Blood oxygenation level-dependent (BOLD)-based techniques for the quantification of brain hemodynamic and metabolic properties - theoretical models and experimental approaches

Abstract

The quantitative evaluation of brain hemodynamics and metabolism, particularly the relationship between brain function and oxygen utilization, is important for the understanding of normal human brain operation, as well as the pathophysiology of neurological disorders. It can also be of great importance for the evaluation of hypoxia within tumors of the brain and other organs. A fundamental discovery by Ogawa and coworkers of the blood oxygenation level-dependent (BOLD) contrast opened up the possibility to use this effect to study brain hemodynamic and metabolic properties by means of MRI measurements. Such measurements require the development of theoretical models connecting the MRI signal to brain structure and function, and the design of experimental techniques allowing MR measurements to be made of the salient features of theoretical models. In this review, we discuss several such theoretical models and experimental methods for the quantification of brain hemodynamic and metabolic properties. The review's main focus is on methods for the evaluation of the oxygen extraction fraction (OEF) based on the measurement of the blood oxygenation level. A combination of the measurement of OEF and the cerebral blood flow (CBF) allows an evaluation to be made of the cerebral metabolic rate of oxygen consumption (CMRO2 ). We first consider in detail the magnetic properties of blood - magnetic susceptibility, MR relaxation and theoretical models of the intravascular contribution to the MR signal under different experimental conditions. We then describe a 'through-space' effect - the influence of inhomogeneous magnetic fields, created in the extravascular space by intravascular deoxygenated blood, on the formation of the MR signal. Further, we describe several experimental techniques taking advantage of these theoretical models. Some of these techniques - MR susceptometry and T2 -based quantification of OEF - utilize the intravascular MR signal. Another technique - quantitative BOLD - evaluates OEF by making use of through-space effects. In this review, we target both scientists just entering the MR field and more experienced MR researchers interested in the application of advanced BOLD-based techniques to the study of the brain in health and disease.

Keywords: MRI; blood; blood oxygenation level dependent (BOLD); brain; cerebral metabolic rate of oxygen consumption (CMRO2); oxygen extraction fraction (OEF); quantitative BOLD (qBOLD); susceptibility.

Figure 1

Time dependence of the signal attenuation functions Γ_FID(t) and Γ_SE(t) (normalized to the characteristic value Γ₀, Eq. [30]) calculated in the Gaussian phase approximation (adapted from (53)).

Figure 2

The RBC shape described by Eq. [31].

Figure 3

The function f(t/t_c) in Eq. [44] (adapted from (42)).

Figure 4

Time dependence of the simulated FID (A) and GESSE (B) signals at different vessel radii R. Input parameters are: OEF = 0.4, ζ = 0.03. Light blue lines correspond to the case D = 0 (static dephasing regime – SDR). All other lines correspond to D = 1μm²/ms. Spin echo time TE = 60ms corresponds to t = 0 in (B) (shown by dashed vertical line). The transverse T₂ relaxation is ignored. (Modified from (100)).

Figure 5

(adapted from (100)). Values of OEF (A, B) and dCBV (C, D) found when fitting the models to simulated datasets over a range of blood vessel radii and using a variety of BOLD models. The input parameters for all simulations are: OEF = 0.4, dCBV = 0.03 (shown by dashed gray lines). The lines are only shown to display trends. Subplots A and C represent results for the FID sequence, subplots B and D represent results for the GESSE sequence. Red lines – static dephasing model, Eqs. [44], [47]; blue lines – “linear local field approximation” (45); green lines – Gaussian phase approximation, Eqs. [54]–[58] (for the latter, dCBV is assumed to be known from independent measurement).

Figure 6

Schematic structure of the GESSE sequence designed to give pixel-wise sampling of the MRI signal around the spin echo; RF –radio frequency pulse, GS – slice selection gradient, GP – phase encoding gradient, and GR – read-out gradient. Both multi-slice 2D (shown here) and 3D versions can be implemented. The signal is sampled only in the presence of same sign read-out gradients. This is especially important in the presence of the macroscopic static magnetic field inhomogeneities, which differently distort images collected in the presence of sign-alternating read-out gradients.

Figure 7

(adapted from (43)). A high resolution image illustrating the structure of the second phantom (left panel) and typical signal behavior (on a logarithmic scale) taken from a voxel in the middle of the phantom (areas with filaments) (right panel).

Figure 8

(adapted from (43)). Maps of the volume fraction ζ (first column), the $R_2^{\prime }$ relaxation rate constant (second column), and the susceptibility difference Δχ (third column).

Figure 9

(adapted from (86)). Representative data and fitting curves obtained with the GESSE sequence (64×64 matrix). (a) signals and the fitted profiles for voxels in GM area (blue line) with dCBV=1.56% and OEF=32.9% and WM area (red line) with dCBV=0.62% and OEF=33.1%; (b) high resolution anatomic T₁ weighted image showing selected voxels; (c) extravascular signal contributions after removing signals from CSF/ISF, intravascular blood and adjusting for the T₂ decay (multiplying by the factor exp(+R₂•TE)), the black solid lines correspond to the extrapolated signal profile from the asymptotic behavior at long echo times; (d) fitting residuals; (e) magnitudes of the CSF/ISF signals; (f) real parts of intravascular blood signals. In all plots x axis corresponds to a gradient echo time elapsed from the SE time (TE=36.4 msec), y axis represents signal in relative units. The echo spacing is 1.2 ms.

Figure 10

The residual of the fitting of the model in Eq. [68] without contribution from ISF/CSF to the signal from a representative pixel (same as in Figure 9).

Figure 11

(adapted from (86)). Representative maps of estimated brain parameters obtained with a high resolution (128 × 128) GESSE sequence. Top leftmost image is a high resolution anatomic image. The rest of the maps are: dCBV fraction (%); OEF (%); R₂ of brain tissue (s⁻¹); CSF/ISF volume fraction; CSF/ISF frequency shift (Hz); $R_2^{\prime }$ of brain tissue (s⁻¹); and brain deoxyhemoglobin concentration C_deoxy (μM).

Figure 12

(adapted from (86)). Histograms of the estimated brain parameters for the study shown in Fig. 11. The histograms represent dCBV (%), OEF (%), CSF/ISF volume fraction, CSF/ISF frequency shift (Hz); R₂ of the brain tissue (s⁻¹), and the concentration of deoxyhemoglobin (μM).

Figure 13

(adapted from (112)). A representative T₁ weighted image and maps of the estimated venous oxygen saturation level Y_v (color bar) from one slice in the same rat under isoflurane and alpha-chloralose anesthesia.

Figure 14

(adapted from (112)). Comparison of Y_v obtained by means of the qBOLD and by direct measurements of the venous oxygen level

Figure 15

(adapted from (147)). Quantification of CMRO₂ in healthy subject using ASL-qBOLD technique during the resting state. (a) T₁-weighted anatomical image; (b) CBF map (in ml/100g/min) delineates the contrast between GM and WM; (c) OEF map is mostly uniform across the whole brain (two spots at the back of brain with extreme high OEF values correspond to large uncompensated B₀ field inhomogeneities); (d) the map of CMRO₂ (in μmol/g/min) demonstrates much higher value of CMRO₂ in GM than in WM.

Figure 16

(adapted from (91)). Images from which venous oxygen saturation during baseline, hypercapnia, and recovery were derived. (A) Sagittal localizer angiogram indicating the locations of SSS; (B) axial magnitude image; (C–E) GRE phase-difference images. Note the change in contrast in vessels during hypercapnia.

Figure 17

(adapted from (162)) TRUST MRI technique Sequence diagram. (a) Pulse sequence diagram for TRUST MRI. The sequence consists of interleaved acquisitions of label and control scans, and each image type is acquired with four different effective TEs ranging from 0 to 160 ms. For each scan, the sequence starts with a presaturation RF pulse to suppress the static tissue signal, followed by a labeling (or control) RF pulse to magnetically label the incoming blood. A brief waiting period (1.2 seconds) is allowed for blood to flow into the imaging slice. Before data acquisition, a non-selective T₂-preparation pulse train is applied to achieve the T₂-weighting. The T₂-preparation scheme, instead of conventional T₂-weighted sequence, is used in order to minimize the blood outflow effect. (b) Positions of the imaging slice (yellow) and the labeling slab (green).

Figure 18

(adapted from (170)). An example of quantitative Y_v (left), OEF (middle), and CMRO₂ (right) maps obtained by QUIXOTIC technique.