Objective To investigate the effect of pelvic rotation around coronal axis on the placement angle of acetabu-lar 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 calcula-tion formula of the dynamic changes of the anterior inclination and abduction angle of the acetabular prosthesis was derived.Mat-Lab 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 α1=arcsin(sinβ1×cosα×cosθ+cosβ1×sinα);When the acetabu-lum axis faces downwards the abduction angle formula is θ1=arccot(cosβ1×cotθ-sinβ1×tanα/sinθ);When the acetabulum axis fac-es upwards the abduction angle formula is θ1=π-abs[arccot(cosβ1×cotθ-sinβ1×tanα/sinθ)]withα being the initial acetabular for-ward angle,θ being the initial acetabular abduction angle,α1 being the forward angle of the acetabular prosthesis after pelvic rota-tion,θ1 being the external expansion angle of the acetabular prosthesis after pelvic rotation and β1 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 in-creases first and then decreases,and the abduction angle continues to increase.When the pelvis is tilted forward,the abduction an-gle 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 ab-duction 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 ante-rior inclination angle and the abduction angle change.
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