NMR simulation analysis of statistical effects on quantifying cerebrovascular parameters

Abstract

Determining tissue structure and composition from the behavior of the NMR transverse relaxation during free induction decay and spin echo formation has seen significant advances in recent years. In particular, the ability to quantify cerebrovascular network parameters such as blood volume and deoxyhemoglobin concentration from the NMR signal dephasing has seen intense focus. Analytical models have been described, based on statistical averaging of randomly oriented cylinders in both the static and slow diffusion regimes. However, the error in estimates obtained from these models when applied to systems in which the statistical assumptions of many, randomly oriented perturbers are violated has not been systematically investigated. Using a deterministic simulation that can include diffusion, we find that the error in estimated venous blood volume fraction and deoxyhemoglobin concentration obtained using a static dephasing regime statistical model is inversely related to the square root of number of blood vessels. The most important implication of this is that the minimum imaging resolution for accurate deoxyhemoglobin and blood volume estimation is not bound by hardware limitations, but rather by the underlying tissue structure.

FIGURE 1

Standard deviation of the relative error in [Hb] (closed) and blood volume fraction (open) is inversely proportional to the square root of the number of vessels with constants of proportionality of 0.54 ± 0.03 and 0.36 ± 0.02, respectively.

FIGURE 2

Simulation and fit time course for vessel network with 92 vessels of 15 μm radius in a 1.5 mm isotropic voxel with (intra) and without intravascular contributions. The inset shows the large deviation due to intravascular component for short times.

FIGURE 3

(a) Average relative error in [Hb] shows sharp underestimation that increases with diffusion and for smaller vessels. (b) Average relative error in blood volume fraction, ς, shows general overestimation for large vessel that is offset by an underestimation for small vessels. The simulation did not include intravascular signal. (c) Average relative error ς shows general underestimation when the intravascular signal is included and the full time course is fit. Simulation done with diffusion values of 0 (□), 0.8 (∇), 1.0 (◊), 1.2 (Δ), and 2.5 (○) μm²/ms.

FIGURE 4

Normalized signal decay due to dephasing and diffusion in the presence of 25 μm radius vessel network. Increasing diffusion of 0, 0.8, 1.0, 1.2, and 2.5 μm²/ms from top to bottom produces a reduced short time regime signal.

FIGURE 5

[Hb] concentrations for 2 μm, 15 μm, and combined vessel networks both with and without vessel contributions. The actual [Hb] and the predicted value using five levels of diffusion are shown.

FIGURE 6

Blood volume concentrations for 2 μm, 15 μm, and combined vessel networks both with and without vessel contributions. The actual blood volume and the predicted value using five levels of diffusion are shown.