Mathematical Model Developments for Thermochemical Ablation
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Thermochemical ablation (TCA) is a novel, conceptual platform of minimally invasive therapy of HCC. In TCA, an acid and a base are mixed immediately prior to injection. As a result, heat is released as exothermal reaction occurs and hot salt solution enters the targeted tissue. Moreover, the by-products create an environment that may increase diameter of lethal zone, and serve as a local diffusion reservoir to reduce the risk of local recurrence. Therefore, a mathematical model is developed to evaluate TCA injections. Governing equations that are derived from mixture theory for our formulation enforce mass, momentum and energy balance. Additional constitutive properties are needed to account for temperature induced changes. Therefore, to describe how the density of the ablative solutions changes with temperature and concentration, the model proposed by Laliberté and Cooper was selected. The Arrhenius equation was modified to account for salt concentration, and then used as dose model for estimating tissue damage. Acquisition of datasets of salt distribution and temperature are required to design and evaluate mathematical models of TCA injections. Thus, testing on a liver mimicking phantom will be important. A procedure was developed to ensure reproducibility, and the porosity of various foams were calculated. This project was completed with contributions from David Fuentes from the University of Texas MD Anderson Cancer Center.