Incorporating vascular-stasis based blood perfusion to evaluate the thermal signatures of cell-death using modified Arrhenius equation with regeneration of living tissues during nanoparticle-assisted thermal therapy

Abstract

Cellular and biological tissue heating may result in reversible (or repairable injury) and irreversible (or lethal) thermal cell-death in living biological tissues. Continuous regeneration of living human tissues due to the continuous supply of oxygen through arterial blood must be taken into account to counter balance the thermal degradation at quasi-static thermal conditions. This study incorporates vascular-stasis based non-linear blood perfusion for magnetic nanoparticle assisted thermal therapy to model the thermal by-stander effect - a hyperthermia-induced deep infiltration of nanoparticles in the targeted tissue domain. Pennes bioheat model based on Fourier heat conduction theory is four-way coupled with Arrhenius and non-Arrhenius kinetic models of cell-death with healthy cells regeneration. In determination of treatment endpoint, the kinetic model must be coupled with quantitative and qualitative pathological biomarkers of thermal damage. Nanoparticle distribution volume increases by 39.62% after possible rupturing of cell membrane during heating. The release of intracellular solution by dead cells during heating promotes nanoparticle migration from the region of higher concentration to the regions of lower concentration thereby 80% enhancement in interstitial space and five-fold increase in diffusion coefficient. For such redistribution phenomenon, the heating time is sufficient to reduce the oxygen in erythrocytes (red blood cells) and maximize the necrosis zone inside tumour. However, at the interface, the regeneration of healthy cells triggers an immune response of biological tissue towards continued heating to suppress, prevent and restrict further accumulation of thermal damage within damage bounds of Ω ≤ 1. While modelling the kinetics of thermal damage of tumour, one must include and should not ignore the partial self-regeneration of connecting normal human tissues at the tumour periphery due to continuous matching of oxygen demands in the healthy tissue by the arterial blood.