Continuum modeling perspectives of non-Fourier heat conduction in biological systems

TL;DR

This paper reviews continuum non-Fourier heat conduction models in biological systems, clarifies misconceptions, and demonstrates their proper application through literature examples, highlighting the importance of correct interpretation of experimental data.

Contribution

It provides a critical review of non-Fourier heat conduction models in biological systems and clarifies common misconceptions in their application.

Findings

Misinterpretations of experimental data lead to incorrect use of non-Fourier models.

Boundary conditions and source terms are key to understanding deviations from Fourier's law.

Proper application of models aligns with experimental observations when misconceptions are addressed.

Abstract

The thermal modeling of biological systems has increasing importance in developing more advanced, more precise techniques such as ultrasound surgery. One of the primary barriers is the complexity of biological materials: the geometrical, structural, and material properties vary in a wide range, and they depend on many factors. Despite these difficulties, there is a tremendous effort to develop a reliable and implementable thermal model. In the present paper, we focus on the continuum modeling of heterogeneous materials with biological origin. There are numerous examples in the literature for non-Fourier thermal models. However, as we realized, they are associated with a few common misconceptions. Therefore, we first aim to clarify the basic concepts of non-Fourier thermal models. These concepts are demonstrated by revisiting two experiments from the literature in which the Cattaneo-Vernotte and the dual phase lag models are utilized. Our investigation revealed that using these non-Fourier models is based on misinterpretations of the measured data, and the seeming deviation from Fourier's law originates in the source terms and boundary conditions.