Towards monitoring critical microscopic parameters for electropermeabilization

TL;DR

This paper investigates how to monitor microscopic cell properties during electropermeabilization therapy by analyzing effective parameters in a homogenization model, enabling better control and understanding of the treatment process.

Contribution

It introduces a homogenization-based approach to infer microscopic cell parameters from macroscopic imaging data in electropermeabilization.

Findings

Proved well-posedness of the physiological cell model.

Established convergence of the dynamical homogenization scheme.

Demonstrated numerical sensitivity of effective parameters to microscopic properties.

Abstract

Electropermeabilization is a clinical technique in cancer treatment to locally stimulate the cell metabolism. It is based on electrical fields that change the properties of the cell membrane. With that, cancer treatment can reach the cell more easily. Electropermeabilization occurs only with accurate dosage of the electrical field. For applications, a monitoring for the amount of electropermeabilization is needed. It is a first step to image the macroscopic electrical field during the process. Nevertheless, this is not complete, because electropermeabilization depends on critical individual properties of the cells such as their curvature. From the macroscopic field, one cannot directly infer that microscopic state. In this article, we study effective parameters in a homogenization model as the next step to monitor the microscopic properties in clinical practice. We start from a physiological cell model for electropermeabilization and analyze its well-posedness. For a dynamical homogenization scheme, we prove convergence and then analyze the effective parameters, which can be found by macroscopic imaging methods. We demonstrate numerically the sensitivity of these effective parameters to critical microscopic parameters governing electropermeabilization. This opens the door to solve the inverse problem of rreconstructing these parameters.