Mathematical modeling of the frozen zone dynamics in hydrogel and biological tissue

Thermal imaging is a convenient technique for cryoablation and cryotherapy [1] but it does not allow for visualization of what is inside. We model thermal field distribution which can help relate surface thermal field images to in-depth temperature field dynamics that show freezing and thawing processes dynamics. We consider the spatio-temporal distribution of temperature using examples of hydrogel and living tissue subjected to a cryoprobe.

Physical and mathematical modeling methods are widely used to test cryoapplication regimes. Mathematical modeling of this heat transfer process in non-uniform materials with temperature-dependent coefficients [2,3] allows us to predict the temperature field of the frozen region and visualise it for any moment of time in all points of the simulated area [4]. This makes it possible to determine the cryoapplication time sufficient to destroy target cells by freezing them to a certain temperature and minimizing damage to healthy cells under various experimental conditions.

[1] G. Kovalev et al., Probl. Cryobiol. Cryomed. 30, 359 (2020).

[2] A. Shitzer, J. Heat. Transf. 133, 011005 (2010).

[3] B. Rubinsky, Annu. Rev. Biomed. Eng. 2, 157 (2000).

[4] O. V. Ivakhnenko, O. F. Todrin, V. Yu. Globa, M. O. Chyzh, G. O. Kovalov, S. N. Shevchenko, bioRxiv:2024.10.19.619201 (2024).