A mathematical model for thermoregulation in endotherms including heat transport by blood flow and thermal feedback control mechanisms

changes in coat, metabolic rate, blood fluxes, ventilation and sweating rates

  • José L. Boldrini Department of Mathematics, State University of Campinas, Campinas, SP, Brazil
  • Matheus P. Viana Department of Developmental and Cell Biology, University of California, Irvine, CA, USA
  • Sérgio F. dos Reis Department of Animal Biology, State University of Campinas, Campinas, SP, Brazil
  • Barbara Henning Graduate Program in Ecology, State University of Campinas, Campinas, SP, Brazil https://orcid.org/0000-0001-6881-9010
Keywords: Thermoregulation in homeothermic endotherms, metabolic rate, vasomotor adjustment, Pennes' bio-heat transfer model, thermoneutral zone, integro-differential equation


Thermoregulation in endotherms allows the maintenance of the body temperature independent of ambient temperature. Experimental data have revealed complex interactions between the physiological mechanisms of thermoregulation and environmental conditions. We derive a nonlinear partial integro-differential dynamical model based on physical first principles and fundamental physiological mechanisms to understand the role of some thermal control mechanisms in the thermoregulation process of endotherms. The model is composed of four layers representing different tissues and it incorporates six thermal feedback control mechanisms. These mechanisms are heat production due to metabolic rate and heat exchange within the body given its internal structure, and the model considers heat exchange due to conduction, heat transport by blood flow, heat exchange with the ambient through convection, radiation, and evaporation from the respiratory tract and superficial evaporation in both passive and active situations. Our model sheds new light on previous explanations about the classic metabolism-ambient temperature U-shaped curve.

How to Cite
Boldrini, José, Matheus Viana, Sérgio dos Reis, and Barbara Henning. 2018. “A Mathematical Model for Thermoregulation in Endotherms Including Heat Transport by Blood Flow and Thermal Feedback Control Mechanisms”. Letters in Biomathematics 5 (1), 129-73. https://doi.org/10.1080/23737867.2018.1497458.