Estimation of contrast agent concentration in intra- and extra-vascular spaces of brain tissue

Abstract

This article presents a new method for estimating the leakage of a contrast agent out of a vessel. The proposed method is developed based on tissue homogeneity (TH) model, modified Patlak model, and Monte Carlo simulation. The analytical methods published in the literature estimate the contrast agent leakage by solving the coupled differential equations associated with the TH model under adiabatic conditions. These methods employ unrealistic simplifying assumptions and become intractable in their applications to the vessels that have a non-uniform permeability. Without making any unrealistic assumptions, our approach simply tracks the passage of the contrast agent through the capillary and its crossing of the vessel walls based on the blood flow in the vessel, the vessel’s permeability, and the condition of the blood–brain barrier (BBB). These are treated as statistical processes that can be modeled reasonably well using the Monte Carlo method. In the proposed approach, the intra- and extra-vascular spaces are divided into multiple compartments, similar to the Patlak model. A real, measured arterial input function (AIF) is used as the capillary input and the concentration of the contrast agent is found as a function of time and distance, inside and outside of the capillary. This is done for normal and abnormal capillaries with uniform and non-uniform permeability. The proposed method generates concentration curves similar to those of the analytical method for simple AIF models. It also generates reasonable concentration curves for a real AIF. The proposed method does not fit a mathematical function to the measured AIF and does not make unrealistic simplifying assumptions. It is not therefore prone to the fitting errors and generates more realistic and more accurate results than the analytical methods.