Three‐compartment T1 relaxation model for intracellular paramagnetic contrast agents

Abstract

The goal of this work was to elaborate a model describing the effective longitudinal relaxation rate constant R(1) for (1)H(2)O in three cellular compartments experiencing possible equilibrium water exchange, and to apply this model to explain the effective R(1) dependence on the overall concentration of a cell-internalized Gd(3+)-based contrast agent (CA). The model voxel comprises three compartments representing extracellular, cytoplasmic, and vesicular (e.g., endosomal, lysosomal) subcellular spaces. Relaxation parameters were simulated using a modified Bloch-McConnell equation including magnetization exchange between the three compartments. With the model, several possible scenarios for internalized CA distribution were evaluated. Relaxation parameters were calculated for contrast agent restricted to the cytoplasmic or vesicular compartments. The size or the number of CA-loaded vesicles was varied. The simulated data were then separately fitted with empirical mono- and biexponential inversion recovery expressions. The voxel CA-concentration dependencies of R(1) can be used to qualitatively and quantitatively understand a number of different experimental observations reported in the literature. Most important, the simulations reproduced the relaxivity "quenching" for cell-internalized contrast agent that has been observed.