An ODE-SDE Model for Ct-DNA dynamics

PujanShrestha

Texas A&M University

"An ODE-SDE Model for Ct-DNA dynamics"

Effective cancer therapies, while continuously improving, are often constrained by lower detection limits of disease. Tumor-immune dynamics in this limit present one of the most pressing knowledge gaps as cancer ultimate escape or elimination are often determined following an intervening period of population equilibrium sustained at low population size. Population dynamics in this small-population limit are affected by intrinsic noise in the tumor-immune interaction, as are estimates of population disease burden by extrinsic noise in acquiring such estimates through associated biomarkers. We present a modeling framework that investigates the interactions between tumor cells and the immune system in the small population regime, focusing on how these interactions influence biomarker levels. The framework combines deterministic elements, which describe tumor growth and immune responses, with stochastic components that capture the inherent variability in biomarker release. We use a system of ordinary differential equations (ODEs) to represent the tumor-immune dynamics between an adaptive immune compartment, immunogenic tumor cells, and evasive tumor cells. The immune system’s role in controlling tumor growth is reflected in the tumor-immune interaction terms. Apoptotic death via tumor-immune interactions and necrotic death via the tumor competition under a shared carrying capacity both contribute to the release of a tumor biomarker. We focus on applying our model to ct-DNA, wherein we frame ct-DNA dynamics using a stochastic differential equation (SDE). This SDE framework accounts for the variability in ct-DNA release due to the dynamic tumor-immune interactions, as well as inherent biological noise, such as DNA degradation and clearance. By coupling the ODE system of equations for tumor-immune dynamics with the SDE for ct-DNA release, we can use the model to study the fluctuations in ct-DNA levels driven by tumor-immune dynamics and exogenous sampling noise.
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