Note: This discussion is about an older version of the COMSOL Multiphysics® software. The information provided may be out of date.
Discussion Closed This discussion was created more than 6 months ago and has been closed. To start a new discussion with a link back to this one, click here.
equation system
Posted 2013年8月21日 GMT-4 13:55 Version 4.3b 3 Replies
Please login with a confirmed email address before reporting spam
∇·((σi +σe)∇φe)=−∇·(σi∇Vm)
I have two spheres one within the other as geometry. Inside the smaller sphere I want to introduce Vm as a point source and set it to 1 Volt and measure the potentials φe on the larger sphere's surface. I assume isotropy and give conductance values constant for now.
How can I enter this equation in COMSOL and do this simulation?
Thanks,
Gizem
Please login with a confirmed email address before reporting spam
Gizem,
given your description I am wondering if you need to implement equations. Your task seems to be electrostatics and even if you don't have the AC/DC module this is comprised in the basic module.
Cheers
Edgar
--
Edgar J. Kaiser
emPhys Physical Technology
Please login with a confirmed email address before reporting spam
bidomain model of the heart and after modeling my aim is to find the
forward matrix that represents the relationship between the transmembrane voltages inside the heart and the potentials on torso surface.
Therefore, according to the theory part of my work, I should follow the following steps ;
For my problem it is impossible to assign the transmembrane voltages (TMV) to several nodes of the cardiac mesh and solve the forward problem. Only the gradient of TMV can produce electrocardiography, therefore the TMV distribution must be a steady function.
1) A coarse mesh should be introduced on a sphere geometry ( we assume that sphere represents heart )
2) Then, we should set TMV in one node to 1, the rest of the nodes having the TMV of 0.
3) These TMV distributions should be interpolated to the 'fine' finite element mesh where the whole forward computation could be performed.
4) The impressed currents were calculated from this distribution of TMV .
5) The equation which represents my problem is ; ∇·((σi +σe)∇φe)=−∇·(σi∇Vm). In this equation Vm represents transmembrane voltage and φe represents the torso potentials. σi∇Vm part of the equation is impressed current density which is talked at step 4.
6) As geometry, until step 4 I want to do everything on a single sphere ( which represents the heart ), after that in order to find the φe on torso I need to use bidomain equation ∇·((σi +σe)∇φe)=−∇·(σi∇Vm) and introduce another sphere which encircles the sphere represents the heart.
7) For each Vm which I set to 1, I need to calculate the φe on the torso surface from the same coordinates and these φe values will represent a single column of the transfer matrix.
As boundary conditions: on heart surface I use dirichlet boundary condition, and on torso surface I use neumann boundary condition. Also, for now we assume isotropy and take σi and σe constant in bidomain equation.
I hope I could explain my problem in a simple way.
Please login with a confirmed email address before reporting spam
Regards,
Gizem