Enhanced modeling of spatiotemporal distribution of PET tracers in solid tumors and estimation of transport parameters

Objectives To model distribution of PET tracer uptake via a comprehensive equation used for solute transport modeling in solid tumors, and to utilize this framework for enhanced estimation of kinetic parameters and to additionally estimate diffusion coefficients in the interstitium.

Methods Dynamic PET imaging commonly invokes simplified tracer kinetic modeling that involves ODEs. This work emphasizes that tracer delivery and drug delivery to solid tumors, the former used in diagnostic imaging and the latter in therapy, are determined by similar underlying tumor transport phenomena. We utilize a comprehensive model of solute transport, the convection-diffusion-reaction (CDR) equation as common in simulation of drug delivery. Incorporating PDEs, this framework enables simultaneous modeling of tracer distribution over time and space. We performed extensive simulations of dynamic FMISO PET, including realistic noise levels and distinct capillary network distributions. In the inverse problem, the Levenberg-Marquardt method was utilized in order to minimize the objective function, and to estimate the kinetic parameters as well as the diffusion coefficient.

Results Tracer diffusion (neglected by the conventional ODE framework) can impact estimation of the kinetic parameters of interest (while effect of convection is not significant in clinical scan times). The proposed diffusion-incorporated PDE framework renders itself to enhanced parameter estimates. Furthermore, the diffusion coefficient itself can be estimated from PET images, which to our knowledge has not been achieved in past work.

Conclusions The proposed comprehensive modeling framework naturally couples temporal and spatial distributions via utilization of interstitial diffusion modeling. It enables enhanced kinetic parameter estimates, as well as estimation of the diffusion coefficient from radiotracer imaging.

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