¹⁶ except for a few adjustments to accommodate the content of this study. ${\text{Y}}_{\text{a}}^{\text{norm}}$ and ${\text{CBV}}_0^{\text{norm}}$ were set to 1 and 0.055, respectively, for the comparison with the extended model. δCBV was directly measured, and thus the exponent relating CBF to total CBV, $\text{Φ}$ , was omitted from the simulation. In human functional studies, the value of ${\text{Φ}}_{\text{v}}$ varies from 0 to 0.42, reported by different groups.^26,34–36 This relatively large variation could be partially attributed to different types of functional stimuli used in different studies. ²⁶ Hua et al.^26,36 conducted a black-and-white checkerboard visual stimulation study and reported ${\text{Φ}}_{\text{v}}=0.42$ . In this present study, we adopted this value because we used the identical functional stimuli as their study. In addition, we simulated ${\text{Φ}}_{\text{v}}$ in the range of 0–0.5 to further investigate the potential impacts of ${\text{Φ}}_{\text{v}}$ variations on the results of the G-B model.

To apply the G-B model to the mildly hypoxic conditions, ${\text{Y}}_{\text{a},0}^{\text{hypo}}$ was directly measured. ${\text{CBV}}_0^{\text{hypo}}$ was calculated as in the extended model. The resting extravascular rate of signal decay, ${\text{R}}_{2\text{E},0}^{\text{*}}$ , during hypoxia was estimated by calculating its change from the normoxic ${\text{R}}_{2\text{E},0}^{\text{*}}$ using equation (A10) in the original G-B model. ¹⁶ Other variables were assumed to remain constant from normoxia to hypoxia based on assumptions and findings of previous studies.^37–39

The effects of physiological variations were also considered for the G-B model. In the original G-B model, a thorough analysis was conducted in normoxia, and variables including hematocrit (Hct), venous fraction of baseline total blood volume ( ${\text{ω}}_{\text{v}}$ ), ${\text{ R}}_{2\text{E},0}^{\text{*}}$ and ${\text{Φ}}_{\text{v}}$ were found to have greater impacts on the δCMRO₂ estimates. ¹⁶ Therefore, we varied these four variables and explored the resulting δCMRO₂ in both oxygen conditions. The variables and the ranges of variations used in the simulation of the G-B model are listed in Table 2.

Table 2.

Variables used in the G-B model.

Variable	Standard value (range tested)	Description
${\text{Y}}_{\text{a}}^{\text{norm}}$	1	Arterial oxygen saturation during normoxia
${\text{CBV}}_0^{\text{norm}}$	0.055	Baseline total CBV during normoxia 29
${\text{ω}}_{\text{a}}$	0.2	Arterial fraction of baseline total CBV 16
${\text{ω}}_{\text{c}}$	0.4 (0.5–0.3)	Capillary fraction of baseline total CBV 16
${\text{ω}}_{\text{v}}$	0.4 (0.3–0.5)	Venous fraction of baseline total CBV 16
${\text{Φ}}_{\text{c}}$	0.21 (0.05–0.25)	Exponent relating CBF to capillary CBV 16
${\text{Φ}}_{\text{v}}$	0.42 (0–0.5)	Exponent relating CBF to venous CBV26,36
${\text{OEF}}_0$	0.4	Resting oxygen extraction fraction16,86
κ	0.4	Fraction of capillary blood considered to be “arterial” 16
$\text{Hct}$	0.44 (0.35–0.5)	Resting hematocrit of arteries and veins16,37
${\text{R}}_{2\text{E},0}^{\text{*}}$	25.1 (20–30)	Resting extravascular rate of signal decay in normoxia 16
Λ	1.15	Intravascular to extravascular spin density ratio 16
γ	2.68 × 108	Gyromagnetic ratio of protons
Δχ	2.64 × 10−7	Susceptibility of fully deoxygenated blood 16
B0	3 T	Magnetic field strength
SO2,off	0.95	Blood saturation for equal tissue-blood susceptibility 16

Once the visual task-induced δCMRO₂ was estimated, the flow-metabolism coupling ratio, $\text{n}=\text{δCBF}/{\text{δCMRO}}_2$ , was calculated for both normoxic and hypoxic conditions. Finally, outliers were removed based on three standard deviations, and group averages were calculated.

Results

The average %SpO₂ of the subjects during normoxic and mildly hypoxic conditions was $97.9\text{\%}\pm 0.2\text{\%}$ and $86.8\text{\%}\pm 1.8\text{\%}\hspace{0.17em}(\text{mean}\pm \text{SD})$ , respectively. Inhaling the mildly hypoxic gas mixture significantly decreased the ${\text{\%SpO}}_2(p<0.001)$ in all subjects without causing adverse effects or attention loss during the process. The average %SpO₂ measured in the mildly hypoxic environment was used as the value of ${\text{Y}}_{\text{a}}^{\text{hypo}}$ for the calculation of δCMRO₂ for all subjects.

Figure 1 shows the quantitative δCBV, δCBF and δBOLD maps of a representative subject performing the graded visual tasks in both mildly hypoxic and normoxic environments. The functional maps were superimposed on the anatomical map of this subject. Functional activations were observed in the V1 of this subject for all stimulus frequencies and oxygen conditions. All other subjects exhibited similar activation patterns. On average, mild hypoxia caused significant decreases $(p<0.01)$ in the activation regions of CBV, CBF and BOLD compared with normoxia. An ROI was determined as the voxels that were activated during all visual stimulations for both oxygen conditions. The average number of voxels contained in the ROIs of the subjects’ V1s was $54.5\pm \mathrm{31.4\hspace{0.17em}}(\text{mean}\pm \text{SD})$ .

Figure 1.

The quantitative δCBV, δCBF and δBOLD maps of a representative subject with activations evoked by visual stimulations at 1, 4 and 8 Hz in normoxic and mildly hypoxic environments. The functional maps were overlaid on the subject’s anatomical image. The functionally activated voxels were determined using a general linear model with p < 0.05 as statistically significant.

Figure 2 shows the quantitative δCBV, δCBF, δBOLD and M maps of a representative subject during the hypercapnia challenge. Hypercapnia challenge caused general signal increases in V1 in all contrasts as expected. M^hypo was calculated from M using equation (12). The average M and M^hypo of the subjects were $0.11\pm 0.05$ and $0.21\pm 0.09(\text{mean}\pm \text{SD})$ , respectively.

Figure 2.

The quantitative δCBV, δCBF, δBOLD and M maps of a representative subject during the hypercapnia challenge. The functional maps were overlaid on the subject’s anatomical image. The activated voxels of the δCBV, δCBF and δBOLD maps were determined using a general linear model with p < 0.05 as statistically significant.

Figure 3(a) shows the average visual task-induced δCBV, δCBF and δBOLD measured using the simultaneous acquisition technique. For both the normoxic and hypoxic conditions, δCBV, δCBF and δBOLD increased with the visual stimulus frequency and attained their peak values at 8 Hz. During mild hypoxia, statistically significant decreases in δBOLD were found ( $p<0.005$ for all visual stimulus frequencies), while no statistically significant difference was observed for δCBV ( $p>0.34$ for all visual stimulus frequencies) or δCBF ( $p>0.5$ ) for all visual stimulus frequencies), compared with the measurements during normoxia.

Figure 3.

The average (a) δCBV, δCBF and δBOLD measured by the simultaneous acquisition technique; (b) δCMRO₂ and n estimated using the extended model; (c) δCMRO₂ and n estimated using the G-B model evoked by visual stimulation at 1, 4 and 8 Hz in normoxic and mildly hypoxic environments.

Figure 3(b) shows the average visual task-induced δCMRO₂ and n estimated using the extended model under normoxic and mildly hypoxic conditions. For the normoxic condition, δCMRO₂ attained its maximum value at 4 Hz, and n changed nonlinearly with the visual stimulus frequency as expected. For the mildly hypoxic condition, δCMRO₂ and n were distinct from those observed during normoxia. Specifically, δCMRO₂ increased with the visual stimulus frequency, and n attained its peak value at 4 Hz during mild hypoxia. Furthermore, statistically significant decreases in δCMRO₂ were found ( $p<0.05$ for all visual stimulus frequencies) while statistically significant increases in n were observed ( $p<0.01$ for all visual stimulus frequencies).

Figure 3(c) shows the average visual task-induced δCMRO₂ and n estimated using the G-B model under normoxic and mildly hypoxic conditions. Overall, the two models generated comparable results. Compared with the extended model, the results of the G-B model exhibited smaller error bars and flatter trends, indicating that the G-B model was less sensitive to intersubject variations and visual stimulus frequencies. However, no statistically significant difference between δCMRO₂ ( $p>0.4$ for all visual stimulus frequencies) or n ( $p>0.2$ for all visual stimulus frequencies) estimated using these two models was observed.

The effects of physiological variations on δCMRO₂ induced by visual stimulation at 4 Hz were used as an example for representation. The results produced by other stimulus frequencies had similar patterns (data not shown). Figure 4(a) shows the effects of physiological variations on the hypoxic δCMRO₂ calculated using the extended model. δCMRO₂ was positively related with $\frac{{\text{CBV}}_0^{\text{hypo}}}{{\text{CBV}}_0^{\text{norm}}}$ and β and negatively related with α and ${\text{Y}}_{\text{v},0}$ , as expected from equations (9) and (12). Within the tested ranges, varying β had the greatest impact on the hypoxic δCMRO₂. Despite all physiological variations, the hypoxic δCMRO₂ was less than the normoxic δCMRO₂ induced by the same visual task.

Figure 4.

The effects of physiological variations on the δCMRO₂ induced by visual stimulation at 4 Hz estimated using (a) the extended model and (b) the G-B model. The blue (red) lines represent the normoxic (hypoxic) δCMRO₂ estimated using the standard values. The blue (red) bars represent the ranges of the normoxic (hypoxic) δCMRO₂ estimated due to physiological variations. With the extended model, all variables including $\frac{{\text{CBV}}_0^{\text{hypo}}}{{\text{CBV}}_0^{\text{norm}}}$ , α, ${\text{Y}}_{\text{v},0}^{\text{norm}}$ (and accordingly ${\text{Y}}_{\text{v},0}^{\text{hypo}}$ ) and β were tested. With the G-B model, variables including Hct, ω_v, ${\text{R}}_{2\text{E},0}^{\text{*}}$ or ${\text{Φ}}_{\text{v}}$ were tested. These variables were chosen because they were found to have greater impacts on δCMRO₂ than other variables in previous studies under normoxic conditions.

Figure 4(b) shows the effects of physiological variations on both normoxic and hypoxic δCMRO₂ calculated using the G-B model. δCMRO₂ was positively related with Hct, ${\text{ω}}_{\text{v}}$ and ${\text{R}}_{2\text{E},0}^{\text{*}}$ and negatively related with ${\text{Φ}}_{\text{v}}$ . Similar to the findings of the original G-B model, ¹⁶ ${\text{Φ}}_{\text{v}}$ had the greatest impact on both normoxic and hypoxic δCMRO₂. Moreover, as ${\text{Φ}}_{\text{v}}$ decreased to 0, the difference in the δCMRO₂ between the two oxygen availabilities reduced. Nevertheless, the trend of lower δCMRO₂ during hypoxia compared to normoxia remained despite all physiological variations.

Discussion

In this study, an extended calibrated BOLD model incorporating the dynamic measurement of δCMRO₂ in a hypoxic environment was developed and cross-validated with a multicompartment BOLD model. ¹⁶ A simultaneous acquisition technique that allows the CBV-, CBF- and BOLD-weighted signals to be measured in a single experiment ¹⁷ was implemented. The CBF-CMRO₂ relationship was investigated with graded visual stimulation tasks in both normoxic and mildly hypoxic environments.

Effects of mild hypoxia on visual task-induced δCBV, δCBF and δBOLD

As essential parameters for δCMRO₂ estimation, the effects of mild hypoxia on task-induced δCBV, δCBF and δBOLD deserve close attention. Our observations regarding the measurements of δCBV, δCBF and δBOLD evoked by the graded visual stimuli in normoxia agreed well with previous findings.^9,40,41 However, to the best of our knowledge, no prior work on the responses of CBV, CBF and BOLD to graded stimuli during mild hypoxia has been reported. Our data indicated that mild hypoxia did not influence the task-induced δCBV or δCBF values for any of the tested stimulus frequencies, which have been demonstrated with monotonic stimuli in several positron emission tomography (PET)^13,42 and MRI^14,43–45 studies in humans. In addition, our data suggested a significant decrease in task-induced δBOLD during mild hypoxia for all stimulus frequencies, consistent with previous findings of experiments with monotonic stimuli.^14,46–48

A confounding factor for accurate measurements of CBV, CBF and BOLD is the fluctuation in the arterial CO₂ pressure (PaCO₂) during mild hypoxia, which could not be directly recorded in the current experimental setting. Inhalation of 12%O₂ has been shown to decrease PaCO₂ to $34–35\text{\hspace{0.17em}mmHg}$ ⁴⁹ and lead to mild hypocapnia. While hypoxia may dilate blood vessels and raise the baseline CBF, hypocapnia counteracts both effects. ⁵⁰ In relation to functional activation, however, disparate BOLD responses have been reported during hypocapnia. For example, when the end tidal CO₂ pressure (PetCO₂), a noninvasive surrogate of PaCO₂, was less than 30 mmHg, Posse et al. ⁴⁹ observed a decrease in the visual stimulus-induced δBOLD, while Cohen et al. ⁵⁰ observed the opposite results. Despite the various impacts of hypocapnia, a minimal decrease of 2–3 mmHg in PaCO₂ is believed to induce only a minor impact, if any, on the overall task-induced responses of the brain during mild hypoxia.^13,43,44 Nevertheless, future studies would benefit from monitoring or controlling PetCO₂^51–53 during gas-related procedures.

Separate from CO₂ perturbation, accurate measurements of CBV, CBF and BOLD can also be affected if hypoxia had caused changes in the blood relaxation times. The blood ${\text{T}}_2^{\text{*}}$ decreased quadratically with Y,^54,55 and by 2–3 ms during mild hypoxia at 3T, as observed in previous studies.^44,56 Such a small decrease was insufficient to affect the sensitivity of BOLD signals or explain the significant decreases in the task-induced δBOLD during mild hypoxia. ¹⁴ Using bovine blood sample, Lu et al. ⁵⁷ observed that the blood T₁ decreased with Y and by approximately 3–4% during mild hypoxia at 3T. In human subjects, Tadamura et al. ⁵⁸ observed that the blood T₁ was negatively correlated with PaO₂. Nöth et al. ⁵⁹ further suggested that these competing effects of blood T₁ may cancel out when ${\text{Y}}_{\text{a}}^{\text{hypo}}$ was reduced by 9–14%. In our experiment, the TI₁ values, measured in 3 random subjects, were not significantly different between normoxia and mild hypoxia. In addition, Villien et al. ⁶⁰ reported that no significant difference in gray matter tissue T₁ was observed before and after altitude. These findings indirectly suggested that the changes in blood T₁ during mild hypoxia did not significantly affect the measurements of CBV and CBF. Furthermore, Ho et al. ⁴⁷ performed a simulation to show that the error in task-induced δVASO was within an acceptable range when decreased T₁ and ${\text{T}}_2^{\text{*}}$ during mild hypoxia were considered.

Effects of mild hypoxia on the CBF-CMRO₂ relationship

In normoxic environment, the visual task-induced δCMRO₂ varied nonlinearly with the stimulus frequency, with the maximum value occurring at 4 Hz. In addition, the flow-metabolism coupling relationship, n, varied nonlinearly with the stimulus frequency. These trends in δCMRO₂ and n were consistent with the results of earlier MRI and PET studies.^29,61 In the mildly hypoxic environment, δCMRO₂ and n exhibited different trends with the stimulus frequency compared with the normoxic environment. Specifically, δCMRO₂ increased with the stimulus frequency, and n attained its peak value at 4 Hz during mild hypoxia. Moreover, the amplitudes of the visual task-induced δCMRO₂ significantly decreased for all stimulus frequencies. Thus, significantly increased mismatches between δCBF and δCMRO₂ during mild hypoxia were clearly observed. The literature on stimulus-induced δCMRO₂ is very sparse. Only one study investigated the effect of mild hypoxia on δCMRO₂ evoked by a monotonic stimulation task; this study estimated δCMRO₂ based on an analytical model, which considers the contributions of both extravascular and intravascular (i.e. arterial and venous) compartments to the BOLD signal, and reported results similar to ours. ¹⁴ The authors suggested that the decrease in the task-induced δCMRO₂ was likely associated with the combined effects of an increased baseline CMRO₂ and the constant demand for the absolute CMRO₂ evoked by the same task in the mildly hypoxic environment. ¹⁴

Overall, mild hypoxia caused significant alterations in both the amplitude and trend of the CMRO₂ response to graded visual stimuli but did not impact the CBF response under the same condition. Thus, our observations did not support the hypothesis that a tightly coupled relationship between CBF and CMRO₂ exists during functional tasks and is subject to certain diffusion rules in the brain.^61–64 In contrast, our experiment demonstrated that CBF is regulated by factors other than CMRO₂ during brain stimulation under low oxygen availability.

The extended model versus the G-B model

The extended model is an extension of the Davis model, which has been the mostly applied method to study the relationship between δCBF and δCMRO₂ during neuronal activations. While it is credited for its robustness and simplicity, the Davis model considers only extravascular contributions to the BOLD signal. On the other hand, the G-B model considers contributions from the extravascular and intravascular (i.e. arterial, capillary and venous) compartments to the BOLD signal and incorporates information including vessel size, blood volume exchange effect, and so on. ¹⁶ As broad and exquisite as it is, the G-B model relies extensively on prior knowledges and assumptions regarding multiple variables and relationships. In this study, these two models were cross-validated and generated comparable results on the estimated δCMRO₂ evoked by visual stimulations at different oxygen availabilities.

For the extended model, $\frac{{\text{CBV}}_0^{\text{hypo}}}{{\text{CBV}}_0^{\text{norm}}}$ was expected to increase slightly, if any, during hypoxia and was varied in the range of 1.0–1.1 based on previous measurements.^38,65,66 ${\text{Y}}_{\text{v},0}^{\text{norm}}$ was varied from 0.6 to 0.7, and accordingly ${\text{Y}}_{\text{v},0}^{\text{hypo}}$ from 0.5 to 0.6, based on findings with multiple MRI approaches. ⁶⁷ $\text{α}$ was varied from 0.2 to 0.4, based on an animal study, which showed that $\text{α}$ increased from 0.23 to 0.34 when PaO₂ decreased from 100 to 60 mmHg (corresponding to ${\text{Y}}_{\text{a}}^{\text{hypo}}=0.9–1$ ). ²² Variations in ${\text{Y}}_{\text{v}}$ , $\frac{{\text{CBV}}_0^{\text{hypo}}}{{\text{CBV}}_0^{\text{norm}}}$ or $\text{α}$ did not affect the normoxic δCMRO₂ and caused minor effects on the hypoxic δCMRO₂. In normoxia, $\text{β}=1.5$ fitted reasonably well with theoretical stimulations. ¹⁶ In hypoxia, $\text{β}$ was expected to decrease slightly due to the contribution of larger arterioles to the BOLD signal. We thus varied $\text{β}$ from 1.3–1.6 and found that it had a larger impact on the hypoxic δCMRO₂ than did other variables. However, none of these physiological variations altered the decreased visual task-induced δCMRO₂ observed in hypoxia when compared with normoxia (Figure 4(a)).

For the G-B model, physiological variations can occur in all variables used for the simulation. In the original G-B model, a thorough analysis has been conducted to examine the effects of physiological variations on the estimated δCMRO₂ in normoxia. ¹⁶ To avoid redundancy, we selected the four variables (i.e. $\text{Hct}$ , ${\text{ω}}_{\text{v}}$ , ${\text{R}}_{2\text{E},0}^{\text{*}}$ and ${\text{Φ}}_{\text{v}}$ ) that were identified to have the greatest impacts on the results and varied them in the ranges provided by previous studies.^16,37 Our analysis showed that none of the physiological variations altered the current results. However, ${\text{Φ}}_{\text{v}}$ had the greatest impact on the estimated δCMRO₂ compared to the other variables in both oxygen availabilities. This result was consistent with the analysis conducted by Griffeth and Buxton. ¹⁶ The values of ${\text{Φ}}_{\text{v}}$ reported in the literature vary among different studies. For example, Chen and Pike ³⁴ used graded dual tasks of blue-and-yellow checkerboard visual stimulation and finger-to-thumb apposition and reported an average ${\text{Φ}}_{\text{v}}=0.23$ . Hua et al.^26,36 reported ${\text{Φ}}_{\text{v}}=0.42$ by performing a black-and-white checkerboard visual stimulation. Recently, Wesolowski et al. ³⁵ reported ${\text{Φ}}_{\text{v}}\approx 0$ using red LED goggles visual stimulation. Hua et al. ²⁶ argued that these relatively large variations of ${\text{Φ}}_{\text{v}}$ could be partially attributed to different types of functional stimuli. Indeed, different functional stimuli could cause distinct activation patterns,^68,69 which could result in different ${\text{Φ}}_{\text{v}}$ values. ³⁵ Thus, in this study, we adopted ${\text{Φ}}_{\text{v}}=0.42$ from Hua et al.^26,36 because we used the identical functional stimuli as their study. By using a smaller ${\text{Φ}}_{\text{v}}$ (such as ${\text{Φ}}_{\text{v}}=0.2$ originally used by the G-B model), simulations of the G-B model yielded higher values of δCMRO₂ and smaller differences between the δCMRO₂ of the two oxygen conditions. Nevertheless, the fundamental finding of reduced δCMRO₂ during hypoxia compared to normoxia preserved (Figure 4(b)). In the future, experiments using other types of functional stimuli shall be conducted to further validate the extended model with the G-B model in conditions of lower ${\text{Φ}}_{\text{v}}.$

Efficacy and limitations

We explicitly implemented a simultaneous acquisition technique, first suggested and validated by Yang et al., ¹⁷ to acquire the CBV-, CBF- and BOLD-weighted signals simultaneously as opposed to in separate trials. This time-efficient methodology eliminated intrasubject variations in task performance over multiple trials, thus improving the precision of δCMRO₂ interpretation. Although this simultaneous acquisition technique has been widely adopted by multiple studies,^{9,10,29,70–72} it was limited to single-slice acquisition—the amount of information extracted from the brain images is spatially confined. To overcome this problem, Cheng et al. ⁷³ introduced a 3D triple acquisition pulse sequence that allowed 3D acquisition of the CBF, CBV and BOLD signals, a technique with potential utility in future CMRO₂-related studies.

We directly measured δCBV in this study. The measurement of δCBV has frequently been omitted in relevant studies, mainly for two reasons. On one hand, measuring δCBV is time-consuming because without a simultaneous acquisition technique, a separate trial is required. On the other hand, δCBV is believed to have a power-law relationship with δCBF: $\text{CBV}=0.80{\text{CBF}}^{0.38}$ , first described by Grubb et al. based on experiments with rhesus monkeys. ⁷⁴ However, subsequent PET and MRI studies with human subjects demonstrated that in the power-law relationship described by

$$(1+\text{δCBV})={(1+\text{δCBF})}^{\text{Φ}}$$

(14)the coefficient Φ varied for different regions and physiological states.^29,75,76 In this study, the average Φ calculated using equation (14) during visual stimulation was $\left(\text{mean}\pm \text{SD}\right)0.48\pm 0.16$ and $0.46\pm 0.13$ in normoxia and mild hypoxia, respectively. The average Φ measured during the hypercapnia challenge was $(\text{mean}\pm \text{SD})0.50\pm 0.38$ . Similar to previous findings,^77,78 no statistically significant difference was observed between stimuli and hypercapnia $\left(p=0.8\right)$ . However, a slight decrease $(p=0.16)$ was observed during mild hypoxia compared to normoxia. Our measurements of Φ were largely consistent with previous findings.^{9,10,29,71,79,80} Although Grubb et al. ⁷⁴ reported a fitted $\text{Φ}=0.38$ , van Zijl et al. ⁷⁹ refitted their data with $\text{Φ}=0.5$ and obtained a correlation coefficient greater than 0.9. In PET studies, Ito et al. ⁷⁷ reported a fitted $\text{Φ}=0.30$ , while Lin et al. ²⁹ recalculated their average data using equation (14) and found an average $\text{Φ}=0.51$ . Nevertheless, the CBV measured using the VASO technique can be confounded by the inflow effects of the fresh blood,^71,81 resulting in an overestimated Φ. However, this will not alter our fundamental conclusion regarding the hypoxia effects on the CBF–CMRO₂ relationship. Still, the accuracy of CBV measurements can be further improved by varying TR or TI^71,81 in future studies.

Most of the variables used in the two models were global and group-average values, which may blur intersubject and/or regional variations of the results. For instance, in the extended model, the values of ${\text{Y}}_{\text{a},0}^{\text{norm}}$ and ${\text{Y}}_{\text{a},0}^{\text{hypo}}$ were adopted from Xu et al. ⁸² because the corresponding ${\text{Y}}_{\text{a},0}^{\text{norm}}$ and ${\text{Y}}_{\text{a},0}^{\text{hypo}}$ values in the two studies were comparable. However, these values were group averages estimated from the sagittal sinus. Since ${\text{ Y}}_{\text{v},0}$ can vary across subjects ⁸³ and brain regions, ⁸⁴ using adopted values could cause inaccurate global and/or regional estimations of M^hypo and δCMRO₂. In future studies, individually determined and voxel-based methods for estimating variables could be implemented to enhance the accuracies of the two models.

Finally, this study was limited to dynamic estimation of the fractional changes of CMRO₂. The effects of hypoxia on the baseline CMRO₂ were unknown. Thus, interpretations of the findings of this study should be limited to the scope of the fractional changes in the flow-metabolism relationship caused by mild hypoxia. To further explore the mechanism underlying the effects of hypoxia on the CMRO₂ behaviors, paradigms investigating the effects of hypoxia on the baseline physiologies and/or methods allowing CMRO₂ quantification in absolute values ⁸⁵ should be considered in future studies.