Simulating the time evolving geometry, mechanical properties, and fibrous structure of bioprosthetic heart valve leaflets under cyclic loading

Abstract

Currently, the most common replacement heart valve design is the 'bioprosthetic' heart valve (BHV), which has important advantages in that it does not require permanent anti-coagulation therapy, operates noiselessly, and has blood flow characteristics similar to the native valve. BHVs are typically fabricated from glutaraldehyde-crosslinked pericardial xenograft tissue biomaterials (XTBs) attached to a rigid, semi-flexible, or fully collapsible stent in the case of the increasingly popular transcutaneous aortic valve replacement (TAVR). While current TAVR assessments are positive, clinical results to date are generally limited to <2 years. Since TAVR leaflets are constructed using thinner XTBs, their mechanical demands are substantially greater than surgical BHV due to the increased stresses during in vivo operation, potentially resulting in decreased durability. Given the functional complexity of heart valve operation, in-silico predictive simulations clearly have potential to greatly improve the TAVR development process. As such simulations must start with accurate material models, we have developed a novel time-evolving constitutive model for pericardial xenograft tissue biomaterials (XTB) utilized in BHV (doi: 10.1016/j.jmbbm.2017.07.013). This model was able to simulate the observed tissue plasticity effects that occur in approximately in the first two years of in vivo function (50 million cycles). In the present work, we implemented this model into a complete simulation pipeline to predict the BHV time evolving geometry to 50 million cycles. The pipeline was implemented within an isogeometric finite element formulation that directly integrated our established BHV NURBS-based geometry (doi: 10.1007/s00466-015-1166-x). Simulations of successive loading cycles indicated continual changes in leaflet shape, as indicated by spatially varying increases in leaflet curvature. While the simulation model assumed an initial uniform fiber orientation distribution, anisotropic regional changes in leaflet tissue plastic strain induced a complex changes in regional fiber orientation. We have previously noted in our time-evolving constitutive model that the increases in collagen fiber recruitment with cyclic loading placed an upper bound on plastic strain levels. This effect was manifested by restricting further changes in leaflet geometry past 50 million cycles. Such phenomena was accurately captured in the valve-level simulations due to the use of a tissue-level structural-based modeling approach. Changes in basic leaflet dimensions agreed well with extant experimental studies. As a whole, the results of the present study indicate the complexity of BHV responses to cyclic loading, including changes in leaflet shape and internal fibrous structure. It should be noted that the later effect also influences changes in local mechanical behavior (i.e. changes in leaflet anisotropic tissue stress-strain relationship) due to internal fibrous structure resulting from plastic strains. Such mechanism-based simulations can help pave the way towards the application of sophisticated simulation technologies in the development of replacement heart valve technology.

Keywords: Bioprosthetic heart valve; Simulation; Soft tissue mechanics; Time evolving properties.

Figure 1:

A) The 3D unloaded geometry of a BHV leaflet before and after cyclic loading, with the color indicating the local root mean squared curvature. The most significant change in geometry is in the belly region. B) BHV leaflet collagen fiber architecture, showing that the collagen fiber architecture is convected by the dimensional changes. The grayscale scale bar shows the orientation index (OI), which is the proportional to the angle containing 50 % of fibers. The lack of changes in the OI suggests that minimal damage to the collagen fiber architecture has occurred.

Figure 2:

We speculate that the effects of cyclic loading on BHVs can be divided into three stages: early, intermediate and late. Figure reproduced from [38]

Figure 3:

The framework for using the effective constitutive model to improve the efficiency of using complex meso- or multi-scale models (micro-models) in numerical simulations. Here, A) effective constitutive models act as an intermediate step between micro-models and numerical simulations, where micro-models inform the changes to the effective constitutive model, and the effective constitutive model is then used for the FE simulation. B) An example of how this may be implemented for a time-evolving simulation is shown.

Figure 4:

The inter–ensemble interactions can be separated into rotational and extensional effects. Figure reproduced from [38].

Figure 5:

Illustration of the permanent set effect under cyclic uniaxial loading showing A) the relation between the reference configurations during cyclic loading. Figure reproduced from [38], B) the transfer of mass fraction of the EXL matrix to the loaded configuration Ω(s) from the original state Ω₀ and C) the resulting in changes in the unloaded geometry of the tissue.

Figure 6:

Flowchart explaining the execution of the different components of the time dependent simulation framework.

Figure 7:

Flowchart explaining how the geometry is updated

Figure 8:

(a) Arrows representing circumferential direction in the leaflet, (b) Arrows representing radial direction in the leaflet, (c) Circumferential stretch in uncycled, fully loaded state, referenced to the uncycled, unloaded configuration, (d) Radial stretch in uncycled, fully loaded state, referenced to the uncycled, unloaded configuration, (e) Circumferential stretch in cycled, fully loaded state, referenced to cycled, unloaded state, (f) Radial stretch in cycled, fully loaded state, referenced to cycled, unloaded state. Note that by 50 million cycles, the circumferential and radial stretches have been substantially reduced due to the effects of plastic deformation.

Figure 9:

Time evolution of the circumferential plastic stretch in unloaded state. Here, the plasticity effects were highest in the belly region and the free edge.

Figure 10:

Time evolution of the radial plastic stretch in unloaded state. Plasticity was highest in the belly region.

Figure 11:

Time evolution of the plasticity-induced shear angle α in unloaded state. Shear angle magnitudes were highest near the leaflet attachments.

Figure 12:

Time evolution of the Mean curvature in unloaded state. Curvature was highest in the belly region and the center of the free egde.

Figure 13:

Time evolution of the collagen fiber Normalized Orientation Index in unloaded state. Significant plasticity-induced collagen fiber reorientation occurred near the belly region and the free edge. Note that these changes were not associated with any damage mechanisms

Figure 14:

Time evolution effects on the S_cc in the fully loaded state. The high circumferential stress regions were the same as the regions with highest plasticity in the circumferential direction: the belly region and the free edge. These changes are a coupled results of both the changes in leaflet geometry and tissue properties with cyclic loading.

Figure 15:

Time evolution effects on the S_cc in the fully loaded state. The high circumferential stress regions were the same as the regions with highest plasticity in the radial direction: the lateral portions of the belly region. These changes are a coupled results of both the changes in leaflet geometry and tissue properties with cyclic loading.

Figure 16:

A) BHV leaflet with a few key locations highlighted B) Triple point height in the unloaded configuration showing decay with time C) Plastic stretch in circumferential and radial directions with time at the marked locations in the BHV leaflet. Most of the dimensional changes occur in the first 20–30 million cycles. D) Peak stretch in the current loaded configuration with reference to the current unloaded configuration with time at a few key locations in the BHV leaflet. The reduction in peak stretches demonstrates significant stiffening in the BHV leaflet.

Figure 17:

The fully loaded state of the single cycle simulations of intact tri-leaflet valves with the collagen fiber architecture of A) a uniform collagen fiber orientation distribution, B) exogenously cross-linked bovine pericardium valve, and C) the native porcine aortic valve. A) and B) result in mostly homogeneous stress distributions with A) showing stress concentrations are the commissure regions, while C) results in a very heterogeneous stress distribution and the belly region caving in. The top row shows the side view of the valves at 80 mmHg and the bottom row shows the top-down view.

Figure 18:

BHV fatigue as a multiscale process