Quarterly of Applied Mathematics

Quarterly of Applied Mathematics

Online ISSN 1552-4485; Print ISSN 0033-569X



Towards monitoring critical microscopic parameters for electropermeabilization

Authors: H. Ammari, T. Widlak and W. Zhang
Journal: Quart. Appl. Math. 75 (2017), 1-17
MSC (2010): Primary 35B30, 35R30
DOI: https://doi.org/10.1090/qam/1449
Published electronically: July 27, 2016
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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 solving the inverse problem of reconstructing these parameters.

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Additional Information

H. Ammari
Affiliation: Department of Mathematics, ETH Zürich, Rämistrasse 101, CH-8092 Zürich, Switzerland
Email: habib.ammari@math.ethz.ch

T. Widlak
Affiliation: Department of Mathematics and Applications, École Normale Supérieure, 45, rue d’Ulm, 75230 Paris Cedex 05, France
Email: thomas.widlak@ens.fr

W. Zhang
Affiliation: Department of Mathematics and Applications, École Normale Supérieure, 45, rue d’Ulm, 75230 Paris Cedex 05, France
Email: wenlong.zhang@ens.fr

DOI: https://doi.org/10.1090/qam/1449
Keywords: Electropermeabilization, cell membrane, homogenization, sensitivity of effective parameters
Received by editor(s): March 24, 2016
Published electronically: July 27, 2016
Additional Notes: This work was supported by the ERC Advanced Grant Project MULTIMOD–267184.
Article copyright: © Copyright 2016 Brown University

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