Millán Vaquero Ricardo Manuel, Vais Alexander, Dean Lynch Sean, Rzepecki Jan, Friese Karl-Ingo, Hurschler Christof, Wolter Franz-Erich
J Biomech Eng. 2016 Sep 1;138(9). doi: 10.1115/1.4034005.
We present processing methods and visualization techniques for accurately characterizing and interpreting kinematical data of flexion-extension motion of the knee joint based on helical axes. We make use of the Lie group of rigid body motions and particularly its Lie algebra for a natural representation of motion sequences. This allows to analyze and compute the finite helical axis (FHA) and instantaneous helical axis (IHA) in a unified way without redundant degrees of freedom or singularities. A polynomial fitting based on Legendre polynomials within the Lie algebra is applied to provide a smooth description of a given discrete knee motion sequence which is essential for obtaining stable instantaneous helical axes for further analysis. Moreover, this allows for an efficient overall similarity comparison across several motion sequences in order to differentiate among several cases. Our approach combines a specifically designed patient-specific three-dimensional visualization basing on the processed helical axes information and incorporating computed tomography (CT) scans for an intuitive interpretation of the axes and their geometrical relation with respect to the knee joint anatomy. In addition, in the context of the study of diseases affecting the musculoskeletal articulation, we propose to integrate the above tools into a multiscale framework for exploring related data sets distributed across multiple spatial scales. We demonstrate the utility of our methods, exemplarily processing a collection of motion sequences acquired from experimental data involving several surgery techniques. Our approach enables an accurate analysis, visualization and comparison of knee joint articulation, contributing to the evaluation and diagnosis in medical applications.
我们提出了基于螺旋轴精确表征和解释膝关节屈伸运动运动学数据的处理方法和可视化技术。我们利用刚体运动的李群，特别是其李代数来自然地表示运动序列。这使得我们能够以统一的方式分析和计算有限螺旋轴（FHA）和瞬时螺旋轴（IHA），而无需冗余自由度或奇点。应用基于李代数中勒让德多项式的多项式拟合来提供给定离散膝关节运动序列的平滑描述，这对于获得稳定的瞬时螺旋轴以进行进一步分析至关重要。此外，这允许对多个运动序列进行高效的整体相似性比较，以便区分几种情况。我们的方法结合了基于处理后的螺旋轴信息专门设计的患者特定三维可视化，并纳入计算机断层扫描（CT）扫描，以便直观地解释轴及其相对于膝关节解剖结构的几何关系。此外，在研究影响肌肉骨骼关节的疾病的背景下，我们建议将上述工具集成到一个多尺度框架中，以探索分布在多个空间尺度上的相关数据集。我们通过示例处理从涉及几种手术技术的实验数据中获取的一组运动序列，展示了我们方法的实用性。我们的方法能够对膝关节运动进行准确的分析、可视化和比较，有助于医学应用中的评估和诊断。
