The Effect of Fractional Derivatives on Thermo-Mechanical Interaction in Biological Tissues during Hyperthermia Treatment Using Eigenvalues Approach

Abstract

This article studies the effects of fractional time derivatives on thermo-mechanical interaction in living tissue during hyperthermia treatment by using the eigenvalues approach. A comprehensive understanding of the heat transfer mechanism and the related thermo-mechanical interactions with the patient’s living tissues is crucial for the effective implementation of thermal treatment procedures. The surface of living tissues is traction-free and is exposed to a pulse boundary heat flux that decays exponentially. The Laplace transforms and their associated techniques are applied to the generalized bio-thermo-elastic model, and analytical procedures are then implemented. The eigenvalue approach is utilized to obtain the solution of governing equations. Graphical representations are given for the temperature, the displacement, and the thermal stress results. Afterward, a parametric study was carried out to determine the best method for selecting crucial design parameters that can improve the precision of hyperthermia therapies.

Keywords

• living tissue
• fractional time derivatives
• analytical solutions
• thermo-mechanical interactions
• Laplace transform
• thermal relaxation time