Incorporating cross-voxel exchange into the analysis of dynamic contrast-enhanced imaging data: theory, simulations and experimental results

Abstract

Predictions of tumour perfusion are key determinants of drug delivery and responsiveness to therapy. Pharmacokinetic models allow for the estimation of perfusion properties of tumour tissues but many assume no dispersion associated with tracer transport away from the capillaries and through the tissue. At the level of a voxel, this translates to assuming no cross-voxel tracer exchange, often leading to the misinterpretation of derived perfusion parameters. Tofts model (TM), a compartmental model widely used in oncology, also makes this assumption. A more realistic description is required to quantify kinetic properties of tracers, such as convection and diffusion. We propose a Cross-Voxel Exchange Model (CVXM) for analysing cross-voxel tracer kinetics. In silico datasets quantifying the roles of convection and diffusion in tracer transport (which TM ignores) were employed to investigate the interpretation of Tofts’ perfusion parameters compared to CVXM. TM returned inaccurate values of and where diffusive and convective mechanisms are pronounced (up to 20% and 300% error respectively). A mathematical equation, developed in this work, predicts and gives the correct physiological interpretation of Tofts’ Finally, transport parameters were derived from dynamic contrast enhanced-magnetic resonance imaging of a TS-415 human cervical carcinoma xenograft by using TM and CVXM. The latter deduced lower values of and compared to TM (lower by up to 63% and 76% respectively). It also allowed the detection of a diffusive flux (mean diffusivity 155 μm2 s−1) in the tumour tissue, as well as an increased convective flow at the periphery (mean velocity 2.3 μm s−1 detected). The results serve as a proof of concept establishing the feasibility of using CVXM for accurately determining transport metrics that characterize the exchange of tracer between voxels. CVXM needs to be investigated further as its parameters can be linked to the tumour microenvironment properties (permeability, pressure…), potentially leading to enhanced personalized treatment planning.