The role of disc-type crystal shape for micromechanical predictions of elasticity and strength of hydroxyapatite biomaterials
The role of disc-type crystal shape for micromechanical predictions of elasticity and strength of hydroxyapatite biomaterials
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DOI：
10.1098/rsta.2010.0005
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发表时间：
2010-04-28
期刊：
影响因子：
5
通讯作者：
Dormieux, Luc
中科院分区：
文献类型：
--
作者：
Fritsch, Andreas;Hellmich, Christian;Dormieux, Luc
陶瓷骨生物材料的成功设计面临着两个相互竞争的要求的挑战：一方面，此类材料需要坚硬且坚固，这意味着目标是低孔隙率（孔径在10-100毫米范围内）；另一方面，骨生物材料需要具有生物活性（特别是血管化），这表明此类材料具有高孔隙率。总之，关于孔隙率如何驱动陶瓷骨生物材料（组织工程支架）的刚度和强度特性的可靠信息非常令人感兴趣。在此背景下，数学模型越来越多地被引入该领域。最近，自洽连续微观力学公式已被证明是预测羟基磷灰石生物材料的刚度和强度的有效且可靠的工具，作为生物材料特定孔隙率以及单个羟基磷灰石晶体的“通用”特性（其刚度、强度和形状）的函数。然而，精确的晶体形状可以通过特定的椭圆体形状来适当地近似：虽然之前已经表明球形形状不能产生令人满意的结果，并且针状形状是合适的选择，但我们在这里专注于圆盘型晶体形状，因为除了针之外，在羟基磷灰石生物材料的显微照片中也经常报道板状晶体形状。基于盘的模型对羟基磷灰石生物材料的刚度和强度的大量实验数据的预测几乎达到了非常令人满意的基于针的模型的质量。这表明，只要晶体形状明显是非球形，如果基于连续微观力学、根据其微观形态和孔隙率来预测羟基磷灰石生物材料的刚度和强度，其精确形状就是次要的。
The successful design of ceramic bone biomaterials is challenged by two competing requirements: on the one hand, such materials need to be stiff and strong, which would suggest a low porosity (of pore sizes in the 10-100 mm range) to be targeted; on the other hand, bone biomaterials need to be bioactive (in particular vascularized), which suggests a high porosity of such materials. Conclusively, reliable information on how porosity drives the stiffness and strength properties of ceramic bone biomaterials (tissue engineering scaffolds) is of great interest. In this context, mathematical models are increasingly being introduced into the field. Recently, self-consistent continuum micromechanics formulations have turned out as expressedly efficient and reliable tools to predict hydroxyapatite biomaterials' stiffness and strength, as a function of the biomaterial-specific porosity, and of the 'universal' properties of the individual hydroxyapatite crystals: their stiffness, strength and shape. However, the precise crystal shape can be suitably approximated by specific ellipsoidal shapes: while it was shown earlier that spherical shapes do not lead to satisfactory results, and that acicular shapes are an appropriate choice, we here concentrate on disc-type crystal shape as, besides needles, plates are often reported in micrographs of hydroxyapatite biomaterials. Disc-based model predictions of a substantial set of experimental data on stiffness and strength of hydroxyapatite biomaterials almost attain the quality of the very satisfactory needle-based models. This suggests that, as long as the crystal shape is clearly non-spherical, its precise shape is of secondary importance if stiffness and strength of hydroxyapatite biomaterials are predicted on the basis of continuum micromechanics, from their micromorphology and porosity.