Bioheat equation - Revision history

MihaR at 20:27, 23 March 2020

2020-03-23T20:27:37Z

MihaR at 20:25, 23 March 2020

2020-03-23T20:25:33Z

MihaR: Created page with "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 c..."

2020-03-23T20:24:25Z

Created page with "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 c..."

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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 sources.

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

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
<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 the 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"/>

<figure id="fig:brainBioheat">
[[File:BrainBioheat.png|thumb|upright=2|<caption>
</caption>]]
</figure>

=References=
<references/>

@@ Line 4: / Line 4: @@
 </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 sources.
+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
 <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 the FEM elements used in the referenced article with constants set to the default values from table 2 of the article.
+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"/>

@@ Line 1: / Line 1: @@
 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 sources.
@@ Line 19: / Line 24: @@
 Obtained solution is displayed on <xr id="fig:brainBioheat"/>
 =References=
 <references/>