A Mesh-Free Approach to Incorporate Complex Anisotropic and Heterogeneous Material Properties into Eye-Specific Finite Element Models.

Commercial finite element modeling packages do not have the tools necessary to effectively incorporate the complex anisotropic and heterogeneous material properties typical of the biological tissues of the eye. We propose a mesh-free approach to incorporate realistic material properties into finite element models of individual human eyes. The method is based on the idea that material parameters can be estimated or measured at so called control points, which are arbitrary and independent of the finite element mesh. The mesh-free approach approximates the heterogeneous material parameters at the Gauss points of each finite element while the boundary value problem is solved using the standard finite element method. The proposed method was applied to an eye-specific model a human posterior pole and optic nerve head. We demonstrate that the method can be used to effectively incorporate experimental measurements of the lamina cribrosa micro-structure into the eye-specific model. It was convenient to define characteristic material orientations at the anterior and posterior scleral surface based on the eye-specific geometry of each sclera. The mesh-free approach was effective in approximating these characteristic material directions with smooth transitions across the sclera. For the first time, the method enabled the incorporation of the complex collagen architecture of the peripapillary sclera into an eye-specific model including the recently discovered meridional fibers at the anterior surface and the depth dependent width of circumferential fibers around the scleral canal. The model results suggest that disregarding the meridional fiber region may lead to an underestimation of local strain concentrations in the retina. The proposed approach should simplify future studies that aim to investigate collagen remodeling in the sclera and optic nerve head or in other biological tissues with similar challenges.

Stent and leaflet stresses in a 26-mm first-generation balloon-expandable transcatheter aortic valve.

OBJECTIVE: Transcatheter aortic valve replacement is established therapy for high-risk and inoperable patients with severe aortic stenosis, but questions remain regarding long-term durability. Valve design influences durability. Increased leaflet stresses in surgical bioprostheses have been correlated with degeneration; however, transcatheter valve leaflet stresses are unknown. From 2007 to 2014, a majority of US patients received first-generation balloon-expandable transcatheter valves. Our goal was to determine stent and leaflet stresses in this valve design using finite element analyses. METHODS: A 26-mm Sapien Transcatheter Heart Valve (Edwards Lifesciences, Inc, Irvine, Calif) underwent high-resolution microcomputed tomography scanning to develop precise 3-dimensional geometry of the leaflets, the stent, and the polyethylene terephthalate elements. The stent was modeled using 3-dimensional elements and the leaflets were modeled using shell elements. Stent material properties were based on stainless steel, whereas those for leaflets were obtained from surgical bioprostheses. Noncylindrical Sapien valve geometry was also simulated. Pressure loading to 80 mm Hg and 120 mm Hg was performed using ABAQUS finite element software (Dassault Systèmes, Waltham, Mass). RESULTS: At 80 mm Hg, maximum principal stresses on Sapien leaflets were 1.31 megaspascals (MPa). Peak leaflet stress was observed at commissural tips where leaflets connected to the stent. Maximum principal stresses for the stent were 188.91 MPa and located at stent tips where leaflet commissures were attached. Noncylindrical geometry increased peak principal leaflet stresses by 16%. CONCLUSIONS: Using exact geometry from high-resolution scans, the 26-mm Sapien Transcatheter Heart Valve showed that peak stresses for both stent and leaflets were present at commissural tips where leaflets were attached. These regions would be prone to leaflet degeneration. Understanding stresses in first-generation transcatheter valves allows comparison to future designs for relative durability.

Stent and Leaflet Stresses in 29-mm Second-Generation Balloon-Expandable Transcatheter Aortic Valve.

BACKGROUND: Equipoise of transcatheter aortic valve replacement with surgical aortic valve replacement in intermediate-risk patients has been demonstrated. As transcatheter aortic valve replacement usage expands, questions regarding long-term durability become paramount. Valve design impacts durability with regions of increased leaflet stress being vulnerable to early failure. However, transcatheter aortic valve (TAV) leaflet stresses are unknown. The objective of this study was to determine stent and leaflet stresses of second-generation balloon-expandable TAV. METHODS: Commercial 29-mm Edwards Sapien XT (Edwards Lifesciences, Irvine, CA) valves underwent high-resolution microcomputed tomography scanning to develop precise three-dimensional geometric mesh. Compressed and uncompressed TAVs were modeled under systemic pressure using finite element software. Material properties of stent were based on cobalt-chromium, whereas those for leaflets were obtained from surgical bioprostheses. RESULTS: Maximum and minimum principal stresses on uncompressed Sapien XT TAV were 1.63 MPa and -0.36 MPa on leaflets and 93.3 MPa and -105.6 MPa on stent at diastolic pressure. Peak leaflet stress was observed at commissural tips where leaflets connected to the stent. For compressed TAV to 26 mm, maximum and minimum principal stresses were 1.55 MPa and -0.63 MPa on leaflets and 526.1 MPa and -902.2 MPa on stent at diastolic pressure. Peak leaflet stress was located at similar position and also along the suture line with the Dacron (C. R. Bard, Haverhill, PA). CONCLUSIONS: Stress analysis of two extreme deployed geometries of 29-mm Edwards Sapien XT using exact geometry from high-resolution scans demonstrated that peak stresses for TAV leaflets were present at commissural tips where leaflets were attached. These regions would be mostly likely to initiate degeneration.

Biomechanics of Failed Pulmonary Autografts Compared to Native Aortic Roots.

BACKGROUND: Progressive autograft dilatation after a Ross operation suggests that remodeling does not effectively reproduce native aortic root biomechanics. In the first of this two-part series, we compared mechanical properties of explanted autografts to pulmonary roots at pulmonary pressures. The goal of this study was to compare mechanical properties of explanted autografts to native aortic roots at systemic pressures. METHODS: Autograft specimens were obtained from patients undergoing reoperation after Ross operation. For comparison, native aortic roots were obtained from unused donor hearts. Biaxial stretch testing was performed to determine tissue mechanical properties. Tissue stiffness was determined at patient-specific physiologic stresses corresponding to systemic pressures (80 and 120 mm Hg) and hypertensive state (200 mm Hg). RESULTS: Nonlinear stress-strain curves were present for both failed autografts and native aortic roots. Explanted autografts were significantly more compliant than native aortic roots at 80 mm Hg (1.53 ± 0.68 versus 2.99 ± 1.34 MPa; p = 0.011), 120 mm Hg (2.54 ± 1.18 versus 4.93 ± 2.21 MPa; p = 0.013), and 200 mm Hg (4.79 ± 2.30 versus 9.21 ± 4.16 MPa; p = 0.015). Autograft tissue stiffness at 80, 120, and 200 mm Hg was not correlated with age at the time of Ross operation (p = 0.666, p = 0.639, and p = 0.616, respectively) or time in the systemic circulation (p = 0.635, p = 0.637, and p = 0.647, respectively). CONCLUSIONS: Failed pulmonary autografts retained a nonlinear response to mechanical loading typical of healthy arterial tissue. Despite similar wall thickness between autografts and aorta, autograft stiffness in this patient population was significantly reduced compared with native aortic roots. We demonstrated that biomechanical remodeling was inadequate in these specimens to achieve native aortic mechanical properties, which may have resulted in progressive autograft root dilatation.

Biomechanics of Failed Pulmonary Autografts Compared With Normal Pulmonary Roots.

BACKGROUND: Progressive dilatation of pulmonary autografts after the Ross operation may reflect inadequate remodeling of the native pulmonary root to adapt to systemic circulation. Understanding the biomechanics of autograft root dilatation may aid designing strategies to prevent dilatation. We have previously characterized normal human pulmonary root material properties; however, the mechanical properties of failed autografts are unknown. In this study, failed autograft roots explanted during reoperation were acquired, and their material properties were determined. METHODS: Failed pulmonary autograft specimens were obtained from patients undergoing reoperation after the Ross operation. Fresh human native pulmonary roots were obtained from the transplant donor network as controls. Biaxial stretch testing was performed to determine tissue mechanical properties. Tissue stiffness was determined at patient-specific physiologic stresses at pulmonary pressures. RESULTS: Nonlinear stress-strain response was present in both failed autografts and normal pulmonary roots. Explanted pulmonary autografts were less stiff than were their native pulmonary root counterparts at 8 mm Hg (134 ± 42 vs 175 ± 49 kPa, respectively) (p = 0.086) and 25 mm Hg (369 ± 105 vs 919 ± 353 kPa, respectively) (p = 0.006). Autograft wall stiffness at both 8 and 25 mm Hg was not correlated with age at the Ross procedure (p = 0.898 and p = 0.813, respectively) or with time in the systemic circulation (p = 0.609 and p = 0.702, respectively). CONCLUSIONS: Failed pulmonary autografts retained nonlinear response to mechanical loading typical of healthy human arterial tissue. Remodeling increased wall thickness but decreased wall stiffness in failed autografts. Increased compliance may explain progressive autograft root dilatation in autograft failures.

Ascending thoracic aortic aneurysm wall stress analysis using patient-specific finite element modeling of in vivo magnetic resonance imaging.

OBJECTIVES: Rupture/dissection of ascending thoracic aortic aneurysms (aTAAs) carries high mortality and occurs in many patients who did not meet size criteria for elective surgery. Elevated wall stress may better predict adverse events, but cannot be directly measured in vivo, rather determined from finite element (FE) simulations. Current computational models make assumptions that limit accuracy, most commonly using in vivo imaging geometry to represent zero-pressure state. Accurate patient-specific wall stress requires models with zero-pressure three-dimensional geometry, material properties, wall thickness and residual stress. We hypothesized that wall stress calculated from in vivo imaging geometry at systemic pressure underestimates that using zero-pressure geometry. We developed a novel method to derive zero-pressure geometry from in vivo imaging at systemic pressure. The purpose of this study was to develop the first patient-specific aTAA models using magnetic resonance imaging (MRI) to assess material properties and zero-pressure geometry. Wall stress results from FE models using systemic pressure were compared with those from models using zero-pressure correction. METHODS: Patients with aTAAs <5 cm underwent ECG-gated computed tomography angiography (CTA) and displacement encoding with stimulated echo (DENSE)-MRI. CTA lumen geometry was used to create surface contour meshes of aTAA geometry. DENSE-MRI measured cyclic aortic wall strain from which wall material property was derived. Zero- and systemic pressure geometries were created. Simulations were loaded to systemic pressure using the ABAQUS FE software. Wall stress analyses were compared between zero-pressure-corrected and systemic pressure geometry FE models. RESULTS: Peak first principal wall stress (primarily aligned in the circumferential direction) at systolic pressure for the zero-pressure correction models was 430.62 ± 69.69 kPa, whereas that without zero-pressure correction was 312.55 ± 39.65 kPa (P = 0.004). Peak second principal wall stress (primarily aligned in the longitudinal direction) at systolic pressure for the zero-pressure correction models was 200.77 ± 43.13 kPa, whereas that without zero-stress correction was 156.25 ± 25.55 kPa (P = 0.02). CONCLUSIONS: Previous FE aTAA models from in vivo CT and MRI have not accounted for zero-pressure geometry or patient-specific material property. We demonstrated that zero-pressure correction significantly impacts wall stress results. Future computational models that use wall stress to predict aTAA adverse events must take into account zero-pressure geometry and patient material property for accurate wall stress determination.