Couple URIS valve to tissue mechanics

Use Case

This feature would improve the physiological fidelity of cardiac FSI simulations that use unfitted resistive immersed surfaces (URIS) to model the cardiac valves.

Problem

In cardiac FSI simulations that use URIS valves, the force exerted by the blood on the valves is not transferred to the surrounding tissue. This results in a net force by the blood on the tissue, which significantly alters tissue deformation. This is unphysiological, since in reality, closed valves are mechanically supported by the surrounding cardiac tissue, as well as the papillary muscles, and the net force on the tissue is close to zero.

See https://onlinelibrary-wiley-com.stanford.idm.oclc.org/doi/full/10.1002/cnm.70119 for a more complete discussion of this problem.

Solution

Implement the solution proposed in https://onlinelibrary-wiley-com.stanford.idm.oclc.org/doi/full/10.1002/cnm.70119. Essentially, we "add distributed forces acting on the structure to model the attachment of valves to the cardiac walls". This amounts to computing the net force on a URIS valve, then distributing it over a particular region of the tissue domain. Clear equations are provided in the paper. Moreover, they propose an explicit treatment of this extra forcing term and do not observe stability issues. This should make it more straightforward to implement in svMultiPhysics.

Alternatives considered

None. I am not aware of any other proposed solutions to this problem.

Additional context

No response

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