Optimization strategies for evaluation of brain hemodynamic parameters with qBOLD technique

Abstract

Quantitative blood oxygenation level dependent technique provides an MRI-based method to measure tissue hemodynamic parameters such as oxygen extraction fraction and deoxyhemoglobin-containing (veins and prevenous part of capillaries) cerebral blood volume fraction. It is based on a theory of MR signal dephasing in the presence of blood vessel network and experimental method-gradient echo sampling of spin echo previously proposed and validated on phantoms and animals. In vivo human studies also demonstrated feasibility of this approach but also recognized that obtaining reliable results requires high signal-to-noise ratio in the data. In this paper, we analyze in detail the uncertainties of the quantitative blood oxygenation level dependent parameter estimates in the framework of the Bayesian probability theory, namely, we examine how the estimated parameters oxygen extraction fraction and deoxygenated cerebral blood volume fraction depend on their "true values," signal-to-noise ratio, and data sampling strategies. On the basis of this analysis, we develop strategies for optimization of the quantitative blood oxygenation level dependent technique for deoxygenated cerebral blood volume and oxygen extraction fraction evaluation. In particular, it is demonstrated that the use of gradient echo sampling of spin echo sequence allows substantial decrease of measurement errors as the data are acquired on both sides of spin echo. We test our theory on phantom mimicking the structure of blood vessel network. A 3D gradient echo sampling of spin echo pulse sequence is used for the acquisition of the MRI signal that was subsequently analyzed by Bayesian Application Software. The experimental results demonstrated a good agreement with theoretical predictions.

Figure 1

The relative errors as functions of δt/t_c, calculated based on Eqs. 18–22 and the model described in Eqs. 6 and 9; t_c=8 ms, ζ=0.03, R₂=13 s⁻¹, SNR₀=500, T₀=0 (FID experiment), T=10t_c.

Figure 2

The relative errors as functions of 1/ζ. t_c=8 ms; R₂=13 s⁻¹, SNR₀=500, δt = t_c, T₀=0, T=10t_c.

Figure 3

The relative errors as functions of R₂ (A), T (B), and T=0 (C); t_c=8 ms, ζ=0.03, SNR₀=500; T=10t_c (in (A, C); R₂=13 s⁻¹ (in (B, C); T₀=0 (in (A, B)). Solid lines in (A) correspond to the case when R₂ is a fitting parameter; dashed lines correspond to the case when R₂ is considered as a constant known from an independent experiment (the corresponding line for the relative error ε_ζ is not shown because it practically coincides with the solid line). The relative error ε_R2^* in (C) is much smaller than for two other parameters (~ 0.004) and is not shown.

Figure 4

The relative errors as functions of the echo time TE when the measurement starts immediately after 180° pulse (at T₀ = −TE/2); t_c=8 ms, R₂=13 s⁻¹, SNR₀=500, ζ=0.03, T₀=10 t_c.

Figure 5

A representative signal evolution profile (normalized by its value at the spin echo time) from a pixel in the filament region and the fitting curve (solid line). The fitting parameters are:ζ = 0.075, t = 3.49ms, R₂ =11.9s⁻¹. Time t is counting from the spin echo time TE (marked by the vertical dotted line). Due to T₂ relaxation, the maximum of the signal is shifted from the spin echo time TE (t=0).

Figure 6

Maps of the volume fraction ζ (first row), susceptibility difference χ (second row), and relaxation constant $R_2^{\ast }$ (third row) for different initial measurement time T₀: first column - T₀/δt=−14, second column - T₀/δt=0, third column - T₀/δt=+3. The value of χ for fish lines is found to be 0.056 ± 0.003ppm, the value of R₂ is homogeneous across the whole phantom and is equal to 11.9 ± 0.2 s⁻¹.

Figure 7

Typical distributions of the model parameters for the initial measurement time T₀=−14δt. (ζ)_est = (7.58±0.07)·10⁻², (χ)_est = (5.64±0.05)·10⁻²ppm, ${(R_2^{\ast })}_{\mathit{est}}=(33.5\pm 0.03){\text{s}}^{-1}$

Figure 8

Dependence of the model parameters found from experimental data (for a single pixel) on the initial measurement time T₀.

Figure 9

The dependencies on the initial measurement time T₀ of the uncertainties in the model parameters, σ_j, obtained experimentally (symbols) and their theoretical predictions (solid lines).

Figure 10

The comparison of the relative errors ε_ζ (a) and ε_χ (b) as functions of TE (when the measurement starts at T₀=−TE/2). Solid lines - one-compartment model discussed in the main text; dashed lines – two-compartment model (i) - tissue & ISF/CSF; dotted lines – two-compartment model (ii) - tissue & blood; dash-dotted lines – three-compartment model (iii) - tissue & CSI/CSF & blood. t_c=8 ms, R₂=13 s⁻¹, SNR₀=500, ζ=0.03, T=10 t_c, λ=0.1, R_2e = 8s⁻¹.