Effective property method for efficient modeling of non-uniform tissue support in fluid-structure interaction...

Incorporating tissue support in fluid-structure interaction analysis of cardiovascular flows is crucial for accurately representing physiological constraints, achieving realistic vessel wall motion, and minimizing artificial oscillations. The generalized Robin boundary condition, which models tissue support with a spring-damper-type force, uses elastic and damping parameters to represent the viscoelastic behavior of perivascular tissues. Using spatially distributed parameters for tissue support, rather than uniform ones, is more realistic and aligns with the varying properties of vessel walls. However, considering the spatial distribution of both can increase the complexity of preprocessing and numerical implementation. In this work, we develop an effective property method for efficient modeling of non-uniform tissue support and quantifying the contribution of tissue support to the mechanical behaviors of vessel walls.

Based on the theory of linear viscoelasticity, we derive the mathematical formulas for the effective property method, integrating the parameters of generalized Robin boundary condition into vessel wall properties. The pulse wave velocity incorporating the influence of tissue support is also analyzed. Furthermore, we modify the coupled momentum method, originally formulated for elastic problems, to account for the viscoelastic properties of the vessel wall.

The method is verified with three-dimensional fluid-structure interaction simulations, achieving a maximum relative error of less than 2.2% for flow rate and less than 0.7% for pressure. This method shows that tissue support parameters can be integrated into vessel wall properties, resulting in increased apparent wall stiffness and viscosity, and further changing pressure, flow rate, and wave propagation.

In this study, we develop an effective property method for quantitatively assessing the impact of tissue support and for efficiently modeling non-uniform tissue support. Moreover, this method offers further insights into clinically measured pulse wave velocity, demonstrating that it reflects the combined influence of both vessel wall properties and tissue support.