Department of Mechanical Engineering, École Polytechnique de Montréal, P.O. Box 6079, Station Centre-ville, Montréal, Québec H3C3A7, Canada.
Med Biol Eng Comput. 2011 Aug;49(8):967-77. doi: 10.1007/s11517-011-0793-4. Epub 2011 Jul 5.
The distribution of stresses in the scoliotic spine is still not well known despite its biomechanical importance in the pathomechanisms and treatment of scoliosis. Gravitational forces are one of the sources of these stresses. Existing finite element models (FEMs), when considering gravity, applied these forces on a geometry acquired from radiographs while the patient was already subjected to gravity, which resulted in a deformed spine different from the actual one. A new method to include gravitational forces on a scoliotic trunk FEM and compute the stresses in the spine was consequently developed. The 3D geometry of three scoliotic patients was acquired using a multi-view X-ray 3D reconstruction technique and surface topography. The FEM of the patients' trunk was created using this geometry. A simulation process was developed to apply the gravitational forces at the centers of gravity of each vertebra level. First the "zero-gravity" geometry was determined by applying adequate upwards forces on the initial geometry. The stresses were reset to zero and then the gravity forces were applied to compute the geometry of the spine subjected to gravity. An optimization process was necessary to find the appropriate zero-gravity and gravity geometries. The design variables were the forces applied on the model to find the zero-gravity geometry. After optimization the difference between the vertebral positions acquired from radiographs and the vertebral positions simulated with the model was inferior to 3 mm. The forces and compressive stresses in the scoliotic spine were then computed. There was an asymmetrical load in the coronal plane, particularly, at the apices of the scoliotic curves. Difference of mean compressive stresses between concavity and convexity of the scoliotic curves ranged between 0.1 and 0.2 MPa. In conclusion, a realistic way of integrating gravity in a scoliotic trunk FEM was developed and stresses due to gravity were explicitly computed. This is a valuable improvement for further biomechanical modeling studies of scoliosis.
尽管脊柱侧凸的生物力学在脊柱侧凸的发病机制和治疗中具有重要意义，但脊柱侧凸中应力的分布仍不清楚。重力是这些力的来源之一。现有的有限元模型（FEM）在考虑重力时，将这些力施加到患者已经承受重力的射线照片获得的几何体上，这导致与实际的脊柱不同的变形脊柱。因此，开发了一种新的方法来将重力纳入脊柱侧凸躯干 FEM 并计算脊柱中的应力。使用多视图 X 射线 3D 重建技术和表面拓扑结构获取了三个脊柱侧凸患者的 3D 几何形状。使用该几何形状创建了患者躯干的 FEM。开发了一个模拟过程来在每个椎骨水平的重心施加重力。首先，通过在初始几何形状上施加适当的向上力来确定“零重力”几何形状。将应力重置为零，然后施加重力以计算受重力作用的脊柱几何形状。需要优化过程来找到合适的零重力和重力几何形状。设计变量是施加于模型上的力，以找到零重力几何形状。优化后，从射线照片获得的椎体位置与模型模拟的椎体位置之间的差异小于 3 毫米。然后计算了脊柱侧凸中的力和压缩应力。在冠状平面上存在不对称的载荷，特别是在脊柱侧凸曲线的顶点处。脊柱侧凸曲线凹面和凸面之间的平均压缩应力差异在 0.1 到 0.2 MPa 之间。总之，开发了一种在脊柱侧凸躯干 FEM 中集成重力的现实方法，并明确计算了重力引起的应力。这是进一步进行脊柱侧凸生物力学建模研究的有价值的改进。
