Validation of Oxygen Extraction Fraction Measurement by qBOLD Technique

Abstract

Measurement of brain tissue oxygen extraction fraction (OEF) in both baseline and functionally activated states can provide important information on brain functioning in health and disease. The recently proposed quantitative BOLD (qBOLD) technique is MRI-based and provides a regional in vivo OEF measurement (He and Yablonskiy, MRM 2007, 57:115–126). It is based on a previously developed analytical BOLD model and incorporates prior knowledge about the brain tissue composition including the contributions from grey matter, white matter, cerebrospinal fluid, interstitial fluid and intravascular blood. The qBOLD model also allows for the separation of contributions to the BOLD signal from OEF and the deoxyhemoglobin containing blood volume (DBV). The objective of this study is to validate OEF measurements provided by the qBOLD approach. To this end we use a rat model and compare qBOLD OEF measurements against direct measurements of the blood oxygenation level obtained from venous blood drawn directly from the superior sagittal sinus. The cerebral venous oxygenation level of the rat was manipulated by utilizing different anestheisa methods. The study demonstrates a very good agreement between qBOLD approach and direct measurements.

While the dynamic properties of blood oxygenation level dependent (BOLD) contrast in MRI during functional activation have received much consideration, very little attention has been paid to the nature of the BOLD contrast during the resting or baseline level of neuronal activity in the brain. Because “resting brain” is responsible for approximately 20% of total human body oxygen consumption (1,2), understanding brain functioning in the baseline state is important for understanding brain performance in health and disease. One of the important parameters defining oxygen consumption is oxygen extraction fraction (OEF) – the percent of the oxygen removed from the blood by tissue during its passage through the capillary network. Previously, Raichle et al. (2,3) used this parameter to characterize the baseline state of the normal human brain. Such a characterization is germane because OEF maps of normal human subjects, resting quietly with their eyes closed, demonstrate remarkable uniformity (2,4) despite substantial regional variations of cerebral blood flow and the cerebral metabolic rate of oxygen consumption (2,3). This uniformity of the OEF in the absence of specific goal-directed activities supports the hypothesis that an established equilibrium exists between the local metabolic requirements necessary to sustain a long term modal level of neural activity and the level of blood flow in a particular region.

Thus far most quantitative imaging studies mapping tissue OEF were conducted using oxygen-15 based positron emission tomography (PET) imaging techniques (5). The advent of BOLD MR imaging initiated by Ogawa et al. (6) opened new opportunities to noninvasively study brain hemodynamics. BOLD approach capitalizes on the fact that deoxygenated blood has different magnetic susceptibility as compared to oxygenated blood (7), which in turn has magnetic susceptibility similar to the tissue (6). Due to this effect, the deoxyhemoglobin containing part of the blood vessel network in the brain creates mesoscopic field inhomogeneities in the surrounding tissue leading to more rapid MRI signal decay than from standard T2 decay alone. Because these field inhomogeneities are tissue specific, measuring the MRI signal decay rate may provide information on the tissue structure and functioning. Previously this lab has developed a theoretical model of BOLD contrast that analytically connects the BOLD signal to hemodynamic parameters such as the deoxyhemoglobin-containing blood volume (DBV), deoxyhemoglobin concentration, and OEF (8). A subsequent publication (9) quantitatively validated important features of the model in phantom studies and developed a theoretical background and experimental method (based on the Gradient Echo Sampling of Spin Echo (GESSE) sequence) that allows the separation of mesoscopic field inhomogeneity effects from both macroscopic and microscopic inhomogeneities. Such separation allows one to take full advantage of the mesoscopic, tissue-specific magnetic field inhomogeneity effects to extract quantitative information about tissue hemodynamic properties. Earlier attempts (10–13) to directly implement this method in vivo were encouraging but have not produced conclusive results. One reason is that the simplistic model used therein, describing brain tissue as a one compartment structure similar to water in a phantom, is not sufficient to describe real brain tissue. The qBOLD MR signal model (14) of brain tissue incorporates prior knowledge about brain tissue composition and includes contributions from intravascular water in gray (GM) and white (WM) matters, cerebrospinal fluid (CSF), or interstitial fluid (ISF) with a resonance frequency shift, and intravascular venous blood. Using MR images of human brain parenchyma obtained with a 2D GESSE sequence, the qBOLD model demonstrated an ability to measure brain hemodynamic parameters such as DBV, OEF, ISF/CSF volume fraction, and frequency shift in the baseline activity state (14).

While preliminary results (14) obtained from the qBOLD model are in a good agreement with previous PET studies, direct validation against a “gold standard” is necessary for this technique to become a practical tool for clinical and research applications. A validated qBOLD technique would provide a means for cognitive studies and clinical diagnosis that is more widely available to clinicians and researchers than oxygen-15 based PET techniques for the measurement of brain hemodynamics and metabolism. The current study is designed to provide such a validation. In this study, the averaged OEF measurements across the rat brain provided by the qBOLD technique were compared against direct OEF measurements (determined from the arterial-venous oxygenation difference) from the venous blood samples directly drawn from the rat superior sagittal sinus. Cerebral venous blood oxygen level of the rat was manipulated by using different anesthesia methods and different levels of oxygen in the inhaled air.

MATERIALS AND METHODS

Animal Preparation

All experiments were performed on Varian 4.7 Tesla (T) horizontal-bore magnet with an 8-cm-inner diameter gradient and shim assembly controlled by a Varian INOVA console using a 3.5-cm-diameter birdcage transmit/receive RF coil. All surgical procedures were conducted under the guidelines of the Washington University Institutional Animal Care and Use Committee. Twelve male Sprague-Dawley rats weighting 260–400 g were initially anesthetized with a ketamine/xylazine rat “cocktail” at a dose of 72.9 mg/kg⁻¹ ketamine plus 10.4 mg/kg⁻¹ xylazine and were given time to stabilize under the anesthesia. The animals were then restrained in prone position in a stereotaxic head-frame (Kopf Instruments, Tujunga, CA) and anesthesia was maintained by supplying 1.2% isoflurane in 100% O₂ through a nosepiece for the duration of the surgery. Each rat’s head was shaved and a small incision was made along the interaural line on the top of the rat’s head. After carefully removing a small area of scalp and membrane layers, the skull was exposed around the lambda. A 0.3-mm-diameter burr hole was drilled through the skull to expose the superior sagittal sinus. A small amount of Vaseline was applied at the burr-hole site to prevent bleeding. Rats were then intubated through a tracheotomy and mechanically ventilated by a small animal ventilator (Model 680; Harvard Apparatus, Holliston, MA) at a tidal volume of 5 mL/kg and frequency of 75 min/L.

For imaging, the animals were restrained using a laboratory-constructed Teflon head holder with ear and tooth bars. After positioning animal head to the center of the birdcage coil, the whole assembly was transferred into the MR scanner bore. During the whole experiment, the animal’s torso lay on a circulating water pad (Model D10-B3; Thermo Haake, Karlsruhe, Germany) to maintain the body temperature at approximately 37.5°C.

To manipulate the OEF values during the imaging study, two anesthesia methods were used. In the first group (8 rats), 40 mg/kg alpha chloralose was injected 30 min before the start of MR scanning followed by booster injections of 20 mg/kg every half hour using an i.p. line. During scanning, animals were ventilated with 30% O₂ balanced with N₂. In the second group (3 rats), anesthesia was maintained using a continuous flow of 1.2% isoflurane in 100% O₂. In one rat, both anesthesia methods were used sequentially.

Venous blood from superior sagittal sinus was sampled both before and immediately after the MR scan. Venous blood oxygen saturation level, SvO₂, was measured using an i-STAT Portable Clinical Analyzer (Heska, Fort Collins, CO) designed for veterinary purpose. The SvO₂ values are calculated based on the value of the partial oxygen pressure at half-saturation of hemoglobin (P50), blood pH and pCO₂. This device is calibrated for animals like canine, feline, and equine. At normal pH range (pH = 7.4), the P50 for the rat is 32.7 mmHg (15), for the dog it is 31.5 mmHg (16), for the cat it is 34.1 mmHg (17). Therefore, the P50 value for rat blood is within the range of values used for calibration of this blood gas analyzer. To maintain an air tight environment during blood sampling, the following procedure was adopted to eliminate the contamination from air. A specially made 1-mL syringe with 26-gauge needle was used to collect venous blood. Blunted need tip was attached with PE10 tubing, which was positioned inside superior sagittal sinus through the drilled burr-hole. The needle and tubing was filled with heparin flush (10 unit/mL) in advance to eliminate air (O₂) contamination and to prevent blood from clotting. Arterial blood oxygen saturation level, SaO₂, was measured before and immediately after the MR scan using a pulse oximeter placed on the rat’s hind paw.

NMR Experiments and Data Analysis

A 3D version of gradient echo sampling of spin echo sequence (GESSE) with RF spoiling, similar to the 2D version used earlier (14), was used. In the GESSE sequence, a set of gradient echoes is embedded around the spin echo of a single spin-echo sequence. Within the set, each gradient echo has the same phase encoding. This sequence structure allows simultaneous acquisition of a set of images corresponding to different gradient echo times (TE). The signal was sampled only in the presence of positive readout gradients to avoid artifacts due to macroscopic static magnetic field inhomogeneities that differently distort images collected in the presence of positive and negative readout gradients. Compared with the two-dimensional (2D) multi-slice approach, 3D GESSE produces higher SNR images and less signal distortion due to macroscopic field inhomogeneities. Data acquisition was performed using the following acquisition parameters: FOV of 36 × 36 mm², slab thickness 18 mm, sampling matrix of 64 × 64 × 32, TR of 230 ms, 8 acquisitions, total imaging time of 1 hr. The spin echo occurs at the 11th of 31 gradient echoes, corresponding to 56 ms after the RF excitation pulse, and gradient echo spacing is 1.895 ms. To eliminate image wrapping artifacts along the slice selection direction, and to generate a uniform refocusing profile, the slice thickness of the excitation RF pulse was set at 9 mm while the slice thickness for the refocusing pulse is kept at 18 mm. For spoiled single spin echo sequence, the optimal flip angle for excitation RF pulse is cos⁻¹(−e^−TR/T1) (18), which is larger than 90°. In our study, it was experimentally determined to be 110°.

Raw data from Siemens scanner were imported into Matlab (MathWorks Inc., Natick, MA) running on PC with Pentium 4 CPU and 2 GB memory for image reconstruction and processing. To reduce Gibbs ringing artifacts, all images were filtered using a Hanning filter before further processing. A nonlinear least square curve fitting function from the Matlab Optimization Toolbox was used for the fitting of the proposed signal model to the measured signal on a pixel-by-pixel basis. Because the phase of measured signal could be affected by unknown factors such as eddy currents, flow, and subject movement, only the magnitude of the GESSE signal is used in the fitting procedure.

The resultant MR signal was then analyzed using the qBOLD model that includes signals from tissue, deoxygenated blood, and CSF/ISF. Details of the theoretical model (14) are described in the Appendix. Due to the large number of fitting parameters (S₀, Y, DBV, $R_2^t,R_2^e$, Δf, φ, λ, and λ′), a good initial estimate is essential for a robust optimization procedure. Because the deviation from a linear exponential decay for the extravascular MR signal is negligible for the data points beyond 10 ms after the spin echo, a simplified two exponential decay model is first fitted to the data points in this time region. This fit provides initial estimates for S₀, frequency shift Δf, phase shift φ, ISF/CSF signal fraction λ and relaxation rate constant $R_2^e$. Fitting also provides an initial value for brain tissue $R_2^t$. The difference (on a logarithmic scale) between the measured and the extrapolated signal intensity at the spin echo is used to evaluate the initial value for blood volume fraction DBV. The initial value of Y in this estimate is set to a value corresponding to an average OEF of 40%. These initial values are used afterward in a final fitting procedure.

These measurements allow evaluation of a regional blood oxygenation level Y. This parameter was then averaged across the whole brain and compared with SvO₂ obtained directly from the sagittal sinus. Recall that parameter Y is related to the OEF by means of a simple relationship: OEF = (SaO₂ − Y)/ SaO₂, where SaO₂ is the oxygenation level of arterial blood. Hence, as with PET techniques, knowledge of SaO₂ is required to evaluate OEF. In our studies, the arterial oxygen saturation level, measured with a pulse oximeter, was relatively constant (94 ± 3%) across all experimental conditions.

RESULTS AND DISCUSSION

Representative data from a selected voxel obtained from the 3D GESSE sequence for a rat under alpha-chloralose anesthesia is illustrated in Figure 1. The venous blood oxygen saturation level in this rat, measured using the i-STAT analyzer, was 50%. The signal contributions from ISF/CSF and intravascular venous blood are also shown in Figure 1e,f. Only the real part of the blood signal is shown as it contributes most to the total magnitude signal (14). Figure 1c shows the extravascular brain tissue signal after removing the effect of R₂ decay and contributions from ISF/CSF and intravascular blood. The estimated fitting parameters were: DBV of 3.25%, blood oxygenation level of 46%, ISF/CSF frequency shift of 4.9 Hz with 13% contribution to the total signal at the spin echo time.

FIG. 1.

Representative data and fitting curves obtained with the 3D GESSE sequence for a rat under alpha-chloralose anesthesia. Contributions from all compartments are shown. a: Signal (square) and the fitted profile (dashed line) for the selected voxel. b: High resolution anatomic T₁-weighted image with the selected voxel shown by a rectangle. c: The extravascular signal contribution after removing signals from ISF/CSF and intravascular blood and adjusting for the R₂ decay (multiplying by the factor exp[+ R₂ TE]). The solid lines correspond to the extrapolated signal profile from the asymptotic behavior at long echo times, demonstrating the expected quadratic behavior around the spin echo. d: Fitting residual. e: Magnitude of the ISF/CSF signal. f: Real part of the intravascular blood signal.

Figure 2 shows a representative T₁-weighted image and maps of the estimated venous oxygen saturation level from one slice in the same rat under isoflurane and alpha-chloralose anesthesia. Isoflurane is known to slightly elevate cerebral blood flow (CBF) and significantly reduce brain metabolism (19). Alpha-chloralose is known to suppress both CBF and metabolism (20). Hence, we can expect that the venous blood oxygen level under isoflurane anesthesia should be much higher than in the alpha-chloralose case. Measurements based on the qBOLD technique show a fairly homogenous venous blood oxygen saturation level across the brain, with an estimated mean venous O₂ level of 77% under isoflurane anesthesia and 62% under alpha-chloralose anesthesia, which is consistent with the known effects of these anesthetics. Good correspondence is also seen with the venous blood oxygen saturation levels measured using the i-STAT blood gas analyzer (77% and 67%, respectively).

FIG. 2.

Examples of the maps of estimated venous blood oxygen saturation level obtained with the qBOLD technique from the rat under isoflurane (middle) and alpha-chloralose (right) anesthesia. The color bar shows the blood oxygenation level in %. The leftmost image is the T₁-weighted anatomic image. The venous blood oxygen saturation level measured using the i-STAT analyzer was 77% for isoflurane and 67% for alpha-chloralose, respectively. Mean values of venous blood oxygen saturation level calculated from the images shown are 77% under isoflurane anesthesia and 62% under alpha-chloralose anesthesia.

The plot in Figure 3 compares the venous blood oxygen saturation level measured using the qBOLD approach to the direct blood gas analyzer measurement. Because the results from the blood gas analyzer provide only integrated SvO₂ values for the entire brain, the results from the qBOLD measurements are also shown averaged across the entire brain. Over all 13 experiments, the venous oxygen level was varied from 44% to 87% by manipulating the concentration of oxygen in the inhaled air and the type of anesthesia. Overall, the correlation between the two methods was excellent with the regression line Y(qBOLD) = 0.9968 · SvO₂(direct), yielding a R² value of 0.92.

FIG. 3.

Comparison of venous oxygen saturation level [Y × 100%] measured with the qBOLD technique with the oxygenation of venous blood, SvO₂, from blood samples drawn directly from the superior sagittal sinus and measured with a blood gas analyzer (average of before and after MR scan). Because the results from the blood gas analyzer provide only integrated SvO₂ values for the entire brain, the results from the qBOLD measurements are also shown averaged across the entire brain. Data marked with triangles indicate rats anesthetized with isoflurane, circles indicate rats anesthetized with alpha-chloralose, and the solid curve is a linear regression fit to the data.

Figure 4 demonstrates an example of maps corresponding to all other estimated model parameters. Table 1 summarizes values of these parameters from all 13 studies. The results indicate that the transverse relaxation rate constant $(R_2^t)$, the signal fraction (λ ) from the ISF/CSF component at the spin echo time, and the frequency shift (Δf) between ISF/CSF and brain tissue are quite uniform across different studies. As compared to human results (14), DBV in rats is more homogeneous and higher by a factor of two. The $R_2^{\prime }$ relaxation rate constant is also higher than in (14) because of higher DBV and stronger magnetic field (4.7T in this study as compared to 3T in human study).

FIG. 4.

Representative maps of rat brain parameters determined from qBOLD model. The top leftmost image is a high resolution T₁-weighted anatomic image. The rest of maps are venous blood oxygenation level (%), DBV fraction (%), apparent R₂ for the combined brain tissue and ISF/CSF (s⁻¹) and R₂ for the brain tissue (s⁻¹), ISF/CSF signal fraction at spin echo time (%), ISF/CSF frequency shift (Hz) and the effective magnetization density (relative to parenchyma tissue) of intravascular blood signal. The rat in this study was under alpha-chloralose anesthesia with direct measured venous blood oxygenation level of 52%.

Table 1.

Estimated Brain Parameters From All 13 Studies Under Different Venous Blood Oxygen Saturation Levels^*

Study	SvO2 (gas, %)	Y (qBOLD, %)	DBV (%)	$R_2^t$ (1/sec)	$R_2^{\prime }$ (1/sec)	λ (CSF) (%)	Δf(Hz)	λ′	$R_2^{\mathit{\text{apparent}}}$ (1/sec)
1	44%	50 ± 21	2.6 ± 1.3	31.5 ± 7.1	6.2 ± 3.6	26.1 ± 10.0	8.0 ± 2.5	0.61 ± 0.36	18.9 ± 3.1
2	50%	53 ± 16	3.6 ± 1.3	33.2 ± 7.1	7.4 ± 2.9	29.1 ± 7.9	8.4 ± 3.0	0.56 ± 0.37	17.1 ± 6.5
3	50%	52 ± 29	3.3 ± 1.3	31.0 ± 6.5	7.5 ± 2.6	23.9 ± 11.6	8.2 ± 2.6	0.66 ± 0.34	19.4 ± 3.1
4	51%	52 ± 12	2.2 ± 1.3	27.3 ± 6.4	6.9 ± 4.3	20.1 ± 10.4	7.2 ± 3.1	0.42 ± 0.40	18.4 ± 2.3
5	52%	58 ± 10	3.5 ± 1.1	33.2 ± 6.0	7.6 ± 2.6	27.1 ± 8.6	8.9 ± 1.7	0.66 ± 0.33	19.6 ± 1.6
6	58%	53 ± 25	2.8 ± 1.4	28.4 ± 7.9	6.8 ± 4.6	24.2 ± 10.9	7.3 ± 3.4	0.55 ± 0.39	18.1 ± 4.1
7	60%	59 ± 10	3.0 ± 1.1	28.8 ± 4.5	5.1 ± 1.6	26.6 ± 8.6	5.7 ± 1.7	0.19 ± 0.32	18.2 ± 1.8
8	61%	62 ± 11	3.4 ± 1.2	29.3 ± 5.5	6.6 ± 2.4	24.1 ± 11.1	6.8 ± 2.4	0.42 ± 0.40	18.9 ± 2.4
9	67%	62 ± 18	3.2 ± 1.4	30.4 ± 8.2	6.9 ± 4.4	25.9 ± 11	8.1 ± 3.2	0.58 ± 0.38	18.7 ± 4.5
10	77%	77 ± 8	4.0 ± 1.5	27.6 ± 5.5	5.2 ± 4.6	28.5 ± 7.9	6.8 ± 2.5	0.26 ± 0.35	18.0 ± 2.9
11	80%	78 ± 8	4.0 ± 1.8	31.1 ± 5.3	5.0 ± 2.9	25.4 ± 7.8	8.5 ± 2.5	0.19 ± 0.26	19.7 ± 2.0
12	83%	84 ± 10	3.0 ± 2.0	26.6 ± 9.1	3.5 ± 3.1	26.3 ± 9.0	6.1 ± 3.4	0.37 ± 0.37	17.1 ± 4.9
13	87%	83 ± 7	3.7 ± 1.6	25.0 ± 2.9	3.3 ± 1.8	26.2 ± 6.3	4.4 ± 1.8	0.10 ± 0.19	17.2 ± 1.4
Mean	–	–	3.3 ± 0.5	29.5 ± 2.5	–	25.6 ± 2.3	7.3 ± 1.3	–	18.4 ± 0.9

^*Y, qBOLD estimated venous blood oxygenation level; DBV, volume fraction of deoxyhemoglobin containing blood (in tissue excluding ISF/CSF); $R_2^t$, transverse relaxation rate constant for parenchyma tissue; $R_2^{\prime }$, reversible transverse relaxation rate constant originating solely from mesoscopic magnetic field inhomogeneities; λ, signal fraction of ISF/CSF at spin echo time; Δf, frequency shift between ISF/CSF and parenchyma tissue; λ′, effective magnetization density (relative to parenchyma tissue) of intravascular blood signal. All parameters are defined in Equation [6]. $R_2^{\mathit{\text{apparent}}}$ – weighted average of the transverse relaxation rate constants of tissue $(R_2^t)$ and ISF/CSF $(R_2^e)$. All data are shown as mean ± standard deviation across the entire brain. Note that SD reflects a natural biological variability characteristic to variability in the tissue structure rather than the measurement error.

The average signal contribution (λ ) of the ISF/CSF component at the spin echo time is approximately 25%. To evaluate the ISF/CSF volume fraction in the brain tissue, we note that there are two competing factors determining the contribution of ISF/CSF to the MRI signal. Because the T1 relaxation time constant of ISF/CSF component is longer than the T1 of tissue, the signal from ISF/CSF is suppressed stronger than the signal from the tissue. This effect however is counteracted due to the fact that T2 relaxation time constant of ISF/CSF component is much longer than the T2 of the tissue. Assuming literature data (21) for tissue T1 of 1600 ms, ISF/CSF T1 of 1850 ms and T2 of 105 ms, and our measured T2 of tissue of 33 ms, we can estimate that the ISF/CSF component in the brain tissue is approximately 11%. This is consistent with our findings in the human brain (14).

The parenchyma tissue T2 value determined in our study (34 ms, see Table 1, Column 5) is significantly lower as compared with literature values (50 ms in Kettunen et al. (22) and 58 ms in Does and Gore (21)). However, the apparent T2 (54 ms), estimated from the weighted average of R2 relaxation rate constants of tissue and ISF/CSF, as listed in the last column of Table 1, is similar to the literature values.

Field difference also leads to linear increase in the frequency shift Δf = 5.25 Hz in (14) as compared to 7.3 Hz in this study. Our data also show some evidence that DBV increases when OEF decreases. This is consistent with the fact that the low OEF corresponds to higher blood flow hence increased blood volume. The parameter λ′ describes the effective magnetization density of blood signal relative to parenchyma tissue. Its value is different from unity because it depends on pulse sequence parameters, tissue, and blood spin densities and T1 and T2 relaxation time constants and blood flow. The variability in λ′ could be attributed to variation of blood inflow effects that affect blood apparent T1 and blood signal suppression by the phase dispersion induced by crusher gradient pair around the refocusing RF pulse. The measurement also indicates that the variation of SvO₂ in the rat brain is 8% and 16% under isoflurane and alpha-chlorase anesthesia, respectively.

Noninvasive measurement of the cerebral oxygen extraction fraction reflects the balance between oxygen delivery and tissue oxygen consumption and is, therefore, important for numerous clinical and research investigations. Approaches using the dependency of blood oxygen level on the blood R2 relaxation rate constant (23), or the susceptibility of the blood in major venous vessels (i.e., jugular veins) (24) have been proposed to estimate the global brain oxygen extraction fraction. The recently proposed qBOLD model (25) allows measurement of regional OEF values, thus providing a new tool for researchers and clinicians that can be readily implemented on commonly available MRI scanners. Previous results (14) obtained on a human whole body 3.0T Trio MRI scanner (Siemens Medical Systems, Erlangen, Germany) were in a good agreement with those well established findings from PET studies. Our current study was designed to validate qBOLD approach for measuring OEF.

Similar to previous validation studies for other modalities (5,26), the averaged OEF measurements across the whole rat brain obtained by the qBOLD technique were compared against a direct OEF measurement, based upon the arterial-venous blood oxygenation difference. Venous blood was sampled from the superior sagittal sinus to ensure measurement of only the blood draining from the brain. Compared with jugular vein sampling, this approach eliminates the contamination of the intracranial blood with blood from extra-cranial sources (27). Although blood obtained from the jugular bulb in primates, including human, is primarily derived from the brain tissue, contamination from extra-cerebral tissue may be as high as 7% (26).

We conclude that our results demonstrate a very good agreement between direct and qBOLD measured OEF, providing solid justification for applying qBOLD technique for in vivo studies.

APPENDIX

A. qBOLD Model

As described in He and Yablonskiy (14), the qBOLD model includes MR signal from parenchymal tissue (gray and white matters), ISF/CSF, and intravascular blood. The normalized MR signal from the parenchyma tissue at the time t (time origin is chosen at the spin echo in GESSE sequence) is (8):

$$s_t(t)=\mathit{\text{exp}}(-R_2^t·t-\mathit{\text{DBV}}·f_c(\delta \omega ·t))$$ [1]

where

$$\begin{array}{c}{f}_c(\delta \omega ·t)=\frac{1}{3}·{\displaystyle {\int }_0^1\mathit{\text{du}}}·(2+u)·\hfill \\ \hfill \sqrt{1-u}·\frac{1-J_0(1.5·\delta \omega ·t·u)}{u^2},\end{array}$$ [2]

J₀ is the zero order Bessel function; DBV is the deoxyhemoglobin-containing blood volume (part of the blood vessel network where deoxygenated blood is present); $R_2^t$ is the tissue transverse relaxation rate constant. The characteristic frequency δω depends upon the blood oxygenation level Y (Y = 1 indicates fully oxygenated blood):

$$\delta \omega =\gamma ·\frac{4}{3}·\pi ·\mathrm{\Delta }{\chi }_0·\mathit{\text{Hct}}·(1-Y)·B_0,$$ [3]

where γ is the nuclear gyromagnetic ratio, Hct - the blood hematocrit level, Δχ₀- the susceptibility difference between completely deoxygenated and completely oxygenated red blood cells, and B₀ is the external magnetic field strength.

The extracellular fluid in the central nervous system, which is composed of both cerebrospinal fluid (CSF) and interstitial fluid (ISF), might have frequency Δf and phase φ shifts from the brain cellular tissue component (similar to a consideration for blood plasma vs. blood cells provided in (28)). Hence, the normalized signal from the “extracellular” space (CSF or ISF) is (14):

$$s_e(t)=\mathit{\text{exp}}(-R_2^e·t-2\pi i·\mathrm{\Delta }f·t-i\mathrm{\varphi }),$$ [4]

where $R_2^e$ is the transverse relaxation rate constant of CSF/ISF.

The intravascular blood signal takes into account the presence of multiple blood vessels with orientations, hence frequencies, uniformly distributed in a voxel (29):

$$\begin{array}{c}{s}_b(t)={\left(\frac{\pi }{3·|\delta \omega ·t|}\right)}^{1/2}\mathit{\text{exp}}(i·\delta \omega ·t/2-R_2^b·t-(R_2^{*b}\hfill \\ \hfill -R_2^b)·|t|)·[C(|3\delta \omega ·t/2{|}^{1/2})-i·\mathit{\text{sign}}(t)·S(|3\delta \omega ·t/2{|}^{1/2})]\end{array}$$ [5]

Functions C(x) and S(x) are Fresnel cosine and sine integral functions, respectively, sign is a sign function (+1 for positive arguments and −1 for negative arguments), and δω is the characteristic frequency shift as defined in Equation [3].

Hence, the complete brain MR signal model adopted in this study is:

$$\begin{array}{c}\overline{S}(t)=S_0·F(t)·\{(1-\lambda -\lambda \prime ·\mathit{\text{DBV}})·s_t+\lambda ·s_e\hfill \\ \hfill +\lambda \prime ·\mathit{\text{DBV}}·s_b\}\end{array}$$ [6]

where parameters λ and λ′ are the fractions of signal from ISF/CSF and blood at spin echo time (t = 0). Comparing with Equation [10] in reference (14), λ′ in Equation [6] is normalized to the deoxyhemoglobin containing blood volume DBV. The function F represents signal decay due to macroscopic field inhomogeneities. It was calculated according to algorithm proposed previously (9) as a product of three sinc functions where field gradients across the voxel were estimated from phase images.

B. Assumptions

Some of the parameters in Equations [1]–[6] are determined through the fitting routine: S₀, DBV, Y, $R_2^t,R_2^e$, λ, λ′, Δf, ϕ. These parameters and the results for their values obtained for each animal are listed in Table 1.

Some of the parameters in Equations [1]–[6] are “assumed” in accordance with the reference and literature data. Among them: Δχ₀ = 0.264 ppm (28); B₀ = 4.73T (our scanner magnetic field); the blood oxygen saturation level dependent transverse relaxation rate constants $R_2^b\text{and}{R}_2^{*b}$ (30):

$$R_2^b({\text{sec}}^{-1})=15+254{(1-Y)}^2.$$ [7]

$$R_2^{*b}({\text{sec}}^{-1})=41+319{(1-Y)}^2$$ [8]

Equations [7] and [8] provide empirical relationships between the transverse relaxation rate constants $R_2^b\text{and}{R}_2^{*b}$ and blood oxygenation level Y. They were established in Ref. (30) for Hct value of 0.4. Although the transverse relaxation time of water protons in the whole blood is dependent on blood Hct value, such dependency is rather insignificant for Hct values around 0.40 (31), This has also been demonstrated by the small changes of transverse relaxation rate measured at Hct of 0.21 and 0.4 at 4.7T (30). Therefore, applying $R_2^b\text{and}{R}_2^{*b}$ values measured at Hct of 0.40 may not create any noticeable measurement error in our experiments.

In our experiments, the Hct value of the blood drawn from superior sagittal sinus was measured for each rat both before and immediately after the MR experiment. The group averaged Hct value was 42 ± 8%. For each individual rat, the measured Hct value normally varies within 3 percentage points, but variation as high as 10 percentage points has also been observed. Due to such variation and because the validation of Hct measurements with I-STAT device on laboratory mice and rats has only been established for group measurements (32), only mean group Hct value is used in our study. At the same time, the Hct value used in Equation [3] of our qBLOD model is the Hct value at the microvascular level. As it is well appreciated (33), the blood Hct level inside the microvasculature is reduced as compared to that of the systemic level to approximately 80–88% with the higher number at the cerebrum. Therefore, to reduce the uncertainties of Hct values, we have adopted the 0.34 value for the Hct in Eq. [3] for all animals.

C. The Role of Accuracy in Assumed Parameters Estimation

Equation [3] allows evaluation of the relative error in blood oxygenation level measurement due to variation in the value of “assumed” parameters. This error can be written as:

$$\left|\frac{\delta Y}{1-Y}\right|=\left|\frac{\delta \mathit{\text{Hct}}}{\mathit{\text{Hct}}}\right|+\left|\frac{\delta \mathrm{\Delta }{\chi }_0}{\mathrm{\Delta }{\chi }_0}\right|$$ [9]

Because the variation of B₀ is at the order of ppm across the brain (excluding the brain surface), its effect on OEF estimation can be ignored. At the same time, relative errors in evaluation of blood Hct and susceptibility difference between fully oxygenated and fully deoxygenated blood, Δχ₀, directly propagate in the relative error in evaluation of blood oxygenation level. This effect should always be taken into account, especially in cases of compromised tissue when variation in Hct level can be expected.