Quantitative BOLD: Mapping of Human Cerebral Deoxygenated Blood Volume and Oxygen Extraction Fraction: Default State

Abstract

Since Ogawa et al. (Proc Natl Acad Sci USA 1990;87:9868–9872) made the fundamental discovery of blood oxygenation level-dependent (BOLD) contrast in MRI, most efforts have been directed toward the study of dynamic BOLD (i.e., temporal changes in the MRI signal during changes in brain activity). However, very little progress has been made in elucidating the nature of BOLD contrast during the resting or baseline state of the brain, which is important for understanding normal human performance because it accounts for most of the enormous energy budget of the brain. It is also crucial for deciphering the consequences of baseline-state impairment by cerebral vascular diseases. The objective of this study was to develop a BOLD MR-based method that allows quantitative evaluation of tissue hemodynamic parameters, such as the blood volume, deoxyhemoglobin concentration, and oxygen extraction fraction (OEF). The proposed method, which we have termed quantitative BOLD (qBOLD), is based on an MR signal model that incorporates prior knowledge about brain tissue composition and considers signals from gray matter (GM), white matter (WM), cerebrospinal fluid (CSF), and blood. A 2D gradient-echo sampling of spin-echo (GESSE) pulse sequence is used for the acquisition of the MRI signal. The method is applied to estimate the hemodynamic parameters of the normal human brain in the baseline state.

The fundamental discovery by Ogawa and coworkers (1) of blood oxygenation level-dependent (BOLD) contrast in MRI opened up broad opportunities to study the hemodynamic properties of the brain. While the “dynamic” properties of BOLD contrast during functional activation have received much consideration, very little attention has been paid to the nature of BOLD contrast during the resting or baseline state of the brain. Raichle et al. (2) identified the baseline state of the normal human brain in terms of the brain tissue oxygen extraction fraction (OEF). OEF maps in subjects who are resting quietly with their eyes closed define a baseline level of neuronal activity. OEF maps in normal resting humans demonstrate remarkable uniformity despite substantial regional variations in CBF and CMRO₂ (3,4). Understanding brain function in the baseline state is important for understanding normal human performance because it accounts for most of the enormous energy budget of the brain, whereas evoked activity represents very small incremental changes (5). Such an understanding is also crucial for deciphering the consequences of baseline-state impairment by diseases of the brain such as stroke (6) and Alzheimer's disease (7,8). Importantly, the OEF has been shown to be an accurate predictor of subsequent stroke occurrence in patients with cerebrovascular disease (9,10). Previous studies were conducted using PET imaging techniques; however, such studies would be more available for research and clinical applications if they could be performed based on MRI methods. One such MRI approach is discussed in this article.

The magnetic field inside practically any system that is put into an MRI scanner is always inhomogeneous. The relative scale of this inhomogeneity compared to an imaging voxel can be roughly divided into three categories: macroscopic, mesoscopic, and microscopic (11). These three types of inhomogeneities all affect MRI signal formation. The macroscopic scale refers to magnetic field changes that occur over distances that are larger than the dimensions of the imaging voxel. Macroscopic field inhomogeneities arise from magnet imperfections, body–air interfaces, large (compared to voxel size) sinuses inside the body, etc. These field inhomogeneities are mostly undesirable in MRI because they generally provide no information of physiologic or anatomic interest. Rather, they lead to effects such as signal loss in gradient-echo (GRE) imaging, and image spatial distortions in both GRE and spin-echo (SE) imaging. The microscopic scale refers to changes in magnetic field over distances that are comparable to atomic and molecular lengths (i.e., over distances that are orders of magnitude smaller than the imaging voxel dimensions). Fluctuating microscopic field inhomogeneities lead to the irreversible signal dephasing characterized by the T₂ relaxation time constant, as well as to the longitudinal magnetization changes characterized by the T₁ relaxation time constant. The mesoscopic scale refers to distances that are smaller than the voxel dimensions but much larger than the atomic and molecular scales. The blood vessel network in brain tissue creates mesoscopic field inhomogeneities that are tissue specific and are responsible for the BOLD contrast. Our laboratory previously developed a theoretical model of BOLD contrast (12) that analytically connects BOLD signal to hemodynamic parameters such as blood volume, deoxyhemoglobin concentration, and OEF. In phantom studies (11) we quantitatively validated important features of the model. We have also proposed 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 (11). 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.

Previous attempts (13–16) to directly implement this method (11) in vivo were encouraging but did not produce conclusive results. One reason is that the simplistic model used in previous studies, which described brain tissue as a one-component structure similar to water in a phantom, is not sufficient to describe real brain tissue. Indeed, it is well known that brain tissue displays multicomponent MR behavior. This issue has been addressed in a number of papers (e.g., Refs. 17 and 18). In white matter (WM), Whittal et al. (18) identified three components as fast, intermediate, and slow, with T₂ = 15, 77, and 250 ms, and fractional weights of 11%, 84%, and 5%, respectively. In gray matter (GM), these authors found fast and intermediate components with T₂ = 15 and 87 ms and fractional weights of 5% and 95%, respectively. Direct measurements of the R₂′ relaxation rate constant in the brain tissue by Fujita et al. (19) demonstrated that the R₂′ measurement depends on the SE time in the GESSE sequence. Fujita et al. (19) correctly attributed this effect to the multicomponent structure of brain tissue, whereas each component has a different T₂ relaxation time constant and fractionally weights the measurement differently for different SE times. In this study we expand the theoretical BOLD model (12) and experimental approach (11) by incorporating the multicomponent/multicompartment structure of the brain tissue.

The objective of this study was to develop a BOLD MR signal model of brain tissue that incorporates prior knowledge about brain tissue composition and includes contributions from GM, WM, CSF, and blood. The model was utilized to estimate hemodynamic parameters of the human brain in the baseline state.

Theory

Because of the paramagnetic nature of heme complexes in deoxygenated red blood cells (20), the presence of a blood vessel network creates an additional decay mechanism for tissue-originated MR signals. This effect is due to inhomogeneous magnetic fields created by red blood cells in the blood (21) and inhomogeneous magnetic fields created by blood vessels in the surrounding tissue (1). These mesoscopic field inhomogeneities are tissue-specific and may provide important information about blood vessel network structure. It is generally assumed that in the presence of a blood vessel network, a free induction decay (FID) MR signal at time t after excitation can be described in terms of a simple linear exponential function:

$$s_t(t)\approx exp(-R_2^{\ast }\cdot t);R_2^{\ast }=R_2+R_2^{\prime }.$$ [1]

The R₂ relaxation rate constant describes the irreversible (with respect to an external 180° radiofrequency (RF) re-focusing pulse) part of the FID MR signal decay, and has contributions from both the internal microscopic tissue T₂ decay and the mesoscopic magnetic field inhomogeneities described above. The $R_2^{\prime }$ relaxation rate constant describes the reversible part of the MR signal decay that originates solely from mesoscopic field inhomogeneities. An analytical theory was developed that predicts how the $R_2^{\prime }$ relaxation rate constant depends on the tissue and blood parameters (12):

$$R_2^{\prime }=\mathrm{\zeta }\cdot \mathrm{\delta }\mathrm{\omega }=\mathrm{\zeta }\cdot \mathrm{\gamma }\cdot \frac{4}{3}\cdot \mathrm{\pi }\cdot \mathrm{\Delta }{\mathrm{\chi }}_0\cdot Hct\cdot (1-Y)\cdot B_0,$$ [2]

where γ is the nuclear gyromagnetic ratio, Hct is the blood hematocrit level, Δχ₀- is the susceptibility difference between completely deoxygenated and completely oxygenated red blood cells, and Y is the blood oxygenation level (Y = 1 indicates fully oxygenated blood). The parameter ζ is sometimes confused with the cerebral blood volume (CBV), which can be defined by other techniques (e.g., PET) and measures the total blood volume. In the proposed MR technique, only blood that has a different magnetic susceptibility compared to the brain parenchyma, due to the presence of deoxyhemoglobin, contributes to the mesoscopic field inhomogeneity-induced signal decay described in Eq. [2]. This deoxyhemoglobin-containing blood constitutes only part of the blood vessel network, namely, the venous blood vessel network and the part of the capillary network adjacent to the venous side (capillary blood becomes deoxygenated as it moves through the capillary bed from arteries to veins). Sometimes the capillary contribution is ignored and parameter ζ is called venous CBV. To avoid confusion, we will call the parameter ζ the deoxygenated blood volume (DBV) with the understanding that the veins are typically the major contributor to ζ.

Equation [2] is in very good agreement with previous numerical results obtained by means of Monte-Carlo computer simulations (22,23). It follows from Eq. [2] that by measuring the $R_2^{\prime }$ relaxation rate constant, one can obtain information about the product of DBV and blood deoxygenation level, but not on each of them separately. Nevertheless, another theoretical prediction (12) presents an opportunity to measure DBV and blood oxygenation level Y independently. This theory predicts that the linear exponential decay of MR signal in Eq. [1] takes place only for times t greater than some characteristic time 1.5 t_c, where

$$t_c^{-1}=\mathrm{\delta }\mathrm{\omega }=\mathrm{\gamma }\cdot \frac{4}{3}\cdot \mathrm{\pi }\cdot \mathrm{\Delta }{\mathrm{\chi }}_0\cdot Hct\cdot (1-Y)\cdot B_0$$ [3]

For shorter times, the signal from brain tissue decays as a quadratic exponential:

$$s_t(t)\approx exp[-0.3\cdot \mathrm{\zeta }\cdot {(\mathrm{\delta }\mathrm{\omega }\cdot t)}^2-R_2^t\cdot t]$$ [4]

with a different dependence on DBV and blood oxygenation level than the simple product of blood volume and blood oxygenation level in the $R_2^{\prime }$ relaxation rate constant. $R_2^t$ is the relaxation rate constant for brain tissue. Phantom studies (11) confirmed this theoretical feature and demonstrated that rather accurate data on blood volume and oxygenation level can be obtained using the theoretical model of Ref. 12. While Eqs. [1] and [4] describe asymptotic behavior of MR signal, the complete solution is given as (12):

$$s_t(t)=exp(-R_2^t\cdot t-\mathrm{\zeta }\cdot f_c(t/t_c));f_c(t/t_c)=\frac{1}{3}\cdot {\int }_0^1\mathit{\text{du}}\cdot (2+u)\cdot \sqrt{1-u}\cdot \frac{1-J_0(1.5\cdot t/t_c\cdot u)}{u^2},$$ [5]

where s_t is the normalized signal, and J₀ is the zero-order Bessel function.

Equation [5] is derived in the framework of a static dephasing regime. Here the presence of susceptibility-induced static magnetic field inhomogeneities causes the MR FID signal to decay much faster than the competing process, the averaging of the water ¹H nuclear spin phases due to molecular diffusion within the inhomogeneous field. Hence, in the static dephasing regime the diffusive motion of water is not relevant to the MR FID signal decay process. The criteria for the validity of the static dephasing regime were discussed in detail in Refs. 11 and 12. The comparison of the static dephasing regime theory with numerical simulations by Boxerman et al. (23), Kiselev and Posse (24), and Fujita et al. (19) confirms that this analytical theory is valid for practically all blood vessels except for capillaries, where the correction for diffusion phenomena should be made for low-field MRI (24–26). This theory is still under development, and in this study we will ignore the corresponding corrections. We only note that at high-field MRI (≥3T) the deviation from the static dephasing regime is not expected to be substantial.

As discussed in the Introduction, the correct model of brain tissue signal should incorporate its multicomponent tissue structure. For an MR experiment with SE times ranging from 25 ms to 80 ms, fast T₂ components in GM and WM (T₂ = ∼15 ms) are practically “invisible” due to T₂ decay and their low concentration. Hence, we will adopt for WM a model that includes only two components with T₂s of approximately 77 and 250 ms. For the GM we will also adopt a model with two components (one with T₂ of approximately 87 ms, and one with T₂ greater than or approximately equal to 250 ms) to account for possible partial-volume effects from CSF. In both WM and GM, the long T₂ components are related to the extracellular fluid in the central nervous system (CNS) and are composed of either CSF or interstitial fluid (ISF) in GM and WM. The interstitial space of the brain communicates freely with the CSF compartment, and hence the composition of the two fluid compartments is relatively similar. However, T₁ and T₂ relaxation time constants of ISF can be substantially different from T₁ and T₂ relaxation time constants of CSF due to contact with the cell membranes and water exchange between ISF and intracellular fluid. In the following text we will refer to the rapidly relaxing component in both GM and WM as “tissue” (abbreviated as “t”), and the slowly relaxing component as “extracellular” (including both CSF and ISF, abbreviated as “e”). The two relaxation rate constants, $R_2^t$ and $R_2^e$, will be considered as phenomenological fitting parameters. Also, given that CSF/ISF has different protein and lipid contents compared to brain cells, we will assume that the CSF/ISF signal 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 Ref. 27). Accordingly, for the normalized signal from the “extracellular” space (CSF or ISF), we adopt the following model:

$$s_e(t)=exp(-R_2^e\cdot t-2\mathrm{\pi }i\cdot \mathrm{\Delta }f\cdot t-i\mathrm{\phi }).$$ [6]

In addition, an intravascular contribution from the venous blood should be taken into consideration. Even though the intravascular blood volume fraction is small, its entire content is subject to mesoscopic field inhomogeneities. Thus, if intravascular blood signal is not properly accounted for, it may confound the estimation of DBV and OEF. In this study we adopt a theoretical model for the intravascular blood signal proposed in Ref. 28 that takes into account the presence of multiple blood vessels with orientations uniformly distributed in a voxel. In this model a normalized signal is

$$s_b(t)={\left(\frac{\mathrm{\pi }}{3\cdot |\mathrm{\delta }\mathrm{\omega }\cdot t|}\right)}^{½}exp(i\cdot \mathrm{\delta }\mathrm{\omega }\cdot t/2-R_2^b\cdot t)\cdot [C({|3\mathrm{\delta }\mathrm{\omega }\cdot t/2|}^{½})-i\cdot \mathit{\text{sign}}(t)\cdot S({|3\mathrm{\delta }\mathrm{\omega }\cdot t/2|}^{½})].$$ [7]

Functions C(x) and S(x) are Fresnel cosine and sine integral functions, respectively, sign is a sign function, and δω is the characteristic frequency shift as defined in Eq. [2].

The transverse relaxation rate constant of venous blood, $R_2^b$, depends on blood oxygen saturation. This dependence was extensively studied in Refs. 27 and 29 at 1.5T and 4.7T. Combining the results of these two studies and assuming the Hct level of 0.34 (30), we adopt for a 3T magnetic field the following equation for the transverse relaxation rate constant $R_2^b$ of the blood:

$$R_2^b({sec}^{-1})=5.0+173\cdot {(1-Y)}^2.$$ [8]

So far we have discussed the influence of intrinsic, tissue-specific magnetic field inhomogeneities on the formation (decay) of the MR signal. Both fluctuating microscopic field inhomogeneities and static mesoscopic field inhomogeneities have been taken into account. However, macroscopic field inhomogeneities also affect signal formation and may compromise hemodynamic parameter quantification if they are not properly recognized (11). Because of differences in the spatial scale of macroscopic and mesoscopic field inhomogeneities, the total FID signal can be represented as a product of the signal that would exist in the absence of macroscopic field inhomogeneities, multiplied by the function F(t), which represents contributions to the signal attenuation caused by macroscopic (b_macro) field inhomogeneities:

$$F(t)=\frac{1}{V}\int exp[-i\cdot \mathrm{\gamma }\cdot b_{\mathit{\text{macro}}}(\overrightarrow{r})\cdot t]\cdot d\overrightarrow{r}$$ [9]

The integral in Eq. [9] is taken over the voxel volume V. The NMR signal correction around the SE can be described by means of the same function Eq. [9] with a shifted argument, F(t – TE).

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

$$\overline{S}(t)=S_0\cdot F(t)\cdot \{(1-\mathrm{\lambda }-{\mathrm{\lambda }}^{\prime })\cdot s_t+\mathrm{\lambda }\cdot s_e+{\mathrm{\lambda }}^{\prime }\cdot s_b\}$$ [10]

where parameters λ and λ′ are the fractions of signal from ISF/CSF and blood at t=0 (note that they are different from the true volume fraction of corresponding components). The values of λ and λ′ depend on the longitudinal and transverse relaxation rate constants of brain tissue components, the timing details of the pulse sequence, and the relative spin densities of the tissue components. For an SE sequence, t = 0 is chosen at the SE time. In the GRE or FID sequence, t = 0 corresponds to the time of the excitation RF pulse.

Materials and Methods

MR Experiments

This study was approved by the Institutional Review Board of Washington University, and written informed consent was obtained from each recruited subject. A total of nine studies were conducted on normal healthy volunteers. All images were acquired on a 3T Allegra head scanner (Siemens Medical Systems, Erlangen, Germany). To reduce motion artifacts, a vacuum mold pillow was used as a head restrainer. During the study the volunteers were instructed to rest quietly with their eyes open.

A GESSE sequence with RF spoiling similar to that used in a previous study (11) was employed. In the GESSE sequence a set of GREs are embedded around the SE of a single SE sequence. Within the set, each GRE has the same phase encoding. This sequence structure allows simultaneous acquisition of a set of images corresponding to different GRE times (TEs). 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 sign-alternating readout gradients. The pulse sequence parameters for six studies were as follows: Multiple 2D 6-mm slices with a field of view (FOV) of 256 × 256 mm² and sampling matrix of 64 × 64 were simultaneously acquired in an interleaved manner with TR of 2000 ms. The GRE train spacing was 1.2 ms with a length of 89 echoes. The SE occurred during the seventh GRE, corresponding to 32.8 ms after the RF excitation pulse. The bandwidth was 1817 Hz per pixel. To compensate for imaging artifacts due to DC offset, each k-space line was acquired twice with the opposite flip angle at subsequent repetitions. Four repetitions with a total acquisition time of 8 min 30 s were used.

Other sets of sequence parameters were also tested in three data sets. In these studies, TR was set at 1000 ms, and slice thickness was 6 mm with 16 repetitions. SE occurred at 36.4 or 67.8 ms after the RF excitation pulse. The FOV was 256 × 224 mm² (81.3% FOV in the phase-encoding direction) with a sampling matrix of 128 × 104 or 64 × 52. The echo train spacing was 3.92 ms with a bandwidth of 331 Hz per pixel. The use of longer echo spacing helps to reduce imaging artifacts that arise from eddy-current effects due to fast readout gradient switching, and to enable low ADC bandwidth for improved SNR. During these studies, for each odd repetition all acquisition windows and readout gradients were shifted by half the echo spacing so that an effective temporal resolution of 1.96 ms was achieved. The effective echo train length was 62.

For field mapping, a double-echo GRE pulse sequence was used to acquire 3D high-resolution images. The MRI parameters were TR = 20 ms, TE = 4.92 and 12.30 ms, and spatial resolution = 1.0 × 1.0 × 2.0 mm³.

Data Processing

Raw data from the Siemens scanner were imported into Matlab (MathWorks Inc., Natick, MA, USA) running on a 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 to fit the proposed signal model to the measured signal on a pixel-by-pixel basis. Since the phase of measured signal can be affected by unknown factors, such as eddy currents, flow, and patient movement, only the magnitude of the GESSE signal is used in the fitting procedure.

To evaluate the function F(t) in Eq. [9], the magnetic field distribution was calculated from the MR signal phase difference between the two echoes in high-resolution 3D images. The phase images were preliminary unwrapped by a customized 3D phase unwrapping program that combines the merits of mask-cut and quality-guided unwrapping algorithms as described in Ref. 31. The phase of MR signal is affected by both mesoscopic and macroscopic field inhomogeneities. Mesoscopic field inhomogeneities create phase changes on the scale of the characteristic size of blood vessels, while macroscopic field inhomogeneities change on a much larger scale (the size of the imaging voxel). Blood vessels that are much smaller than the voxel size in the high-resolution field mapping sequence will not contribute to the phase difference map because their effect will be averaged out by Fourier reconstruction. To filter out effects of mesoscopic field inhomogeneities originating from the blood vessels that are on the order of the voxel size in the high-resolution field mapping sequence, the phase difference map for each GESSE voxel is fitted into a quadratic polynomial model using base functions x, y, z, xy, yz, xz, x²-y², and z²-x²-y². This procedure not only removes the contribution of mesoscopic field inhomogeneities, it also effectively reduces the influence of noise on the calculated function F(t) in Eq. [9].

Because of the large number of fitting parameters used (S₀, δo, ζ, $R_2^t$, $R_2^e$, Δf, φ, and λ), a good initial estimate is essential for a robust optimization procedure. Since the deviation from a linear exponential decay for the extravascular MR signal is negligible for t > 1.5t_c, a simplified two exponential decay model (with an F factor as described in Eq. [9] to account for macroscopic field inhomogeneities) is first fitted to the data points beyond 10 ms after the SE. 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 extrapolated signal intensities at the SE is used to evaluate the initial value for blood volume fraction ζ. The initial value of δω in this estimate is set to a value corresponding to an average OEF of 40%. These initial values are used afterwards for a final fitting procedure.

The OEF is calculated from the deoxygenated blood oxygenation level, Y, and oxygen saturation level of arterial blood, Y_a = SO₂/100:

$$OEF=1-Y/Y_a,Y=1-\mathrm{\delta }\mathrm{\omega }/(\mathrm{\gamma }\cdot \frac{4}{3}\cdot \mathrm{\pi }\cdot \mathrm{\Delta }{\mathrm{\chi }}_0\cdot Hct\cdot B_0)$$ [11]

Under normal conditions SO₂ is very close to 100%, and Eq. [11] can be replaced by the approximation OEF = 1−Y. However, for accurate clinical or research evaluations, an exact Eq. [11] should be used, provided that the arterial oxygen saturation is measured by other means (e.g., by a simple pulse oximeter). Parameter ζ defines the volume fraction of cerebral deoxygenated blood in the brain tissue excluding the ISF/CSF:

$$DBV=\mathrm{\xi }.$$ [12]

The parameters δω and ζ are the only two fitting parameters that define OEF and DBV in Eqs. [11] and [12]. A number of other tissue characteristics can also be evaluated from our data. The value of deoxyhemoglobin concentration in the brain tissue can be estimated from the model parameters via

$$C_{\mathit{\text{deoxy}}}=DBV\cdot (1-Y)\cdot n_{Hb}\cdot Hct=\frac{DBV\cdot \mathrm{\delta }\mathrm{\omega }\cdot n_{Hb}}{\mathrm{\gamma }\cdot 4/3\cdot \mathrm{\pi }\cdot \mathrm{\Delta }{\mathrm{\chi }}_0\cdot B_0},$$ [13]

where n_Hb is the total intracellular Hb concentration, 5.5 × 10⁻⁶ mol/mL (27). In order to evaluate numerical values of OEF and deoxyhemoglobin concentration, an independent measurement of the Hct is required. In this work we assume an Hct ratio in small vessels of 0.34 (30), which is typical for healthy humans. For the susceptibility difference between completely deoxygenated and completely oxygenated red blood cells we use the value of 0.264 ppm (27).

To evaluate the DBV and the regional cerebral deoxyhemoglobin concentration per unit of brain volume including both brain tissue and ISF/CSF, the following correction should be made:

$$DBV\Rightarrow DB{V}^{\prime }=DBV\cdot (1-{\mathrm{\lambda }}_0);C_{\mathit{\text{deoxy}}}\Rightarrow C_{\mathit{\text{deoxy}}}^{\prime }=C_{\mathit{\text{deoxy}}}\cdot (1-{\mathrm{\lambda }}_0)$$ [14]

where λ₀ is the true volume fraction of ISF/CSF. It can be inferred from the following equation, which takes into account the parameters of the GESSE sequence and tissue component magnetic properties:

$${\mathrm{\lambda }}_0=\frac{n_t\cdot m_t\cdot \mathrm{\lambda }}{n_{CSF}\cdot m_{CSF}\cdot (1-\mathrm{\lambda })+n_t\cdot m_t\cdot \mathrm{\lambda }},$$ [15]

where n_t and n_csf are the relative spin densities for brain tissue and ISF/CSF, respectively. In Eq. [15] the contribution from intravascular blood is ignored because the blood signal fraction is quite small compared to the signal from brain tissue. In our calculations we assume n_t = 0.66 (an average value for mixed brain tissue (17)). The parameters m_t and m_CSF represent the steady-state magnitudes of the magnetization at the SE time for a GESSE sequence with the excitation flip angle α:

$$m=\frac{1-2exp(-(T_R-TE/2)/T_1)+exp(-T_R/T_1)}{1+exp(-T_R/T_1)\cdot cos\alpha }\cdot exp(-TE/T_2).$$ [16]

Where m, T₁ and T₂ are values of parameter m, the longitudinal and transverse relaxation times for the corresponding component (tissue or ISF/CSF). For the longitudinal relaxation time, T₁, of ISF/CSF, blood, and brain tissue we used 3700 ms, 1627 ms, and 1000 ms, respectively (32,33). Since the blood volume fraction is small, the fraction of intravascular blood signal can be approximately expressed as:

$${\mathrm{\lambda }}^{\prime }=m_b\cdot n_b\cdot (1-\mathrm{\lambda })\cdot \mathrm{\zeta }$$ [17]

Results

Representative signal-intensity evolution profiles from two selected voxels in GM and WM obtained with the GESSE sequence are illustrated in Fig. 1. The residual profiles shown in Fig. 1d indicate that the fitting error of the quantitative BOLD (qBOLD) theoretical model, Eq. [10], is comparable to the background noise level. An interesting observation is a rather large (as compared to the noise level), sharp peak in the residual at the SE. Its intensity can be as high as 1% of the total signal and it is usually larger in the GM than in the WM (as in the example shown in Fig. 1d). This peak most likely originates from water components with short T₂ relaxation time constants, but it can also have contributions from lipids and metabolites. The signal contributions from ISF/CSF and intravascular venous blood are illustrated in Fig. 1e and f, which indicate a significantly higher ISF/CSF signal fraction in GM regions than in WM. Only the real part of the blood signal is shown, because it contributes most to the total magnitude signal. Figure 1c shows the extravascular brain tissue signal after the effect of R₂ decay and contributions from ISF/CSF and intravascular blood are removed. DBVs of 1.56% and 0.62% were obtained for the GM and WM voxels, respectively. The other estimated fitting parameters for the GM voxel are: OEF = 32.9%, frequency shift = 4.6 Hz, and ISF/CSF signal contribution at SE time = 4.9%. For the WM voxel, the rest of the fitting parameters are: OEF = 33.1%, frequency shift = 4.5 Hz, and ISF/CSF signal fraction = 4.0% at SE time. Sampled data points within the initial 2 ms were discarded to stabilize the eddy-current effect. Meanwhile, data points at the last 10 ms were usually discarded due to a low signal-to-noise ratio (SNR).

Fig. 1.

Representative data and fitting curves obtained with the GESSE sequence (matrix = 64 × 64, TR = 2000 ms). a: Signals and the fitted profiles for voxels in the GM area (blue line) with DBV = 1.56% and OEF = 32.9%, and the WM area (red line) with DBV = 0.62% and OEF = 33.1%. b: High-resolution anatomic T₁-weighted image showing selected voxels. c: Extravascular signal contributions after removing signals from ISF/CSF and intravascular blood, and adjusting for the R₂ decay (multiplying by the factor exp(+R₂ TE)). The black solid lines correspond to the extrapolated signal profile from the asymptotic behavior at long TEs. d: Fitting residuals. e: Magnitudes of the ISF/CSF signals. f: Real parts of intravascular blood signals. In all plots the x-axis corresponds to a GRE time elapsed from the SE time (TE = 36.4 ms), and the y-axes represent signals in relative units. The echo spacing is 1.2 ms.

Figure 2 shows maps of the estimated brain parameters from a high-resolution GESSE study using a 128 × 128 sampling matrix with a total acquisition time of 27 min. All maps are filtered with a 2D Gaussian filter with standard deviation (SD) of 2 voxels (4 mm). In the maps of DBV, ISF/CSF volume fraction, and brain tissue deoxyhemoglobin concentration, the contrast is sufficient to resolve GM and WM. Meanwhile, the maps of OEF and frequency shift are relatively uniform. In the map of ISF/CSF volume fraction, the scale stops at 40% in order to enhance the contrast in areas that consist mainly of GM and WM.

Fig. 2.

Representative maps of estimated brain parameters obtained with a high-resolution (128 × 128) GESSE sequence. The top leftmost image is a high-resolution anatomic image. The rest of the maps are DBV fraction (%), OEF (%), R₂ of brain tissue (s⁻¹), ISF/CSF volume fraction, ISF/CSF frequency shift (Hz), R₂′ of brain tissue (s⁻¹), and brain deoxyhemoglobin concentration (μM).

Voxels close to the brain surface are contaminated by partial-volume effects from the fat signal of the skull and Fourier leakage from image reconstruction. These problems are compounded by the fact that around the brain surface, B₀ field inhomogeneities may be higher and the corresponding field maps are less accurate due to low SNR. Voxels in this area are also more susceptible to patient movement. We normally observed higher than average fitting residuals near the brain surface, and therefore these areas were excluded from the postprocessing and the maps in Fig. 2. Future studies can minimize fat contamination by applying a fat saturation magnetization preparation pulse or Dixon water–fat separation techniques.

Figure 3 illustrates histograms of the estimated brain parameters across three slices from the study shown in Fig. 2. Although the contrast between GM and WM for most parameters is highly visible in 2D maps, the combined histograms show little sign of clearly separated peaks. This may result from the partial-volume effect and Fourier leakage such that the MR signal may contain contributions from both GM and WM. Therefore, there exists a large transition area between pure GM and WM that leads to a more or less smoothed histogram. From the histograms, the averaged DBV is 1.08% ± 0.52%; the OEF is 47.9% ± 7.2%; the ISF/CSF volume fraction is 14.4% ± 9.5%; the frequency shift between ISF/CSF and brain tissue is 5.25 ± 0.58 Hz; the R₂ of brain tissue is 14.9 ± 0.2 s⁻¹; and the concentration of deoxyhemoglobin is 9.7 ± 4.2 μM.

Fig. 3.

Histograms of the estimated brain parameters for the study shown in Fig. 2. The histograms represent the DBV (%), OEF (%), ISF/CSF volume fraction, ISF/CSF frequency shift (Hz), R₂ of the brain tissue (s⁻¹), and concentration of deoxyhemoglobin (μM).

Figure 4 displays the results from studies using the GESSE pulse sequence with a low-resolution (64 × 64) sampling matrix. For the given slice, the images represent a T₁-weighted anatomic image (from the high-resolution field map), DBV map, OEF map, brain tissue R₂ map, ISF/CSF volume fraction map, ISF/CSF and water frequency shift map, brain tissue $R_2^{\prime }$ map, and deoxyhemoglobin concentration map. Even this relatively low-resolution study successfully resolved the contrast in DBV and deoxyhemoglobin concentration between GM and WM. In comparison with the study shown in Fig. 3, partial-volume effects become more dominant near the surface of the brain, as demonstrated in the map of brain tissue R₂ map and ISF/CSF volume fraction map.

Fig. 4.

Representative maps of brain parameters obtained with a low-resolution (64 × 64) GESSE sequence. The top leftmost image is a high-resolution anatomic image. The rest of the maps are DBV fraction (%), OEF (%), R₂ for brain tissue (s⁻¹), ISF/CSF volume fraction, ISF/CSF frequency shift (Hz), $R_2^{\prime }$ of brain tissue (s⁻¹), and brain deoxyhemoglobin concentration (μM).

In some of the studies a careful inspection of the DBV and OEF maps reveals that in areas with quite low DBV values, abnormal values of OEF can be observed. In such areas the value of the reversible transverse relaxation rate constant $R_2^{\prime }$ is very low. From Eq. [2], $R_2^{\prime }$ is proportional to the product of DBV and OEF. Hence, the uncertainty of DBV value estimation (the relative uncertainty can be high because the DBV value is small) may result in high error in OEF estimation.

Table 1 summarizes the results from all nine studies. Each shaded group represents data from the same subject obtained from two studies conducted approximately 1 hr apart. Studies 1 and 2 employed different acquisition matrices but the same TR and GRE spacing. To estimate the mean tissue parameters for WM and GM, we used the following procedure: Because of partial-volume effects and Fourier reconstruction leakage, the measured MR signal from any given voxel may be contaminated by the signals from adjacent voxels. These signal contamination effects are more severe in GM areas due to their smaller size. Therefore, in order to differentiate the parameters from relatively uncontaminated GM and WM, we included only regions that were relatively far away from the GM/WM boundaries and boundaries with CSF. The deep WM areas can be easily segmented manually. GM areas are very thin, and we segmented them by applying a threshold to the DBV map such that only areas with DBV value larger than 1.2% were selected. Given that the average DBV value in the GM areas is on the order of 1.6–1.9% with an SD of about 0.3–0.5%, this thresholding procedure removed only a very small fraction of GM voxels and did not substantially affect the results for the DBV estimates.

Table 1. The Estimated Brain Parameters From all Nine Studies^*.

Study	DBV GM (%)	DBV WM (%)	OEF (%)	$R_2^{\prime }$ GM (sec−1)	$R_2^{\prime }$ WM (sec−1)	dHb GM (μM)	dHb WM (μM)
1a	1.62 ± 0.33	0.62 ± 0.08	34.5 ± 5.7	2.5 ± 0.9	0.68 ± 0.31	10.8 ± 2.5	3.7 ± 0.9
2	1.66 ± 0.32	0.70 ± 0.06	34.9 ± 5.7	2.4 ± 0.8	0.77 ± 0.35	11.0 ± 2.4	4.5 ± 0.8
3	1.74 ± 0.47	0.56 ± 0.10	36.4 ± 7.5	2.5 ±1.3	0.72 ± 0.27	11.2 ± 2.8	4.5 ±1.0
4	1.93 ± 0.48	0.60 ± 0.12	32.5 ± 7.8	3.1 ± 2.1	0.68 ± 0.53	11.2 ± 3.6	4.1 ± 1.3
5	1.93 ± 0.48	0.63 ± 0.10	35.1 ± 7.1	3.2 ± 1.9	0.82 ± 0.62	12.2 ± 3.4	4.2 ±1.4
6	1.77 ± 0.47	0.55 ± 0.08	36.0 ± 6.7	3.5 ± 2.5	0.54 ± 0.25	14.2 ± 4.8	3.8 ±1.0
7	1.82 ± 0.43	0.44 ± 0.14	42.7 ± 9.7	3.2 ±1.7	0.54 ± 0.32	13.8 ± 3.9	3.8 ±1.2
8	1.73 ± 0.47	0.47 ± 0.16	44.5 ±10	3.2 ± 1.6	0.71 ± 0.31	13.1 ± 4.0	4.9 ±1.8
9a	1.58 ± 0.32	0.69 ± 0.11	47.9 ± 7.2	2.6 ±1.4	1.60 ± 0.76	14.1 ± 2.8	6.3 ± 1.1
Mean ± SD	1.75 ± 0.13	0.58 ± 0.09	38.3 ± 5.3	2.9 ± 0.4	0.68 ± 0.10	12.4 ± 1.4	4.4 ± 0.8

^*Each shaded group represents data from the same subject obtained from two studies conducted approximately one hour apart. Studies 1, 2, and 9 were acquired using a window shifting scheme with TR of 1000 msec and effective echo spacing 1.96 msec. The rest of the studies were acquired with TR of 2000 msec and echo spacing of 1.2 msec.

^aHigh resolution (2×2×6 mm³) studies. The rest of the studies were acquired with a 64 × 64 matrix.

Discussion

Quantitative measurements of human CBV and OEF have been carried out by many researchers using mostly PET and optical spectroscopy approaches. It is well established from PET studies that there exists a contrast of CBV between GM and WM. At the same time, OEF maps are largely flat. Our data are in agreement with these well established findings.

The results shown in Table 1 demonstrate that OEF variation across the brain in each study was small (less than 20% of the mean value). This result is consistent with previous reports (2). To test the reproducibility of the technique, on three occasions two data sets were acquired from the same subjects at a time interval of about 1 hr (marked shaded in Table 1). For these studies the variation was small for each subject, which indicates the reliability of the proposed method. Table 1 also demonstrates that the OEF varied among subjects (average OEF values as high as 47.9% and as low as 32.5% were detected). For the entire group the average OEF value was 38.3% ± 5.3%. This variation may reflect differences in the subjects' physiological condition. Both the mean OEF values and intersubject variability are consistent with previous results from PET studies in normal volunteers. Indeed, Carpenter et al. (34), Yamauchi et al. (35), Diringer et al. (36), and Raichle et al. (2) reported OEF values of 35% ± 7%, 42.6% ± 5.1%, 41% ± 6%, and 40% ± 9%, correspondingly. We should also note that accounting for arterial blood oxygen saturation level (Eq. [11]) may result in slightly different values of the estimated OEF. This may not be very important for normal subjects, since their saturation level is close to 100%, but it could have a significant impact on certain categories of patients.

Our DBV estimations from both GM and WM areas did not vary substantially across the subjects. The average measured DBV values of 1.75% ± 0.13% in GM area and 0.58% ± 0.09% in deep WM demonstrate the expected contrast between these tissues. It has been reported that the capillary volume fraction is about 200–300% greater in GM than in WM (37,38). Similarly, the total blood volume determined by an MRI approach is about two to three times larger in GM than in WM (39), which is consistent with our results. To further compare our results with those from other techniques, we must re-emphasize that the DBV measured by our approach based on the BOLD phenomena is different from the CBV reported by other methods. As explained above, our approach evaluates only the blood volume occupied by deoxygenated blood. Most noninvasive measurements of CBV have come from PET studies that evaluated the sum of arterial, venous, and capillary blood pools.

To compare our results with global measurements of CBV, we need to know the blood distribution among different components of the blood vessel network. However, such quantitative information is rather limited. Generally, the blood vessel network is divided into five groups (40). The first group comprises large cerebral arteries, such as the arteries of the circle of Willis, and their peripheral and basal branches. The second group comprises small (terminal) arteries and pre-arterioles. The third group comprises all structural units of the cerebral vascular system that are involved in the exchange between blood and tissue (arterioles, metarterioles, arteriolar-venular anastomoses, true capillaries, and venules). The fourth group comprises the terminal cerebral veins, and the fifth group consists of large collecting veins at the base of the brain. A previous study of a canine brain (40) found that groups 1–5 contained 10%, 17%, 29%, 19%, and 25% of the total brain blood volume, respectively. Studies on microvascular corrosion casts of human (41,42) and chinchilla (43) CNS using optical and/or scanning electron microscopy indicate similarities in the morphological characteristics and distribution patterns of the microvascular network between humans and other mammals, although definitive volume fractions have not been determined. Because the arterial blood does not contribute to the BOLD effect, the second and at least one-third of the third group should be excluded from consideration. Also, the first and fifth groups are largely located outside of the brain tissue.

Hence, the BOLD-sensitive blood may occupy only about 59% of the total CBV, which is within the range reported by Lee et al. (44) and van Zijl et al. (45). Our DBV measurements predict a total blood volume of approximately 3.0% in GM and 1.0% in WM, which is consistent with previous MRI data (39) and is in the range of reported PET data (Carpenter et al. (34), Diringer et al. (36), and Derdeyn et al. (6) reported global CBV values of 4.5%, 3%, and 2.7%, respectively).

The average value of deoxyhemoglobin concentration from nine studies was 12.4 ± 1.4 μM at GM and 4.4 ± 0.8 μM at WM. Following the same argument used for the DBV analysis, the total deoxyhemoglobin concentration in GM (including the contribution from the fifth vessel group) would be about 20 μM, which is in good agreement with the results of a previous near-infrared spectroscopy study (46). The average value of $R_2^{\prime }$ is 2.9 ± 0.4 s⁻¹ in GM and 0.68 ± 0.10 s⁻¹ in WM. The value of GM $R_2^{\prime }$ is consistent with the reported value of 2.48 ± 0.35 s⁻¹ (47). To the best of our knowledge, no such data exist for WM.

In our model, signal with a long T₂ is attributed to CSF or ISF. Figures 2 and 4 indicate that the ISF/CSF signal fraction in GM is quite high in the cortical sulci regions and around the midline, which results mainly from the partial-volume effect of bulk CSF. The CSF/ISF contribution for WM regions is also substantial (about 5%), in good agreement with previous studies by Whittal et al. (18). We note again that the T₁ and T₂ of ISF can be substantially different from the T₁ and T₂ of CSF due to water exchange between the intra- and extracellular fluids. However, the dynamic range of our measurements (about 100 ms in the GESSE sequence) does not allow reliable differentiation between the T₂ values of CSF and ISF.

The existence of multiple water resonance frequencies in human and rat brains was also reported in previous studies (48,49), which indicated that about 14% of voxels in the rat brain had two or more resolved components. Although the large frequency shift observed in a 1.5T human brain study was attributed to the bulk magnetic susceptibility shift due to large blood vessels with specific orientations, their results nevertheless indicate the existence of a frequency difference between ISF/CSF and brain tissue. In addition to the multicompartment characteristic of the brain water NMR signal, several researchers also noticed the existence of multiple water reference signals when phase correction was applied to spectroscopy data (50,51). They attributed the unwanted phase jumps in the water signal to the presence of a second signal that resonates close to the main water resonance. Our study demonstrates that the frequency shift between ISF/CSF and parenchyma occurs across the entire brain. Excluding areas in the vicinity of major venous blood vessels, the map of frequency shift is relatively uniform, with a value of 5.4 ± 0.8 Hz. The existence of this frequency shift can be explained by the different protein and lipid concentrations in brain tissue and ISF/CSF—an effect similar to that considered previously for red blood cells vs. plasma in blood (27).

In previous studies based on the GESSE sequence or modifications (13,14,52), no significant difference in the DBV of brain GM/WM was detected. Their estimates of DBV are significantly higher than our results. This is probably due to several factors. First, the MR signal model adopted in Refs. 13, 14, and 52 ignores the contribution from ISF/CSF and intravascular blood. As illustrated in Fig. 1e and f, such contributions are comparable to signal changes due to mesoscopic field inhomogeneities. We compared our results from the qBOLD model with those obtained when a single-compartment model (Eq. [5]) with the macroscopic field inhomogeneity correction factor (Eq. [9]) was used. Unlike the residual resulting from fitting the complete qBOLD model, a single-component model demonstrates the presence of a substantial systematic residual (Fig. 5). For the same imaging slice shown in Fig. 1, the estimates for OEF and DBV are substantially different (DBV = 7.8% ± 1.8% and OEF = 20.8% ± 10.1% for the single-compartment model vs. DBV = 1.6% ± 0.9% and OEF = 40.3% ± 7.2% for the qBOLD model). These results demonstrate a significant overestimation of DBV and a significant underestimation of OEF when a single-compartment model is used.

Fig. 5.

Residuals after fitting a one-compartment BOLD model (Eq. [5]) with the correction factor F(t) (Eq. [9]) to the same data set as in Fig. 1.

Second, the approach adopted in Refs. 13, 14, and 52 utilizes asymptotic properties of the MR signal at the SE and long GRE times, as originally proposed in phantom studies (11). However, in contrast to phantom experiments, the in vivo signal during a SE may be considerably contaminated by small amounts of lipids and metabolites in the tissue, as shown in Fig. 1c and d. Hence, one can introduce substantial errors into the estimation of DBV by simply measuring the distance between the extrapolated line and the signal intensity at the SE time on a logarithmic scale. Because of the R₂ difference between brain tissue and deoxygenated blood, the degree of this error would depend on the SE time. As pointed out by Fujita et al. (19), when the two-staged estimation method is applied without considering multiple T₂ decay components, the estimated $R_2^{\prime }$ from the long time-scale behavior will depend on the chosen fitting interval, leading to errors in estimation of DBV and OEF. Our approach is free from these problems because it utilizes a more realistic brain tissue model and fits data to the whole qBOLD model (Eq. [10]), incorporating the exact effects of mesoscopic field inhomogeneities (Eq. [5]), instead of using only asymptotic forms. In particular, our curve-fitting approach automatically filters out high-frequency contributions from metabolites and lipids.

Another drawback of using asymptotic signal behavior for parameter estimation is increased sensitivity to low image SNR. As demonstrated in Eqs. [1] and [4], the characteristic function of randomly oriented cylindrical objects behaves as a quadratic exponential decay for short time scales (t/t_c < 1.5) and linear exponential decay for long time scales (t/t_c >1.5). Decay data collected at long time scales before and after the SE can only determine the RF reversible decay R₂′, which is proportional to the product of DBV and OEF. The short time-scale quadratic exponential behavior that is crucial for separating the effects of DBV and OEF is confined to the region within 2–3 t_c around the SE (about 15 ms for healthy human subjects at 3T). Therefore, the accuracy of independent DBV and OEF estimation is determined mainly by the SNR and the number of the sampled data points within this interval (assuming there are enough sampling data points outside this area to determine the rest of the parameters). Acquiring more sampling points within this region (i.e., by increasing temporal resolution, as in our method) substantially improves the accuracy of DBV and OEF estimation.

We also note that our approach is based on a theoretical assumption of the static dephasing regime for MR signal formation in the presence of the blood vessel network (11). This assumption may not hold for capillaries, and hence the signal $R_2^{\prime }$ decay rate may be smaller than predicted by Eq. [2]. Theoretical considerations by Kiselev and Posse (23) and Fujita et al. (19) suggest that water diffusion may play an important role in extravascular MR signal formation from the capillary network, especially if long SE times are used. The signal deviates more from the static dephasing regime behavior with increasing SE time and decreasing vessel size. According to numerical simulations, our method may underestimate the contribution to DBV from the capillary network. Substantial improvement can be achieved by shortening the SE time in the GESSE sequence. Also, further improvements could be made to incorporate the effects of molecular diffusion into the model.

Another important assumption of our theoretical model is the presence of randomly oriented blood vessels in the voxel (Eqs. [5] and [7]). We expect that for the large voxels used in this study (about 100 mm³), this assumption should be valid for most regions of the brain. However, some voxels may have large blood vessels with preferential orientations. In this case the theory can be modified to incorporate a distribution of blood vessel orientations (with the penalty of having additional fitting parameters). As another approach, the intravascular blood signal could be substantially suppressed with the use of crusher gradients (average blood flow in the fourth and fifth groups of the blood vessel network is 8–20 mm/s). However, this suppression does not affect extravascular mesoscopic effects, and their anisotropy should still be taken into consideration. The influence of molecular diffusion and blood vessel orientation on our MR signal model will be the subject of future studies.

Summary and Conclusions

In this study we developed an MR signal model of brain tissue, termed the qBOLD model, that generalizes our previously proposed theoretical model of the BOLD effect (12). The model is based on a multicomponent approach that includes contributions from intracellular water, ISF or CSF with a resonance frequency shift, and intravascular blood. This model analytically connects the BOLD effect to hemodynamic parameters, such as the DBV, deoxyhemoglobin concentration, and OEF. Using MR images of human brain parenchyma obtained with a modified GESSE sequence, our model-based multivariable curve-fitting approach quantifies brain parameters such as the DBV, OEF, ISF/CSF volume fraction, and frequency shift simultaneously. Given the proper temporal resolution and sufficient SNR, DBV contrast between GM and WM can be successfully resolved. At the same time, the brain signal model also quantifies the volume fraction and frequency shift of the extracellular space (ISF and CSF), which may prove useful for studying the development of brain edema or other diseases. The developed model and postprocessing approach can also be used to map cerebral DBV and OEF during functional activation for BOLD fMRI studies.

These analytical concepts and experimental results provide a promising platform for MR-based in vivo quantification of tissue hemodynamics. Quantitative measurements of this type are essential if MRI is to play an important role in evaluating the brain's baseline activity in health and disease. When this method is validated, it will provide an extraordinary tool for cognitive studies and clinical diagnosis that will be more widely available to clinicians and researchers than oxygen-15-based PET for the measurement of brain hemodynamics and metabolism.