Nonlinear bioheat model for dynamics of hypothermia and frostbite. Ⅰ. Modeling aspects

Tyler Fara; Malgorzata Peszynska; Tyler Fara; Malgorzata Peszynska

doi:10.3934/mbe.2026009

Mathematical Biosciences and Engineering

2026, Volume 23, Issue 1: 210-241. doi: 10.3934/mbe.2026009

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Research article

Nonlinear bioheat model for dynamics of hypothermia and frostbite. Ⅰ. Modeling aspects

Tyler Fara ,
Malgorzata Peszynska ^,

Department of Mathematics, Oregon State University, 2000 S.W. Campus Way, Corvallis, OR 97331, USA

Received: 16 August 2025 Revised: 29 October 2025 Accepted: 17 November 2025 Published: 04 December 2025

We propose a new bioheat model for thermoregulation in the human body in response to cold environments, with emphasis on hypothermia and frostbite in exposed extremities. The model couples the bioheat transfer equation in the extremity with a differential equation that describes the core temperature. We used simulations to illustrate the connection between microscale vascular exchange and the effective perfusion term in the bioheat transfer equation. The nonlinear coupling proposed here incorporates physiologically motivated feedback laws for local and reflex vasoconstriction, as well as heat exchange with the environment. We illustrated the model numerically with realistic scenarios of thermoregulation regarding the thermal response of the body, which involves preservation of core temperature despite an increased frostbite risk. The model provides a robust framework for predictive studies of cold‐induced injuries.
- Thermoregulation,
- frostbite,
- hypothermia,
- coupled system,
- nonlinear boundary conditions,
- finite elements,
- multiscale modeling
Citation: Tyler Fara, Malgorzata Peszynska. Nonlinear bioheat model for dynamics of hypothermia and frostbite. Ⅰ. Modeling aspects[J]. Mathematical Biosciences and Engineering, 2026, 23(1): 210-241. doi: 10.3934/mbe.2026009

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Abstract

We propose a new bioheat model for thermoregulation in the human body in response to cold environments, with emphasis on hypothermia and frostbite in exposed extremities. The model couples the bioheat transfer equation in the extremity with a differential equation that describes the core temperature. We used simulations to illustrate the connection between microscale vascular exchange and the effective perfusion term in the bioheat transfer equation. The nonlinear coupling proposed here incorporates physiologically motivated feedback laws for local and reflex vasoconstriction, as well as heat exchange with the environment. We illustrated the model numerically with realistic scenarios of thermoregulation regarding the thermal response of the body, which involves preservation of core temperature despite an increased frostbite risk. The model provides a robust framework for predictive studies of cold‐induced injuries.

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