剛体ばねモデルによる腰椎固定インプラントの力学的解析

Abstract

Pedicle screw fixation is a typical surgical method for lumbar scoliosis using spinal instruments such as metal screws, connectors, and rods. In correcting scoliosis, this method is stronger than other methods. However, screw loosening or rod breaking happens occasionally.In this study, a whole lumbar and instruments were modeled by rigid bodies and springs in three dimensions. An abdominal pressure and muscle forces acted on this model. Inserted pedicle loads and corrected lumbar postures were estimated using this model.Five lumbar vertebrae and ten screws are modeled as rigid bodies, and soft tissues and rods are represented as springs. A ligament is modeled by a linear spring for a tensile deformation, and an intervertebral disc is simplified as three axial springs and three torsional springs.A screw and a connector are combined as one rigid body. The 40-mm-long screw passes through 29 mm of cancellous bone in the vertebral body, 9 mm of subcortical bone in the pedicle, and 2 mm of cortical bone on the surface of the vertebra. These three kinds of bone are replaced with pullout, radial, and torsional springs, respectively. Each spring constant is obtained from experimental data in the literature. The spring constant of the rod is assumed to be equivalent to the uniform column beam.Muscle forces in daily simple motions are obtained from the three-dimensional musculoskeletal model developed in the previous study. The simple motions are represented by a flexion of 30 degrees, a right lateral bending of 20 degrees, and a counterclockwise rotation of 10 degrees.The relative displacements (3 D.O.F. times 15 rigid bodies) and angles (3 times 15) are calculated applying the Runge-Kutta-Gill method. The initial load of the calculation is the gross weight of the upper body (0.25 kN) .The following three types of fixation for scoliosis with a Cobb’s angle of 30 degrees were simulated: (a) screws inserted into both sides of L1-5; (b) both sides of L1, 3, and 5; and (c) only the right side of L1-5. In the case of (a) and (b), the relative displacements and rotation angles are almost the same values, but pullout forces on L3 in (b) are close to the maximum limitation (1.0 kN) . In (c), the radial forces are very large. These estimates indicate that only case (a) can correct the scoliosis without loosening the screws. Additionally, since all the corrected postures are lumbar coupled motions, the above results show that three-dimensional models are available.The force of the connection along the rod between the connector and the rod needs 1.2 kN, and the moment around the rod needs 1.8 Nm in simple motions. In order to prevent this force and moment from exceeding a fatigue stress (Ti-6Al-4V: 0.54 GPa), the diameter of the rod should be at least 4.2 mm. This design is given only by modeling of the instruments and of the in vivo conditions such as an abdominal pressure and muscle forces.