Indication of BOLD-Specific Venous Flow-Volume Changes from Precisely Controlled Hyperoxic vs. Hypercapnic Calibration

Abstract

Deriving cerebral metabolic rate of oxygen consumption (CMRO₂) from blood oxygenation level-dependent (BOLD) signals involves a flow-volume parameter (α), reflecting total cerebral blood volume changes, and a calibration constant (M). Traditionally, the former is assumed a fixed value and the latter is measured under alterations in fixed inspired fractional concentrations of carbon dioxide. We recently reported on reductions in M-variability via precise control of end-tidal pressures of both hypercapnic (HC) and hyperoxic (HO) gases. In light of these findings, our aim was to apply the improved calibration alternatives to neuronal activation, making use of their distinct vasoactive natures to evaluate the α-value. Nine healthy volunteers were imaged at 3 T while simultaneously measuring BOLD and arterial spin-labeling signals during controlled, graded, HC, and HO, followed by visual (VC) and sensorimotor cortices (SMC) activation. On the basis of low M- and CMRO₂-variability, the comparison of these calibration alternatives accurately highlighted a reduced venous flow—volume relationship (α = 0.16 ± 0.02, with α_VC = 0.12 ± 0.04, and α_SMC = 0.20 ± 0.02), as appropriate for BOLD modeling.

Keywords

BOLD calibration end-tidal control flow—volume relationship hypercapnic hyperoxic

Introduction

In spite of the blood oxygenation level-dependent (BOLD) signal being the predominant imaging technique to explore human neuronal activation, the metabolic and hemodynamic changes at its basis still elude precise quantification and understanding. Primarily driven by changes in cerebral blood flow (CBF), the BOLD contrast is also modulated by volume and metabolism changes. Hence, the flow—volume relationship (typically characterized by the parameter α), the deoxyhemoglobin (dHb) baseline level, the cerebral metabolic rate of oxygen consumption (CMRO₂), and its coupling to CBF (ψ) are crucial to the quantification of the BOLD phenomenon.

Although the CMRO₂ response to neuronal activation can be measured by tracer kinetics such as positron emission tomography (¹⁵O-PET; Mintun et al, 2001) or nuclear magnetic resonance (¹⁷O-, ¹³C-, and ³¹P-NMR; Herman et al, 2006), these approaches are costly, complex, and offer limited spatial resolution and signal-to-noise ratio. Positron emission tomography also requires a radiotracer and long scan times over which physiological states might change. Near-infrared spectroscopy (Boas et al, 2003), inherently sensitive to oxygenated and deoxygenated hemoglobin (oHb and dHb, respectively), allows estimating CMRO₂ indirectly from hemodynamic parameters, yet also on a limited spatial resolution. In addition, requiring knowledge of blood flow, the technique is complicated by the need to use a multi-modality approach to measure CBF concurrently (e.g., with functional magnetic resonance imaging (fMRI)). In vivo magnetic resonance (MR)-oximetry together with phase-contrast and pulsed arterial spin-labeling (ASL) flow imaging (Chen and Pike, 2010a) have been applied to quantify changes in global CMRO₂ (e.g., under baseline or hypercapnic (HC) state) but not regional changes (e.g., localized to neuronal activity).

Because of its relative simplicity, availability, and good spatial resolution, BOLD-calibrated fMRI has recently taken precedence in human brain studies for the estimation of CMRO₂. In this context, the extensively used dHb dilution model enables CMRO₂ calculations by integrating the physiological processes giving rise to BOLD (Hoge et al, 1999a; Davis et al, 1998). Given that almost all venous dHb is generated from the metabolic extraction of O₂, variations in venous dHb concentration ([dHb]_v) are quantified from relative changes in CBF, cerebral blood volume (CBV), and CMRO₂. The biophysical model requires simultaneous acquisition of BOLD and CBF under conditions of calibration and neuronal activation. Calibration of the BOLD—CBF relationship at resting-state CMRO₂ typically relies on the induction of changes in CBF from the manipulation of the arterial partial pressure of carbon dioxide (PaCO₂). A common method to elevate PaCO₂ is to transiently increase the fractional concentration of CO₂ in inspired gas (F_ICO₂). Under this traditional HC technique, the resulting calibration (M)-value is prone to large intra- and inter-subject as well as inter-session variations (Chiarelli et al, 2007b, c ; Leontiev and Buxton, 2007). The accurate determination of the M-value in individual subjects and brain regions (Chiarelli et al, 2007a; Ances et al, 2008) is critical as it can bias CMRO₂-estimates (Chiarelli et al, 2007b). Another uncertainty arises from the derivation, in lieu of measurement, of volume changes from flow data based on a power—law relationship (α) observed in anesthetized monkeys under global CO₂ challenges (Grubb et al, 1974), recently demonstrated by fMRI, NMR, PET, and optical studies to overestimate changes residing in the venous vasculature holding partially deoxygenated blood (i.e., venules, veins, and with smaller weighting, arterioles and capillaries) specifically responsible for the BOLD contrast (Chen and Pike, 2009, 2010b; Ito et al, 2003; Lee et al, 2001; Hillman et al, 2007). In expanding the dHb dilution model to include several physical effects not included in its original mathematical form, this flow-volume change has recently been reported to be the parameter with the largest impact on the model's accuracy (ψ_v, or uncorrected typo φ_v, in Figure 6a of Griffeth and Buxton, 2011), the later being optimized under reduced input value (Figure 7b of Griffeth and Buxton, 2011).

In the context of the widely used dHb dilution model, we recently introduced a precise, repeatable computer-controlled iso-oxic HC method for reduced methodological variations in calibration and M-estimates (Mark et al, 2010, 2011). Because M represents the theoretical maximum achievable BOLD signal at baseline dHb, it would ideally be more accurately found at high HC levels (Hoge et al, 1999a). However, large rises in PaCO₂ are poorly tolerated as they cause distressing feelings of breathlessness. A change in BOLD signal can also be induced at isocapnia (i.e., baseline PaCO₂) with a transient increase in arterial blood O₂ content from elevated levels of fractional inspired concentration of oxygen (F_IO₂; Chiarelli et al, 2007c). Isocapnic changes in F_IO₂ are not sensed by subjects and thus well tolerated. We hence also reported that a precisely controlled isocapnic hyperoxic (HO) stimulus is a robust, rapid, well-tolerated technique of further reducing M-variability in fMRI calibration (Mark et al, 2011). Our aim in the current study was to apply these diminished method-dependent variations in the calibration data to neuronal activation, taking advantage of their distinct vasoactive natures, and reduced M- and CMRO₂-variability, in order to estimate the flow—volume relationship (i.e., α-value). We thus applied computer-controlled graded HC and HO levels as well as visual and sensorimotor stimulation during the same scanning session in the same group of subjects. We hypothesized that improved methodology of these two alternative calibrations would yield sufficiently low variability in M- and CMRO₂-estimates to allow a novel and complementary approach to accurately evaluate α in individual brain regions.

Materials and methods

The experimental protocol was approved by the Research Ethics Board of the Montreal Neurological Institute (MNI, Montreal, Canada) and the computerized end-tidal gas-targeting system (RespirAct™, Thornhill Research, Toronto, Canada) was approved for this study under an investigational device exemption by Health Canada. Signed informed consent was obtained from 11 nonsmoking healthy adults. Subjects were instructed not to consume caffeine on the day of their scan. Two subjects were excluded from the study as their scans showed excessive head motion. We therefore included data from nine subjects (five females; mean age 26 years; range 18 to 30 years).

Experimental Protocol

All MR scans were performed on a Siemens 3 T TIM Trio system (Siemens, Erlangen, Germany) with a 32-channel phased array head-coil. The functional acquisitions covered nine oblique axial slices (4 × 4 × 6 mm³; interslice gap of 1 mm) positioned to include both visual and sensorimotor cortices (VC and SMC, respectively) based on a high-resolution three-dimensional T₁-weighted data set (1 × 1 × 1 mm³) and a BOLD functional localization scan. During the localizer, subjects were instructed to perform voluntary bilateral cyclic finger tapping (trained to keep pace at ~ 3 Hz before scanning) coincident with the presentation of a maximal contrast black/white checkerboard of eight reversals per second in one OFF/ON/OFF block of 6-seconds/11-seconds/6-seconds. Each subject was then scanned under randomized levels of isocapnic HO and iso-oxic HC protocols obtained from an automatic respiratory modulation of end-tidal partial pressures (P_ET), as described previously (Mark et al, 2011). The HO consisted of isocapnic (P_ETCO₂ maintained at baseline) step increases in P_ETO₂ of 140, 240, and 340 mmHg from baseline. The HC protocol consisted of iso-oxic (P_ETO₂ maintained at baseline) increases in P_ETCO₂ of 3, 5, 7, and 9 mmHg from baseline. Each challenge was preceded by a 60-seconds steady-state level where P_ETCO₂ and P_ETO₂ were clamped at resting levels observed for each subject during spontaneous ventilation. Imaging lasted for 6 minutes and consisted of one OFF/ON/OFF block of 60-seconds/120-seconds/120-seconds. Subsequent to this calibration procedure, each subject was scanned under simultaneous visual and sensorimotor activation while acquiring ASL frames with identical MRI sequence and imaging parameters as under the respiratory tasks. Subjects were presented with a maximal contrast black/white checkerboard (alternating at 8 contrast-reversals per second, in four OFF/ON/OFF blocks of 24-seconds/48-seconds/24-seconds) and instructed to perform voluntary bilateral sequential finger-to-thumb apposition coincident with the visual stimulus. To maintain attention over the resting period subjects were asked to fixate upon a black triangle at the screen center. Subjects were also instructed to maintain a constant breathing rate during the neuronal scans to minimize PaCO₂ fluctuations because of slow variations in breathing at rest and involuntary increase from the motor task or anxiety. Pilot studies showed high reproducibility for these tasks under the chosen region of interests (ROIs; see ‘Data Analysis' section for a description of these ROIs), as demonstrated before (Leontiev et al, 2007). After the scan, all except two subjects reported following every instruction given (i.e., hence rejected from neuronal data set, N = 7). Minimal fluctuations in P_ETCO₂ were observed in all analyzed subjects during the neuronal tasks (i.e., below the ± 1 mmHg sensitivity of our gas controller), in agreement with others (Chiarelli et al, 2007a).

Magnetic Resonance Imaging Parameters

A multislice-pulsed ASL echo planar imaging sequence was used for simultaneous CBF and BOLD measurement, as previously described (Mark et al, 2011). The pulsed ASL sequence was based on QUIPSS II (Wong et al, 1998) with ASSIST background suppression (Ye et al, 2000) and two presaturation asymmetric BASSI pulses (Warnking and Pike, 2006) in the imaging region followed by an adiabatic BASSI inversion pulse in the labeling region (thickness of 150 mm, gap of 5 mm) and inversion times of 700 milliseconds and 1,400 milliseconds. An echo planar imaging readout (2,170 Hz/pixel) was used with an echo time of 25 milliseconds. A repetition time of 3 seconds allowed the acquisition of 120 frames for each respiratory challenge and 128 frames for the neuronal tasks.

Data Analysis

CBF images were formed by subtracting adjacent nonselective (control) and selective (tag) frames, whereas BOLD images were obtained from their average. Differences in frame timing were corrected using sinc interpolation, which also removed the potential contamination of ASL data by BOLD (Lu et al, 2006). Motion correction parameters were estimated using AFNI's 3dvolreg software (Cox, 1996). Frames with estimated translation > 1 mm or rotation >1° were excluded from the analysis, a situation never exceeding three frames at any challenge level. All data were spatially smoothed with a three-dimensional Gaussian filter of 6 mm full-width half-maximum. Drift was removed by subtracting from each voxels time course the low-frequency components of its discrete cosine transform, with a cutoff frequency of one-half of the stimulation paradigm frequency.

Areas of statistically significantly BOLD and CBF activation were identified based on the generalized linear model assuming a gamma variate hemodynamic response function using fMRIstat (Worsley et al, 2002). Signal changes under both respiratory and neuronal stimulation were calculated in statistically thresholded t-maps (at significance level of P < 0.05, corrected for multiple comparisons). To investigate specific brain regions, we manually separated the activation maps for each subject into ROIs encompassing VC and SMC.

Time courses of CBF and BOLD percentage responses for each subject, obtained in the VC and SMC, were temporally low-pass-filtered (Hanning, full-width half-maximum 6-seconds). Mean CBF and BOLD responses (ΔBOLD and ΔCBF, respectively) were normalized to their corresponding baseline values (BOLD₀ and CBF₀). The amplitude of the steady-state response to each respiratory and neuronal task was computed as the signal intensity averaged across the time points representing the plateau portion of the response (i.e., Respiratory tasks: rejecting frames in the initial 24-seconds of the ON period, Neuronal tasks: a 24-seconds period starting 12-seconds after stimulus onset).

Cerebral Metabolic Rate of Oxygen Consumption and ψ-Estimates

For each subject, we estimated changes in the CMRO₂ and its coupling relationship (ψr) to CBF under neuronal activation in the ROI corresponding to VC and SMC (index i) based on the dHb dilution model (Hoge et al, 1999a; Davis et al, 1998), using group and subject M-values (M_Group and M_Subject, respectively, index j) obtained under HC and HO calibration (index k):

\begin{aligned} {\frac{Δ C M R O_{2}}{C M R O_{2, 0}} |}_{i, j, k} & = [1 - (Δ B O L D / B O L D_{0} |_{i}) / M_{i, j, k}]^{1 / β} \cdot \\ [1 + Δ C B F / C B F_{0} |_{i}]^{1 - α / β} - 1 \end{aligned}

(1)

Ψ |_{i, j, k} = \frac{Δ C M R O_{2} / C M R O_{2, 0} |_{i, j, k}}{Δ C B F / C B F_{0} |_{i}}

(2)

where β, a constant linking blood oxygenation to relaxivity (Boxerman et al, 1995), is estimated to be 1.3 at 3T (Buxton, 2003). To account for the CBV contribution to the BOLD signal, the α-parameter was, in turn, (1) assumed a reduced value previously shown to reflect the venous compartment (α = 0.20; Chen and Pike, 2009, 2010b; Mark et al, 2011), (2) assumed the widely used total blood volume value (α = 0.38; Grubb et al, 1974; see ‘Assumed α-Parameter' section), and (3) estimated from an unconstrained nonlinear least-square curve-fit (trust—region—reflective method, weighted by the inverse standard deviation of the measurements) that optimizes the agreement between HC and HO calibrated data (see ‘Optimized α-Parameter' section). M-values were estimated from linear fits of the slope between changes in BOLD and the denominators of equations (1) and (2) in (Mark et al, 2011) representing changes in blood flow under HC and deoxyhemoglobin under HO. Separate brain regions (i.e., VC and SMC defined by the ROI selection, see ‘Data Analysis' section) were used to derive M_Subject-values based on (1) individual data points across graded HO or HC levels, and M_Group-values based on (2) the entire data set (i.e., all graded HC or HO levels across all subjects). The errors on M-values, representing the 95% confidence intervals of the mean (CI_m) of the fit of the slope, as well as the errors on functional BOLD and CBF responses were propagated into the variance of CMRO₂-estimates for each subject (as described in Appendix A).

To evaluate the extent to which lower variability in M-values translates to reduced variability in CMRO₂- and ψ-estimates, individual results of equations (1) and (2) were averaged across subjects and the variability was quantitatively assessed based on the percent coefficient of variation (CoV).

Results

MR Responses

On average across subjects, visual stimulation led to BOLD- and CBF-activated areas of 51.6 ± 8.4 cm³ and 35.9 ± 5.0 cm³, respectively, whereas sensorimotor stimulation led to a corresponding 58.6 ± 12.8 cm³ and 30.5 ± 7.6 cm³ (e.g., Figure 1). The selection of statistical significance for ROI definition resulted in an adequate number of activated voxels for robust and low variability MR signal changes in both cortices. The t-map thresholding method is biased toward voxels with the highest signals, and hence holds widespread use in fMRI studies due to their limited signal-to-noise ratio. The slightly enlarged spatial extent of BOLD vs. CBF activation might have originated from the use of a common threshold for BOLD and CBF, the latter based on a lower signal-to-noise ratio perfusion measurement, or from enhanced extravascular BOLD effects around large veins and sagittal sinus. The analysis did not substantially change upon overlapping BOLD and CBF ROIs (resulting in 85% and 81% common voxels in VC and SMC, respectively) and the need for consistency in the ROI definition used for M calculations (with HO being non-vasoactive; Mark et al, 2011) justified keeping them separate. The group averaged steady-state MR responses in both cortices (BOLD_VC = 1.41 ± 0.01%, CBF_VC = 55.3 ± 0.6% and BOLD_SMC = 0.83 ± 0.01%, CBF_SMC = 43.6 ± 0.5%) are in general agreement with previous fMRI studies using similar stimulation conditions (Stefanovic et al, 2006; Hoge et al, 1999b; Davis et al, 1998; Leontiev et al, 2007; Kim et al, 1999; Kastrup et al, 2002).

Figure 1

Blood oxygenation level-dependent (BOLD; top) and cerebral blood flow (CBF; bottom) visual and sensorimotor activation maps in a single subject. The color range represents the percentage signal change from baseline.

Estimates of Oxidative Metabolism and Metabolism-Flow Coupling

Figure 2 shows individual BOLD and CBF changes induced under visual and sensorimotor stimulation, along with iso-metabolic contours from HC and HO group-calibrations assuming venous CBV contribution (i.e., α = 0.20). Individual neuronal activation results falling on positive contours (shown in 10% increments) indicate increased oxidative metabolism that enhances metabolic dHb production and attenuates BOLD compared with the calibration condition (iso-metabolic contour = 0%). The functional data appear to follow the principle direction of the across-subject-averaged group-calibrated metabolism-flow coupling ratios (ψ shadowed regions). In both cortices, these averaged ψ-estimates (reproduced in Figures 3A and 3B against individual changes in CMRO₂ and CBF), agree relatively well under the HC and HO calibrations (i.e., compared with when assuming α = 0.38, shown in Figures 3C and 3D and discussed in ‘Assumed α-Parameter' section) and fall in the range reported in fMRI and PET studies (ψ ~ [0.25 to 0.5], Figure 3 of Buxton, 2010).

Figure 2

Blood oxygenation level-dependent (BOLD) and cerebral blood flow (CBF) signal changes in the (left: A, C) visual cortex and (right: B, D) sensorimotor cortex for each subject (black markers, N = 7). Iso-cerebral metabolic rate of oxygen consumption contours under (top: A, B) hypercapnic (HC: dotted blue) and (bottom: C, D) hyperoxic (HO: dotted red) group-calibration were obtained from equation (1) using the corresponding M_Group under venous (α = 0.20) cerebral blood volume assumption. Error bars indicate the standard deviation of the steady-state values over the averaged stimulation blocks. Across-subject-averaged ψ-estimates are shown as shadowed regions (mean ± s.e.).

Figure 3

Cerebral metabolic rate of oxygen consumption (CMRO₂) and cerebral blood flow (CBF) signal changes in the (left: A, C) visual cortex and (right: B, D) sensorimotor cortex for each subject (N = 7). Cerebral metabolic rate of oxygen consumption estimates were obtained from equation (1) under hypercapnic (HC: blue markers) and hyperoxic (HO: red markers) group-calibration under (top: A, B) venous (α = 0.20) and (bottom: C, D) total (α = 0.38) cerebral blood volume assumption. Error bars indicate the s.e. with error propagation (Appendix A). Across-subject-averaged ψ-estimates are shown as shadowed regions (mean ± s.e.).

As summarized in Table 1a, the average CMRO₂- and ψ-estimates found under the alternative calibrations, under an assumed α of 0.20, display reduced variability (ѱ ~ CoVψ ~ 6% to 11% under HC and ~3% to 8% under HO) compared with those previously reported by fMRI studies using fixed inspired HC calibration (reaching ~65%; Hoge et al, 1999b; Stefanovic et al, 2006; Chiarelli et al, 2007a; Leontiev et al, 2007; Kim et al, 1999) or absolute-relaxation-rates calibration (up to ~40%; Fujita et al, 2006). This improvement arises from improved accuracy in M-values under precise end-tidal HC gas manipulation (CoV_M,HC ~13% to 14%), even more pronounced under HO manipulation (CoV_M,HO ~ 6%), vs. quoted F_ICO₂ studies (CoV_M,HC ~ 20% to 75%). Our further reduction in variability under HO calibration (CoV_HO/HC ~0.3 to 0.8) is displayed graphically as narrower errors in Figures 2, 3A, and 3B. Findings obtained under the traditionally assumed α-value of 0.38 are detailed separately in the section ‘Assumed α-Parameter‘.

Table 1

Summary of across-subject group fitted M-values (m ± CI_m, where m is the mean and CI_m the 95% confidence interval of the mean), averaged percentage change in CMRO₂- and ψ-estimates (m ± s.e.) under HC and HO group calibration in the VC and SMC, for (a) venous CBV (α = 0.20) and (b) total CBV (α = 0.38; N = 7).

Group calibration	M_Group (%)	ΔCMRO₂/CMRO_2,0 (%)	ψ
(a) Venous (α = 0.20)
VC
HC	5.5 ± 0.7	15.2 ± 1.7	0.28 ± 0.03
HO	5.2 ± 0.3	13.0 ± 0.9	0.24 ± 0.02
CoV_HO/HC	0.5	0.6	0.8
SMC
HC	5.0 ± 0.7	18.1 ± 1.1	0.40 ± 0.03
HO	5.0 ± 0.3	18.2 ± 0.6	0.40 ± 0.01
CoV_HO/HC	0.4	0.5	0.3
(b) Total (α = 0.38)
VC
HC	6.4 ± 0.8	12.3 ± 1.3	0.23 ± 0.02
HO	5.2 ± 0.3	6.4 ± 0.8	0.12 ± 0.01
CoV_HO/HC	0.5	1.2	1.0
SMC
HC	5.8 ± 0.8	14.7 ± 0.9	0.32 ± 0.02
HO	5.0 ± 0.3	12.4 ± 0.5	0.27 ± 0.01
CoV_HO/HC	0.4	0.7	0.6

CBV, cerebral blood volume; CMRO₂, cerebral metabolic rate of oxygen consumption; CoV, coefficient of variation; HC, hypercapnic; HO, hyperoxic; SMC, sensorimotor cortex; VC, visual cortex.

The reduction in variability offered by HO vs. HC is given as the ratio of the coefficients of variability (CoV_HO/HC = CoV_HO/CoV_HC).

As detailed in Table 2 for the case of an assumed α of 0.2, precise end-tidal gas control also resulted in low variability of individual subjects M-values in both cortices (CoV_Msubject ~20% to 40% and, better yet, CoV_Msubject ~20%). This enabled a per-subject calibration for quantification of individual differences in functional responses. To date, most fMRI-calibrated studies using fixed inspired fractional concentrations of carbon dioxide (F_ICO₂) challenges have only used group-calibration due to excessively large variance on individual M-values. The few attempted per-subject calibrations under similar visual and sensorimotor stimulation led to large variability in across-subject-averaged CMRO₂ (CoV_CMRO2 ~ 60%) and hence in ψ coupling (up to CoV_ψ ~ 50%; Kastrup et al, 2002; Chiarelli et al, 2007a). In contrast, the variability on our per-subject-calibrated CMRO₂ averages is much reduced in the SMC (CoV_CMRO2 ~24% and further improved CoV_CMRO2 ~13%) and even more so in the VC (~7% and ~ 3%, respectively). Also, our group- vs. per-subject-calibration estimated averages (Tables 1a and 2, respectively) are in better agreement under HO than under HC, as expected, given the independence of the former on individual vascular differences.

Table 2

Summary of per-subject fitted M-values (m ± CI_m, where m = mean and CI_m = 95% confidence interval of the mean), averaged percentage change in CMRO₂- and ψ-estimates (m ± s.e.) under HC and HO per-subject calibration in the VC and SMC, for venous CBV (α = 0.20; N = 6, one subject excluded due to significant activation under only two HC levels).

Per-subject calibration	M_Subject(% range)	ΔCMRO₂/CMRO_2,0 (%)	ψ
Venous (α = 0.20)
VC
HC	(4.1 ± 1.7–8.1 ± 2.0)	9.7 ± 6.3	0.20 ± 0.11
HO	(4.6 ± 0.9–5.7 ± 1.3)	12.7 ± 4.3	0.25 ± 0.07
CoV_HO/HC	0.3–0.9	0.5	0.5
SMC
HC	(3.7 ± 0.7–8.3 ± 3.1)	15.3 ± 3.7	0.34 ± 0.09
HO	(4.2 ± 1.0–6.5 ± 1.2)	17.8 ± 2.3	0.40 ± 0.06
CoV_HO/HC	0.2–1.0	0.5	0.6

CBV, cerebral blood volume; CMRO₂, cerebral metabolic rate of oxygen consumption; CoV, coefficient of variation; HC, hypercapnic; HO, hyperoxic; SMC, sensorimotor cortex; VC, visual cortex.

The reduction in variability offered by HO vs. HC is given as the ratio of the CoV (CoV_HO/HC = CoV_HO/CoV_HC).

Discussion

Obtaining a clearer understanding of BOLD signal changes upon neuronal activation requires an investigation of the underlying CBF, CBV, and CMRO₂ changes involved. To accurately estimate the latter, fMRI studies based on the widely used dHb dilution model must pay special attention to (1) the assumed α-parameter, describing the power—law relationship between CBV and CBF changes, and (2) the estimated calibration M-value.

Most often in applying the dHb dilution model to derive CMRO₂ estimates, CBV changes are derived from CBF measurements through a power—law relationship described by an α-parameter (equation (1)). The ubiquitous value used (α = 0.38), originally derived from primate whole brain PET data (Grubb et al, 1974), has recently been shown to yield an overestimation of M and an underestimation of CMRO₂ under HC calibration (Figure 5 of Chen and Pike, 2009). Accrued evidence of a lower value (α ~ 0.20), which reflects venous rather than total volume changes as appropriate for BOLD signals, have since then been provided by fMRI, NMR, and PET studies based on observations of the major portion of volume changes residing in arterial compartments (Chen and Pike, 2009, 2010b; Ito et al, 2003; Lee et al, 2001; Kim et al, 2007). In vivo high-resolution laminar optical imaging and microscopy of the rat cortex have also revealed significant activation-related CBV changes in the capillaries (Villringer et al, 1994) and arterioles, whereas venous dilation was found to be negligible (Hillman et al, 2007). On account of these reports, we assumed a reduced α-value of 0.20 in our original estimates and then compared these to calculations based on the traditional value of 0.38 (see ‘Assumed α-Parameter’ section). Our comparative calibration study further offers an insightful investigation into this parameter as it affects M calculations under HC, but not under HO (equations (1) and (2), respectively, in Mark et al, 2011), and consequently impacts differently these alternative estimations of CMRO₂ (i.e., CMRO₂ in equation (1) herein also has an α-dependence, irrespective of the M calibration model used). Although previous calibrated fMRI studies, based on HC (Kim et al, 1999; Stefanovic et al, 2004; Chen and Pike, 2009) or absolute-relaxation-rates calibration (Fujita et al, 2006), have considered the effects of the α-value on the metabolism-flow coupling, none have included a comparison across calibration technique, investigated the HO substitute, carefully controlled end-tidal gases nor compared brain regions. Hence, rather than only relying on assumed values from previous studies, we also estimated the α that maximized the agreement between our alternative calibrated results in a least-square curve-fit sense (see the section ‘Optimized α-Parameter‘).

Figure 5

Sensitivity of across-subject-averaged (A) M- and (B) cerebral metabolic rate of oxygen consumption (CMRO₂)-estimates on assumed α-parameter, in the visual cortex (VC; blue line) and sensorimotor cortex (SMC; green line) under hypercapnic (HC: dotted line) and hyperoxic (HO: solid line) group-calibration. Results of optimized agreement between calibration alternatives are indicated by the respective arrows (weighted least-square curve-fit ± 95% confidence interval of the fit).

The calibration M-value has a large impact on CMRO₂-estimates (Chiarelli et al, 2007c; Fujita et al, 2006) as it modulates the contribution coming from the BOLD response (equation (1)). Hence, given the importance of obtaining precise M-estimates for an accurate estimation of α, careful control of iso-oxic HC gas delivery was applied to minimize the technical contribution to variance found under the traditional F_ICO₂ calibration method. A further reduction in M-variability was achieved under precise control of a novel calibration replacement, HO with strict maintenance of isocapnia (CoV_HO/HC on M_Group = 0.4 to 0.5 and M_Subject= [0.2 to 1.0] in Tables 1a and 2, respectively). Being non-vasoactive and removing potential confounding effects of blood flow changes, HO calibration (1) is based on higher signal-to-noise ratio measurement of ΔP_ETO₂ (see M derivation in Appendix of Mark et al, 2011), in contrast to perfusion imaging used under HC, and (2) eliminates the variability in individual vascular reactivity associated with HC (Table 2: reduced range of M_Subject-values under HO). As discussed previously, any potential CBF reduction, unlikely under robust isocapnic HO end-tidal control, would have been below the detection limit of our ASL measurement (Mark et al, 2011). If present at all, a slight vasoconstriction would simply require a post hoc correction to the M-values (as described in Chiarelli et al, 2007c). Furthermore, although this corrective term would be expected to introduce further variability under a fixed inspired methodology, our precise control of end-tidal gases would most likely yield a small and predictable correction factor that would only scale our M-values and leave the variability unaffected. The reduced M-variability offered by the precise control of either HC or better-suited HO gases yielded lower variability in oxidative metabolism and metabolism-flow coupling estimates than reported with F_ICO₂ manipulation (see ‘Estimates of Oxidative Metabolism and Metabolism-Flow Coupling’ section). As detailed below, a sensitivity analysis was performed to further investigate the extent to which improvement in M carries through derivations of CMRO₂-changes in response to neuronal activation, key before discussing the impact of the commonly assumed α-value (see ‘Assumed α-Parameter' section) or directly evaluating this parameter (see ‘Optimized α-Parameter' section).

Sensitivity Analysis: M- vs. Cerebral Metabolic Rate of Oxygen Consumption-Variability

The extent to which variability in M affects that of CMRO₂ was carefully examined through simulations based on error propagation in equation (1) (detailed in Appendix A). We recalculated CMRO₂ for each subject under both calibrations keeping the respective M_Group constant in magnitude but letting its variability span a range of CoV_M,HC of up to 25%, double our worse result, yet only a third of the range found under F_ICO₂-calibrated fMRI studies (i.e., up to CoV_M,HC ~75%; Hoge et al, 1999b; Stefanovic et al, 2006; Chiarelli et al, 2007a; Leontiev et al, 2007; Kim et al, 1999). The resulting across-subject averaged coefficient of variability on CMRO₂ is displayed in Figure 4 for the VC. A similar sensitivity behavior was found in the SMC (not shown), as expected given the similitude of our results in both ROIs (see ‘MR Responses' section and Table 1a) and for different values of α (not shown).

Figure 4

Sensitivity of variability in cerebral metabolic rate of oxygen consumption (CMRO₂) (coefficient of variation CoV_CMRO2) on variability in M-value (CoV_M), under hypercapnic (HC: blue line) and hyperoxic (HO: red line) group calibration. Results obtained in the present study, as reported in Table 1a, are indicated by the respective markers.

Compared with HC calibration, HO is seen to (1) propagate to higher levels of CoV_CMRO2 (i.e., red line), yet (2) have resulted in reduced variability in the current study (i.e., red marker). The increased sensitivity to M-variability arises from slightly lower magnitudes in M-values (Table 1a: M_HO = 5.2% vs. M_HC = 5.5%) that result in smaller CMRO₂ magnitudes with larger CoV_CMRO2 for equivalent absolute error. Despite the presence of this slight masking effect, HO still provided an improvement over HC in the current study by showing a much reduced variability in M (Table 1a: CoV_M,HO ~ 6% vs. CoV_M,HC ~ 13%) and hence in CMRO₂ (CoV_CMRO2 ~ 7% vs. CoV_CMRO2 ~ 11%).

The above analysis demonstrates the importance of reducing the variability in M measurement, dictated by the specific calibration methodology used, as it greatly impacts the accuracy of CMRO₂-estimates. Our precisely controlled HC, and particularly HO, calibration consistently yielded lower variability in M than traditional gas manipulation. We thereby report a reduction in CoV_CMRO2 (and consequently in CoV_ψ) despite two important facts. First, our error estimates include error propagation throughout the calibrated model rather than, as is often done, neglecting it or reporting instead the confidence interval of linear fits. Second, our M-values are generally lower than typically reported (Hoge et al, 1999a, b ; Davis et al, 1998; Ances et al, 2008; Leontiev et al, 2007; Kim et al, 1999; Chiarelli et al, 2007a), hence, prone to the aforementioned masking effect.

Assumed α-Parameter

When compared with HC results found under the assumption of a venous CBV (i.e., α = 0.20; Table 1a), the commonly adopted value (i.e., α = 0.38) shows the expected overestimation in M, with corresponding underestimation in CMRO₂ and ψ (Table 1b). However, M-estimates under HO calibration remain unchanged as they are independent of α. As a consequence of the opposing effects of M and α in deriving CMRO₂-estimates (equation (1)), the larger a hence causes greater underestimation in CMRO₂ and ψ under HO than HC, which now deviate (Figures 3C and 3D). The closer agreement between the calibration alternatives under reduced α (Figures 3A and 3B) provides additional, independent, support for the appropriateness of considering venous rather than total contributions to CBV changes in modeling the BOLD response.

A self-compensation of α-uncertainties occurs in the HC scheme from having this parameter appear in both M and CMRO₂ expressions, as described previously (Davis et al, 1998; Chen and Pike, 2009; Mark et al, 2011). In other words, under HC, both calibration and activation tasks involve CBF changes, and hence, assumptions relating these to CBV changes. In contrast, CMRO₂-estimates under the HO model might be more sensitive to α-inaccuracies due to the lack of a CBF change under the HO calibration (i.e., relies on direct plasmatic O₂ enhancement rather than vasoaction). Consequently, the marked reduction in variability offered by HO over HC when considering a reduced α reflecting venous CBV (Table 1a: CoV_HO/HC = [0.3 to 0.8]) partly vanishes as α is increased toward its representation of total CBV (Table 1b: CoV_HO/HC = [0.6 to 1.2]). However, this potential self-correction under HC (1) applies only when M is estimated, rather than assumed as is often done, via HC calibration during the same scanning session as the neuronal task (i.e., calibration and activation data must incorporate the same bias) and (2) assumes α holds similar values under the distinct physiological mechanisms involved in focal neuronal vs. global HC conditions (Ito et al, 2003; Chen and Pike, 2009, 2010b; Ho et al, 2011). The α-independence of calculated M_HO-values, by avoiding the issue surrounding α-uncertainties due to region-specific vascularization (Ances et al, 2008; Chen and Pike, 2009), remains a plausible argument for the much simplified HO model for calibrated BOLD-fMRI.

The trend we observe in ψ between brain region, with lower estimates residing in the VC compared with the SMC (Table 1a: ψ_VC = [0.24 to 0.28] and ψ_SMC = 0.40) agrees with previous F_ICO₂ studies from our group (Stefanovic et al, 2006). This difference is most likely due to the extended vascularization of the VC, yielding a correspondingly higher M-value in this region (Table 1a: M_VC = [5.2 to 5.5]% and M_SMC = 5.0%; Stefanovic et al, 2006; Chiarelli et al, 2007a). Based on their specific vascular composition, brain regions might be affected differently by the non-vasoactive nature of HO, compared with the vasodilatory one of HC. As an illustration, the assumption of an overestimated blood volume contribution (i.e., α = 0.38) is likely responsible for the larger discrepancy between HC and HO coupling estimates in the highly vascularized VC (Figure 3C), compared with the less vascularized sensorimotor region (Figure 3D). Appropriately reducing CBV (i.e., α = 0.20) thereby moderates this regional effect, with largest impact in the VC (Figures 3A vs. 3B). As α is increased, the lack of self-compensation for uncertainties in this parameter under HO explains the divergence of the results being accentuated in the VC (Table 1b: CoV_HO/HC = [1.0 to 1.2]) compared with the SMC (Table 1b: CoV_HO/HC= [0.6 to 0.7]).

The large range of ψ-values being reported by calibrated fMRI studies (ψ = [0.2 to 0.5], in Chiarelli et al, 2007a, b ; Davis et al, 1998; Hoge et al, 1999b; Kastrup et al, 2002; Kim et al, 1999; Leontiev and Buxton, 2007; Leontiev et al, 2007; Stefanovic et al, 2004) and non-MRI studies (as low as ψ = 0.1, in Fox et al, 1988; Mintun et al, 2001) could originate from (1) measurement techniques or (2) intrinsic differences in subjects and brain regions (Leontiev et al, 2007; Buxton, 2010). Improved calibration, as outlined here, reduces the component of variability arising from measurement techniques to allow the investigation of actual physiological characteristics (Ances et al, 2008; Chiarelli et al, 2007a) of individual brain region (described above) and subject (detailed in ‘Estimates of Oxidative Metabolism and Metabolism-Flow Coupling' section). This capability is of prime importance in investigating both the metabolism-flow coupling and the flow—volume relationship, underlying all fMRI physiological models.

Optimized α-Parameter

The improved agreement between CMRO₂-estimates from alternative calibrations under a reduced flow—volume relationship (i.e., α = 0.20 vs. 0.38, see the section ‘Assumed α-Parameter‘) forms an independent corroborating evidence of previous reports obtained from direct CBF and venous CBV measurement under graded visual and sensorimotor (α = 0.23 ± 0.05; Chen and Pike, 2009) as well as hypocapnic and HC stimulation (α = 0.18 ± 0.02; Chen and Pike, 2010b). Because of the distinct vasoactive nature of the calibration gases used, the current study offers a complementary insight into the α-parameter. Figure 5 indicates the α-values which yield the best agreement between HC and HO results for each stimulated cortex. The slight dissimilarity between the optimized values observed from the M compared with the CMRO₂ graph (α_VC = 0.12 vs. 0.10 and α_SMC = 0.20 vs. 0.21) arises from the specific origin of the calculation, being either from calibration data alone (i.e., for M) or a combination of neuronal and calibration data (i.e., for CMRO₂). Assuming α holds similar values under the distinct physiological mechanisms involved in focal neuronal vs. global HC conditions is most likely valid (as described in the section ‘Assumed α-Parameter’ in terms of the self-corrective feature of the HC-model). This similitude has been demonstrated for total volume changes with PET studies (Ito et al, 2003) and for venous changes by the aforementioned fMRI studies (Chen and Pike, 2009, 2010b), not surprisingly given venous vessels respond mainly biomechanically to changes in flow. Note that the HC curve in Figure 5B reproduces the behavior originally provided with the first introduction of the dHb dilution model (Figure 1 of Davis et al, 1998). In performing the above comparison between calibration alternatives, both are presumed iso-metabolic, an assumption that merits further investigation given maintained metabolism is more certain for HO than HC (Mark et al, 2011).

The tendency of a lower α in the VC compared with the SMC (α= 0.12 ± 0.04 vs. 0.20 ± 0.02, respectively), is not statistically significant (P =0.42 paired two-tailed Student's t-test), as reported previously (α = 0.18 ± 0.04 vs. 0.31 ± 0.10, respectively; Chen and Pike, 2009). As alluded to in the section ‘Assumed α-Parameter', a potential explanation for this difference lies in the specific vasculature of these brain regions. As arteries are the primary contributor to total volume change (Lee et al, 2001; Kim et al, 2007), it is conceivable that the aggregation of vessels in the occipital cortex, because of the presence of superficial veins that do no exhibit significant vasodilation under activation (Hillman et al, 2007), elicit relatively less volume changes than those in the SMC, a counter-intuitive argument given veins hold the largest volume of blood at rest. Nevertheless, because of the lack of statistical significance, a fit across the combined cortex regions results in an α-value of 0.16 ± 0.02 that could be used across the brain. This finding is in agreement with the value of 0.14 recently found to both improve the accuracy, and capture several physical effects not included in the original formulation, of the dHb dilution model (Griffeth and Buxton, 2011). Our results add further, independent, support to the mounting evidence of venous volume changes being lesser than arterial ones, of significant importance to calibrated BOLD-fMRI studies.

Conclusions

We document, for the first time, simultaneous BOLD and CBF measurement under neuronal and precisely controlled HC and HO challenges in the same group of healthy humans. In the context of BOLD calibration, precise end-tidal control of both respiratory alternatives provided an invaluable tool to reduce the variability in M- and CMRO₂-estimates to accurately evaluate the flow—volume relationship described by the α-parameter. This rigorous comparison of calibration alternatives indicates the appropriateness of using venous rather than total volume changes in the pursuit of evaluating oxidative metabolism in calibrated BOLD-fMRI studies, essential to understanding the BOLD phenomenon and rendering fMRI more quantitative.

Footnotes

The authors declare no conflict of interest.

Appendix A. Error Analysis

The description of the error propagation analysis performed starts by first rewriting equation (1) as:

where, C = 1 + ΔCMRO₂/CMRO_2,0, B = 1 + ΔBOLD/BOLD₀, F = 1 + ΔCBF/CBF₀.

Measured changes in BOLD, CBF, and M along with their respective variances (σ_B², σ_F² and σ_M²) are then used to derive the variance in the estimate for CMRO₂:

where,

The covariance in MR measurement (σ_BF²) appears since BOLD and CBF signal changes, obtained from the same acquired frames (see ‘Data Analysis' section), might be highly correlated. However, based on our experimental results, this contribution (equation A2d) is more than a 100 times smaller than that of the M factor (equation A2c), whereas contributions from individual BOLD (equation A2a) and CBF (equation A2b) variances are also negligible (more than 200 and 50 times smaller compared with the M factor). The error propagation is hence effectively uniquely restricted to the variance in M, which overly dominates and dictates the total uncertainty in CMRO₂-estimates in the present study.

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