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Looking for an Efficient and Safe Hyperthermia Therapy: Insights from a Partial Differential Equations Based Model

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Abstract

In the present study, we formulate a boundary value problem that characterizes the light and heat transfer processes in a tissue during a hypothetical superficial hyperthermia therapy. The heating process is represented with a partial differential equations system (PDEs) consisting in the diffusion and bio-heat equations whereas the tissue damage process is modeled with the Arrhenius integral equation. The PDEs system is discretized using the method of lines to obtain an ordinary differential equations system that approximates the original PDEs. The resulting model is then numerically solved to obtain (1) the spatio-temporal distribution of both absorbed light and heat, (2) the volume of tissue effectively treated, and (3) the degree of thermal damage reached. Finally, we define an optimization problem to find a set of relevant parameter values that maximize the therapeutic effect while minimizing damage to healthy tissue. The results of this work could be useful for preclinical level research, in particular for the study of strategies that modify the physical properties of the target tissue for a safe and efficient heat therapy.

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Acknowledgments

The author’s work was supported by Administrative Department for Science, Technology and Innovation, and the Deanship for Engineering Students, Universidad de Los Andes.

Thanks Hernán Estrada for conceiving the original idea for this project.

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Authors and Affiliations

  1. Department of Biomedical Engineering, Universidad de Los Andes, Bogotá, 641014, Colombia

    Maria C. Quintero & Juan M. Cordovez

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  1. Maria C. Quintero
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  2. Juan M. Cordovez
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Correspondence to Maria C. Quintero.

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Quintero, M.C., Cordovez, J.M. Looking for an Efficient and Safe Hyperthermia Therapy: Insights from a Partial Differential Equations Based Model. Differ Equ Dyn Syst 25, 137–150 (2017). https://doi.org/10.1007/s12591-015-0256-8

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