Comprehensive modeling of the spatiotemporal distribution of PET tracer uptake in solid tumors based on the convection-diffusion-reaction equation

In this paper, the distribution of PET tracer uptake is elaborately modeled via a general equation used for solute transport modeling. This model can be used to incorporate various transport parameters of a solid tumor such as hydraulic conductivity of the microvessel wall, transvascular permeability as well as interstitial space properties such as pressure. This is especially significant because tracer delivery and drug delivery to solid tumors are determined by similar underlying tumor transport phenomena, and quantifying the former can enable enhanced prediction of the latter. First, based on a mathematical model of angiogenesis, the capillary network of a solid tumor and normal tissues around it were generated. The coupling mathematical method, which simultaneously solves for blood flow in the capillary network as well as fluid flow in the interstitium, is used to compute pressure and velocity distributions. Subsequently, we applied a comprehensive convection-diffusion-reaction equation to accurately model distribution of PET tracer uptake, specifically FMISO in this work, within solid tumors. The abovementioned use of partial differential equations (PDEs), beyond ordinary differential equations (ODEs) as commonly invoked in tracer kinetic modeling, enables simultaneous modeling of tracer distribution over both time and space. For different angiogenetic structures, the intravascular pressure and interstitial pressure were elaborately calculated across the domain of interest, and used as input to model tracer distribution. The results can be utilized to comprehensively assess the impact of various parameters on the spatiotemporal distribution of PET tracers.