Numerical Approximation of Elasticity Tensor Associated With Green-Naghdi Rate

How to implement user-defined fiber-reinforced hyperelastic materials in finite element software

Finite element modeling is often used in biomechanical engineering to evaluate medical devices, treatments and diagnostic tools. Using an adequate material model that describes the mechanical behavior of biological tissues is essential for a reliable outcome of the simulation. Pre-programmed material models for biological tissues are available in many finite element software packages. However, since these pre-programmed models are presented to the user as a black box, without the possibility to modify the material description, many researchers turn to implementing their own material formulations. This is a complex undertaking, requiring extensive knowledge while documentation is limited. This paper provides a detailed description, at the level of the biomedical engineer, of the implementation of a nonlinear hyperelastic material model using user subroutines in Abaqus®, in casuUANISOHYPER_INV and UMAT. The Gasser-Ogden-Holzapfel material model is used as an example, resulting in four implementation variations: the built-in implementation, a UANISOHYPER_INV formulation, a UMAT with analytical tangent stiffness formulation and a UMAT with numerical tangent stiffness formulation. In addition, three different element formulations are used: a continuum compressible, a continuum incompressible and a plane stress incompressible. All cases are thoroughly verified by applying a series of deformations on a single cube element and by simulating an extension-inflation experiment with non-homogeneous deformations and multiple elements. In these test cases, stresses, displacements, reaction forces, the required number of iterations and the total CPU time were compared. The results show that the four implementation variations are very similar, with total relative errors between 10^-3 and 10^-15, number of iterations that varied by maximum one iteration, and a comparable CPU time. In addition to this detailed overview, the user subroutines are added as supplementary material to this tutorial, which can be used as the ideal starting point for biomechanical engineers to implement their own material models at different levels of complexity.

The role of stress concentration in calcified bicuspid aortic valve

Calcific aortic valve disease (CAVD) is the most common valvular heart disease in the aging population, and is now believed to be a slow, progressive, yet actively regulated process. The disease progression can be divided into two phases: initiation phase associated with lipid deposition and inflammation response, and the later propagation phase with active calcification growth. It has been hypothesized that elevated mechanical stress plays a major role in both phases of disease progression. In order to identify a direct link between leaflet stress and calcification development, we performed patient-specific finite-element (FE) analyses of six bicuspid aortic valves (BAV), where the leaflets, raphe and calcifications were all considered. The results showed that during the initiation phase, calcium buildup is likely to occur along the leaflet-root attachment curve (ATC), and the commissures, which are subject to the most drastic changes in stress during the cardiac cycle. During the propagation phase, the presence of calcification would lead to local stress concentration along its boundary, hence further calcification growth. Three patterns of calcification formation were identified on BAV leaflets: 'radial', which extended radially from ATC into the leaflet belly region; 'commissure to commissure', which extended circumferentially along the coaptation; and 'raphe', which located in the vicinity of the raphe. Furthermore, we found a strong correlation between regions with a high risk of calcium buildup and regions with elevated mechanical stress. The high-risk regions predicted at diastole on the non-calcified leaflet from FE models agreed reasonably well with the in vivo calcification locations, which indicates that patient-specific FE modelling could help us to evaluate the potential risk of calcification formation in the early stage of CAVD.

Numerical Parametric Study of Paravalvular Leak Following a Transcatheter Aortic Valve Deployment Into a Patient-Specific Aortic Root

Paravalvular leak (PVL) is a relatively frequent complication after transcatheter aortic valve replacement (TAVR) with increased mortality. Currently, there is no effective method to pre-operatively predict and prevent PVL. In this study, we developed a computational model to predict the severity of PVL after TAVR. Nonlinear finite element (FE) method was used to simulate a self-expandable CoreValve deployment into a patient-specific aortic root, specified with human material properties of aortic tissues. Subsequently, computational fluid dynamics (CFD) simulations were performed using the post-TAVR geometries from the FE simulation, and a parametric investigation of the impact of the transcatheter aortic valve (TAV) skirt shape, TAV orientation, and deployment height on PVL was conducted. The predicted PVL was in good agreement with the echocardiography data. Due to the scallop shape of CoreValve skirt, the difference of PVL due to TAV orientation can be as large as 40%. Although the stent thickness is small compared to the aortic annulus size, we found that inappropriate modeling of it can lead to an underestimation of PVL up to 10 ml/beat. Moreover, the deployment height could significantly alter the extent and the distribution of regurgitant jets, which results in a change of leaking volume up to 70%. Further investigation in a large cohort of patients is warranted to verify the accuracy of our model. This study demonstrated that a rigorously developed patient-specific computational model can provide useful insights into underlying mechanisms causing PVL and potentially assist in pre-operative planning for TAVR to minimize PVL.

Evaluation of transcatheter heart valve biomaterials: Computational modeling using bovine and porcine pericardium

OBJECTIVE

The durability of bioprosthetic heart valve (BHV) devices, commonly made of bovine (BP) and porcine (PP) pericardium tissue, is partly limited by device calcification and tissue degeneration, which has been associated with pathological levels of mechanical stress. This study investigated the impacts of BP and PP tissues with different thicknesses and tissue mechanical properties in BHV applications.

METHODS

Second Harmonic Generation (SHG) imaging was employed to visualize the collagen fibers on each side of the pericardium. Structural constitutive modeling that incorporates collagen fiber distribution obtained from multiphoton microscopy for each tissue type were derived to characterize the corresponding biaxial mechanical testing data collected in a previous study. The models were verified through finite element (FE) simulations of the biaxial test and implemented in valve closing simulations.

RESULTS

Smooth side collagen fibers were found to correlate with the mechanical response. BHVs with adult (ABP) and calf (CBP) BP tissues had lower maximum principal stresses than those with PP and fetal (FBP) BP tissues. Collagen fiber orientation along the circumferential axis resulted in lower maximum principal stresses and more uniform and symmetric stress distributions throughout the valve.

CONCLUSIONS

The use of PP and FBP tissue resulted in higher peak stresses than ABP and CBP tissues in the given valve design. Additionally, ensuring collagen fiber orientation along the circumferential axis led to lower maximum stresses felt by the valve leaflets, which could also improve BHV durability.