An open-source computational framework for immersed fluid-structure interaction modeling using FEBio and MFEM

TL;DR

This work introduces an open-source immersed FSI framework that couples MFEM with FEBio to enable robust, large-deformation cardiovascular simulations using a fictitious-domain, distributed Lagrange multiplier approach. A fully implicit monolithic scheme with variational multiscale stabilization solves the coupled incompressible fluid and nearly-incompressible solid problems, with the fluid represented by MFEM and the solid by FEBio’s rich constitutive models. The MFEMiFSI plugin architecture enables seamless integration, parallel execution, and extension to additional solid formulations, supported by a dedicated FSI-constraint matrix assembly workflow. Numerical tests across static benchmarks, open/closed valve scenarios, oscillating leaflets, free-falling spheres, and 3D semilunar valve dynamics validate accuracy, convergence, and the method’s capability to capture complex valve mechanics and jet dynamics. By combining open-source, hardware-accelerator-ready fluid solvers with sophisticated biomechanics modeling, the framework provides a practical platform for high-fidelity, patient-relevant FSI analyses in biomechanics and cardiovascular research.

Abstract

Fluid-structure interaction (FSI) simulation of biological systems presents significant computational challenges, particularly for applications involving large structural deformations and contact mechanics, such as heart valve dynamics. Traditional ALE methods encounter fundamental difficulties with such problems due to mesh distortion, motivating immersed techniques. This work presents a novel open-source immersed FSI framework that strategically couples two mature finite element libraries: MFEM, a GPU-ready and scalable library with state-of-the-art parallel performance developed at Lawrence Livermore National Laboratory, and FEBio, a nonlinear finite element solver with sophisticated solid mechanics capabilities designed for biomechanics applications developed at the University of Utah. This coupling creates a unique synergy wherein the fluid solver leverages MFEM's distributed-memory parallelization and pathway to GPU acceleration, while the immersed solid exploits FEBio's comprehensive suite of hyperelastic and viscoelastic constitutive models and advanced solid mechanics modeling targeted for biomechanics applications. FSI coupling is achieved using a fictitious domain methodology with variational multiscale stabilization for enhanced accuracy on under-resolved grids expected with unfitted meshes used in immersed FSI. A fully implicit, monolithic scheme provides robust coupling for strongly coupled FSI characteristic of cardiovascular applications. The framework's modular architecture facilitates straightforward extension to additional physics and element technologies. Several test problems are considered to demonstrate the capabilities of the proposed framework, including a 3D semilunar heart valve simulation. This platform addresses a critical need for open-source immersed FSI software combining advanced biomechanics modeling with high-performance computing infrastructure.

Figures (18)

• Figure 1: Diagram of the plugin's design interfacing with FEBio and MFEM.
• Figure 2: (a) Problem setup and boundary conditions for the immersed annular solid in static equilibrium test case. The orange region is the fluid domain, while the yellow region is the solid domain. Note that $\hat{e}_{()}$ denotes a unit vector in a coordinate direction. (b) Snapshot of the fluid pressure throughout the domain from the N=256 mesh.
• Figure 3: Convergence results for the immersed annular solid disk in static equilibrium problem.
• Figure 4: Snapshot of the numerical solution for the open valve test problem on mesh M3 at time $t=2.25$ s (peak inflow) zoomed in around the leaflets.
• Figure 5: Time history of the (a) x- and (b) y-displacement of the tip of the top leaflet compared with a reference ALE-FSI simulation from kamensky_immersogeometric_2015. M1, M2, and M3 correspond to the sequence of quadrilateral fluid meshes considered of size $129 \times 32$, $256\times 64$, and $512 \times 128$ elements respectively.

Theorems & Definitions (5)

• Remark 2.1
• Remark 2.2
• Remark 2.3
• Remark 2.4
• Remark 3.1