Bonifasi-Lista Carlos, Cherkaev Elena, Yeni Yener N
Department of Bioengineering, University of Utah, 72 South Central Campus Drive, Room 2646, Salt Lake City, UT 84112, USA.
J Biomech Eng. 2009 Dec;131(12):121003. doi: 10.1115/1.4000082.
This work deals with the study of the analytical relations between porosity of cancellous bone and its mechanical properties. The Stieltjes representation of the effective shear complex modulus of cancellous bone is exploited to recover porosity. The microstructural information is contained in the spectral measure in this analytical representation. The spectral function can be recovered from the effective measurements over a range of frequencies. The problem of reconstruction of the spectral measure is very ill-posed. Regularized algorithm is derived to ensure stability of the results. The proposed method does not use any specific assumptions about the microgeometry of bone. The approach does not rely on correlation analysis, it uses analytical relationships. For validation purposes, complex shear modulus over a range of frequencies was calculated by the finite element method using micro-computed tomography (micro-CT) images of human cancellous bone. The calculated values were used in numerical algorithm to recover bone porosity. At the microlevel, bone was modeled as a heterogeneous medium composed of trabeculae tissue and bone marrow treated as transversely isotropic elastic and isotropic viscoelastic materials, respectively. Recovered porosity values are in excellent agreement with true porosity found from the corresponding micro-CT images.
这项工作致力于研究松质骨孔隙率与其力学性能之间的解析关系。利用松质骨有效剪切复模量的斯蒂尔杰斯表示来恢复孔隙率。微观结构信息包含在这种解析表示的谱测度中。谱函数可从一系列频率上的有效测量值中恢复。谱测度的重建问题是严重不适定的。推导了正则化算法以确保结果的稳定性。所提出的方法不使用关于骨微观几何形状的任何特定假设。该方法不依赖于相关性分析，而是使用解析关系。为了进行验证，使用人体松质骨的微观计算机断层扫描（micro-CT）图像，通过有限元方法计算了一系列频率上的复剪切模量。计算值被用于数值算法中以恢复骨孔隙率。在微观层面，骨被建模为一种非均匀介质，由小梁组织和骨髓组成，分别视为横向各向同性弹性材料和各向同性粘弹性材料。恢复的孔隙率值与从相应微观CT图像中得到的真实孔隙率非常吻合。
