Kewei Li

Simulated elliptical bioprosthetic valve deformation: Implications for asymmetric transcatheter valve deployment

The asymmetric, elliptical shape of a transcatheter aortic valve (TAV), after implantation into a calcified aortic root, has been clinically observed. However, the impact of elliptical TAV configuration on TAV leaflet stress and strain distribution and valve regurgitation is largely unknown. In this study, we developed computational models of elliptical TAVs based on a thin pericardial bioprosthetic valve model recently developed. Finite element and computational fluid dynamics simulations were performed to investigate TAV leaflet structural deformation and central backflow leakage, and compared with those of a nominal symmetric TAV. From the results, we found that for a distorted TAV with an elliptical eccentricity of 0.68, the peak stress increased significantly by 143% compared with the nominal circular TAV. When the eccentricity of an elliptical TAV was larger than 0.5, a central backflow leakage was likely to occur. Also, deployment of a TAV with a major calcified region perpendicular to leaflet coaptation line was likely to cause a larger valve leakage. In conclusion, the computational models of elliptical TAVs developed in this study could improve our understanding of the biomechanics involved in a TAV with an elliptical configuration and facilitate optimal design of next-generation TAV devices.

Simulated Transcatheter Aortic Valve Deformation: A Parametric Study on the Impact of Leaflet Geometry on Valve Peak Stress

In this study, we developed a computational framework to investigate the impact of leaflet geometry of a transcatheter aortic valve (TAV) on the leaflet stress distribution, aiming at optimizing TAV leaflet design to reduce its peak stress. Utilizing a generic TAV model developed previously [Li and Sun, Annals of Biomedical Engineering, 2010. 38(8): 2690-2701], we first parameterized the 2D leaflet geometry by mathematical equations, then by perturbing the parameters of the equations, we could automatically generate a new leaflet design, remesh the 2D leaflet model and build a 3D leaflet model from the 2D design via a Python script. Approximately 500 different leaflet designs were investigated by simulating TAV closure under the nominal circular deployment and physiological loading conditions. From the simulation results, we identified a new leaflet design that could reduce the previously reported valve peak stress by about 5%. The parametric analysis also revealed that increasing the free edge width had the highest overall impact on decreasing the peak stress. A similar computational analysis was further performed for a TAV deployed in an abnormal, asymmetric elliptical configuration. We found that a minimal free edge height of 0.46 mm should be adopted to prevent central backflow leakage. This increase of the free edge height resulted in an increase of the leaflet peak stress. Furthermore, the parametric study revealed a complex response surface for the impact of the leaflet geometric parameters on the peak stress, underscoring the importance of performing a numerical optimization to obtain the optimal TAV leaflet design. Copyright

An exponential constitutive model excluding fibres under compression: Application to extension–inflation of a residually stressed carotid artery

Detailed information on the three-dimensional dispersion of collagen fibres within layers of healthy and diseased soft biological tissues has been reported recently. Previously we have proposed a constitutive model for soft fibrous solids based on the angular integration approach which allows the exclusion of any compressed collagen fibre within the dispersion. In addition, a computational implementation of that model in a general purpose finite element program has been investigated and verified with the standard fibre-reinforcing model for fibre contributions. In this study, we develop the proposed fibre dispersion model further using an exponential form of the strain-energy function for the fibre contributions. The finite element implementation of this model with a rotationally symmetrical dispersion of fibres is also presented. This includes explicit expressions for the stress and elasticity tensors. The performance and implementation of the new model are demonstrated by means of a uniaxial extension test, a simple shear test, and an extension–inflation simulation of a residually stressed carotid artery segment. In each example we have obtained good agreement between the finite element solution and the analytical or experimental results.

Characterization of biomechanical properties of aged human and ovine mitral valve chordae tendineae.

The mitral valve (MV) is a highly complex cardiac valve consisting of an annulus, anterior and posterior leaflets, chordae tendineae (chords) and two papillary muscles. The chordae tendineae mechanics play a pivotal role in proper MV function: the chords help maintain proper leaflet coaptation and rupture of the chordae tendineae due to disease or aging can lead to mitral valve insufficiency. Therefore, the aim of this study was to characterize the mechanical properties of aged human and ovine mitral chordae tendineae. The human and ovine chordal specimens were categorized by insertion location (i.e., marginal, basal and strut) and leaflet type (i.e., anterior and posterior). The results show that human and ovine chords of differing types vary largely in size but do not have significantly different elastic and failure properties. The excess fibrous tissue layers surrounding the central core of human chords added thickness to the chords but did not contribute to the overall strength of the chords. In general, the thinner marginal chords were stiffer than the thicker basal and strut chords, and the anterior chords were stiffer and weaker than the posterior chords. The human chords of all types were significantly stiffer than the corresponding ovine chords and exhibited much lower failure strains. These findings can be explained by the diminished crimp pattern of collagen fibers of the human mitral chords observed histologically. Moreover, the mechanical testing data was modeled with the nonlinear hyperelastic Ogden strain energy function to facilitate accurate computational modeling of the human MV.

A discrete fibre dispersion method for excluding fibres under compression in the modelling of fibrous tissues

Recently, micro-sphere-based methods derived from the angular integration approach have been used for excluding fibres under compression in the modelling of soft biological tissues. However, recent studies have revealed that many of the widely used numerical integration schemes over the unit sphere are inaccurate for large deformation problems even without excluding fibres under compression. Thus, in this study, we propose a discrete fibre dispersion model based on a systematic method for discretizing a unit hemisphere into a finite number of elementary areas, such as spherical triangles. Over each elementary area, we define a representative fibre direction and a discrete fibre density. Then, the strain energy of all the fibres distributed over each elementary area is approximated based on the deformation of the representative fibre direction weighted by the corresponding discrete fibre density. A summation of fibre contributions over all elementary areas then yields the resultant fibre strain energy. This treatment allows us to exclude fibres under compression in a discrete manner by evaluating the tension–compression status of the representative fibre directions only. We have implemented this model in a finite-element programme and illustrate it with three representative examples, including simple tension and simple shear of a unit cube, and non-homogeneous uniaxial extension of a rectangular strip. The results of all three examples are consistent and accurate compared with the previously developed continuous fibre dispersion model, and that is achieved with a substantial reduction of computational cost.

Quantification of structural compliance of aged human and porcine aortic root tissues

The structural compliance of the aortic root has a significant implication for valve procedures such as transcatheter aortic valve implantation and valve-sparing aortic root replacement. However, a detailed quantification of human aortic root structural compliance, particularly in different regions, has been incomplete. In this study, the structural properties of human aortic roots (81 ± 8.74 years, n = 10) were characterized and compared with those of porcine ones (6-9 months, n = 10) using a vessel pressure-inflation test. The test involved tracking three-dimensional deformation of the markers affixed on the different surface regions of the aortic roots, including the three sinuses: the noncoronary sinus (NCS), the left-coronary sinus (LCS), and the right-coronary sinus (RCS), and at three regions along the longitudinal direction of each sinus: the upper sinus (US), the middle sinus (MS), and the lower sinus (LS), and the ascending aorta (AA) region above the NCS. We found that tissue stiffness in physiological pressure range was similar among the three human sinuses. A variation in regional structural stiffness of human aorta was observed. In the circumferential direction, the LS regions were the stiffest in the LCS and RCS, whereas NCS had relatively uniform stiffness. In the longitudinal direction, the human AA regions were more compliant than all sinuses. There was a significant difference in tissue stiffness between human and porcine aortic tissues, suggesting that the mechanical properties of porcine tissues may not be analogous to aged human ones.

Hemodynamic Impact of Transcatheter Aortic Valve Deployment Configuration

Transcatheter aortic valve (TAV) replacement holds promise for a large number of patients who otherwise have limited or no treatment options. However, it also poses various challenges, due to its unique disease treatment mechanism. Successful TAV deployment and function are heavily reliant on the tissue-stent interaction [1,2]. For patients with aortic stenosis, heavy calcium deposition on the valve leaflets and the aortic root can also cause distortion of TAV geometries, resulting in a valve of an elliptical shape [3–5] instead of a nominal circular shape. In a recent study by Schultz et al. [5], the geometry and apposition of the TAV after implantation in 30 patients with aortic stenosis were evaluated using multislice computed tomography. The results indicated that none of the TAV frames reached exactly nominal designed dimensions. The difference between the orthogonal smallest and largest diameters of TAV cross section at the ventricular end was 4.4 mm, which was clearly an asymmetric elliptical shape [5]. In this study, we sought to develop computational models of valve hemodynamics under clinically relevant deployment scenarios.

Simulated Transcatheter Aortic Valve Flow: Implications of Elliptical Deployment and Under-Expansion at the Aortic Annulus: SIMULATED TRANSCATHETER AORTIC VALVE FLOW

Clinical use of transcatheter aortic valves (TAVs) has been associated with abnormal deployment, including oval deployment and under-expansion when placed into calcified aortic annuli. In this study, we performed an integrated computational and experimental investigation to quantify the impact of abnormal deployment at the aortic annulus on TAV hemodynamics. A size 23 mm generic TAV computational model, developed and published previously, was subjected to elliptical deployment at the annulus with eccentricity levels up to 0.68 and to under-expansion of the TAV at the annulus by up to 25%. The hemodynamic performance was quantified for each TAV deployment configuration. TAV opening geometries were fabricated using stereolithography and then subjected to steady forward flow testing in accordance with ISO-5840. Centerline pressure profiles were compared to validate the computational model. Our findings show that slight ellipticity of the TAV may not lead to degeneration of hydrodynamic performance. However, under large ellipticity, increases in transvalvular pressure gradients were observed. Under-expanded deployment has a much greater negative effect on the TAV hemodynamics compared with elliptical deployment. The maximum turbulent viscous shear stress (TVSS) values were found to be significantly larger in under-expanded TAVs. Although the maximum value of TVSS was not large enough to cause hemolysis in all cases, it may cause platelets activation, especially for under-expanded deployments.

Measuring aortic sinus pressure-inflation response using three dimensional marker tracking

In this study, we investigated the mechanical properties of porcine aortic sinus using a three-dimensional marker measuring technique called the direct linear transformation (DLT) method. By recording pressure-inflation tests of five porcine aortic roots with the use of two cameras simultaneously, we were able to obtain stress and strain responses of aortic sinus upon applied luminal pressures and compare them with previously published planar biaxial results of the same tissue. We found that the roots were stiffer in the circumferential direction for the middle region of the non-coronary sinus for all specimens. The magnitude of stress at 30% strain was higher than that observed using planar biaxial testing.

Quasi-static simulation of mitral valve edge to edge repair

Edge-to-edge repair (ETER) technique alters mitral valve inflow in the diastolic phase and thus the stress distribution on each leaflet, especially the area near sutured edges. In the present study, we performed finite element simulations of ETER mitral valve during the diastolic phase under different pressures. We conducted planar biaxial mechanical testing to obtain the material properties of native mitral leaflets. The test data were characterized by the Fungelastic model. Fung-elastic model with material parameters from experiments was implemented into FE models of ETER mitral valve to study leaflet deformation. The simulation results indicate the high stress regions occurred in the areas near sutured edges and the vicinity of commissures.