Introduction

In the modelling of human gait, few joints are as complicated in mechanical effect as the hip. It trades torque back and forth with the ankle plantar flexors, swinging the limb and placing the foot, while balancing the trunk on its proverbial shoulders. Whilst the approximation of the knee and ankle as single-axis hinge joints may or may not be an over-simplification, the normal functioning hip joint is undeniably a three-axis ball-and-socket, flexing, rotating and abducting in response to external forces and internal muscle-based activations. With great degrees of freedom, however, comes great responsibility (of gait biomechanists to correctly locate this joint centre).

Small changes in model geometry can lead to large changes in calculated forces and moments; perturbation of the hip joint centre (HJC) by as little as two centimetres can alter the moment arms and force generation capacity of a modelled limb by as much as 50 % (Delp and Maloney, 1993). Correct estimation of subject-specific hip geometry is essential for accurate estimation of contact forces, themselves crucial for understanding mechanobiological processes or hip arthroplasty implant mechanics (Lenaerts et al., 2009). The HJC location in gait models also influences the definition of the knee joint coordinate system (Kainz et al., 2015), affecting similar factors for knee flexion (and thereby knee arthroplasty and knee osteoarthritis modelling too). Locating an individual’s HJC becomes relatively trivial using 3D imaging, such as MRI or CT scans, commonly defined as the centre of a sphere fitted to the femoral head or acetabulum (or concentric circles on the shadow of the same feature on an X-ray) (Bell et al., 1989). However, it is not always feasible to obtain medical images for this purpose, necessitating other approaches to predict the HJC location within the pelvis coordinate system.

Regression equations that describe the position of the HJC in the pelvis frame have been established and used predominantly in gait analysis over the past 40 years. Tylkowski and Andriacchi, for example, developed regression equations (whether explicit linear models or simple average proportions) to describe the most-likely position of the HJC based on external landmarks such as the anterior superior iliac spines (ASIS) or pubic symphysis (PS) (Andriacchi and Strickland, 1985, Tylkowski et al., 1982). This work was further developed by others, like Bell, who generated new estimates of the coefficients for Tylkowski’s equations and extended Andriacchi’s approach into a third dimension (Bell et al., 1989), or Seidel, who passed over the use of inter-ASIS distance for non medial–lateral placement, adding measurements of the height and depth of the pelvis to the equation (Seidel et al., 1995). These methods each have advantages and drawbacks; pelvic depth is difficult to accurately measure in-vivo, but its exclusion results in larger uncertainties of the depth of the HJC. Seidel’s equation was based on 65 adult pelves, representing a larger population than the 31 adult pelves used by Bell. Seidel’s pelvic examinations were also more thorough than Bell’s orthogonal radiographs, given that said pelves were removed and fully de-fleshed before measurement.

Worth noting is a related study conducted by Hara et al. (Hara et al., 2016) (using data from the same forensic institute); however, their best solutions for HJC estimation all involved entire lower-limb measurements, rather than purely pelvic landmarks. We would also be remiss to not mention our prior efforts to predict the HJC using statistical shape models using the MAP Client Lower-Limb Scaling Workflow (Zhang et al., 2016, Bahl et al., 2019). Here we have used 159 CT-segmented cadaveric pelves to assess the accuracy and generate new estimates of coefficients for the regression models described above.

Dataset

Under ethics approval, the Victorian Institute of Forensic Medicine (Melbourne, Australia) provided de-identified computerised tomography (CT) scans of 159 cadavers. These were made up of 86 male and 73 female cadavers, with an average age of 57 ± 19 years. This sample represented a mature adult western population from an urban environment.

Landmark measurements

CT images were used to generate estimates of landmark locations for each cadaveric pelvis; including the left and right Anterior and Posterior Superior Iliac

Results

Each set of new parameters is reported below, along with error reduction. Mean absolute error for each method is tabulated at the end of this section.

Discussion

It follows that a model based on a larger sample may describe more inter-subject variation than a similar model based on a smaller sample, and thereby result in lower average error (particularly on subjects that were not part of the sample used to create it). Our results support this being the case, with our improved regression equation values reducing errors in hip joint centre estimation for all approaches. Our improvement may also be due to the method with which we measured the HJC location