Statistical multi-level shape models for scalable modeling of multi-organ anatomies

Abstract

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.

Keywords: computational anatomy; computational morphometrics; foot and ankle; hierarchical statistical models; hip and pelvis; shape and relative pose models; statistical shape modeling; vertebra.