Verification of a Finite Volume Solver for Active and Passive Cardiac Material Behaviour

VERIFICATION OF A FINITE VOLUME SOLVER FOR ACTIVE AND PASSIVE CARDIAC MATERIAL BEHAVIOUR Aaron Mullen-Hales VERIFICATION OF A FINITE VOLUME SOLVER FOR ACTIVE AND PASSIVE CARDIAC MATERIAL BEHAVIOUR 20th Openfoam Workshop hosted by AIT Austria Institute of Technology 30th June – 4th July, Vienna, Austria Aaron Mullen-Hales Philip Cardiff School of Mechanical and Materials Engineering, University College Dublin Background and Motivation 3 Cardiac Xenotransplantations Simulations 4 Pig To Human Heart Transplants Verification of Cardiac Mechanics Software 5 •To be confident in our simulation software that is accurate we need to verify it. •Land et al. (2015) [1] and Arostica et al. (2025) [2] Benchmarks for an idealised ventricle to verify solid mechanics. •Traditionally FEM has been used for these benchmarking problems, we are using FVM in OpenFOAM. •Why use FVMs? [3] 6 Verification of Cardiac Mechanics Software Mathematical and Numerical Models 7 Governing equations •Conservation of Linear Momentum: •Total Lagrangian form: [4] 8 Jacobian Free Newton Krylov Methods 9 Krylov Methods - JFNK Case •In our case we have: •Krylov subspace: •We set: 16 Krylov Methods - JFNK Case Minimise Update u 17 Krylov Methods - Implementation with GMRES 18 Material Model 19 Guccione Material Model Cauchy stress: Strain energy function: Where: •Model depends on the fibers of the heart. •Electro-mechanical coupling implemented. 20 FVM Discretisation 21 FVM Discretisation •A 2nd order cell centered FVM discretisation is employed, and the discretised governing equations are solved iteratively. •Rhie chow stabilisation is implemented to avoid checkerboarding in our meshes. 22 Rhie Chow Stabilisation We have been using two different values of the scaling stiffness parameter K, which depend on the stiffness of the problems that will be explored. Or 23 24 Test Cases 25 32 33 Volume Locking: Analysis of Bulk Modulus sensitivity 34 Next step P1 35 Treating pressure as an additional unknown in the solver to hopefully avoid volume locking . Problem 2 From Land et al. Inflation of a Ventricle 36 Idealised Ventricle Mesh Land et al. 37 Problem 2 Set Up 38 39 Bulk Modulus Sensitivity Analysis and Comparison With Land et al. (2015) 40 Bulk: 1e5 41 Rhie Chow Analysis Rhie Chow Coef = 1000 Rhie Chow Coef = 1 48 Rhie Chow Coef = 1 49 50 Rhie Chow Coef = 1000 51 52 Problem 2.5 Fictitious Problem 53 Problem 2.5 Set Up •This problem was set up to explore the effects of anisotropy and electromechanical coupling. •The problem has the same constitutive/material properties as problem 3. •The problem has an active contraction equal to zero. •This was so we can check the anisotropy of the problem to see if the issue lies with electromechanical coupling or not. •We compare the results of our model with the results of an identical problem within FEBio [5]. •FEBio have created a model and have benchmarked their results to Land et al. successfully. 54 Bulk sensitivity Analysis comparison with FEbio's model 55 2e4 mesh1 FEBio Our model FEBio Our model 56 2e5 mesh2 FEBio Our model FEBio Ours FEBio Ours FEBio Ours Ours Ours FEBio FEBio Ours FEBio 57