Three-dimensional dynamic analysis of the effect of pelvic rotation around coronal axis on acetabular prosthesis / 中华骨科杂志

ABSTRACT

Objective:To investigate the effect of pelvic rotation around coronal axis on the placement angle of acetabular prosthesis after total hip arthroplasty.Methods:According to Murary's definition, the angle between the acetabular axis and the sagittal plane was defined as the acetabular abduction angle, and the angle between the acetabular axis and the coronal plane as the anterior inclination angle. A simple mathematical solid geometry model was established by using the mathematical software GeoGebra to simulate the dynamic changes of the acetabular prosthesis when it rotated around the coronal axis, and the calculation formula of the dynamic changes of the anterior inclination and abduction angle of the acetabular prosthesis was derived. MatLab software was used to generate the function graph of pelvis forward inclination and abduction angle and deduce the motion of acetabular prosthesis.Results:The dynamic changes of acetabular tilt angle and abduction angle when the pelvis rotated around the coronal axis were functionally related to the anterior-posterior tilt of the pelvis in a nonlinear pattern. When the pelvis rotates around the coronary axis, the anterior inclination angle formula is α 1=arcsin (sinβ 1×cosα×cosθ+cosβ 1×sinα); When the acetabulum axis faces downwards the abduction angle formula is θ 1=arccot (cosβ 1×cotθ-sinβ 1×tanα/sinθ); When the acetabulum axis faces upwards the abduction angle formula is θ 1=π-abs[arccot (cosβ 1×cotθ-sinβ 1×tanα/sinθ)] withα being the initial acetabular forward angle, θ being the initial acetabular abduction angle, α 1 being the forward angle of the acetabular prosthesis after pelvic rotation, θ 1 being the external expansion angle of the acetabular prosthesis after pelvic rotation and β 1 being the rotation angle of the pelvis around the coronal axis. When the pelvis is tilted backward, the anterior inclination angle of the acetabular prosthesis increases first and then decreases, and the abduction angle continues to increase. When the pelvis is tilted forward, the abduction angle decreases first and then increases, and the anterior inclination angle continues to decrease to negative. Conclusion:When the initial anterior inclination angle and abduction angle of acetabular prosthesis change, the curve of anterior inclination and abduction angle change accordingly. The larger the initial anterior inclination angle is, the faster it reaches its peak value, and the larger the peak value is, the faster the abduction angle changes. The larger the initial abduction angle is, the slower the initial anterior inclination angle and the abduction angle change.