Explicit formula of finite difference method to estimate human peripheral tissue temperatures during exposure to severe cold stress

• A model based on bio-heat equation has been formulated for the estimation of temperature distribution in the dermal regions of human body.
• The explicit formula of FDM has been used to solve the model for reasonable and realistic results.
• Conditions for the prediction of frostbite and other cold injuries at the human peripheral tissues were discussed in the model.
• The study may be helpful to understand the thermal behaviour of tissues in laser therapies and other medical science problems.

During cold exposure, peripheral tissues undergo vasoconstriction to minimize heat loss to preserve the maintenance of a normal core temperature. However, vasoconstricted tissues exposed to cold temperatures are susceptible to freezing and frostbite-related tissue damage. Therefore, it is imperative to establish a mathematical model for the estimation of tissue necrosis due to cold stress. To this end, an explicit formula of finite difference method has been used to obtain the solution of Pennes' bio-heat equation with appropriate boundary conditions to estimate the temperature profiles of dermal and subdermal layers when exposed to severe cold temperatures. The discrete values of nodal temperature were calculated at the interfaces of skin and subcutaneous tissues with respect to the atmospheric temperatures of 25 °C, 20 °C, 15 °C, 5 °C, −5 °C and −10 °C. The results obtained were used to identify the scenarios under which various degrees of frostbite occur on the surface of skin as well as the dermal and subdermal areas. The explicit formula of finite difference method proposed in this model provides more accurate predictions as compared to other numerical methods. This model of predicting tissue temperatures provides researchers with a more accurate prediction of peripheral tissue temperature and, hence, the susceptibility to frostbite during severe cold exposure.