Mathematical Modeling of 3D Tissue Engineering Constructs
Tissue engineering represents a new field aiming at developing biological substitutes to restore, maintain, or improve tissue functions. In this approach, scaffolds provide a temporary mechanical and vascular support for tissue regeneration while tissue ingrowth is being formed. The design of optimized scaffolds for tissue engineering applications is a key topic of research, as the complex macro- and micro-architectures required for a scaffold depends on the mechanical and vascular properties and physical and molecular queues of the surrounding tissue at the defect site. One way to achieve such hierarchical designs is to create a library of unit cells, which can be assembled through a computational tool.
Besides presenting an overview scaffold designs based hyperbolic surfaces, this chapter investigates the use of two different types of triply periodic minimal surfaces, Schwarz and Schoen, in order to design better biomimetic scaffolds with high surface-to-volume ratio, high porosity, and good mechanical properties. The effect of two parametric parameters (thickness and surface radius) is also evaluated regarding its porosity and mechanical behavior.
KeywordsTissue engineering Scaffold design Triply periodic minimal surfaces Schwartz surfaces Schoen surfaces
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