Finite Element Analysis (FEA) of the aortic valve can be used to predict leaflet stress, strain, and deformation throughout the cardiac cycle. This is particularly relevant for congenital valve variants such as bicuspid and quadricuspid aortic valves, where altered leaflet geometry can produce asymmetric mechanical loading and localized stress concentrations.
Aicha Boualiane and Lotfi Hamza Cherif developed patient-specific three-dimensional models of tricuspid (TAV), bicuspid Type 0 (BAV Type 0), bicuspid Type 1 (BAV Type 1), and quadricuspid (QAV) aortic valves. Geometries reconstructed from transesophageal echocardiography (TEE) images using MATLAB and Blender were analyzed with FEATool Multiphysics for finite element simulation of valve stress and strain under changing pressure loads throughout the cardiac cycle. The simulations showed clear morphology-dependent differences, with the asymmetric BAV and QAV configurations developing greater stress concentrations and more localized deformation than the TAV model.
The modeling workflow began with TEE image acquisition, image post-processing, and segmentation of the valve anatomy. MATLAB and Blender were then used to construct the valve geometries before the finite element stage. The paper presents the FEA workflow as a sequence covering mesh generation, definition of valve behavior, initial conditions, boundary conditions, and finite element solution. FEATool Multiphysics was used as the finite element simulation environment for three-dimensional biomechanical analysis of aortic valve leaflet stress, strain, and deformation under time-dependent pressure loading. The valves were assigned initial stresses and subjected to a surface-dependent variable pressure profile as a boundary condition. This allowed the analysis to follow changes in leaflet stress and deformation as the transvalvular loading changed rather than treating the valve as a single static load case.
The simulations combined linear elastic and nonlinear hyperelastic material descriptions. Two numerical solution approaches were used: the linear MUMPS solver and the nonlinear FEniCS solver. The paper reports that both were employed to ensure convergence of the results. Mesh sensitivity was also examined using characteristic mesh sizes of 1.24, 0.62, and 0.31 mm, with von Mises stress, first principal stress, and first principal strain compared for each valve type. This provided a direct check on the sensitivity of the principal biomechanical quantities to mesh refinement without making the stress and strain comparison dependent on a single discretization.
The FEATool results highlighted how strongly valve morphology influenced the mechanical response. For the tricuspid valve, leaflet stresses at peak systole and diastole were comparatively moderate and distributed in a more homogeneous and symmetric pattern. The congenital variants produced less uniform behavior. BAV Type 0 showed a more even strain distribution between its cusps, whereas BAV Type 1 exhibited an asymmetric strain pattern with a peak around the fused cusp and raphe. The asymmetric QAV geometry similarly produced several regions of elevated stress concentration. Overall, the BAV and QAV models showed larger deformation peaks than the TAV model.
These differences allowed the researchers to identify mechanically vulnerable regions that would be difficult to characterize from valve geometry alone. The paper relates the higher and more localized mechanical loading in congenital variants to mechanisms that may contribute to valve degeneration and calcification, particularly where repeated leaflet loading is concentrated. Rather than treating TAV, BAV, and QAV as geometrically different versions of the same mechanical system, the simulations demonstrate that their distinct morphologies produce distinct stress and strain environments. The resulting framework is intended to support patient-specific assessment of valve biomechanics and potentially inform more individualized evaluation and treatment planning.
In this study, FEATool Multiphysics was used for three-dimensional finite element analysis of patient-specific aortic valve biomechanics. The workflow included reconstructed valve geometries, time-dependent pressure loading, stress and strain evaluation, mesh sensitivity analysis, and linear and nonlinear solver approaches. The application provides an example of using FEATool for biomechanical and structural mechanics simulations involving complex anatomical geometry and changing loads over the cardiac cycle. Related FEATool examples include Stress Analysis of a Thick Plate, which demonstrates three-dimensional stress analysis under a pressure load, and Deformation of a Spanner, which demonstrates three-dimensional structural analysis with imported geometry. These examples do not reproduce the valve model, but provide useful starting points for related FEATool structural mechanics workflows.
See the linked references for more detailed information about this research.
References
- A. Boualiane, L. H. Cherif. Biomechanical Analysis of Stresses and Strains of the Healthy Aortic Valve and Its Congenital Variants Throughout the Cardiac Cycle: A Finite Element Approach, International Journal for Numerical Methods in Biomedical Engineering, 42(4), e70168, 2026, doi: 10.1002/cnm.70168.