Gu Dongyun, Chen Yazhu, Dai Kerong, Zhang Su, Yuan Jianbin
Department of Orthopaedics & Bone and Joint Research Center, Shanghai 9th People's Hospital, Shanghai Jiaotong University School of Medicine, Shanghai 200011, China.
Med Eng Phys. 2008 Oct;30(8):1024-31. doi: 10.1016/j.medengphy.2007.12.013. Epub 2008 Feb 13.
The acetabular cartilage surface plays an important role in hip joint biomechanics, locomotion and lubrication, but few studies has focused on its geometric morphometry. The aim of this study was to present a novel, accurate mathematical representation of the acetabular cartilage surface based on a new method, combined with a reverse engineering technique, surface-fitting algorithms and mathematical curve surface theory. By using a three-dimensional (3D) laser scanner, a 3D triangulated mesh surface approximation of acetabular cartilage was created. Using surface-fitting algorithms and mathematical curve surface theory, two main curvature parameters, Gaussian curvature and mean curvature at each point on the surface of the acetabular cartilage, were calculated. The distribution patterns of both parameters over the curved surface were elucidated and the eigenvalues of the surface were calculated to determine the shape of the acetabular cartilage surface. By statistically analyzing 25 specimens, it was found that the shape of the acetabular cartilage surface was not theoretically spherical but rotational ellipsoidal, which is a novel mathematical description. The surface-fitting error of a rotational ellipsoid shape was significantly smaller than that of a spherical shape for representing the acetabular cartilage surface (p<0.001). The highest surface-fitting error for a spherical shape was seen in the roof area of the acetabular cartilage, where a rotational ellipsoid surface presented a better anatomical fit. The results will not only be helpful in gaining a new anatomical understanding of the acetabular cartilage surface, but will also be usable in the construction of a precise 3D numerical model in simulation studies of the hip joint.
髋臼软骨表面在髋关节生物力学、运动和润滑方面发挥着重要作用，但很少有研究关注其几何形态测量。本研究的目的是基于一种新方法，结合逆向工程技术、曲面拟合算法和数学曲线曲面理论，提出一种新颖、准确的髋臼软骨表面数学表示方法。通过使用三维（3D）激光扫描仪，创建了髋臼软骨的3D三角网格表面近似。利用曲面拟合算法和数学曲线曲面理论，计算了髋臼软骨表面各点的两个主要曲率参数，即高斯曲率和平均曲率。阐明了这两个参数在曲面上的分布模式，并计算了表面的特征值以确定髋臼软骨表面的形状。通过对25个标本进行统计分析，发现髋臼软骨表面的形状在理论上不是球形而是旋转椭球形，这是一种新颖的数学描述。对于表示髋臼软骨表面，旋转椭球体形状的曲面拟合误差明显小于球体形状（p<0.001）。球体形状的最高曲面拟合误差出现在髋臼软骨的顶部区域，而旋转椭球表面在此处呈现出更好的解剖学拟合。这些结果不仅有助于对髋臼软骨表面获得新的解剖学认识，还可用于髋关节模拟研究中精确3D数值模型的构建。
