The Pennes' bioheat equation is a standard model for temperature distrubution in living tissues, that enhances diffusion equation with a linear term describing blood flow and a constant metabolic heat source.

\[ \rho c \frac{\partial T}{\partial t} = \nabla(\lambda \nabla T) + W_b (T_a -T) + Q_m \]

This example implements the stationary form of bioheat equation

\[ \nabla(\lambda \nabla T) + W_b (T_a -T) + Q_m = 0 \] with Robin boundary conditions \[ \lambda \frac{\partial T}{\partial \hat{n}} = h_s(T - T_{ext}) \] on a human brain model ^[1]. Simulation nodes are based on FEM elements used in the referenced article with constants set to the default values from table 2 of the article.

Obtained solution is displayed on Figure 1

References

↑ Mario Cvetković, Dragan Poljak, Akimasa Hirata, The electromagnetic-thermal dosimetry for the homogeneous human brain model, Engineering Analysis with Boundary Elements, Volume 63, 2016, Pages 61-73, ISSN 0955 7997, https://doi.org/10.1016/j.enganabound.2015.11.002.

[Cvetkovic2016-1] Mario Cvetković, Dragan Poljak, Akimasa Hirata, The electromagnetic-thermal dosimetry for the homogeneous human brain model, Engineering Analysis with Boundary Elements, Volume 63, 2016, Pages 61-73, ISSN 0955 7997, https://doi.org/10.1016/j.enganabound.2015.11.002.

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