Evaluation of MRI Models in the Measurement of CMRO₂ and Its Relationship With CBF

Abstract

The aim of this study was to investigate the various MRI biophysical models in the measurements of local cerebral metabolic rate of oxygen (CMRO₂) and the corresponding relationship with cerebral blood flow (CBF) during brain activation. This aim was addressed by simultaneously measuring the relative changes in CBF, cerebral blood volume (CBV), and blood oxygen level dependent (BOLD) MRI signals in the human visual cortex during visual stimulation. A radial checkerboard delivered flash stimulation at five different frequencies. Two MRI models, the single-compartment model (SCM) and the multi-compartment model (MCM), were used to determine the relative changes in CMRO₂ using three methods: [1] SCM with parameters identical to those used in a prior MRI study (M = 0.22; α = 0.38); [2] SCM with directly measured parameters (M from hypercapnia and α from measured δCBV and δCBF); and [3] MCM. The magnitude of relative changes in CMRO₂ and the nonlinear relationship between CBF and CMRO₂ obtained with Methods [2] and [3] were not in agreement with those obtained using Method [1]. However, the results of Methods [2] and [3] were aligned with positron emission tomography findings from the literature. Our results indicate that if appropriate parameters are used, the SCM and MCM models are equivalent for quantifying the values of CMRO₂ and determining the flow-metabolism relationship.

The relationship between increases in the local cerebral metabolic rate of oxygen (CMRO₂) and increases in cerebral blood flow (CBF), which occur in response to focal neuronal activation has been a topic of long-standing interest. Techniques for measuring the percent changes (δ) in CMRO₂ and CBF using positron emission tomography (PET) and functional MRI (fMRI) of the human brain have been developed to understand hemodynamic and metabolic processes of neuronal activity. Comparison studies have shown that fMRI and PET are comparable and equivalent in the measurements of δCBF (1,2). However, it has been noted that a significant discrepancy exists between PET and fMRI measurements of δCMRO₂. PET and fMRI also differ in their measurement of the relationship between the δCMRO₂ and δCBF observed during brain activation. Specifically, the δCMRO₂ values measured by fMRI are consistently larger than those measured using PET. More problematic, the flow-metabolic relationships determined by PET and fMRI appeared to be different in previous studies. For example, using a visual stimulation paradigm, a nonlinear flow and metabolic relationship was repeatedly observed with PET (3,4) while a linear correlation between δCMRO₂ and δCBF was found with an fMRI study (5). To our knowledge, this discrepancy has not been fully addressed by neuroimaging community.

PET measurements of hemodynamics and metabolism are based on autoradiographic principles and can provide full quantification in physiological units. The original PET observations of δCBF:δCMRO₂ uncoupling (3,6) were made using a comprehensive tracer kinetic model which requires explicit measurements of CBF, cerebral blood volume (CBV), and oxygen extraction fraction (OEF). With a visual stimulation paradigm at 10 Hz, CMRO₂ increased slightly by 5.0 ± 0.2% while CBF increased dramatically by 50.0 ± 6.9% were measured by PET (3). Using a simplified PET model for quantification of CMRO₂, Vafaee and Gjedde (4) found that the δCBF:δCMRO₂ coupling ratio changes nonlinearly with the visual stimulation rate. At rates below 4 Hz, CBF and CMRO₂ both rose, with a coupling ratio of ∼2:1. As the rate was increased to more than 4 Hz, CMRO₂ fell while CBF continued to rise, resulting in a highly nonlinear relationship. As expected, the results from PET methods (3,4,7) at rates above 4 Hz were consistent with each other.

Blood oxygenation level dependent contrast (BOLD)-based fMRI was exploited to create an expanded biophysical model which allowed changes in CMRO₂ to be estimated from the BOLD signal (8). The model was further refined by Davis et al. (9). Applying Davis’s model to a similar visual stimulation paradigm that was used previously in PET (4), Hoge et al. (5) reported a fMRI measurement of δCMRO₂ consistent with PET results at 4 Hz, but not at higher frequencies. At 8–10 Hz, it is unexpectedly found that the CMRO₂ increases measured by fMRI (5) were five times larger than those measured by PET (16–30% vs 3–6%) (3,4,7). A more striking finding from the fMRI measurements is the observed linear coupling between flow and metabolism (5), which is inconsistent with the nonlinear coupling relationship that is observed in PET results (3,4).

There has been speculation regarding the source of this unexpected discrepancy between fMRI and PET findings. With developments in fMRI imaging techniques, new methods and strategies for δCMRO₂ measurement continue to evolve. Recently, the development of new fMRI models has revealed that δCMRO₂ values reported in prior fMRI studies (5) may have been erroneously calculated due to improper parameter estimations stemming from two sources. First, in the study (5), the intravascular and extravascular contributions to the BOLD effect were assumed to be combined into a single compartment. This assumption left the basal BOLD relaxation rate, M (see definition in Eq. [4] below), not clearly defined. Davis et al. (9) used the strategy of induced CO₂ challenge for calibration of the M values. The determined δCMRO₂ was highly dependent on the calibrated M value (10); therefore, an improper M value can result in an erroneous estimation of δCMRO₂. The M value reported for linear δCBF:δCMRO₂ coupling by Hoge et al. (5) was 0.22, but recent observations suggest that the value is much lower (M < 0.15) (10-12). Larger M values have been reported to yield higher δCMRO₂ magnitudes and greater linearity in δCBF: δCMRO₂ coupling (10). By shifting M to the range lower than 0.15, nonlinear δCBF:δCMRO₂ coupling relationships were exposed (10). Second, it was assumed in the study (5) that there is a constant relationship between δCBV and δCBF. As typically applied, δCBF is explicitly measured using the arterial spin labeling (ASL) technique (13), but δCBV is estimated based on the power-law relationship of Grubb et al. (14) with a constant power (α = 0.38). However, recent observations show that the α value can vary depending on the experimental conditions (e.g., stimulus frequency and duration) (15-17). The use of Grubb’s power law relationship has been reported to result in systematic misestimating of regional δCBV and δCMRO₂ during focal brain activation (18). It is reasonable to hypothesize that by using more appropriate values for the parameters M and α, the disparity in PET and fMRI measurements of δCMRO₂ magnitude and the relationship between flow and metabolism will be reduced.

An alternative strategy for estimating δCMRO₂ using BOLD fMRI has recently been proposed by Lu et al. (19). In contrast to the previous fMRI model (9), the new method (19) calculates the two components (intravascular and extravascular) of BOLD contributions separately. For each component, the analytical expression for the BOLD signals is clearly defined, thus eliminating the CO₂ calibration. Furthermore, rather than computing δCBV from δCBF using Grubb’s power law as done with the previous fMRI model (9), the new method (19) determines δCBV experimentally through the measurement of the vascular space occupancy (VASO) (20). Applying the alternative MRI model to a fixed frequency (8 Hz) visual stimulation paradigm, Lu et al. (19) obtained δCMRO₂ values that were more consistent with prior PET measurements (3,4,7) than were the prior fMRI observations (5).

The purpose of the current study was to evaluate and directly compare various fMRI models that can be used to determine CMRO₂ and to determine their relationship with CBF. Specifically, two fMRI models, the single-compartment model (SCM) developed by Davis et al. (9) and the multicompartments model (MCM) developed by Lu et al. (19), were considered in this study. Both models were used to estimate δCMRO₂ in an experimental paradigm for which PET studies have reported nonlinear changes in δCBF:δCMRO₂ coupling (4). The changes in CBV, CBF, and BOLD induced by the visual stimuli were simultaneously measured. The changes in CMRO₂ were calculated in three different ways: (i) application of SCM with parameters (M = 0.22; α = 0.38) identical to those used in the prior fMRI study (5); (ii) application of SCM with parameters M and α measured from hypercapnia and VASO, respectively; and (iii) application of MCM. The three strategies were used to find δCMRO₂ and determine its relationship with δCBF. These findings were compared with each other and also with results from previous PET studies (4,7).

METHODS

Subjects

Eight healthy volunteers (four men and four women) between the ages of 23 and 36 participated in this study. This protocol was approved by the Internal Reviewed Board of University of Texas Health Science Center at San Antonio. Informed written consent was obtained from each volunteer.

fMRI Data Acquisition

MRI experiments were performed on a 3 Tesla (T) Siemens Trio MRI scanner (Siemens, Erlangen, Germany) with simultaneous VASO, ASL, and BOLD measurement using a pulse sequence described previously (21). A standard Transmit/Receive head coil was used. A single oblique axial slice (6 mm in thickness) encompassing the primary visual cortex was chosen for functional imaging. Images were acquired with a field-of-view (FOV) of 26 cm and in-plane matrix size of 64 × 64. The echo time (TE) was 9.4 ms for VASO images, 11.6 ms for perfusion images, and 28.1 ms for BOLD images, with the repetition time (TR) was 2000 ms. The inversion time for VASO images (TI₁; blood nulling point) was determined empirically by searching for the minimal signal intensity in the sagittal sinus area in the inversion recovery sequence (∼680 ms). For ASL images, (TI₂) was 1200 ms. The inversion slab thickness was 100 mm. During an inversion recovery cycle, three images sensitive to VASO, ASL, and BOLD, respectively, were collected. High-resolution T₁-weighted anatomical images were obtained with TR/TE/flip angle = 500 ms/11 ms/90°, slice thickness = 6 mm, in-plane resolution = 1 × 1 mm².

Hypercapnia

The basal BOLD relaxation rate, M, was measured by CO₂ challenge. Mild hypercapnia (5% CO₂, 20% O₂, balance N₂) was induced through administration of a mixture of CO₂ and air through a nonrebreathing face mask (Hudson RCI, Model 1059, Temecula, CA) with two blocks of 3 min off/3 min on. At baseline, the subjects were inhaling medical air (human oxygen grade compressed air). During hypercapnic perturbations, the CO₂ gas was combined with medical air in a Y-connector. End-tidal CO₂ was monitored by means of a nasal cannula with an aspirator. The sequence and imaging parameters for hypercapnic data acquisition were identical to those used in functional studies, as described above.

Stimulus Conditions

The stimulus was generated with a Dell personal computer (Dimension 2400, Austin, TX, 60 Hz monitor refresh rate) and was back-presented on a screen inside the scanner using a DLP projector (LP70; InFocus, Wilsonville, OR) with a synchronization range of 15–100 kHz horizontal and 43.5–130 Hz vertical. The stimulus consisted of a black-and-white radial checkerboard pattern with an outer diameter of 10.0 cm and an inner diameter of 0.5 cm. It contained 16 concentric rings, with each ring consisting of 18 segments of equal size, alternating in intensity (black and white). A cross-hair (0.5 cm) was located at the center of the circle. Subjects viewed the screen by means of a mirror above their heads while they lay in the scanner. The stimulus was presented at approximately 45 to 48 cm from the eyes. Its contrast was reversed at specified frequencies. Stimulus presentation was automatically synchronized with data acquisition. During the functional study, subjects were shown the checkerboard flashing at frequencies of 1, 4, 8, 16, and 32 Hz, with 1 Hz defined as one contrast reversal per second. Four of the subjects were shown the stimulus in ascending order (1, 4, 8, 16, and 32 Hz), whereas the other four were shown the stimulus in descending order (32, 16, 8, 4, and 1 Hz). The procedure was used to make the current fMRI study comparable to the prior PET literature (7). The visual stimulation paradigm consisted of a 3-min visual stimulus at each frequency alternating with 3-min baseline condition (resting). The total scan time for the functional study was 30 min.

Data Analysis

Data were processed and analyzed using MATLAB 7 (Math Works, Natick, MA). Two image pairs (8 s) acquired after the onset and cessation of each stimulus period were excluded from data analysis to account for the transition time of the hemodynamic response. The VASO image series was obtained by adding the adjacent slab-selective and nonselective images acquired from the first echo in the inversion recovery sequence.

Based on the VASO images, δCBV during hypercapnia or visual activation can be determined using the following equation (20):

$$\delta \mathit{CBV}=-\left(\frac{C_{\mathit{par}}}{C_{\mathit{blood}}\cdot {\mathit{CBV}}_{\mathit{rest}}}-1\right)\cdot \delta \mathit{VASO}$$ [1]

where C_par = 0.89 and C_blood = 0.87 are the water contents in milliliters water/milliliter substance for parenchyma and blood, respectively (22). The average basal CBV (CBV_rest) was measured as 0.055 ml blood/ml parenchyma (23,24).

The ASL/BOLD image series was obtained by subtracting/adding the adjacent slab-selective and nonselective images from the second/ third echo in the sequence.

The M value, defined in Ref. (5) and as shown in Equation [4] below, was calculated from relative BOLD, CBV, and CBF (activation compare with resting) during hypercapnia by using the following equation:

$$\frac{\mathit{BOLD}}{{\mathit{BOLD}}_{\mathit{rest}}}-1=M\cdot \left(1-\left({\frac{\mathit{CBV}}{\mathit{CBV}}}_{\mathit{rest}}\right)\cdot {\left(\frac{\mathit{CBF}}{{\mathit{CBF}}_{\mathit{rest}}}\right)}^{-\beta }\right)$$ [2]

where “rest” denote to the baseline signal of a relevant parameter. By inserting BOLD/BOLD_rest = 1 + δBOLD, CBV/CBV_rest = 1 +δCBV, and CBF/CBF_rest = 1 +δCBF into Equation [2], one can obtain:

$$\delta \mathit{BOLD}=M\cdot (1-(1+\delta \mathit{CBV})\cdot {(1+\delta \mathit{CBF})}^{-\beta })$$ [3]

where

$$M=\mathit{TE}\cdot A\cdot {\mathit{CBV}}_{\mathit{rest}}\cdot {\left[\mathit{dHb}\right]}_{\mathit{rest}}^{\beta }$$ [4]

in which, A is a field strength and sample-specific proportionality constant, [dHb] is the concentration of deoxyhemoglobin and β is a constant, in the range 1 < β < 2, depending on the average blood volume within a tissue sample (β = 1 for vessels > 8 μm radius; β = 2 for vessels ≤ 8 μm radius) (8). Monte Carlo simulations given β ⊃1.5 (9), and this β value was used in the study by Hoge et al. (5) and will be used in this present study as well.

For functional studies, Student’s t-tests were used to compare “baseline” and each frequency “stimulus” signals. The threshold was set to t = 3.0 (P < 0.005, the reported P values were not corrected for multiple comparisons). For each subject, the VASO, ASL, and BOLD functional maps as well as the high-resolution T₁-weighted anatomical images were normalized to a standard brain co-ordinance (Talairach space). The functional maps were then registered to the anatomical images using a Convex Hull algorithm (25). Only those common activation areas (in a total volume of 5.15 ± 0.69 cc that includes 52 ± 7 voxels) that passed the statistically significant threshold for all the VASO, ASL, and BOLD functional maps across all five visual stimulation frequencies were used for calculating the average values of the δCBV, δCBF, and δBOLD, respectively. The three functional quantities were then used to calculate the δCMRO₂ with the following three methods.

Method [1]: SCM (9) With Parameters M and α Identical to Those Used in Prior fMRI Studies (5)

As shown in the Equation [2] in Ref. (9) and Equations [6] and [9] in Ref. (5), the BOLD signals related to relative CMRO₂, CBF and CBV can be expressed as follows:

$$\begin{array}{cc}\hfill & \frac{\mathit{BOLD}}{{\mathit{BOLD}}_{\mathit{rest}}}-1\hfill \\ \hfill & =M\cdot \left(1-\left(\frac{\mathit{CBV}}{{\mathit{CBV}}_{\mathit{rest}}}\right)\cdot {\left(\frac{\mathit{CBF}}{{\mathit{CBF}}_{\mathit{rest}}}\right)}^{-\beta }{\left(\frac{{\mathit{CMRO}}_2}{{\mathit{CMRO}}_{2,\mathit{rest}}}\right)}^{\beta }\right)\hfill \end{array}$$ [5]

Therefore, the relative CMRO₂ can be derived from Equation [5] as follows:

$$\begin{array}{cc}\hfill & \frac{{\mathit{CMRO}}_2}{{\mathit{CMRO}}_{2,\mathit{rest}}}\hfill \\ \hfill & ={\left(1-\frac{\left(\frac{\mathit{BOLD}}{{\mathit{BOLD}}_{\mathit{rest}}}-1\right)}{M}\right)}^{\frac{1}{\beta }}\cdot {\left(\frac{\mathit{CBV}}{{\mathit{CBV}}_{\mathit{rest}}}\right)}^{\frac{1}{\beta }}\cdot \left(\frac{\mathit{CBF}}{{\mathit{CBF}}_{\mathit{rest}}}\right)\hfill \end{array}$$ [6]

By assuming that there is a consistent power-law relationship between relative CBV and CBF (14):

$$\left(\frac{\mathit{CBV}}{{\mathit{CBV}}_{\mathit{rest}}}\right)={\left(\frac{\mathit{CBF}}{{\mathit{CBF}}_{\mathit{rest}}}\right)}^{\alpha }$$ [7]

Equation [6] can be expressed as follows (5,9):

$$\frac{{\mathit{CMRO}}_2}{{\mathit{CMRO}}_{2,\mathit{rest}}}={\left(1-\frac{\left(\frac{\mathit{BOLD}}{{\mathit{BOLD}}_{\mathit{rest}}}-1\right)}{M}\right)}^{\frac{1}{\beta }}\cdot {\left(\frac{\mathit{CBF}}{{\mathit{CBF}}_{\mathit{rest}}}\right)}^{1-\frac{\alpha }{\beta }}$$ [8]

By inserting BOLD/BOLD_rest = 1 + δBOLD, CMRO₂/CMRO_2rest = 1 + δCMRO₂ and CBF/CBF_rest = 1 + δCBF into Equation [8], one can obtain:

$$\delta {\mathit{CMRO}}_2={\left(1-\frac{\left(\delta \mathit{BOLD}\right)}{M}\right)}^{\frac{1}{\beta }}\cdot {(1+\delta \mathit{CBF})}^{1-\frac{\alpha }{\beta }}-1$$ [9]

where M = 0.22, α = 0.38 and β = 1.5 (5).

Method [2]: SCM (9) With Measured Parameters (M and δCBV)

With direct measurement of CBV and by inserting BOLD/BOLD_rest = 1 + δBOLD, CBV/CBV_rest = 1 +δCBV, CMRO₂/CMRO_2rest = 1 + δCMRO₂ and CBF/CBF_rest = 1 + δCBF into Equation [6], one can obtain:

$$\begin{array}{cc}\hfill \delta {\mathit{CMRO}}_2& ={\left(1-\frac{\left(\delta \mathit{BOLD}\right)}{M}\right)}^{\frac{1}{\beta }}\cdot \hfill \\ \hfill & \times {(1+\delta \mathit{CBV})}^{-\frac{1}{\beta }}\cdot (1+\delta \mathit{CBF})-1\hfill \end{array}$$ [10]

where M and δCBV were measured from the hypercapnic challenge and VASO experiments, respectively.

Method [3]: MCM (19)

In this model, the BOLD signal has been separated into intravascular and extravascular components. For the intravascular component, the ratio of the water volume distribution in arteriole to that in venule is approximately 0.3: 0.7 (26). The δBOLD in a voxel can be written as:

$$\delta \mathit{BOLD}=\frac{0.3\cdot \left(\Delta x\right)\cdot M_a{e}^{-R_{2a}^{\ast ,\mathit{rest}}\mathit{TE}}+0.7\cdot M_v\cdot (x^{\mathit{act}}\cdot e^{-R_{2v}^{\ast ,\mathit{act}}\mathit{TE}}-x^{\mathit{rest}}\cdot e^{-R_{2v}^{\ast ,\mathit{rest}}\mathit{TE}})+M_t{e}^{-R_{2,t}^{\ast ,\mathit{rest}}\mathit{TE}}[e^{-\Delta R_{2t}^{\ast }\mathit{TE}}(1-x^{\mathit{act}})-(1-x^{\mathit{rest}})]}{0.3\cdot x^{\mathit{rest}}\cdot M_a{e}^{-R_{2a}^{\ast ,\mathit{rest}}\mathit{TE}}+0.7\cdot x^{\mathit{rest}}\cdot M_v{e}^{-R_{2v}^{\ast ,\mathit{rest}}\mathit{TE}}+(1-x^{\mathit{rest}})\cdot M_t{e}^{-R_{2,t}^{\ast ,\mathit{rest}}\mathit{TE}}}$$ [11]

where act is used to refer to a variable in the activation state. The quantity x is the water fraction of blood in the voxel, and Δx can be obtained from δVASO using the following equation:

$$\Delta x=x^{\mathit{act}}-x^{\mathit{rest}}=\left(\frac{C_{\mathit{par}}-{\mathit{CBV}}_{\mathit{rest}}\cdot C_{\mathit{blood}}}{C_{\mathit{par}}}\right)\cdot \delta \mathit{VASO}$$ [12]

where $R_{2a}^{\ast }$, $R_{2v}^{\ast }$, and $R_{2t}^{\ast }$ are the effective relaxation rates of arteriole, venule, and pure tissue, respectively. Also, M_a, M_v, and M_t are the magnetizations of arteriole, venule, and tissue, respectively, which can be determined as follows:

$$M_i=\frac{1-e^{-R_{1i}\cdot \mathit{TR}}}{1-\cos \left(\mathit{FA}\right)e^{-R_{1i}\cdot \mathit{TR}}}\cdot \sin \left(\mathit{FA}\right)(\mathrm{i}=\mathrm{a}\mathrm{v}\text{or}\mathrm{t})$$ [13]

Where FA is the flip angle of the RF pulse and R_1i is the longitudinal relaxation rate (equal to 1/T_1i). At 3T, T₁ values are 1200 ms and 1627 ms for tissue and blood, respectively (27).

For the intravascular component at 3T, $R_2^{\ast }$ is quadratic and proportional to the [dHb] and can be uniquely determined from the arterial (Y_a) and venous (Y_v) blood oxygenation (28):

$$R_{2i}^{\ast }=18.82+188.28\cdot {(1-Y_i)}^2(\mathrm{i}=\mathrm{a}\text{or}\mathrm{v})$$ [14]

where 1 — Y_i is proportional to [dHb]_i. For the extravascular component, $\Delta R_{2t}^{\ast }$ is assumed to be linearly proportional to the [dHb] based on the theoretical framework proposed by Yablonskiy and Haacke (29):

$$\begin{array}{cc}\hfill \Delta R_{2t}^{\ast }=0.7\cdot \gamma \cdot B_0\cdot \frac{4}{3}\pi \cdot \Delta \chi \cdot & \mathit{Hct}\cdot ({\mathit{CBV}}_{\mathit{act}}\cdot (1-Y_v^{\mathit{act}})\hfill \\ \hfill & -{\mathit{CBV}}_{\mathit{rest}}\cdot (1-Y_v^{\mathit{rest}}))\hfill \end{array}$$ [15]

It should be pointed out that this equation uses static dephasing regime and the diffusion in the presence of field inhomogeneity is neglected. Monte Carlo simulations (30) have shown that, when considering the diffusion effects, the exponent of [dHb] may be slightly greater than 1, especially for magnetic field of 1.5T or lower. Here, a linear relationship is assumed because (i) at 3T, the exponent is approaching 1; (ii) the static dephasing regime provides an analytical expression that is feasible for model calculation. In Equation [15], γ = 2.67 × 10⁸ rad/sec/T and B₀ = 3T. The quantity Δχ = 0.31 ppm (31) is the susceptibility difference between fully oxygenated and deoxygenated blood. The hematocrit of blood in the microvascular is represented by Hct = 0.36. $Y_v^{\mathrm{act}}$ can be calculated from δBOLD by assuming Y_a = 1.00 (completely oxygenated blood) and $Y_v^{\mathrm{rest}}=0.61$ Based on Fick’s principle, the relationship between Y_v and OEF is given by the following:

$${\mathit{OEF}}_i=1-Y_v^j(\mathrm{j}=\text{rest or act})$$ [16]

Quantification of CMRO₂ can be achieved using the following equation:

$${\mathit{CMRO}}_{2,j}={\mathit{CBF}}_j\cdot {\mathit{OEF}}_j\cdot \mathit{Ca}$$ [17]

where Ca is the arterial oxygen content. Assuming Ca is constant, δCMRO₂ can be calculated by this equation:

$$\delta {\mathit{CMRO}}_2=(1+\delta \mathit{OEF})\cdot (1+\delta \mathit{CBF})-1$$ [18]

Once accomplished computing the individual δCMRO₂, the functional maps of VASO, ASL, and BOLD were averaged and registered onto the average anatomical images. Furthermore, the δCBF:δCMRO₂ coupling ratio (n =δCBF/δCMRO₂) was calculated for δCMRO₂ values determined by all three methods described above. The relationships of the δCMRO₂ values and the coupling ratio n with the visual stimulation frequencies were plotted.

RESULTS

Figure 1 shows the BOLD, ASL, and VASO functional maps averaged over the eight subjects at five visual stimulus frequencies. As expected, brain activation was found in the visual cortex area in all functional maps.

FIG. 1.

The functional maps of the BOLD, ASL, and VASO signal averaged over eight subjects at five stimulus frequencies (1, 4, 8, 16, and 32 Hz). The activation area (in color) were generated by the t-test method (P < 0.005) superimposed onto T₁-weighted anatomical images.

The values of the δCBV, δCBF, δBOLD, and δOEF in the primary visual cortex at five stimulus frequencies (1–32 Hz) are shown in Table 1. The changes of these three functional quantities all reach a maximum at 8 Hz, as clearly shown in Figure 2. The δCBF values are positively correlated to δBOLD (r = 0.99) as well as to δCBV (r = 0.93).

Table 1.

Averaged Values (Mean ± SE) of δCBV, δCBF, δBOLD, and δOEF at Five Stimulus Frequencies

	δCBV (%)	δCBF (%)	δBOLD (%)	δOEF (%)
1 Hz	16.2 ± 1.9	35.1 ± 5.9	1.1 ± 0.2	-16.3 ± 1.0
4 Hz	21.5 ± 1.7	51.0 ± 6.8	1.9 ± 0.2	-22.3 ± 1.0
8 Hz	37.7 ± 2.9	68.2 ± 6.1	2.8 ± 0.1	-34.4 ± 2.0
16 Hz	34.1 ± 1.9	59.8 ± 4.1	2.5 ± 0.2	-31.6 ± 1.0
32 Hz	32.3 ± 1.8	53.8 ± 5.0	2.3 ± 0.2	-30.0 ± 1.0

FIG. 2.

The averaged values (N = 8) of δCBF, δBOLD, and δCBV in the primary visual cortex versus stimulus frequency.

The averaged δCBV, δCBF, and δBOLD from our hyper-capnic challenge were 14.9 ± 4.2%, 37.3 ± 6.4%, and 2.7 ± 0.3%, respectively. The M value, which was computed individually with Equation [3] and averaged, was 0.098 ± 0.002. This value matches well with what was expected (9-12) and it has been adopted for the calculation of δCMRO₂ using Methods [2] and [3].

Figure 3 shows the values of δCMRO₂ calculated by Methods [1], [2], and [3] at the five stimulus frequencies (1–32 Hz). For comparison, the value measured by previous PET studies is also shown in the figure. Methods [2] and [3] agree well with other in that δCMRO₂ was observed to depend on stimulus-rate for both methods. These findings are also aligned with previous PET results: they are all peaked at 4 Hz. In contrast, the value of δCMRO₂ obtained by Method [1] peaked at 8 Hz, and the values are substantially larger than all other methods for the frequencies that were measured. Using Student’s t-test, no statistically significant difference was found between the δCMRO₂ values determined by Methods [2] and [3], for any of the five frequencies (P > 0.5).

FIG. 3.

The averaged values (N = 8) of δCMRO₂ obtained by Methods [1], [2], and [3] versus stimulus frequency. ‡Adapted from Vafaee et al. (7); §Adapted from Vafaee and Gjedde. (4). Color figure can be viewed in the online issue, which is available at www. interscience.wiley.com.

Figure 4 shows the δCBF:δCMRO₂ coupling ratio calculated by Methods [1], [2], and [3] at the five stimulus frequencies (1–32 Hz). The values measured by a prior PET study (4) are also shown in the figure. The rate-response functions for the δCBF:δCMRO₂ coupling ratio computed in Methods [2] and [3] were highly nonlinear (close coupling at 1 and 4 Hz; uncoupling at 8 Hz and higher) and virtually identical to the PET-derived response function (4). In contrast, the rate-response functions for these same variables computed by Method [1] showed linear coupling throughout the five stimulus frequencies, differing from the results produced by Methods [2] and [3] and PET (4).

FIG. 4.

The averaged values (N = 8) of the coupling ratio (n = δCBF/δCMRO₂) obtained by Methods [1], [2], and [3] versus stimulation frequency. The PET data adopted from Vafaee and Gjedde. (4).

DISCUSSION

In the present study, BOLD, ASL, and VASO fMRI data were obtained at rest and during visual stimulation at five frequencies ranging from 1 to 32 Hz. These data were modeled to compute δCBF, δCBV, δCMRO₂ and the δCBF: δCMRO₂ coupling ratio.

The δCBF, δCBV and δBOLD values obtained at these frequencies were in excellent agreement with the rate-response function for this stimulation paradigm, which was first determined by CBF PET (32) and subsequently by many other studies using a variety of modalities and physiological measurements. The rate-response function has proven to be a very useful and popular imaging paradigm because for interstimulus intervals greater than the neuronal relative refractory period, stimulation rate and the integrated electrophysiological response are linearly related (32).

The rate-response functions for δCMRO₂ and the δCBF:δCMRO₂ coupling ratio computed in Methods [2] and [3] were not only in agreement with each other, but they also matched well with previous PET results. In contrast, the rate-response functions for these same variables computed in Method [1] showed significant discrepancies. These discrepancies are likely due to the inaccurate values for the parameters M and α used in the Method [1].

One of the key assumptions in Method [1] involves the use of M as a lumped parameter that includes CBV_rest, resting-state [dHb], field strength and TE. The inappropriate use of M has been considered to be a major cause of error in the SCM (10,12). This suspicion was further confirmed by the present data. The M value (M = 0.22) reported by Hoge et al. (5) was much larger compared with the present measurement (M = 0.098) and previous measurement by Davis et al. (9) (M = 0.079). The larger discrepancy could be due to longer TE which Hoge and his co-workers used (50 ms vs 28.1 ms), and their low δCBF relative to δBOLD (ex. their δBOLD was 41% lower than ours [1.6% vs 2.7%], but δCBF was 73% lower [10% vs 37%]). By adjusting M from 0.22 to 0.098 in Method [1] of SCM with the fixed α value (α = 0.38), the δCMRO₂ declined from range of 21.1–34.5% to 15.3–18.1%, and the maximal δCMRO₂ shifted from 8 Hz to 4 Hz (see Fig. 5).

FIG. 5.

SCM sensitivity to M and α in the determination of δCMRO₂. ‡Adapted from Vafaee et al. (7); §Adapted from Vafaee and Gjedde. (4).

The other substantive approximation used by Method [1] is the estimation of δCBV from δCBF using the power-law relationship of Grubb et al. (14), rather than explicit measurement of δCBV. The α value used for previous fMRI studies (5,9) was fixed at 0.38 regardless of the different visual stimulation frequency rates used in the studies. There are reported data to show that the α value may varied at different experimental conditions (15,16). In a relevant PET study of human visual stimulation with different frequency rates (2 Hz and 8 Hz), Ito et al. (15) calculated the α value to be 0.30 by assuming that the universal power-law relationship of Grubb et al. is valid at all conditions (rest, 2Hz and 8 Hz). From the date shown in Figure 2 in the study by Ito et al. (15), if one fit the power-law relationship based on individual date sets (either rest, 2 Hz, or 8Hz), different α values would result. By taking the average date shown in Table 2 in Ref. (15), we compared their individual stimulus (i.e., 2 and 8 Hz) to the baseline ((1 + δCBV) = (1 + δCBV)^α)), and found that the α varied with frequency rates as α = 0.65 and 0.37, at 2 and 8 Hz, respectively. The average α is 0.51, which is consistent with that in a prior MRI report (α = 0.50) (17) and in the present study (the simulated α across the five frequencies is 0.58) as well. In an animal fMRI study, Kida et al. (16) observed that the relationship between δCBF and δCBV varied dynamically from stimulation onset for all stimulus durations due to different pace of increase in CBF and CBV responding to the stimulus. Consequently, the α value response to the stimulus is dynamic: the value of α ranged between 0.1 and 0.2 after stimulation onset and at the peak or plateau of the δCBF, but increased to 0.4 after stimulation offset, primarily because of rapid and slow decays in δCBF and δCBV, respectively. Considering the fact of that α depends on the experimental condition, special caution should be taken when estimating δCBV from the measurement of δCBF.

In the present study, we further examined the impact of δCBV variation on the determination of δCMRO₂. By substituting the measured δCBV into SCM with a fixed M (M = 0.22), the magnitude of δCMRO₂ decreased from the range 21.1–34.5% to 18.2–25.4%, and the maximal δCMRO₂ shifted from 8 Hz to 4 Hz (see Fig. 5). The results demonstrated above strongly indicated that both α and M can impact not only the magnitude of δCMRO₂, but also its rate-response function. It is a crucial to use the proper parameters (M and α) in the SCM to obtain accurate measurements of δCMRO₂.

With MCM, the intravascular and extravascular contributions to the BOLD effect are modeled separately. For each compartment, the analytical expression for BOLD signals is explicitly defined, thereby eliminating the estimation of M. Although some other estimates must be made for MCM, quantities such as CBV_rest, C_blood, and arteriole: venule (A:V) ratio (0.3:0.7), have physiological or MR physics-related meanings. In contrast to the M value, theyare well known from the literature or can be determined individually. Nevertheless, the MCM sensitivity to the aforementioned assumptions was evaluated in the present study by computing δCMRO₂ while varying these parameters. The CBV_rest (0.055) used in the present study was obtained from a most recent MRI and PET CBV study (23,24). The value was reported to vary from 0.047 to 0.055 by prior PET and fMRI studies (23,24,33). We estimated the δCBV and δCMRO₂ with varied CBV_rest, ranging from 0.047 to 0.063 (0.055 ± 0.008). The results show that either δCBV or δCMRO₂ curvature (δCBV peaking at 8 Hz and δCMRO₂ peaking at 4 Hz) determined by MCM was not sensitive to the assumed CBV_rest (results of δCMRO₂ are shown in Fig. 6a), and thereby the nonlinear δCBF: δCMRO₂ coupling relationship. Neither the δCMRO₂ curvature, nor the δCBF:δCMRO₂ coupling was sensitive to the varied C_blood (±15%) or A:V ratio (see Fig. 6b,c). Although the δCMRO₂ magnitudes were somewhat influenced by the varied parameters, the effects were small compared with the use of inappropriate M and α values in the SCM (Method [1]), and they did not cause the δCMRO₂ values to deviate greatly from PET results (see Figs. 5, 6b,c).

FIG. 6.

a- c: MCM sensitivity to CBV_rest (a), C_blood (b), and Arteriole: Venule (AV) ratio (c) in the determination of δCMRO₂. The PET data adopted from Vafaee et al. (7).

New evidence suggests that the VASO signal may have contributions from other physiologic sources under certain circumstances. In particular, VASO experiments conducted at short TR may have residual contributions from blood inflow (34). We note that this effect appears to be resolution dependent, with a considerable reduction in the flow effect as the voxel size increases. The voxel size we chose in the study (4.1 × 4.1 × 6.0 mm³, volume 101 mm³) was for being comparable to the PET literature. We extrapolated (linearly) the data in Figure 7 in Ref. (34) to the spatial resolution used in this study and found that the expected VASO signals showed virtually no inflow effect for voxel sizes above 90 mm³, suggesting that the VASO signals observed in our data can be primarily attributed to the CBV effect. The obtained δCBV values (16.2–37.7%) were in reasonable agreement with previous studies in human and animals (35,36). Nonetheless, it should be pointed out that the δCBV can be overestimated when the VASO signal contains other contributions, especially at higher spatial resolutions, as shown by another study (56% with volume 19.21 mm³) (37). In addition, the dynamic contribution of cerebrospinal fluid (CSF) to the VASO signal has also been considered (38). We estimated the δCBV and δCMRO₂ by including both the resting and changing fractional CSF contributions (x_c,rest and Δx_c/x_c,rest, respectively), based on Equation [2] in Scouten and Constable (38) and assuming longitudinal magnetizations per unit of water in blood at inversion time M_b(TI) = 0. The results are shown in Figure 7a that the variation of the x_c,rest (0 to 0.1, Δx_c/x_c,rest = 0, values taken from Scouten and Constable) (38) does not have significant impact on δCBV for both magnitude (P > 0.5) and curvature (δCBV peaking at 8 Hz). Similar results are obtained for δCMRO₂ magnitude (P > 0.5) as well as curvature (δCMRO₂ peaking at 4 Hz), either with SCM or MCM (only MCM results are shown in Fig. 7b for simplicity). The variation with both x_c,rest (0 to 0.1) and Δx_c/x_c,rest (-2% to -10%, values takenfrom Scouten and Constable) (38) increases δCBV and further drops down δCMRO₂. Only Δx_c/x_c,rest = -2% is presented in the Figure 7c,d because δCMRO₂ become more negative when Δx_c/x_c,rest < -2% (especially at higher frequencies), which is not physiologically reasonable. Nonetheless, the curvatures of both δCBV and δCMRO₂ do not altered, either. Therefore, the inclusion of CSF fraction, either at resting or changing state, does not affect our conclusion of nonlinear flow-metabolism coupling.

FIG. 7.

Evaluation of resting (x_c,rest) and changing (Δx_c/x_c,rest) CSF contribution to VASO signal. a,b: δCBV (a) and δCMRO₂ (with MCM; b) across the stimulus frequencies as a function of x_c,rest without fractional CSF changes (Δx_c/x_c,rest = 0). c: δCBV, and (d) δCMRO₂ (with MCM), across the stimulus frequencies as a function of x_c,rest with fractional CSF changes (Δx_c/x_c,rest = -2%). The PET data adopted from Vafaee et al. (7).

Our study has shown that with proper choices of parameters, the results from the SCM Method [2] and MCM fMRI models are comparable. Our data further suggests that CBF and CMRO₂ do not necessarily rise proportionally with neuronal activation, and therefore, it is unlikely that the CBF elicitation is directly coupled to oxygen demand. The exact mechanisms causing the frequency-varying δCMRO₂ response and nonlinear coupling between δCBF and δCMRO₂ remain unclear. The behaviors of the frequency-varying flow-metabolism coupling could be regulated by Ca²⁺ oscillating frequency (39). CBF response to neuronal activation has been observed to be regulated by astrocyte-mediated Ca²⁺ influx (40). In the study by Hajnóczky et al. (39), it was demonstrated that cytosolic Ca²⁺ ([Ca²⁺]_c) oscillations can be transmitted to mitochondria, as mitochondrial Ca²⁺ ([Ca²⁺]_m) oscillates, further regulating NADH oscillations (the reduced form of NAD⁺, nicotinamide adenine dinucleotide) through a Ca²⁺-sensitive mitochondrial dehydrogenase pathway. Based on fundamental biochemistry, it’s well known that CMRO₂ can then be regulated by NADH concentration by means of mitochondrial electron transfer chain. At low frequency, the NADH oscillations can be tuned to [Ca²⁺]_m oscillations and the NADH spikes are in phase with those of [Ca²⁺]_m. However, in the higher range of [Ca²⁺]_m oscillating frequencies, the NADH spikes start to run together, owing to relatively slow reoxidation phase (Figures 4 and 7 in Ref. 39). Because δCBF response is regulated by Ca²⁺ influx, whereas δCMRO₂ is correlated with NADH concentration, the dissociation of δCBF:δCMRO₂ coupling, which starts at 8 Hz, could reflect the inconsistent pace between Ca²⁺ and NADH oscillations. Future studies are suggested to explore the relationship between Ca²⁺/NADH oscillations and δCBF:δCMRO₂ coupling associated with physiological activations.

Overall, it is very encouraging to see that the rate-response function measured in this present fMRI study (Methods [2] and [3]) matches well with PET literature, even though different groups of subjects were used for these two different imaging modalities. It is our expectation that a direct comparison study with PET and fMRI by using the same group of subjects (hence eliminating intrasubject variation) and an identical visual task, will yield a better quantitative agreement in the determination of CMRO₂ and its relationship with flow. This direct comparison study is undertaken in our laboratory to further support and validate the fMRI models in these physiological measurements.

CONCLUSIONS

Both MRI single-component and multicomponent models have been evaluated in the measurements of CMRO₂ and its relationship with CBF. In the present study, fMRI-derived measurements of δCMRO₂ and its relationship with flow were brought into much closer agreement with PET-derived measures by choosing proper MRI models and parameters. This agreement paves the way for further fMRI studies of the hemodynamic and metabolic processes involved in neuronal activation.