Gradient of contact stress in normal and dysplastic human hips

The stress gradient index (Gp) is introduced for the assessment of dysplasia in human hip joint. The absolute value of Gp is equal to the magnitude of the gradient of the contact stress at the lateral acetabular rim. The parameter Gp normalized with respect to the body weight (WB) is determined from the standard anteroposterior radiographs of adult human hips and pelvises using the mathematical model. The average value of Gp/WB was determined for the group of dysplastic hips and for the group of normal hips. In the group of normal hips the average value of Gp/WB is smaller (−0.445×105 m−3) than in the group of dysplastic hips (+1.481×105 m−3). The difference is statistically significant P<0.001. The average value of Gp/WB changes its sign at the value of the centre-edge angle ϑCE≈20∘ which is usually considered as the boundary value of ϑCE (lower limit) for the normal hips. Accordingly we suggest a new definition for the hip dysplasia with respect to the size and sign of the normalized stress gradient index Gp/WB. The hips with positive Gp/WB are considered to be dysplastic while the hips with negative Gp/WB are considered to be normal. The statistically significant correlation between the value of the Harris hip score, used in the clinical assessment of the hip dysplasia, and the normalized stress gradient index was found.