Microscale modeling of layered fibrous networks with applications to biomaterials for tissue engineering
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Many important biomaterials are composed of multiple layers of networked fibers. A prime example is in the field of tissue engineering, in which damaged or diseased native tissues are replaced by artificial tissues that are grown on fibrous polymer networks. For load bearing tissues, it is critical that the mechanical behavior of the engineered tissue be similar to the behavior of the native tissue that it will replace. In the case of soft tissues such as heart valves, the macroscale mechanical behavior is highly anisotropic and nonlinear. This behavior is a result of complex deformations of the collagen and elastin fibers that form the extracellular matrix (ECM). The microstructure of engineered tissues must be properly designed to reproduce this unique macroscopic behavior. While there is a growing interest in modeling and simulation of the mechanical response of this class of biomaterials, a theoretical foundation for such simulations has yet to be firmly established. This work introduces a method for modeling materials that have a layered, fibrous network microstructure. Methods for characterizing the complex network geometry are first established. Then an algorithm is developed for generating realistic network geometry that is a good representation of electrospun tissue scaffolds, which serve as the primary synthetic structure on which engineered tissues are grown. The level of fidelity to the real geometry is a significant improvement on previous representations. This improvement is important, since the scaffold geometry has a strong influence over the macroscopic mechanical behavior of the tissue, cell proliferation and attachment, nutrient and waste flows, and extracellular matrix (ECM) generation. Because of the importance of scaffolds in tissue formation and function, this work focuses on characterizing scaffold network geometry and elucidating the impact of geometry on macroscale mechanics. Simulation plays an important role in developing a detailed understanding of scaffold mechanics. In this work, Cosserat rod theory is used to model individual fibers, which are connected to form a network that is treated as a representative volume element (RVE) of the material. The continuum theory is the basis for a finite element discretization. The nonlinear equations are solved using Newton's method in a parallel implementation that is capable of accurately capturing the large, three-dimensional fiber rotations and large fiber stretches that result from the large macroscopic deformations experienced by these biomaterials in their natural environment. Comparisons of simulation results with existing analytical models of soft tissues show that these models can predict the behavior of scaffold networks with reasonable accuracy, despite the significant differences between soft tissue and scaffold network microstructural geometry. The simulations also reveal how macroscale loading is related to the microscale fiber deformations and the load distribution among the fibers. The effects of different characteristics of the microstructural geometry on macroscopic behavior are explored, and the implications for the design of scaffolds that produce the desired macroscopic behavior are discussed. Overall, the improved modeling of electrospun scaffolds presented in this work is an important step toward designing more functional engineered tissues.