On the theoretical basis of perfusion measurements by dynamic susceptibility contrast MRI

Abstract

A quantitative analysis was undertaken to calibrate the perfusion quantification technique based on tracking the first pass of a bolus of a blood pool contrast agent. A complete simulation of the bolus passage, of the associated changes in the T 2 and T* 2 signals, and of the data processing was performed using the tracer dilution theory, an analytical theory of the MR signal from living tissues and numerical simulations. Magnetic resonance imaging (MRI) of the first passage of a bolus of a blood pool contrast agent is a promising method for assessment of regional perfusion (1,2). This method implies a measurement of the contrast agent concentration time course in both a volume of interest (VOI) and a feeding artery. The quantification of the perfusion is achieved by comparison of these data sets. The underlying theory rests on two basic assumptions. First, it is assumed that the measured MR signal is proportional to the concentration of the contrast agent, with a universal proportionality coefficient for both the VOI and a reference voxel in the artery. Second, the kinetic of the contrast agent is described in terms of a linear model. The aim of this work is to demonstrate that the former assumption is invalid in proton MRI: the relationship between the MRI signal and the concentration of the contrast agent in the VOI significantly differs from that in the reference voxel. It depends on the MRI pulse sequence and the vascular composition of the investigated tissue.The reason for such variability in the MRI signal is the contribution of the extravascular protons. These parenchymal protons are dephased by the blood pool contrast agent through the inhomogeneous, long-ranged, susceptibilityinduced magnetic field. Thus, their contribution to the MR signal follows the time course of the contrast agent concentration with a specific functional dependence that significantly differs from the relaxation effect of the contrast agent in blood. This peculiarity is not accounted for in the present theory (1,3).Until now, theoretical interest has been focused on the so-called deconvolution procedure in the presence of noise. This issue is well understood (3) and is not considered here. The presented results were obtained for a noisefree simulation. This allows analysis of the inherent accuracy of the method. The obtained theoretical predictions are compared with published experimental data (4 -6). METHODS Tracer Dilution TheoryLet us start with a brief review of the tracer dilution theory (7). Consider a VOI and a voxel inside a properly chosen supplying artery. Let us denote as c a (t) and c(t) the concentrations of the contrast agent in the artery and in blood in the studied tissue, respectively. The concentration c(t) linearly depends on the history of c a (t). This is expressed as a convolution with a kernel h(t) which describes the blood transport:[1]In practical calculations the lower limit in this integral can be replaced with the moment of bolus injection. The function h(t) possesses a propertywhich reflects the fact t...

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