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Initial conditions problem

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I wish to model a muscle tissue (solid domain) which contains a capillary blood vessel (fluid domain). I’m not interested in the blood flow.
The geometry is in the attached file.

I want to model the pressure the fluid is exerting on the vessel wall (blood pressure). At first I thought of using the structural mechanics modulo alone, using the load option in the subdomain settings , but as this load is force/length or force/area it is not suitable for me to use…. (blood pressure is in Pa and can’t be translated to N/m2 as the dimension of depth of the cardiovascular system are not proper to model…)

This led me to the conclusion I need a model of structural-fluid interaction, but I wish to model only blood pressure and not velocity…

I’ve tried to use the built in structural-fluid interaction modulo in comsol which comes with the ALE… and after defining the subdomain and boundary settings without defining any initial values… I got an error message regarding initial solutions…

My questions are:
In structural mechanics module in the subdomain settings: when do I need to use the “initial stress and strain” definitions? When do I need the “init” tab (and what pressure is mentioned there?)

In the fluid domain (incompressible NS): When do I need the “init” tab (and what pressure is mentioned there?)

In what cases is the ALE (comsol coupled structural-fluid interaction) is better than user coupling of the structural and fluid mechanics models?

Also, which solver will be best?
Help will be most appreciated,

Yael


4 Replies Last Post Dec 27, 2009, 5:11 a.m. EST
Ivar KJELBERG COMSOL Multiphysics(r) fan, retired, former "Senior Expert" at CSEM SA (CH)

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Posted: 1 decade ago Dec 21, 2009, 11:11 a.m. EST
Hi

You have many questions here, I cannot answer all just now, but this one puzzles me:

"At first I thought of using the structural mechanics modulo alone, using the load option in the subdomain settings , but as this load is force/length or force/area it is not suitable for me to use…. (blood pressure is in Pa and can’t be translated to N/m2 as the dimension of depth of the cardiovascular system are not proper to model…)"

In 2D, what you are seeing is a cut view of a pseudo 3D system of of 1[m] normalised depth, therefore pessures are in [N/m] or =[N/m^2]=[Pa] for a 1m deep system. Normally blod pressure (range) is known, even average velocity, transverse to your cut view.
I believe this should allow you to do quite some analysis, no?

Your structural fluids issue is, in my understanding, linked to the large displacement you might get for such soft "materail" as muscle and blod vessels. Have you been reading the newly arrived, and excellent book on this subject ?: Modelling of Transport Processes, Application to biomedical Systems by A. Datta and V. Rakesh

Initial stress and strain are there to have non zero values at first solver step, but you can also "build" them up by a first static analysis, and then restart from there for further processing.
If you know the initial values, i.e. of blod is usually 37°C, no need to start at 0°K, otherwise you need some extra time to get to the equilibrium first.

Many times I leave them as defined by default, its only when solving takes time or the convergene is poor I start to check them over

Good luck
Ivar
Hi You have many questions here, I cannot answer all just now, but this one puzzles me: "At first I thought of using the structural mechanics modulo alone, using the load option in the subdomain settings , but as this load is force/length or force/area it is not suitable for me to use…. (blood pressure is in Pa and can’t be translated to N/m2 as the dimension of depth of the cardiovascular system are not proper to model…)" In 2D, what you are seeing is a cut view of a pseudo 3D system of of 1[m] normalised depth, therefore pessures are in [N/m] or =[N/m^2]=[Pa] for a 1m deep system. Normally blod pressure (range) is known, even average velocity, transverse to your cut view. I believe this should allow you to do quite some analysis, no? Your structural fluids issue is, in my understanding, linked to the large displacement you might get for such soft "materail" as muscle and blod vessels. Have you been reading the newly arrived, and excellent book on this subject ?: Modelling of Transport Processes, Application to biomedical Systems by A. Datta and V. Rakesh Initial stress and strain are there to have non zero values at first solver step, but you can also "build" them up by a first static analysis, and then restart from there for further processing. If you know the initial values, i.e. of blod is usually 37°C, no need to start at 0°K, otherwise you need some extra time to get to the equilibrium first. Many times I leave them as defined by default, its only when solving takes time or the convergene is poor I start to check them over Good luck Ivar

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Posted: 1 decade ago Dec 21, 2009, 1:26 p.m. EST
Thank you, Ivar.
Well, actually I have made some progress since my message was posted. I’ve realized I can change the thickness of the cross section: I’ve changed it to 150 ?m, so now it fits better with my model dimensions (160 ?m *120 ?m). After changing the thickness I found it logical to use the blood pressure value…
As I’m not interested in the blood flow but rather interested in the heat exchange and the load blood exerts on the vessel wall, I’ve decided not to use the fluid application: I’me using the structural mechanics plane strain modulo and bioheat equation from the heat transfer.

Well, the initial values were more of a problem related to the structural analysis… I have started my transient analysis with the steady state solution… For now, I’m using a displacement in the x direction (which is constant in time). I receive a solution for transient analysis of 1 sec using the steady state as initial value, and for transient analysis of 100 sec using the solution of 1 sec as initial value. But trying to solve for 200 sec using the 100 sec solution I receive the error:
“ Error:
Time 0:
Failed to find consistent initial values.
Last time step is not converged.”
What can be the reason for this?

Best,
Yael
Thank you, Ivar. Well, actually I have made some progress since my message was posted. I’ve realized I can change the thickness of the cross section: I’ve changed it to 150 ?m, so now it fits better with my model dimensions (160 ?m *120 ?m). After changing the thickness I found it logical to use the blood pressure value… As I’m not interested in the blood flow but rather interested in the heat exchange and the load blood exerts on the vessel wall, I’ve decided not to use the fluid application: I’me using the structural mechanics plane strain modulo and bioheat equation from the heat transfer. Well, the initial values were more of a problem related to the structural analysis… I have started my transient analysis with the steady state solution… For now, I’m using a displacement in the x direction (which is constant in time). I receive a solution for transient analysis of 1 sec using the steady state as initial value, and for transient analysis of 100 sec using the solution of 1 sec as initial value. But trying to solve for 200 sec using the 100 sec solution I receive the error: “ Error: Time 0: Failed to find consistent initial values. Last time step is not converged.” What can be the reason for this? Best, Yael

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Posted: 1 decade ago Dec 21, 2009, 6:24 p.m. EST
Well, trying to solve the transient problem using time steps of 0:10:1000 I’ve managed to get a solution (using the steady state as initial value).

I’ve added now the bioheat from the heat transfer modulo and created a coupled problem (structural and thermal). Trying to solve the coupled problem I think that the thermal solution that is received in the coupled problem is less accurate than in the thermal problem modeled by itself… or at least this is how it is visualized in the thermal map…

Can it be? Is there a tradeoff in accuracy when solving coupled problems?
Well, trying to solve the transient problem using time steps of 0:10:1000 I’ve managed to get a solution (using the steady state as initial value). I’ve added now the bioheat from the heat transfer modulo and created a coupled problem (structural and thermal). Trying to solve the coupled problem I think that the thermal solution that is received in the coupled problem is less accurate than in the thermal problem modeled by itself… or at least this is how it is visualized in the thermal map… Can it be? Is there a tradeoff in accuracy when solving coupled problems?

Ivar KJELBERG COMSOL Multiphysics(r) fan, retired, former "Senior Expert" at CSEM SA (CH)

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Posted: 1 decade ago Dec 27, 2009, 5:11 a.m. EST
Hi again

For me the "accuracy" is always linked to the way you solve a problem, you add in always assumptons and simplifcatons, i.e. using a segregated solver part of the "problem" ignores/freezes certain phenomena while solving for the others.

Ideally, you should mange to explain any difference seen, to be able to judge where is the "truth", but sometimes this remains "in thory" ;)

Try to reproduce the effect for a very simple case, is it still there?, can you explain it analytically ?

Good luck
Ivar


Hi again For me the "accuracy" is always linked to the way you solve a problem, you add in always assumptons and simplifcatons, i.e. using a segregated solver part of the "problem" ignores/freezes certain phenomena while solving for the others. Ideally, you should mange to explain any difference seen, to be able to judge where is the "truth", but sometimes this remains "in thory" ;) Try to reproduce the effect for a very simple case, is it still there?, can you explain it analytically ? Good luck Ivar

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