Difference between revisions of "Bioheat equation"
From Medusa: Coordinate Free Mehless Method implementation
| Line 4: | Line 4: | ||
</figure> | </figure> | ||
| − | 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 constant metabolic heat | + | 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. |
\[ | \[ | ||
| Line 21: | Line 21: | ||
on a human brain model | on a human brain model | ||
<ref name="Cvetkovic2016"> | <ref name="Cvetkovic2016"> | ||
| − | 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.</ref>. Simulation nodes are based on | + | 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.</ref>. 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 <xr id="fig:brainBioheat"/> | Obtained solution is displayed on <xr id="fig:brainBioheat"/> | ||
Latest revision as of 21:27, 23 March 2020
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.
