Influence of stent height upon stresses on the cusps of closed bioprosthetic valves

A finite element model of a bioprosthetic heart valve was developed to determine the influence of the stent height on leaflet stresses under various pressure loading conditions after valve closure. A nonlinear solution was used to obtain the stresses in the leaflets for stent heights of 14.6 mm, 19.0 mm and 22.0 mm respectively. The basic assumptions included an elliptic-paraboloid for a relaxed leaflet shape, a rigid stent, isotropic leaflet material property with a Poisson's ratio of 0.45, a uniform leaflet thickness and a stress dependent Young's modulus. The model predicted an increase of stresses on the closed leaflets as the stent height was reduced. This observation appears to mitigate, to some extent, the hemodynamic benefits thought to accompany the reduction of stent height of bioprosthetic valves.     

Stress distribution on the cusps of a polyurethane trileaflet heart valve prosthesis in the closed position.

In this paper, a finite element analysis of the stress distribution on the cusps of a polyurethane trileaflet heart valve prosthesis in the closed position is presented. The geometry of the valve was modified from a relationship proposed by Ghista and Reul (J. Biomechanics 10, 313-324, 1977). The effects of variations in stent height, leaflet thickness and coaptation area on the stress distribution were also analyzed. Analyses were performed with both rigid and flexible stents for the trileaflet valve in order to delineate the effect of stent flexibility on the leaflet stress distribution. The results showed that regions of stress concentration were present near the commissural attachment similar to those predicted with the bioprostheses. The stresses on the leaflets were reduced by increasing the stent height with both rigid and flexible stents. Selectively increasing the leaflet thickness near the commissures and also increasing the coaptation area did not prove to reduce the leaflet stresses when the stent flexibility was taken into account. The possible effect of high stresses on the structural integrity of polyurethane leaflets and its relationship with calcification is yet to be investigated.     

A reduced-order modeling for efficient design study of artificial valve in enlarged ventricular outflow tracts

A computational approach is proposed for efficient design study of a reducer stent to be percutaneously implanted in enlarged right ventricular outflow tracts (RVOT). The need for such a device is driven by the absence of bovine or artificial valves which could be implanted in these RVOT to replace the absent or incompetent native valve, as is often the case over time after Tetralogy of Fallot repair. Hemodynamics are simulated in the stented RVOT via a reduce order model based on proper orthogonal decomposition, while the artificial valve is modeled as a thin resistive surface. The reduced order model is obtained from the numerical solution on a reference device configuration, then varying the geometrical parameters (diameter) for design purposes. To validate the approach, forces exerted on the valve and on the reducer are monitored, varying with geometrical parameters, and compared with the results of full CFD simulations. Such an approach could also be useful for uncertainty quantification.     

Effect of fiber orientation on the stress distribution within a leaflet of a polymer composite heart valve in the closed position

Polymer trileaflet valves offer natural hemodynamics with the potential for better durability than commercially available tissue valves. Strength and durability of polymer-based valves may be increased through fiber reinforcement. A finite element analysis of the mechanics of a statically loaded polymer trileaflet aortic heart valve has been conducted. A parametric analysis was performed to determine the effects of fiber orientation and volume density in a single and double ply model. A maximum stress value of 1.02MPa was obtained in the non-reinforced model for a transvalvular load (downstream-upstream) of 120mmHg. The maximum stress on the downstream side of the leaflet was approximately twice the maximum stress on the upstream side, and always occurred on the interface with the valve stent. The single ply model reduced the stress on the polymer matrix, with the maximum reduction of at least 64% occurring when the fiber orientation was such that the fibers ran perpendicular to the stent edge. The double ply model further reduced the stress on the polymer matrix, with the maximum reduction of greater than 86% now occurring when the fibers are oriented most perpendicular to one another.     

A model of stress-induced geometrical remodeling of vessel segments adjacent to stents and artery/graft anastomoses

The mismatch between the elastic properties and initial geometry of a host artery and an implanted stent or graft cause significant stress concentration at the zones close to junctions. This may contribute to the often observed intimal hyperplasia, resulting in late lumen loss and eventual restenosis. This study proposes a mathematical model for stress-induced thickening of the arterial wall at the zones close to an implanted stent or graft. The host artery was considered initially as a cylindrical shell with constant thickness that was clamped to the stent or graft, which was assumed to be non-deformable in the circumferential direction. It was assumed that the abnormal circumferential and axial stresses due to the bending of the arterial wall cause wall thickening that tends to restore the stress state close to that existing far from the junction. The linear equations of a cylindrical shell with variable thickness were coupled to an evolution equation for the wall thickness. These equations were solved numerically and a parametric study was performed using finite difference method and explicit time step. The results show that the remodeling process is self-limiting and leads to local thickening that gradually decreases with distance from the edge of the stent/graft. Model predictions were tested against morphological findings existing in the literature. Recommendations on stent designs that reduce stress concentrations are discussed.     

Developmental Patterns of Tree Dimensions in a Neotropical Deciduous Forest1

For 26 tree species in very dry tropical forest in Mexico, the developmental trends of relationships among trunk diameter, tree height, and crown diameter were inferred from a one‐time measurement of dispersed individuals across the size range from saplings to large, mature trees. On hillside sites in this high diversity forest, maximum dimensions were usually <10‐m height, 4‐m crown diameter, and 0.3‐m trunk diameter. The relationship of height to trunk diameter was characterized by an asymptotic, three‐parameter model. Crown diameter was a linear function of trunk diameter. The parameter values for both models varied widely among the species. In general, the dispersion among species of the height–crown diameter relationship increased linearly with trunk diameter (up to 0.2 m). Arborescent cacti were distant from other species at all sizes, although they were well modeled using the same equations. Empirical and theoretical features and limitations of the present and previous models, including mechanical buckling and water‐stress theories, are considered.     

Mechanical stresses in abdominal aortic aneurysms: influence of diameter, asymmetry, and material anisotropy

Biomechanical studies suggest that one determinant of abdominal aortic aneurysm (AAA) rupture is related to the stress in the wall. In this regard, a reliable and accurate stress analysis of an in vivo AAA requires a suitable 3D constitutive model. To date, stress analysis conducted on AAA is mainly driven by isotropic tissue models. However, recent biaxial tensile tests performed on AAA tissue samples demonstrate the anisotropic nature of this tissue. The purpose of this work is to study the influence of geometry and material anisotropy on the magnitude and distribution of the peak wall stress in AAAs. Three-dimensional computer models of symmetric and asymmetric AAAs were generated in which the maximum diameter and length of the aneurysm were individually controlled. A five parameter exponential type structural strain-energy function was used to model the anisotropic behavior of the AAA tissue. The anisotropy is determined by the orientation of the collagen fibers (one parameter of the model). The results suggest that shorter aneurysms are more critical when asymmetries are present. They show a strong influence of the material anisotropy on the magnitude and distribution of the peak stress. Results confirm that the relative aneurysm length and the degree of aneurysmal asymmetry should be considered in a rupture risk decision criterion for AAAs.     

The Cardiocoil stent-artery interaction

An analytical approach for the mechanical interaction of the self-expanding Cardiocoil stent with the stenosed artery is presented. The damage factor as the contact stress at the stent-artery interface is determined. The stent is considered as an elastic helical rod having a nonlinear pressure-displacement dependence, while the artery is modeled by an elastic cylindrical shell. An influence of a moderate relative thickness of the shell is estimated. The equations for both the stent and the artery are presented in the stent-associated helical coordinates. The computational efficiency of the model enabled to carry out a parametric study of the damage factor. Comparative examinations are conducted for the stents made of the helical rods with circular and rectangular cross sections. It was found, in particular, that, under same other conditions, the damage factor for the stent with a circular cross section may be two times larger than that for a rectangular one.     

Finite element analysis of the mitral apparatus: annulus shape effect and chordal force distribution

This study presents a three-dimensional finite element model of the mitral apparatus using a hyperelastic transversely isotropic material model for the leaflets. The objectives of this study are to illustrate the effects of the annulus shape on the chordal force distribution and on the mitral valve response during systole, to investigate the role of the anterior secondary (strut) chordae and to study the influence of thickness of the leaflets on the leaflets stresses. Hence, analyses are conducted with a moving and fixed saddle shaped annulus and with and without anterior secondary chordae. We found that the tension in the secondary chordae represents 31% of the load carried by the papillary muscles. When removing the anterior secondary chordae, the tension in the primary anterior chordae is almost doubled, the displacement of the anterior leaflet toward the left atrium is also increased. The moving annulus configuration with an increasing annulus saddle height does not give significant changes in the chordal force distribution and in the leaflet stress compared to the fixed annulus. The results also show that the maximum principle stresses in the anterior leaflet are carried by the collagen fibers. The stresses calculated in the leaflets are very sensitive to the thickness employed.     

A multi-scale mechanobiological model of in-stent restenosis: deciphering the role of matrix metalloproteinase and extracellular matrix changes

Since their first introduction, stents have revolutionised the treatment of atherosclerosis; however, the development of in-stent restenosis still remains the Achilles' heel of stent deployment procedures. Computational modelling can be used as a means to model the biological response of arteries to different stent designs using mechanobiological models, whereby the mechanical environment may be used to dictate the growth and remodelling of vascular cells. Changes occurring within the arterial wall due to stent-induced mechanical injury, specifically changes within the extracellular matrix, have been postulated to be a major cause of activation of vascular smooth muscle cells and the subsequent development of in-stent restenosis. In this study, a mechanistic multi-scale mechanobiological model of in-stent restenosis using finite element models and agent-based modelling is presented, which allows quantitative evaluation of the collagen matrix turnover following stent-induced arterial injury and the subsequent development of in-stent restenosis. The model is specifically used to study the influence of stent deployment diameter and stent strut thickness on the level of in-stent restenosis. The model demonstrates that there exists a direct correlation between the stent deployment diameter and the level of in-stent restenosis. In addition, investigating the influence of stent strut thickness using the mechanobiological model reveals that thicker strut stents induce a higher level of in-stent restenosis due to a higher extent of arterial injury. The presented mechanobiological modelling framework provides a robust platform for testing hypotheses on the mechanisms underlying the development of in-stent restenosis and lends itself for use as a tool for optimisation of the mechanical parameters involved in stent design.     

A two-dimensional finite element analysis of a bioprosthetic heart valve

A finite element scheme has been developed using total Lagrangian techniques for the two-dimensional analysis of bioprosthetic heart valve leaflets undergoing large deformation. Two models of a leaflet, namely a radial and a circumferential slice, have been analysed. The attachment of the slice to the stent was simulated by progressive contact on a circular former and the coaptation of the leaflets in the centre of a heart valve by a straight line of contact. For the circumferential model, different initial configurations have been considered. The prolapse pressure under which the heart valve closes has been shown to be small in comparison with the normal pressure a heart valve sustains. The regions of the valve that are most heavily stressed are subjected to a strong component of bending. The amount is sensitive to the details of the boundary conditions and to the initial configuration of the valve. These observations are likely to be significant in the use of this kind of stress analysis to improve the design of this type of valve.     

3D computational parametric analysis of eccentric atheroma plaque: influence of axial and circumferential residual stresses

Plaque rupture plays a role in the majority of acute coronary syndromes. Rupture has usually been associated with stress concentrations, which are mainly affected by the plaque geometry and the tissue properties. The aim of this study is to evaluate the influence of morphology on the risk of plaque rupture, including the main geometrical factors, and to assess the role of circumferential and axial residual stresses by means of a parametric 3D finite element model. For this purpose, a 3D parametric finite element model of the coronary artery with eccentric atheroma plaque was developed. Healthy (adventitia and media in areas without atheroma plaque) and diseased (fibrotic and lipidic) tissues were considered in the model. The geometrical parameters used to define and design the idealized coronary plaque anatomy were the lipid core length, the stenosis ratio, the fibrous cap thickness, and the lipid core ratio. Finally, residual stresses in longitudinal and circumferential directions were incorporated into the model to analyse the influence of the important mechanical factors in the vulnerability of the plaque. Viewing the results, we conclude that residual stresses should be considered in the modelling of this kind of problems since they cause a significant alteration of the vulnerable plaque region limits. The obtained results show that the fibrous cap thickness and the lipid core length, in combination with the lipid core width, appear to be the key morphological parameters that play a determinant role in the maximal principal stress (MPS). However, the stenosis ratio is found to not play a significant role in vulnerability related to the MPS. Plaque rupture should therefore be observed as a consequence, not only of the cap thickness, but as a combination of the stenosis ratio, the fibrous cap thickness and the lipid core dimensions.     

Impact of stents and flow diverters on hemodynamics in idealized aneurysm models

Cerebral aneurysms constitute a major medical challenge as treatment options are limited and often associated with high risks. Statistically, up to 3% of patients with a brain aneurysm may suffer from bleeding for each year of life. Eight percent of all strokes are caused by ruptured aneurysms. In order to prevent this rupture, endovascular stenting using so called flow diverters is increasingly being regarded as an alternative to the established coil occlusion method in minimally invasive treatment. Covering the neck of an aneurysm with a flow diverter has the potential to alter the hemodynamics in such a way as to induce thrombosis within the aneurysm sac, stopping its further growth, preventing its rupture and possibly leading to complete resorption. In the present study the influence of different flow diverters is quantified considering idealized patient configurations, with a spherical sidewall aneurysm placed on either a straight or a curved parent vessel. All important hemodynamic parameters (exchange flow rate, velocity, and wall shear stress) are determined in a quantitative and accurate manner using computational fluid dynamics when varying the key geometrical properties of the aneurysm. All simulations are carried out using an incompressible, Newtonian fluid with steady conditions. As a whole, 72 different cases have been considered in this systematic study. In this manner, it becomes possible to compare the efficiency of different stents and flow diverters as a function of wire density and thickness. The results show that the intra-aneurysmal flow velocity, wall shear stress, mean velocity, and vortex topology can be considerably modified thanks to insertion of a suitable implant. Intra-aneurysmal residence time is found to increase rapidly with decreasing stent porosity. Of the three different implants considered in this study, the one with the highest wire density shows the highest increase of intra-aneurysmal residence time for both the straight and the curved parent vessels. The best hemodynamic modifications are always obtained for a small aneurysm diameter.     

Study of the evolution of the shear stress on the restenosis after coronary angioplasty

In this article, we analyze the influence of fluid dynamics variables on the development of obstructive coronary artery disease in the medium term after percutaneous coronary intervention with stent implantation. We have analyzed a group of seven patients and the study is focused on the mid-right coronary artery. In these patients we have studied the relationship between wall shear stress and arterial wall thickness both immediately after stent implantation and six months later. The realistic three-dimensional (3D) reconstruction of the arteries is performed with the data obtained with intravascular ultrasound (IVUS) and angiography. The commercial code Fluent is used to solve the Navier-Stokes equations. Special attention is paid to the shear stress on the wall arteries and the corresponding thickness. The results show that there is a negative correlation for most of the cases between the wall shear stress and increase in wall thickness. A model is proposed to study the instability at the wall, and qualitative agreement is found.     

Bayesian sensitivity analysis of a model of the aortic valve

Understanding the mechanics of the aortic valve has been a focus of attention for many years in the biomechanics literature, with the aim of improving the longevity of prosthetic replacements. Finite element models have been extensively used to investigate stresses and deformations in the valve in considerable detail. However, the effect of uncertainties in loading, material properties and model dimensions has remained uninvestigated. This paper presents a formal statistical consideration of a selected set of uncertainties on a fluid-driven finite element model of the aortic valve and examines the magnitudes of the resulting output uncertainties. Furthermore, the importance of each parameter is investigated by means of a global sensitivity analysis. To reduce computational cost, a Bayesian emulator-based approach is adopted whereby a Gaussian process is fitted to a small set of training data and then used to infer detailed sensitivity analysis information. From the set of uncertain parameters considered, it was found that output standard deviations were as high as 44% of the mean. It was also found that the material properties of the sinus and aorta were considerably more important in determining leaflet stress than the material properties of the leaflets themselves.     

Straightening of curved pattern of collagen fibers under load controls aortic valve shape

The network of collagen fibers in the aortic valve leaflet is believed to play an important role in the strength and durability of the valve. However, in addition to its stress-bearing role, such a fiber network has the potential to produce functionally important shape changes in the closed valve under pressure load. We measured the average pattern of the collagen network in porcine aortic valve leaflets after staining for collagen. We then used finite element simulation to explore how this collagen pattern influences the shape of the closed valve. We observed a curved or bent pattern, with collagen fibers angled downward from the commissures toward the center of the leaflet to form a pattern that is concave toward the leaflet free edge. Simulations showed that these curved fiber trajectories straighten under pressure load, leading to functionally important changes in closed valve shape. Relative to a pattern of straight collagen fibers running parallel to the leaflet free edge, the concave pattern of curved fibers produces a closed valve with a 40% increase in central leaflet coaptation height and with decreased leaflet billow, resulting in a more physiological closed valve shape. Furthermore, simulations show that these changes in loaded leaflet shape reflect changes in leaflet curvature due to modulation of in-plane membrane stress resulting from straightening of the curved fibers. This effect appears to play an important role in normal valve function and may have important implications for the design of prosthetic and tissue engineered replacement valves.     

Patient-specific modeling of biomechanical interaction in transcatheter aortic valve deployment

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.     

3D models for vascular lumen segmentation in MRA images and for artery-stenting simulation

Arterial stenoses and aneurysms are increasingly treated using stents. The goal of this work is to facilitate the pre-operative choice of the stent's length and diameter. Two models are used to accomplish this task: a deformable cylindrical simplex (DCS) model of the arterial intra-luminal wall and a right generalized cylinder (RGC) model representing the stent's geometrical properties. An angiographic 3D image is first segmented using the DCS model to create a patient-specific vascular model. The RGC model of a folded stent is then slid along the vessel centerline until an interactively chosen delivery location, and the model's geometry is modified to simulate the unfolding of the stent. Lastly, the DCS model is re-meshed to fit the shape of the unfolded-stent model and thus to simulate the shape of the arterial lumen boundaries after stenting. Accuracy of the segmentation was quantitatively evaluated in images of arterial phantoms with stenoses ranging from 50 to 95%. Mean error of the resulting diameter estimation was 4.24%. The simulation of the stent insertion is qualitatively illustrated using data of a patient with an aneurysm in the aorta arch.     

On the biaxial mechanical properties of the layers of the aortic valve leaflet

All existing constitutive models for heart valve leaflet tissues either assume a uniform transmural stress distribution or utilize a membrane tension formulation. Both approaches ignore layer specific mechanical contributions and the implicit nonuniformity of the transmural stress distribution. To begin to address these limitations, we conducted novel studies to quantify the biaxial mechanical behavior of the two structurally distinct, load bearing aortic valve (AV) leaflet layers: the fibrosa and ventricularis. Strip biaxial tests, with extremely sensitive force sensing capabilities, were further utilized to determine the mechanical behavior of the separated ventricularis layer at very low stress levels. Results indicated that both layers exhibited very different nonlinear, highly anisotropic mechanical behaviors. While the leaflet tissue mechanical response was dominated by the fibrosa layer, the ventricularis contributed double the amount of the fibrosa to the total radial tension and experienced four times the stress level. The strip biaxial test results further indicated that the ventricularis exhibited substantial anisotropic mechanical properties at very low stress levels. This result suggested that for all strain levels, the ventricularis layer is dominated by circumferentially oriented collagen fibers, and the initial loading phase of this layer cannot be modeled as an isotropic material. Histological-based thickness measurements indicated that the fibrosa and ventricularis constitute 41% and 29% of the total layer thickness, respectively. Moreover, the extensive network of interlayer connections and identical strains under biaxial loading in the intact state suggests that these layers are tightly bonded. In addition to advancing our knowledge of the subtle but important mechanical properties of the AV leaflet, this study provided a comprehensive database required for the development of a true 3D stress constitutive model for the native AV leaflet.     

Modeling active muscle contraction in mitral valve leaflets during systole: a first approach

The present study addresses the effect of muscle activation contributions to mitral valve leaflet response during systole. State-of-art passive hyperelastic material modeling is employed in combination with a simple active stress part. Fiber families are assumed in the leaflets: one defined by the collagen and one defined by muscle activation. The active part is either assumed to be orthogonal to the collagen fibers or both orthogonal to and parallel with the collagen fibers (i.e. an orthotropic muscle fiber model). Based on data published in the literature and information herein on morphology, the size of the leaflet parts that contain muscle fibers is estimated. These parts have both active and passive materials, the remaining parts consist of passive material only. Several solid finite element analyses with different maximum activation levels are run. The simulation results are compared to corresponding echocardiography at peak systole for a porcine model. The physiologically correct flat shape of the closed valve is approached as the activation levels increase. The non-physiological bulging of the leaflet into the left atrium when using passive material models is reduced significantly. These results contribute to improved understanding of the physiology of the native mitral valve, and add evidence to the hypothesis that the mitral valve leaflets not are just passive elements moving as a result of hemodynamic pressure gradients in the left part of the heart.