Smooth leaflets with curved belly and attachment edge profiles promote adaptive remodeling in tissue-engineered heart valves: an in silico study

Fig. 1. TEHV design variations, with their two-letter nomenclature, based on the attachment shape and belly curvature as well as one-letter nomenclature for each group of three valve geometries with a similar design feature. Obtained valve geometries for Design 1 (a) and Design 2 (b)

Fig. 2. Design features used to generate geometrical variations (a), boundary conditions in simulations (b), profile of pressure on the leaflets (c), definition of regions and orientations in the valves (d), and depiction of measures used for macroscopic evaluation of valves after remodeling (e)

Fig. 3. Von Mises stress distributions in TEHVs with different geometries in loaded configuration; under pulmonary pressure before remodeling (a and d), after remodeling under pulmonary pressure conditions (b and e), and after remodeling under aortic pressure loading (c and f). The top row depicts Design 1 (a–c), and the bottom row depicts Design 2 (d– f)

Fig. 4. Global and local analysis of the maximal von Mises stress before remodeling under pulmonary conditions and after remodeling under pulmonary and aortic conditions. Peak stress in the whole leaflet (a and e), the commissure region (b and f), the tip region (c and f), and in the belly region (d and h) are shown, both for Design 1 (a–d) and Design 2 (e–h)

Fig. 5. Maximum principal logarithmic strain distributions in TEHVs with different geometries in loaded configuration; under pulmonary pressure before remodeling (a and d), after remodeling under pulmonary pressure conditions (b and e), and after remodeling under aortic pressure loading (c and f). The top row depicts Design 1 (a–c), and the bottom row depicts Design 2 (d–f)

Fig. 6. Mean radial and circumferential logarithmic strain before remodeling under pulmonary conditions in the belly region of geometries of Design 1 (a) and Design 2 (b)

Fig. 7. Assessment of leaflet retraction after remodeling under both pulmonary and aortic pressure conditions. The decline in belly profile length (a and e) or free edge length (b and f) in the leaflets. The directional compaction in the belly region of the leaflets (c and g) and the developed valve insufficiency presented as regurgitant orifice area (d and h)

Fig. 8. Collagen fiber orientation after remodeling under pulmonary and aortic pressure conditions in Design 1 (a and b) and aortic conditions in Design 2 (c). Cellular stress fiber orientation after remodeling under pulmonary and aortic conditions in Design 1 (d and e) and aortic conditions in Design 2 (f). Orientation parameters of the collagen fiber distribution in pulmonary or aortic pressure conditions in Design 1 (g) and Design 2 (h)

Fig. 9. Cost function results of TEHV design variations. Baseline evaluation, as well as evaluations of variations of geometries with additional coaptation, lower cell contractility, stiffer material, and thinner leaflets for Design 1 (a) and Design 2 (b). The implementation of thin leaflets in aortic conditions led to excessive deformation preventing convergence of the simulations

Fig. 10. The effect of variations in coaptation (a) and leaflet thickness (b) on retraction and radial and circumferential strain

Fig. 11. A general optimal valve design has been defined. Tailoring the valve for pulmonary conditions to prevent retraction involves using thinner and softer leaflets. Conversely, tailoring the geometry for aortic pressure conditions to prevent stress concentrations requires thicker and stiffer leaflets