Partitioned Fluid-Solid-Growth Interaction Using the Equilibrated Constrained Mixture Model

Introduction:: Growth and remodeling (G&R) are commonly triggered mechanically through fluid-structure interaction by a combination of pressure-induced intramural stress and flow-induced wall shear stress [1]. Previous G&R models rely on simplifying assumptions for fluid dynamics of blood inside the vessel. We propose to combine fluid- structure interaction and G&R in a novel fluid-solid-growth (FSGe) framework, using a mechanobiologically equilibrated version of the constrained mixture theory [2].

Materials and Methods:: We solve the incompressible Navier-Stokes equations to obtain velocity and pressure inside the blood vessel. We pass local fluid pressure and wall shear stress to our large-deformation solid G&R model at the fluid-solid interface. As the solid model, we use a fast and efficient formulation of the constrained mixture theory that assumes that each G&R state is mechanobiologically equilibrated [3]. A shear-to-intramural gain ratio controls the importance of wall shear stress and intramural stress stimuli. Both fields are coupled in a partitioned scheme, separating fluid and solid time scales (seconds vs. weeks).

Results, Conclusions, and Discussions:: The computational cost of our coupling scheme is comparable to a fluid-structure-interaction simulation with a hyperelastic solid material. We compare our coupled FSGe method to G&R models with different fluid approximations for pressure and wall shear stress [4]. Our examples include aneurysmal formation (see Figure), stenosis formation, and distortions of blood flow for various Reynolds numbers. Simplified fluid dynamics in cardiovascular G&R models can provide a good approximation in many scenarios. However, we show that local fluid dynamics can significantly influence the long-term G&R state in blood vessels.

Acknowledgements (Optional): : This work was supported by NIH Grants K99HL161313, R01HL139796, R01HL159954, the Additional Ventures Foundation Cures Collaborative, and the Stanford Maternal and Child Health Research Institute.

References (Optional): : [1] Figueroa CA et al. Comput Methods Appl Mech Eng, 198:3583-3602 (2009)
[2] Latorre M, Humphrey JD. J Appl Math Mech, 98:2048-2071 (2018)
[3] Latorre M, Humphrey JD. Comput Methods Appl Mech Eng, 368:113156 (2020)
[4] Latorre M et al. Biomech Model Mechanobiol, 21(3):827-848 (2022)