Vrtovec Tomaz, Likar Bostjan, Pernus Franjo
University of Ljubljana, Faculty of Electrical Engineering, Trzaska 25, SI-1000 Ljubljana, Slovenia.
Phys Med Biol. 2008 Apr 7;53(7):1895-908. doi: 10.1088/0031-9155/53/7/006. Epub 2008 Mar 10.
The purpose of this study is to present a framework for quantitative analysis of spinal curvature in 3D. In order to study the properties of such complex 3D structures, we propose two descriptors that capture the characteristics of spinal curvature in 3D. The descriptors are the geometric curvature (GC) and curvature angle (CA), which are independent of the orientation and size of spine anatomy. We demonstrate the two descriptors that characterize the spinal curvature in 3D on 30 computed tomography (CT) images of normal spine and on a scoliotic spine. The descriptors are determined from 3D vertebral body lines, which are obtained by two different methods. The first method is based on the least-squares technique that approximates the manually identified vertebra centroids, while the second method searches for vertebra centroids in an automated optimization scheme, based on computer-assisted image analysis. Polynomial functions of the fourth and fifth degree were used for the description of normal and scoliotic spinal curvature in 3D, respectively. The mean distance to vertebra centroids was 1.1 mm (+/-0.6 mm) for the first and 2.1 mm (+/-1.4 mm) for the second method. The distributions of GC and CA values were obtained along the 30 images of normal spine at each vertebral level and show that maximal thoracic kyphosis (TK), thoracolumbar junction (TJ) and maximal lumbar lordosis (LL) on average occur at T3/T4, T12/L1 and L4/L5, respectively. The main advantage of GC and CA is that the measurements are independent of the orientation and size of the spine, thus allowing objective intra- and inter-subject comparisons. The positions of maximal TK, TJ and maximal LL can be easily identified by observing the GC and CA distributions at different vertebral levels. The obtained courses of the GC and CA for the scoliotic spine were compared to the distributions of GC and CA for the normal spines. The significant difference in values indicates that the descriptors of GC and CA may be used to detect and quantify scoliotic spinal curvatures. The proposed framework may therefore improve the understanding of spine anatomy and aid in the clinical quantitative evaluation of spinal deformities.
本研究的目的是提出一个用于三维脊柱曲率定量分析的框架。为了研究此类复杂三维结构的特性，我们提出了两个描述符，用于捕捉三维脊柱曲率的特征。这两个描述符分别是几何曲率（GC）和曲率角（CA），它们与脊柱解剖结构的方向和大小无关。我们在30张正常脊柱的计算机断层扫描（CT）图像和一张脊柱侧弯的图像上展示了这两个用于表征三维脊柱曲率的描述符。这些描述符是根据通过两种不同方法获得的三维椎体线来确定的。第一种方法基于最小二乘法技术，该技术近似手动识别的椎体中心，而第二种方法基于计算机辅助图像分析，在自动优化方案中搜索椎体中心。分别使用四次和五次多项式函数来描述正常和脊柱侧弯的三维脊柱曲率。第一种方法到椎体中心的平均距离为1.1毫米（±0.6毫米），第二种方法为2.1毫米（±1.4毫米）。沿着正常脊柱的30张图像在每个椎体水平获得了GC和CA值的分布，结果表明，平均而言，最大胸椎后凸（TK）、胸腰段交界（TJ）和最大腰椎前凸（LL）分别出现在T3/T4、T12/L1和L4/L5。GC和CA的主要优点是测量结果与脊柱的方向和大小无关，从而允许进行客观的个体内和个体间比较。通过观察不同椎体水平的GC和CA分布，可以轻松识别最大TK、TJ和最大LL的位置。将脊柱侧弯的GC和CA所获得的曲线与正常脊柱的GC和CA分布进行了比较。值的显著差异表明，GC和CA描述符可用于检测和量化脊柱侧弯的脊柱曲率。因此，所提出的框架可能会增进对脊柱解剖结构的理解，并有助于脊柱畸形的临床定量评估。
