Influence of Material Parameter Variability on the Predicted Coronary Artery Biomechanical Environment via Uncertainty Quantification.

Central to the clinical adoption of patient-specific modeling strategies is demonstrating that simulation results are reliable and safe. Indeed, simulation frameworks must be robust to uncertainty in model input(s), and levels of confidence should accompany results. In this study, we applied a coupled uncertainty quantification-finite element (FE) framework to understand the impact of uncertainty in vascular material properties on variability in predicted stresses. Univariate probability distributions were fit to material parameters derived from layer-specific mechanical behavior testing of human coronary tissue. Parameters were assumed to be probabilistically independent, allowing for efficient parameter ensemble sampling. In an idealized coronary artery geometry, a forward FE model for each parameter ensemble was created to predict tissue stresses under physiologic loading. An emulator was constructed within the UncertainSCI software using polynomial chaos techniques, and statistics and sensitivities were directly computed. Results demonstrated that material parameter uncertainty propagates to variability in predicted stresses across the vessel wall, with the largest dispersions in stress within the adventitial layer. Variability in stress was most sensitive to uncertainties in the anisotropic component of the strain energy function. Moreover, unary and binary interactions within the adventitial layer were the main contributors to stress variance, and the leading factor in stress variability was uncertainty in the stress-like material parameter that describes the contribution of the embedded fibers to the overall artery stiffness. Results from a patient-specific coronary model confirmed many of these findings. Collectively, these data highlight the impact of material property variation on uncertainty in predicted artery stresses and present a pipeline to explore and characterize forward model uncertainty in computational biomechanics.

Influence of material parameter variability on the predicted coronary artery biomechanical environment via uncertainty quantification.

Central to the clinical adoption of patient-specific modeling strategies is demonstrating that simulation results are reliable and safe. Indeed, simulation frameworks must be robust to uncertainty in model input(s), and levels of confidence should accompany results. In this study, we applied a coupled uncertainty quantification-finite element (FE) framework to understand the impact of uncertainty in vascular material properties on variability in predicted stresses. Univariate probability distributions were fit to material parameters derived from layer-specific mechanical behavior testing of human coronary tissue. Parameters were assumed to be probabilistically independent, allowing for efficient parameter ensemble sampling. In an idealized coronary artery geometry, a forward FE model for each parameter ensemble was created to predict tissue stresses under physiologic loading. An emulator was constructed within the UncertainSCI software using polynomial chaos techniques, and statistics and sensitivities were directly computed. Results demonstrated that material parameter uncertainty propagates to variability in predicted stresses across the vessel wall, with the largest dispersions in stress within the adventitial layer. Variability in stress was most sensitive to uncertainties in the anisotropic component of the strain energy function. Moreover, unary and binary interactions within the adventitial layer were the main contributors to stress variance, and the leading factor in stress variability was uncertainty in the stress-like material parameter that describes the contribution of the embedded fibers to the overall artery stiffness. Results from a patient-specific coronary model confirmed many of these findings. Collectively, these data highlight the impact of material property variation on uncertainty in predicted artery stresses and present a pipeline to explore and characterize forward model uncertainty in computational biomechanics.

Implantation of a capsular tension ring during cataract surgery attenuates predicted remodeling of the post-surgical lens capsule along the visual axis.

Introduction: Cataract surgery permanently alters the mechanical environment of the lens capsule by placing a hole in the anterior portion and implanting an intraocular lens (IOL) that has a very different geometry from the native lens. We hypothesized that implant configuration and mechanical interactions with the post-surgical lens capsule play a key role in determining long-term fibrotic remodeling. Methods: We developed the first finite element-growth and remodeling (FE-G&R) model of the post-surgical lens capsule to evaluate how implantation of an IOL with and without a capsular tension ring (CTR) impacted evolving lens capsule mechanics and associated fibrosis over time after cataract surgery. Results: Our models predicted that implantation of a CTR with the IOL into the post-surgical lens capsule reduced the mechanical perturbation, thickening, and stiffening along the visual axis in both the remnant anterior and posterior portions compared to implantation of the IOL alone. Discussion: These findings align with patient studies and suggest that implantation of a CTR with the IOL during routine cataract surgery would attenuate the incidence of visually-debilitating capsule fibrosis. Our work demonstrates that use of such modeling techniques has substantial potential to aid in the design of better surgical strategies and implants.

Considerations for analysis of endothelial shear stress and strain in FSI models of atherosclerosis.

Atherosclerosis is a lipid driven chronic inflammatory disease that is characterized by the formation of plaques at predilection sites. These predilection sites (side branches, curved segments, and bifurcations) have often been associated with disturbed shear stress profiles. However, in addition to shear stress, endothelial cells also experience artery wall strain that could contribute to atherosclerosis progression. Herein, we describe a method to accurately obtain these shear stress and strain profiles. We developed a fluid-structure interaction (FSI) framework for modelling arteries within a commercially available package (Abaqus, version 6.14) that included known prestresses (circumferential, axial and pressure associated). In addition, we co-registered 3D histology to a micro-CT-derived 3D reconstruction of an atherosclerotic carotid artery from a cholesterol-fed ApoE-/- mouse to include the spatial distribution of lipids within a subject-specific model. The FSI model also incorporated a nonlinear hyperelastic material model with regionally-varying properties that distinguished between healthy vessel wall and plaque. FSI predicted a lower shear stress than CFD (~-12%), but further decreases in plaque regions with softer properties (~-24%) were dependent on the approach used to implement the prestresses in the artery wall. When implemented with our new hybrid approach (zero prestresses in regions of lipid deposition), there was significant heterogeneity in endothelial shear stress in the atherosclerotic artery due to variations in stiffness and, in turn, wall strain. In conclusion, when obtaining endothelial shear stress and strain in diseased arteries, a careful consideration of prestresses is necessary. This paper offers a way to implement them.

Altered stress field of the human lens capsule after cataract surgery.

The lens capsule of the eye is important in focusing light onto the retina during the process of accommodation and, in later life, housing a prosthetic lens implanted during cataract surgery. Though considerable modeling work has characterized the mechanics of accommodation, little has been done to understand the mechanics of the lens capsule after cataract surgery. As such, we present the first 3-D finite element model of the post-surgical human lens capsule with an implanted tension ring and, separately, an intraocular lens to characterize the altered stress field compared to that in a model of the native lens capsule. All finite element models employed a Holzapfel hyperelastic constitutive model with regional variations in anisotropy. The post-surgical lens capsule demonstrated a dramatic perturbation to the stress field with mostly large reductions in stresses (except at the equator where the implant contacts the capsule) compared to native, wherein maximal changes in Cauchy stress were -100% and -145% for the tension ring and intraocular lens, respectively. However, implantation of the tension ring produced a more uniform stress field compared to the IOL. The magnitudes and distribution of the perturbed stress field may be an important driver of the fibrotic response of inhabiting lens epithelial cells and associated lens capsule remodeling after cataract surgery. Thus, the mechanical effects of an implant on the lens capsule could be an essential consideration in the design of intraocular lenses, particularly those with an accommodative feature.