How does the femoral cortex depend on bone shape? A methodology for the joint analysis of surface texture and shape

Highlights • We consider cohorts of surfaces with scalar data at each vertex: textured surfaces. • The joint analysis of shape and texture is of interest but also inherently ambiguous. • The ambiguity may be resolved using homologies to guide vertex correspondences. • This is an extention of Geometric Morphometric Image Analysis to textured surfaces. • The method reveals how cortical bone depends on shape in the human proximal femur.
Graphical abstract
In humans, there is clear evidence of an association between hip fracture risk and femoral neck bone mineral density, and some evidence of an association between fracture risk and the shape of the proximal femur. Here, we investigate whether the femoral cortex plays a role in these associations: do particular morphologies predispose to weaker cortices? To answer this question, we used cortical bone mapping to measure the distribution of cortical mass surface density (CMSD, mg/cm2) in a cohort of 125 females. Principal component analysis of the femoral surfaces identified three modes of shape variation accounting for 65% of the population variance. We then used statistical parametric mapping (SPM) to locate regions of the cortex where CMSD depends on shape, allowing for age. Our principal findings were increased CMSD with increased gracility over much of the proximal femur; and decreased CMSD at the superior femoral neck, coupled with increased CMSD at the calcar femorale, with increasing neck-shaft angle. In obtaining these results, we studied the role of spatial normalization in SPM, identifying systematic misregistration as a major impediment to the joint analysis of CMSD and shape. Through a series of experiments on synthetic data, we evaluated a number of registration methods for spatial normalization, concluding that only those predicated on an explicit set of homologous landmarks are suitable for this kind of analysis. The emergent methodology amounts to an extension of Geometric Morphometric Image Analysis to the domain of textured surfaces, alongside a protocol for labelling homologous landmarks in clinical CT scans of the human proximal femur.