骨盆沿冠状轴旋转对髋臼假体影响的三维动态分析

Three-dimensional dynamic analysis of the effect of pelvic rotation around coronal axis on acetabular prosthesis

目的探讨骨盆沿冠状轴旋转对全髋关节置换术后髋臼假体安放角度的影响规律。方法根据Murary的定义将髋臼轴与矢状面成角定义为髋臼外展角,髋臼轴与冠状面成角定义为前倾角,利用数学软件GeoGebra建立简易数学立体几何模型,模拟沿冠状轴旋转时髋臼假体的动态变化,推导出髋臼假体前倾角和外展角动态变化的计算公式。采用MatLab软件绘制骨盆前倾角和外展角的函数图并分析髋臼假体的变化规律。结果骨盆沿冠状轴旋转时髋臼前倾角和外展角的动态变化与骨盆前后倾斜度存在函数相关关系,而非线性相关的关系。当骨盆沿冠状轴旋转时前倾角公式为α1=arcsin(sinβ1×cosα×cosθ+cosβ1×sinα);髋臼轴朝下时外展角公式为θ1=arccot(cosβ1×cotθ-sinβ1×tanα/sinθ);髋臼轴朝上时外展角公式为θ1=π-abs[arccot(cosβ1×cotθ-sinβ1×tanα/sinθ)],α为髋臼初始前倾角,θ为髋臼初始外展角,α1为骨盆旋转后髋臼假体前倾角,θ1为骨盆旋转后髋臼假体外展角,β1为骨盆沿冠状轴旋转角。骨盆后倾时髋臼假体前倾角先增后减,外展角持续增大,骨盆前倾时外展角先减后增,前倾角持续减小至负数,前倾角负数时表示髋臼轴朝向后方。结论当髋臼假体初始前倾角和外展角变化时,前倾角与外展角函数曲线发生相应改变;初始前倾角越大,前倾角越快达到峰值,峰值越大,外展角变化趋势越快;初始外展角越大,前倾角与外展角的变化趋势越小。

ObjectiveTo investigate the effect of pelvic rotation around coronal axis on the placement angle of acetabular prosthesis after total hip arthroplasty.MethodsAccording 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.ResultsThe 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 isα1=arcsin(sinβ1×cosα×cosθ+cosβ1×sinα);When the acetabulum axis faces downwards the abduction angle formula isθ1=arccot(cosβ1×cotθ-sinβ1×tanα/sinθ);When the acetabulum axis faces upwards the abduction angle formula isθ1=π-abs[arccot(cosβ1×cotθ-sinβ1×tanα/sinθ)]withαbeing the initial acetabular forward angle,θbeing the initial acetabular abduction angle,α1 being the forward angle of the acetabular prosthesis after pelvic rotation,θ1 being the external expansion angle of the acetabular prosthesis after pelvic rotation andβ1 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.ConclusionWhen 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.