UMATHT for Pennes Equation in Abaqus

This is a UMATHT implementation of the Pennes bioheat equation ; it translates the equation to a form fit for use as an Abaqus subroutine by expressing it in terms of internal energy per mass $U$, thermal flux $\overrightarrow{q}$, and their respective partial derivatives with respect to the temperature and the temperature gradient.

Inputs

Units are given as an indication, adapt to your own model if relevant.

• PROPS(1) : Tissue density [kg/m^3]
• PROPS(2) : Tissue specific heat capacity [J/(kg*K)]
• PROPS(3) : Tissue conductivity [W/(m K)]
• PROPS(4) : Tissue perfusion rate [1/s]
• PROPS(5) : Tissue metabolic heat generation [W/m^3]
• PROPS(6) : Blood density [kg/m^3]
• PROPS(7) : Blood specific heat capacity [J/(kg*K)]
• PROPS(8) : Blood temperature [K]

Citation

Feel free to use this code for your own analyses, and please cite it as C. Marché, "Pennes UMATHT", Gefen Lab, GitHub, 2023. Available: https://github.com/cecilemarche/UMATHT_Pennes.

License

This code is licensed under the CeCILL-B license, Version 2.1. Refer to the license file included with the code for more information on its usage and redistribution.

Reference

Pennes, Harry H. Analysis of Tissue and Arterial Blood Temperatures in the Resting Human Forearm . Journal of Applied Physiology 1, no. 2 (August 1948): 93 122. https://doi.org/10.1152/jappl.1948.1.2.93.