Mathematical modeling and control for cancer treatment with cold atmospheric plasma jet

Cold atmospheric plasma (CAP) jet exhibits remarkable properties that trigger cell death in cancer cells. The effect of CAP on cancer cells is influenced by several factors including plasma jet discharge voltages, gas composition and cancer cell type. Consequently in clinics it becomes challenging to plan plasma cancer treatments for a particular cancer types. To address this, we present preliminary results for an in vitro model which includes an optimal feedback control scheme that can adjust treatment conditions based on the actual cancer cell response. Translation to an in vivo model will be the next objective of the presented project. First, a mathematical model is presented for the dynamic response of cancer cells to CAP jets based on experimental data that provide temporal measurements of cancer cell viability after CAP treatments. A differential equation is developed to model the influence of CAP on the viability of two cancer cell lines, U-87 MG and MDA-MB-231, under varying treatment duration and plasma discharge voltages. Subsequently, a control scheme is presented to determine CAP treatment conditions in an optimal fashion by reducing cancer cell viability less than a prescribed goal while minimizing a weighted sum of the treatment duration and the discharge voltage. This is further extended to a model predictive control framework such that a pre-planned CAP treatment schedule is revised according to the actual cancer cell response. The efficacy of the proposed approach is illustrated by numerical simulations based on experimental data.