Fibre stiffening with a fluid layer

[Bennion]

Hello,

I'm currently trying to model movement of the brain within the skull using the new fluid FSI functionality to capture the mechanics of the surrounding fluid layer (I discussed this briefly with Steve in Dublin).

In reality, this fluid layer contains trabeculae which I'm assuming only offer stiffness in tension, so I'm using a trans iso Mooney-Rivlin as the solid component of the fluid FSI material.

The model runs, but varying the stiffness of the fibres (c5) greatly seems to make very little impact on the results. Looking at the 1st deviatoric principle stress of regions in tension also suggests the fibres are contributing very little.

I would really appreciate your thoughts on whether or not this is likely to be my mistake or if febio won't support this?

Many thanks,

Nick

For reference, this is the material section in question:

<material id="2" name="PAC" type="fluid-FSI">
<fluid type="fluid">
<density>1007</density>
<k>2e+009</k>
<viscous type="Newtonian fluid">
<mu>0.001</mu>
<kappa>0.003</kappa>
</viscous>
</fluid>
<solid type="coupled trans-iso Mooney-Rivlin">
<density>1</density>
<c1>1e-9</c1>
<c2>1e-9</c2>
<c3>10</c3>
<c4>50</c4>
<c5>100000</c5>
<k>1</k>
<lambda>1.01</lambda>
<fiber type="local"> 0, 0</fiber>
</solid>
</material>

[ateshian]

Hi Nick,

The fluid-FSI module was not developed to deal with the type of problem you are trying to solve. The solid material is only meant to regularize the deforming mesh of the fluid domain.

To help you figure out whether there is some usefulness to using the FSI module for this problem, it would be helpful if you could describe the model in greater detail. For example, is the fluid layer separating a deformable brain tissue from the rigid skull? Are you imparting some motion to the skull and examining how the brain motion is deforming the fluid domain?

Also, have you tried running your analysis by changing the values of c1 and c2? If you increase them by orders of magnitude and detect a difference in the solution, it would show that the solid properties do influence the analysis but the tensile response of the fibers is not that significant (e.g., they are not subjected to a lot of tension).

Best,

Gerard

[Bennion]

Hi Gerard,

Thank you very much for your response. I had suspected that that was the case but it's useful to know for certain.

I am trying to model the movement of the brain with res-positioning relative to the gravity. As such, with a body load applied to all structures, the brain 'sinks' slightly into the fluid layer between itself and the rigid skull as you describe. We suspect that the brain is tethered with arachnoid traceculae in regions in tension, limiting this displacement.

I have tried varying c1 and c2 (or E in the neo-Hookean) and it definitely makes a difference. The only problem is that achieving the out-of-plane tensile stiffness seen in the literature means the equivalent compressive stiffness will be too high. Nonetheless I will look into this further.

Many thanks for your help.

Best,

Nick