Bohner M, Baumgart F
Dr. Robert Mathys Foundation, Bischmattstrasse 12, 2544 Bettlach, Switzerland.
Biomaterials. 2004 Aug;25(17):3569-82. doi: 10.1016/j.biomaterials.2003.10.032.
A theoretical approach was used to determine the effect of geometrical factors on the resorption rate of calcium phosphate bone substitutes that are either dense, microporous, and/or contain spherical macropores. Two cases were considered: (a) macroporous blocks that can be invaded by resorbing cells either directly because the structure is fully open-porous, or indirectly after some resorption of the macropores walls and/or interconnections. (b) Microporous or dense blocks/granules that cannot be invaded by resorbing cells, i.e. can only be resorbed from the outside to the inside, layer by layer. The theoretical approach was based on five assumptions: (i) the pores are spherical; (ii) the pores are ordered according to a face-centered cubic packing; (iii) the resorption is surface-controlled; (iv) the resorption is only possible if the surface can be accessed by blood vessels of 50 microm in diameter; and (v) the resorption time of a given amount of calcium phosphate is proportional to the net amount of material. Based on these assumptions, the calculations showed that the resorption time of a macroporous block could be minimized at a specific pore radius. This pore radius depended (i) on the size of the bone substitute and (ii) on the interpore distance. Typical radii were in the range of 100-400 microm. These values are similar to the numerous pore size optima mentioned in the scientific literature. For microporous or dense blocks/granules, the model suggested that a relatively small radius should be preferred. Such a radius leads to an optimum combination of a high surface area favorizing resorption and the presence of large intergranular gaps favorizing blood vessel ingrowth. In that case, the optimum of granule radius is around 100-200 microm. Finally, a very good agreement was found between the predictions of the model and experimental data, i.e. the model explained in all but two cases the results with an accuracy superior to 80%. In conclusion, the model appears to be a useful tool to better understand in vivo results, and possibly better define the geometry and distribution of the pores as well as the size of a bone substitute.
采用理论方法来确定几何因素对致密、微孔和/或含有球形大孔的磷酸钙骨替代物吸收速率的影响。考虑了两种情况：(a) 大孔块状物，由于结构为完全开放多孔，吸收细胞可直接侵入，或者在大孔壁和/或互连结构发生一定程度的吸收后间接侵入。(b) 微孔或致密的块状物/颗粒，吸收细胞无法侵入，即只能从外到内逐层吸收。该理论方法基于五个假设：(i) 孔为球形；(ii) 孔按面心立方堆积排列；(iii) 吸收受表面控制；(iv) 只有当直径为50微米的血管能够接触到表面时才可能发生吸收；(v) 给定数量的磷酸钙的吸收时间与材料的净量成正比。基于这些假设，计算表明大孔块状物的吸收时间在特定孔半径时可达到最小。该孔半径取决于：(i) 骨替代物的尺寸；(ii) 孔间距。典型半径范围为100 - 400微米。这些值与科学文献中提到的众多最佳孔径相似。对于微孔或致密的块状物/颗粒，该模型表明应选择相对较小的半径。这样的半径可使有利于吸收的高表面积与有利于血管长入的大颗粒间隙之间达到最佳组合。在这种情况下，颗粒半径的最佳值约为100 - 200微米。最后，发现模型预测与实验数据之间具有很好的一致性，即除了两个案例外，该模型在所有情况下对结果的解释准确率均超过80%。总之，该模型似乎是一个有用的工具，可以更好地理解体内实验结果，并可能更好地确定孔的几何形状、分布以及骨替代物的尺寸。
