Statistical Shape Modeling of Skeletal Anatomy for Sex Discrimination: Their Training Size, Sexual Dimorphism, and Asymmetry

Abstract

Purpose: Statistical shape modeling provides a powerful tool for describing and analyzing human anatomy. By linearly combining the variance of the shape of a population of a given anatomical entity, statistical shape models (SSMs) identify its main modes of variation and may approximate the total variance of that population to a selected threshold, while reducing its dimensionality. Even though SSMs have been used for over two decades, they lack in characterization of their goodness of prediction, in particular when defining whether these models are actually representative for a given population. Methods: The current paper presents, to the authors' knowledge, the most extent lower limb anatomy shape model considering the pelvis, femur, patella, tibia, fibula, talus, and calcaneum to date. The present study includes the segmented training shapes (n = 542) obtained from 271 lower limb CT scans. The different models were evaluated in terms of accuracy, compactness, generalizability as well as specificity. Results: The size of training samples needed in each model so that it can be considered population covering was estimated to approximate around 200 samples, based on the generalizability properties of the different models. Simultaneously differences in gender and patterns in left-right asymmetry were identified and characterized. Size was found to be the most pronounced sexual discriminator whereas intra-individual variations in asymmetry were most pronounced at the insertion site of muscles. Conclusion: For models aimed at population covering descriptive studies, the number of training samples required should amount a sizeable 200 samples. The geometric morphometric method for sex discrimination scored excellent, however, it did not largely outperformed traditional methods based on discrete measures.

Keywords: PCA data analysis; morphometric analysis; sex discrimination; shape modeling; validation and simulation.

Figure 1

Cumulative variance of the population by number principal components following a principal component analysis (PCA) to describe the different skeletal models.

Figure 2

Accuracy evolution of the SSM-based shape representation (solid curve) and in-sample target accuracy (dotted curve) for different levels of prior knowledge expressed as amounts of training data in the SSM.

Figure 3

Heat maps demonstrating sexual dimorphism and asymmetry in the different anatomical shapes considered. PC scores describing the male and female gender differences obtained following the canonical correlation analysis were amplified with a factor 2 when compared to the overall average shape configuration. Asymmetry findings were projected on the average symmetrical consensus shape.