Mechanical modeling of the maturation process for textile reinforced tissue‐engineered heart valves

Abstract Biohybrid tissue‐engineered implants offer promising possibilities to treat cardiovascular diseases. The ability of tissue‐engineered implants to grow and remodel can be utilized to produce implants that can adapt to changes in the physiological conditions within the patient body. To improve the mechanical properties of the implant, a fibre‐reinforced textile scaffold is used. The embedment of a load‐oriented textile scaffold in the implant acts as biomimetic reinforcement and guides the direction of the extracellular matrix (ECM) growth. Our main objective is to design biohybrid heart valves that can withstand tough physiological loading conditions for decades. That makes it necessary to develop accurate and efficient models to support the design process. In this paper, the focus is on the macro‐mechanical modeling of the maturation process for textile reinforced heart valves. A biohybrid heart valve is modeled as a composite structure. The constitutive model is constructed by defining the total Helmholtz free energy as the sum of energies of the valve constituents. The two main constituents are (i) the extracellular matrix (ECM) and (ii) the fiber‐reinforced textile scaffold. The density of protein fibers such as collagen and elastin fibers are treated as internal variables. We introduce a new approach for modeling the densification of protein fibers during the cultivation process which is capable of considering both static and dynamic cultivation processes. The model considers the density change caused by the immunological response as well as the density change due to mechanical stimulation. The textile scaffold anisotropic behavior is introduced using structural tensors. The constitutive models are then embedded into a special finite element technology with reduced integration that enables efficient computations. The finite element simulation results are then validated using the experimental data provided by BioTex (Institute of Applied Medical Engineering, RWTH Aachen University, Germany). In the end, a finite element simulation for an exemplary valve is presented.