Institut für Theoretische Physik, Friedrich-Alexander-Universität Erlangen-Nürnberg, Erlangen, Germany.
Biomaterials. 2011 Oct;32(29):6875-82. doi: 10.1016/j.biomaterials.2011.06.012. Epub 2011 Jul 12.
Triply-periodic minimal surfaces are shown to be a more versatile source of biomorphic scaffold designs than currently reported in the tissue engineering literature. A scaffold architecture with sheetlike morphology based on minimal surfaces is discussed, with significant structural and mechanical advantages over conventional designs. These sheet solids are porous solids obtained by inflation of cubic minimal surfaces to sheets of finite thickness, as opposed to the conventional network solids where the minimal surface forms the solid/void interface. Using a finite-element approach, the mechanical stiffness of sheet solids is shown to exceed that of conventional network solids for a wide range of volume fractions and material parameters. We further discuss structure-property relationships for mechanical properties useful for custom-designed fabrication by rapid prototyping. Transport properties of the scaffolds are analyzed using Lattice-Boltzmann computations of the fluid permeability. The large number of different minimal surfaces, each of which can be realized as sheet or network solids and at different volume fractions, provides design flexibility essential for the optimization of competing design targets.
三重周期极小曲面在生物形态支架设计方面比目前组织工程文献中的报道更为通用。本文讨论了一种基于极小曲面的片状形态支架结构，与传统设计相比具有显著的结构和力学优势。这些片状固体是通过将立方极小曲面膨胀为有限厚度的薄片而获得的多孔固体，而不是传统的网络固体，其中极小曲面形成固体/空隙界面。使用有限元方法，证明片状固体的机械刚度在广泛的体积分数和材料参数范围内超过了传统的网络固体。我们进一步讨论了用于通过快速原型制造定制设计的机械性能的结构-性能关系。使用格子玻尔兹曼计算来分析支架的传输特性。大量不同的极小曲面，其中每一个都可以作为片状或网络固体来实现，并且在不同的体积分数下，为优化竞争设计目标提供了必要的设计灵活性。
