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Traditionally, two-dimensional conventional radiographs have been the primary tool to measure the complex morphology of the foot and ankle. However, the subtalar, talonavicular, and calcaneocuboid joints are challenging to assess due to their bone morphology and locations within the ankle. Weightbearing computed tomography is a novel high-resolution volumetric imaging mechanism that allows detailed generation of 3D bone reconstructions. This study aimed to develop a multi-domain statistical shape model to assess morphologic and alignment variation of the subtalar, talonavicular, and calcaneocuboid joints across an asymptomatic population and calculate 3D joint measurements in a consistent weightbearing position. Specific joint measurements included joint space distance, congruence, and coverage. Noteworthy anatomical variation predominantly included the talus and calcaneus, specifically an inverse relationship regarding talar dome heightening and calcaneal shortening. While there was minimal navicular and cuboid shape variation, there were alignment variations within these joints; the most notable is the rotational aspect about the anterior-posterior axis. This study also found that multi-domain modeling may be able to predict joint space distance measurements within a population. Additionally, variation across a population of these four bones may be driven far more by morphology than by alignment variation based on all three joint measurements. These data are beneficial in furthering our understanding of joint-level morphology and alignment variants to guide advancements in ankle joint pathological care and operative treatments.

Introduction: Statistical shape modeling (SSM) is a valuable and powerful tool to generate a detailed representation of complex anatomy that enables quantitative analysis of shapes and their variations. SSM applies mathematics, statistics, and computing to parse the shape into some quantitative representation (such as correspondence points or landmarks) which can be used to study the covariance patterns of the shapes and answer various questions about the anatomical variations across the population. Complex anatomical structures have many diverse parts with varying interactions or intricate architecture. For example, the heart is a four-chambered organ with several shared boundaries between chambers. Subtle shape changes within the shared boundaries of the heart can indicate potential pathologic changes such as right ventricular overload. Early detection and robust quantification could provide insight into ideal treatment techniques and intervention timing. However, existing SSM methods do not explicitly handle shared boundaries which aid in a better understanding of the anatomy of interest. If shared boundaries are not explicitly modeled, it restricts the capability of the shape model to identify the pathological shape changes occurring at the shared boundary. Hence, this paper presents a general and flexible data-driven approach for building statistical shape models of multi-organ anatomies with shared boundaries that explicitly model contact surfaces.Methods: This work focuses on particle-based shape modeling (PSM), a state-of-art SSM approach for building shape models by optimizing the position of correspondence particles. The proposed PSM strategy for handling shared boundaries entails (a) detecting and extracting the shared boundary surface and contour (outline of the surface mesh/isoline) of the meshes of the two organs, (b) followed by a formulation for a correspondence-based optimization algorithm to build a multi-organ anatomy statistical shape model that captures morphological and alignment changes of individual organs and their shared boundary surfaces throughout the population.Results: We demonstrate the shared boundary pipeline using a toy dataset of parameterized shapes and a clinical dataset of the biventricular heart models. The shared boundary model for the cardiac biventricular data achieves consistent parameterization of the shared surface (interventricular septum) and identifies the curvature of the interventricular septum as pathological shape differences.

Numerous clinical investigations require understanding changes in anatomical shape over time, such as in dynamic organ cycle characterization or longitudinal analyses (e.g., for disease progression). Spatiotemporal statistical shape modeling (SSM) allows for quantifying and evaluating dynamic shape variation with respect to a cohort or population of interest. Existing data-driven SSM approaches leverage information theory to capture population-level shape variations by learning correspondence-based (landmark) representations of shapes directly from data using entropy-based optimization schemes. These approaches assume sample independence and thus are unsuitable for sequential dynamic shape observations. Previous methods for adapting entropy-based SSM optimization schemes for the spatiotemporal case either utilize a cross-sectional design (ignoring within-subject correlation) or impose other limiting assumptions, such as the linearity of shape dynamics. Here, we present a principled approach to spatiotemporal SSM that relaxes these assumptions to correctly capture population-level shape variation over time. We propose to incorporate modeling the underlying time dependency into correspondence optimization via a regularized principal component polynomial regression. This approach is flexible enough to capture non-linear temporal dynamics while encoding population-specific spatial regularity. We demonstrate our method’s efficacy on synthetic data and left atrium segmented from cardiac MRI scans. Our approach better captures the population modes of variation and a statistically significant time dependency than existing methods.

Statistical shape modeling is an indispensable tool in the quantitative analysis of anatomies. Particle-based shape modeling (PSM) is a state-of-the-art approach that enables the learning of population-level shape representation from medical imaging data (e.g., CT, MRI) and the associated 3D models of anatomy generated from them. PSM optimizes the placement of a dense set of landmarks (i.e., correspondence points) on a given shape cohort. PSM supports multi-organ modeling as a particular case of the conventional single-organ framework via a global statistical model, where multi-structure anatomy is considered as a single structure. However, global multi-organ models are not scalable for many organs, induce anatomical inconsistencies, and result in entangled shape statistics where modes of shape variation reflect both within- and between-organ variations. Hence, there is a need for an efficient modeling approach that can capture the inter-organ relations (i.e., pose variations) of the complex anatomy while simultaneously optimizing the morphological changes of each organ and capturing the population-level statistics. This paper leverages the PSM approach and proposes a new approach for correspondence-point optimization of multiple organs that overcomes these limitations. The central idea of multilevel component analysis, is that the shape statistics consists of two mutually orthogonal subspaces: the within-organ subspace and the between-organ subspace. We formulate the correspondence optimization objective using this generative model. We evaluate the proposed method using synthetic shape data and clinical data for articulated joint structures of the spine, foot and ankle, and hip joint.