Learning spatiotemporal statistical shape models for non-linear dynamic anatomies

Abstract

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.

Strainger Things: Discrete Differential Geometry for Transporting Right Ventricular Deformation Across Meshes

“…Perfect reconstruction was not obtained, as it is not possible to exactly impose a strain field and recover a valid mesh: the strain field must satisfy the discrete Codazzi-Mainardi conditions. Contrary to previous methods [1,7,9,11], we use strain to model cardiac dynamics. While this is very well established in the clinical community, and has strong physiological reasons, the engineering community has focused on modelling displacement, and afterwards computing strain.…”

“…Researchers in medical image analysis have proposed various methods for better considering independent components of shape and deformation when analyzing the cardiac function, such as spatio-temporal statistical shape models [9,1,11]. These approaches describe the pointwise displacement of every point of the mesh.…”