Differential geometry, a possible avenue for thermal ablation in oncology?

TL;DR

This paper proposes a novel hyperthermia therapy model using differential geometry to account for topological defects in tissues, aiming to improve thermal ablation precision in cancer treatment.

Contribution

It introduces a new mathematical framework modeling biological tissues as active liquid crystals with topological defects affecting heat diffusion during therapy.

Findings

Defects create non-Euclidean geometry affecting heat distribution.

Application to liver, prostate, and skin tissues shows potential for targeted ablation.

Model suggests improved precision in destroying cancer cells while sparing healthy tissue.

Abstract

We report a model for hyperthermia therapies based on heat diffusion in a biological tissue containing a topological defect. Biological tissues behave like active liquid crystals with the presence of topological defects which are likely to anchor tumors during the metastatic phase of cancer evolution and the therapy challenge is to destroy the cancer cells without damaging surrounding healthy tissues. The defect creates an effective non-Euclidean geometry for low-energy excitations, modifying the bio-heat equation. Applications to protocols of thermal ablation for various biological tissues (liver, prostate, and skin) is analyzed and discussed.