Effect of reinforcement volume fraction and orientation on a hybrid tissue engineered aortic heart valve with a tubular leaflet design
© Stapleton et al. 2015
Received: 25 March 2015
Accepted: 15 July 2015
Published: 13 August 2015
Transcatheter aortic valve implantation of fibrin-based tissue engineered heart valves with a tubular leaflet construct have been developed as an alternative to invasive traditional surgical heart valve implantation. In general, they are well suited for the pulmonary position, but display insufficient mechanical properties for the aortic position. To enable the application of tissue-engineered valves in the systemic circulation, the tissue is reinforced with a textile scaffold. The current study seeks to compare the effect of varying the fiber volume fraction and orientation of bidirectional textile reinforcement on the closed-valve configuration. An anisotropic large deformation material model based on structural tensors was chosen and the materials were characterized. A finite element model was constructed of the heart valve, and the pinching and suturing of the corners along with application of pressure was simulated. Virtual experiments were conducted with fiber volume fractions of 0.1, 0.01, 0.001, and 0.0001 for ±45° fiber orientations. Furthermore, volume fraction was held at 0.01 and fiber orientations of 0°, ±15°, ±30°, ±45°, ±60°, ±75° and 90° from the tube’s axial direction were simulated and compared. It was shown that increasing the fiber volume fraction decreased the maximum principle strain in the valve, but lead to less closure. Additionally, the effect of fiber orientation affected the strains differently at different locations, depending on the local deformed geometry. This indicates that a non-uniform fiber distribution using tailored fiber placement could be used to optimize reinforcement design.
Valvular heart disease is a steadily increasing socioeconomic burden worldwide. The proportion of valvular surgeries has increased over the past decades and these procedures now account for more than 20% of all cardiac surgeries with the number of replacement per year expected to triple by 2050 . Tissue engineering (TE) of heart valves might overcome the well-known complications of contemporary devices implanted in young and elderly patients such as the need for a life-long anticoagulation therapy in the case of mechanical prostheses [2, 3], the degeneration and therefore limited durability of the biological heart valves [2, 3] and the limited availability of homografts . Furthermore, none of the available prostheses is capable of growth and remodeling. The basic concept of cell-based tissue engineering is to isolate/differentiate and expand tissue-specific cells derived from the patient and to seed them onto suitable matrix scaffolds. Subsequently, following in vitro cultivation and tissue development, the resulting structure is implanted into the recipient’s organism. The ultimate goal is to provide the patient with an implant produced with and by the patient’s own cells, able to remodel and self-repair, with physiological haemocompatibility, biologically and mechanically equivalent to the native tissue. Historically, TE heart valves have been designed to mimic the complex shape of the native valve in the attempt to recreate the natural haemodynamics .
Since experimental testing of tissue-engineered heart valves can be extremely time-consuming and expensive, numerical models are desired to predict the effect of geometrical and material changes on performance. One research group has created a series of models to simulate the closing of fiber-reinforced leaflets  and stentless fiber-reinforced heart valves  using high-performance polyethelyne fibers (HP-PE) in an ethylene-propylene-diene-monomer rubber matrix. These models utilized a continuum rule of mixtures technique to represent the fiber-reinforced rubber material only in elements which contain a fiber. As far as the authors can tell, the formulation did not track the angle change of fibers with loading except through rigid body rotations of the composite elements. Fiber orientation and volume fraction were investigated, and optimization techniques were applied to design the leaflets. Xiong et al.  compared a tubular and a molded geometry for stentless pericardial bioprostheses. An isotropic material model was utilized because the geometry was the focus of the study. More recently, Marom et al.  created a model with fluid–structure interaction (FSI) to determine the correlation between root geometries and coaptation height and stresses. The effect of valve-specific collagen networks were also investigated  by mapping experimentally obtained collagen content and direction to an finite element (FE) model where collagen fibers were represented with beam elements. Cox et al.  created a simple, preliminary, FE model of the tubular heart valve geometry. While all of these modes represent varying degrees of modelling fidelity with aspects similar to the current study, none of them look at the effect of fiber reinforcement orientation for a tubular, tissue-engineered heart valve.
There are many different material models developed for modelling soft, biological materials reinforced by multiple fiber directions (for example [14, 15] and the reader is directed to  for a more exhaustive study). The model chosen for this particular study is based on the model first proposed by Reese et al.  and further developed and/or applied in [18–20]. The fiber directions are captured through so-called structural tensors, and the matrix is represented by a hyperelastic Neo-Hookean model. To compare the effect of different fiber volume fractions and orientations on the closing of the heart valve, an FE model was created to simulate the pinching/stitching and closing of the valve. Several fiber volume fractions and orientations were compared and improvements to the model were suggested.
In order to show the effect of fiber reinforcement volume fraction and orientation on a closed tubular heart valve, a finite element (FE) model was utilized. This section describes first the structural tensor material model adapted from Reese et al.  to describe the fiber-reinforced tissue under large deformation. Next, the material characterization is briefly summarized, and finally the boundary conditions of the model are defined.
Material model formulation
Finite element model
To avoid excessive deformations and concentrated forces, the corner sutures were simulated using a control point-to-surface constraint. A 0.75 × 2 mm square patch adjacent to the slit was coupled with a reference point located at the top midpoint of the patch (Fig. 5). The point was coupled with the translational degrees of freedom of the surface (not rotational), and a continuum distribution using uniform weighting was used. Therefore the surface translations were tied to the control point, but only in an average sense. A similar control point and patch were placed in the center of the leaflet to force the valve closed, thereby bypassing snap-through of the leaflet. Utilizing a control point and load patch allowed applying boundary conditions to the control point without having the entire load applied at a concentrated point on the valve surface.
Initial step: The bottom of the valve was fixed (encastre) and symmetry surfaces were given symmetric boundary conditions perpendicular to the surface. Contact was enforced between the inside valve surface and rigid wall.
Step 1: The control points were given a prescribed a displacement in the x-direction (U x ), bringing them against the contact plane.
Step 2: The control point near the slit was fixed in space (simulating suture to stent) and a uniform pressure of 11 kPa  was applied to the outer surface of the valve.
One of the main difficulties in an implicit simulation of a rather thin-walled, flexible tubular structure is bifurcation of solutions. In many instances during the simulation loading, there were negative eigenvalues indicating buckling or unstable solutions. The first and most obvious case was when initially suturing and pinching the tube. Initial models attempted to pinch the corners and then subsequently applying pressure. This caused snap-through of the tube wall, and convergence was extremely difficult. To avoid snap-through, the control point in the middle of the leaflet was introduced so that it was simultaneously closed and pinched (see Fig. 6).
A 0.7 mm × 3.35 mm slit was inserted on the three corners where a suture is placed to give the tube its valve structure (Fig. 8). While this was not necessarily representative of actual heart valves, it was necessary numerically to avoid elements with excessive distortion which make solution convergence difficult. A physical justification of this practice may lie in the conditioning process of actual heart valves . The construct consisting of cell-laden fibrin and the textile reinforcement is pinched and sutured into place, and the cells grow and multiply in a bioreactor while the valve is opening and closing. During this opening and closing, the pinched corners with a suture are not opening and closing. Therefore, cells are growing in this region in the bent configuration. Therefore, the stresses in the pinched regions in the actual heart valve are unknown, but are probably much less than if the fully-grown material were pinched and sutured. These corner regions are not considered critical in the analysis and the slits are inserted to allow better solution stability.
Geometric and material parameters for the heart valve model
K 1 fi (MPa)
θ i (°)
n el (×103)
Mesh size convergence
0.5, 3, 11, 18, 27, 100
0.01, 0.001, 1 × 10−4, 1 × 10−5
0, ±15, ±30, ±45, ±60, ±75, 90
Finally, the maximum principle strain of heart valves with different fiber volume fractions and orientations was determined. The mesh size used was five elements through the thickness and the remaining two directions roughly 0.23 × 0.23 mm. The results were recorded at 11 kPa of applied pressure. The maximum principle strain contours are presented here and the strain along the leaflet centerline (Fig. 9b) and along the line under the corner stitch were shown because they contained the points of highest strain. However, the magnitudes near the bottom suture and the corner stitch should be considered suspect and useful for more of a qualitative rather than quantitative comparison. For the bottom suture, the bottom surface of the heart valve FE model is fixed. It is expected that a suture line would not be entirely fixed, but allowed some rotation. Therefore, the actual boundary probably lies somewhere between a fixed and a pinned condition. The corner stitch strains are also suspect, because the growth of the tissue takes place in the stitched configuration, which most likely leads to lower strains in the material around this point.
Results and discussion
To compare the effect of reinforcement fiber volume fraction and orientation on the closing of a tubular heart valve, the finite element (FE) model was created and utilized. First, the ability of the model to converge with decreasing mesh size was investigated for the heart valve model without textile reinforcement. Finally, the fiber volume fraction and fiber reinforcement orientation was investigated to show how the fiber reinforcement can be tailored to decrease maximum strain or change valve shape under pressure.
Mesh size convergence
First, the elemental convergence of the heart valve model was studied for a heart valve without fiber reinforcement. The average deviation of the maximum principle strain from the model with the finest mesh (6 elements through the thickness) was used to show elemental convergence.
The average deviation error is plotted in Fig. 9a for different meshes. As can be seen, the average deviation is quite low even for coarse meshes. The spot on the centerline along the bottom suture is the only location where mesh size convergence was not immediately achieved. Since the boundaries were not entirely representative of actual conditions as discussed earlier, the mesh size used was five elements through the thickness with the other dimensions roughly 0.23 × 0.23 mm, resulting in 18,943 elements.
Effect of fiber volume fraction
Another thing to note is that there is a strain peak on the valve side below the stitch. This point shows the influence of the corner control point on the valve lip. The control point is fixed while pressure is applied, so there is an increase of strain here due to the control point keeping the valve up. If this stitch boundary condition were applied to a single point rather than through a control point with loading patch, a much higher strain peak would be seen along with excessive localized deformation. Other than the corners, the second highest strain is located at the base of the valve. Like the corner, strains higher than those allowed by the material are found here. It should be noted that the fixed boundary conditions at the base are probably stiffer than the actual valve. One row of sutures holds the valve to the stent, and the suture probably behaves somewhere in between a fixed and a pinned boundary.
The effect of fiber volume fraction is fairly intuitive. The higher the volume fraction, the stiffer the valve and the lower the strains are generally. Lower strains usually mean higher strength. On the other side, the stiffer the valve the less it closes. The valve with fiber volume fraction of 0.01 still has quite a bit of opening at the top, while the lower volume fractions are completely closed. Due to this tradeoff between strength and closure (or coaption), one needs to define (1) the minimum closure required for the valve to fulfill its function, (2) define the closure time required and then chose the highest volume fraction which fulfills both requirements. In this way, a balance can be found between strength and function.
Effect of fiber orientation
This model serves to compare the effects of fiber volume fraction and orientation on the closed-valve configuration, but there are many aspects of the model that could be improved to move towards a predictive rather than merely comparative model. First, more material data is required for proper modelling of the fiber-reinforced tissue. Some tests with the fiber-reinforced material would be necessary to not only validate the model but also to include more advanced aspects including fiber-matrix coupling and fiber–fiber coupling. This could be done by physical testing or by creating a unit-cell model of the textile in a tissue matrix and then conducting virtual experiments. Additionally, experimental data of a textile-reinforced heart valve would be necessary for a validation of the model.
Furthermore, there could be some improvements on the material modelling. The material model treats the tissue with textile as a homogenous material. For membrane stresses, this is probably a reasonable approximation. However, since the soft tissue grows on the outer surface of the textile, the bending stiffness will be much lower in the actual material. Either a multi-layered continuum model or a shell element with bending stiffness based on textile location would be an improvement. The tissue is in actuality not an isotropic material but anisotropic due to conditioning and the fibrous collagen growth in the loading directions. This would mean that not only is the tissue anisotropic, but the material directions would be spatially varying. A more advanced material model could be implemented and a conditioning simulation could be carried out to obtain the local material anisotropy in the conditioned valve similar to [27, 28]. Additionally, plasticity of the tissue and fibers could be included to more accurately predict failure of the valve.
Finally, some FE improvements would lead to a more realistic description of the problem. Running a dynamic simulation with an explicit solver would help with solution instability and contact convergence, and be able to account for the dynamic pressure application in a real valve. A full model of the heart would include the non-symmetric modes, which may appear under more realistic boundary conditions. All of these improvements should be topics of future work to yield a higher-fidelity prediction for the behavior of textile-reinforced heart valves.
The goal of the current study was to show the effect of changing fiber reinforcement orientation on a textile reinforced tubular heart valve through virtual experimentation. First, a large deformation, anisotropic material model first introduced by Reese et al.  was adapted. This model is based on the concept of structural tensors, which isolates directional components of the right Cauchy-Green tensor and uses a corresponding invariant in the energy formulation. The matrix was modelled as a nearly incompressible Neo-Hookean isotropic material. The many of the coupled and higher order terms were neglected because a lack of sufficient experimental data would make the fitting of many constants non-singular and arbitrary.
A finite element (FE) model was constructed for the heart valve. To improve computational efficiency and avoid asymmetric buckling modes, one-sixth of the tube was modelled. Symmetry boundary conditions were applied on both sides and the bottom was fixed to represent the suture to the stent. This last boundary condition is probably stiffer than a suture would be in reality. Three slits were cut out of the tube where the tube would be pinched and sutured to avoid excessive distortion at one single point. This is justified by the fact that the cells grow in the pinched deformation, making the residual stresses at the corner smaller than represented in the model. The valve was closed and pinched simultaneously to avoid snap-through instability, then a uniform pressure was applied to the outside surface. A contact plane was placed in the middle for contact symmetry.
A few studies were carried out with the FE model. First, elemental convergence was shown by comparing the maximum principle strains of the leaflet centerline. Good convergence was achieved for relatively coarse meshes, but the solution around the stress concentrations required finer meshes. Second, the effect of fiber volume fraction was shown be comparing valves with 0.01, 0.001, 0.0001, and 0.00001 fiber volume fractions for ±45° fiber orientations. An increase in fiber volume fraction reduced the maximum principle strain at critical locations because the valve was stiff enough that it did not fold at a concentrated location. However, higher volume fraction also resulted in less valve closure, illustrating the trade-off between strength and stiffness. A more optimum valve could be constructed by reinforcing critical areas with more fibers and leaving other areas with fewer fibers to achieve better closure. Finally, fiber reinforcement orientations of 0°, ± 15°, ± 30°, ± 45°, ± 60°, ± 75°, and 90° were applied and maximum principle strain distributions were compared. It was shown that the fiber reinforcement stiffened the valve, but different orientations were beneficial at different locations. This suggests the use of fiber placement technology to optimize the fiber direction to increase the strength of a heart valve without adding a large amount of fibers.
SES performed the FE analysis and drafted most of the manuscript. RM performed the tissue tensile tests. SJ developed the textile reinforced heart valve concept. PM participated in the design and coordination of the study, wrote parts of the manuscript, and determined the boundary conditions for the valve. SR conceived much of the study, reviewed and edited the manuscript, and created the material model. All authors read and approved the final manuscript.
This research was funded by the Integrated Interdisciplinary Institute of Technology for Medicine (I3TM) of RWTH Aachen University through Seed-Fund SF_14-4-08, “Hybrid scaffold for a transcatheter tissue-engineered aortic valve”. Additional funding was provided by the People Programme (Marie Curie Actions) of the European Union’s Seventh Framework Programme FP7/2007-2013/under REA Grant Agreement No 317512. The authors would additionally like to thank Bertram Stier, Daniel Höwer, Dennis Della Corte and Deepanschu Sodhani for their helpful discussion and support.
Compliance with ethical guidelines
Competing interests The authors declare that they have no competing interests.
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