For native and engineered biological tissues, there exist many physiological, surgical, and medical device applications where multiaxial material characterization and modeling is required. Because biological tissues and many biocompatible elastomers are incompressible, planar biaxial testing allows for a two-dimensional (2-D) stress-state that can be used to fully characterize their three-dimensional (3-D) mechanical properties. Biological tissues exhibit complex mechanical behaviors not easily accounted for in classic elastomeric constitutive models. Accounting for these behaviors by careful experimental evaluation and formulation of constitutive models continues to be a challenging area in biomechanical modeling and simulation. The focus of this review is to describe the application of multiaxial testing techniques to soft tissues and their relation to modern biomechanical constitutive theories.

Structural finite-element analysis (FEA) has been widely used to study the biomechanics of human tissues and organs, as well as tissue–medical device interactions, and treatment strategies. However, patient-specific FEA models usually require complex procedures to set up and long computing times to obtain final simulation results, preventing prompt feedback to clinicians in time-sensitive clinical applications. In this study, by using machine learning techniques, we developed a deep learning (DL) model to directly estimate the stress distributions of the aorta. The DL model was designed and trained to take the input of FEA and directly output the aortic wall stress distributions, bypassing the FEA calculation process. The trained DL model is capable of predicting the stress distributions with average errors of 0.492% and 0.891% in the Von Mises stress distribution and peak Von Mises stress, respectively. This study marks, to our knowledge, the first study that demonstrates the feasibility and great potential of using the DL technique as a fast and accurate surrogate of FEA for stress analysis.

For more than 40 years, the replacement of diseased natural heart valves with prosthetic devices has dramatically extended the quality and length of the lives of millions of patients worldwide. However, bioprosthetic heart valves (BHV) continue to fail due to structural failure resulting from poor tissue durability and faulty design. Clearly, an in-depth understanding of the biomechanical behavior of BHV at both the tissue and functional prosthesis levels is essential to improving BHV design and to reduce rates of failure. In this study, we simulated quasi-static BHV leaflet deformation under 40, 80, and 120 mm Hg quasi-static transvalvular pressures. A Fung-elastic material model was used that incorporated material parameters and axes derived from actual leaflet biaxial tests and measured leaflet collagen fiber structure. Rigorous experimental validation of predicted leaflet strain field was used to validate the model results. An overall maximum discrepancy of 2.36% strain between the finite element (FE) results and experiment measurements was obtained, indicating good agreement between computed and measured major principal strains. Parametric studies utilizing the material parameter set from one leaflet for all three leaflets resulted in substantial variations in leaflet stress and strain distributions. This result suggests that utilization of actual leaflet material properties is essential for accurate BHV FE simulations. The present study also underscores the need for rigorous experimentation and accurate constitutive models in simulating BHV function and design.

The objective of this study was to develop a patient-specific finite element (FE) model of a human mitral valve. The geometry of the mitral valve was reconstructed from multi-slice computed tomography (MSCT) scans at middle diastole with distinguishable mitral leaflet thickness, chordal origins, chordal insertion points, and papillary muscle locations. Mitral annulus and papillary muscle dynamic motions were also quantified from MSCT scans and prescribed as boundary conditions for the FE simulation. Material properties of the human mitral leaflet tissues were obtained from biaxial tests and characterized by an anisotropic hyperelastic material model. In vivo dynamic closing of the mitral valve was simulated. The closed shape of the mitral valve output from the simulation was similar to the mitral valve geometry reconstructed from MSCT images at middle systole. Forces from the anterolateral and posteromedial papillary muscle groups at middle systole were 4.51 N and 5.17 N, respectively. The average maximum principal stress of the midsection of the anterior mitral leaflet was approximately 160 kPa at the systolic peak. Results demonstrated that the developed FE model could closely replicate in vivo mitral valve dynamic motion during middle diastole and systole. This model may serve as a basis for utilizing computational simulations to obtain a better understanding of mitral valve mechanics, disease and surgical repair.

Geometric features of the aorta are linked to patient risk of rupture in the clinical decision to electively repair an ascending aortic aneurysm (AsAA). Previous approaches have focused on relationship between intuitive geometric features (e.g. diameter and curvature) and wall stress. This work investigates the feasibility of a machine learning approach to establish the linkages between shape features and FEA predicted AsAA rupture risk, and it may serve as a faster surrogate for FEA associated with long simulation time and numerical convergence issues. This method consists of four main steps: (1) constructing a statistical shape model (SSM) from clinical 3D CT images of AsAA patients; (2) generating a dataset of representative aneurysm shapes and obtaining FEA predicted risk scores defined as systolic pressure divided by rupture pressure (rupture is determined by a threshold criterion); (3) establishing relationship between shape features and risk by using classifiers and regressors; and (4) evaluating such relationship in cross validation. The results show that SSM parameters can be used as strong shape features to make predictions of risk scores consistent with FEA, which lead to an average risk classification accuracy of 95.58% by using support vector machine and an average regression error of 0.0332 by using support vector regression, while intuitive geometric features have relatively weak performance. Compared to FEA, this machine learning approach is magnitudes faster. In our future studies, material properties and inhomogeneous thickness will be incorporated into the models and learning algorithms, which may lead to a practical system for clinical applications.

Evaluation and simulation of the multiaxial mechanical behavior of native and engineered soft tissues is becoming more prevalent. In spite of this growing use, testing methods have not been standardized and methodologies vary widely. The strong influence of boundary conditions were recently underscored by Waldman et al. [2002, J. Materials Science: Materials in Medicine 13, pp. 933-938] wherein substantially different experimental results were obtained using different sample gripping methods on the same specimens. As it is not possible to experimentally evaluate the effects of different biaxial test boundary conditions on specimen internal stress distributions, we conducted numerical simulations to explore these effects. A nonlinear Fung-elastic constitutive model (Sun et al., 2003, JBME 125, pp. 372-380, which fully incorporated the effects of in-plane shear, was used to simulate soft tissue mechanical behavior. Effects of boundary conditions, including varying the number of suture attachments, different gripping methods, specimen shapes, and material axes orientations were examined. Results demonstrated strong boundary effects with the clamped methods, while suture attachment methods demonstrated minimal boundary effects. Suture-based methods appeared to be best suited for biaxial mechanical tests of biological materials. Moreover, the simulations demonstrated that Saint-Venant's effects depended significantly on the material axes orientation. While not exhaustive, these comprehensive simulations provide experimentalists with additional insight into the stress-strain fields associated with different biaxial testing boundary conditions, and may be used as a rational basis for the design of biaxial testing experiments.

The objective of this study was to develop a patient-specific computational model to quantify the biomechanical interaction between the transcatheter aortic valve (TAV) stent and the stenotic aortic valve during TAV intervention. Finite element models of a patient-specific stenotic aortic valve were reconstructed from multi-slice computed tomography (MSCT) scans, and TAV stent deployment into the aortic root was simulated. Three initial aortic root geometries of this patient were analyzed: (a) aortic root geometry directly reconstructed from MSCT scans, (b) aortic root geometry at the rapid right ventricle pacing phase, and (c) aortic root geometry with surrounding myocardial tissue. The simulation results demonstrated that stress, strain, and contact forces of the aortic root model directly reconstructed from MSCT scans were significantly lower than those of the model at the rapid ventricular pacing phase. Moreover, the presence of surrounding myocardium slightly increased the mechanical responses. Peak stresses and strains were observed around the calcified regions in the leaflets, suggesting the calcified leaflets helped secure the stent in position. In addition, these elevated stresses induced during TAV stent deployment indicated a possibility of tissue tearing and breakdown of calcium deposits, which might lead to an increased risk of stroke. The potential of paravalvular leak and occlusion of coronary ostia can be evaluated from simulated post-deployment aortic root geometries. The developed computational models could be a valuable tool for pre-operative planning of TAV intervention and facilitate next generation TAV device design.

Objectives Studies have shown that patients harboring bicuspid aortic valve (BAV) or bovine aortic arch (BAA) are more likely to develop ascending aortic aneurysm (AsAA) than the general population. A thorough quantification of the AsAA tissue properties for these patient groups may offer insight into the underlying mechanisms of AsAA development in these patients. Thus, the objective of this study was to investigate and compare the mechanical and microstructural properties of aortic tissues from AsAA patients with and without concomitant BAV or BAA. Materials and methods AsAA (n = 20), BAV (n = 20) and BAA (n = 15) human tissues were obtained from patients who underwent elective AsAA surgery. Planar biaxial and uniaxial failure tests were used to characterize the mechanical and failure properties of the tissues, respectively. Histological analysis was performed to detect the medial degenerative characteristics of aortic aneurysm. Individual layer thickness and composition were quantified for each patient group. Results The circumferential (CIRC) response of the BAV samples was stiffer than both AsAA (p = 0.473) and BAA (p = 0.152) tissues at low load. The BAV tissues were nearly isotropic while AsAA and BAA tissues were anisotropic. The areal strain of BAV samples were significantly less than AsAA (p = 0.041) and BAA (p = 0.004) tissues at a low load. The BAA samples were similar to the AsAA samples in both mechanical and failure properties. On the microstructural level, all samples displayed moderate medial degeneration characterized by elastin fragmentation, cell loss, mucoid accumulation and fibrosis. The ultimate tensile strength of BAV and BAA tissues were also found to decrease with age. Conclusions The BAV tissues were stiffer than both AsAA and BAA tissues, and the BAA tissues were similar to the AsAA tissues. The BAV samples were thinnest with less elastin than AsAA and BAA samples, which may attribute to the loss of extensibility at low load of these tissues. No apparent difference in failure mechanics among the tissue groups suggests that each of the patient groups may have a similar risk of rupture.