Spatiotemporal Cardiac Statistical Shape Modeling: A Data-Driven Approach

Abstract

Clinical investigations of anatomy's structural changes over time could greatly benefit from population-level quantification of shape, or spatiotemporal statistic shape modeling (SSM). Such a tool enables characterizing patient organ cycles or disease progression in relation to a cohort of interest. Constructing shape models requires establishing a quantitative shape representation (e.g., corresponding landmarks). Particle-based shape modeling (PSM) is a data-driven SSM approach that captures population-level shape variations by optimizing landmark placement. However, it assumes cross-sectional study designs and hence has limited statistical power in representing shape changes over time. Existing methods for modeling spatiotemporal or longitudinal shape changes require predefined shape atlases and pre-built shape models that are typically constructed cross-sectionally. This paper proposes a data-driven approach inspired by the PSM method to learn population-level spatiotemporal shape changes directly from shape data. We introduce a novel SSM optimization scheme that produces landmarks that are in correspondence both across the population (inter-subject) and across time-series (intra-subject). We apply the proposed method to 4D cardiac data from atrial-fibrillation patients and demonstrate its efficacy in representing the dynamic change of the left atrium. Furthermore, we show that our method outperforms an image-based approach for spatiotemporal SSM with respect to a generative time-series model, the Linear Dynamical System (LDS). LDS fit using a spatiotemporal shape model optimized via our approach provides better generalization and specificity, indicating it accurately captures the underlying time-dependency.

Keywords: Cardiac Dynamics; Statistical Morphology Analysis; Statistical Shape Modeling.

Fig. 1.

Time-varying LDS model

Fig. 2.. PDM Examples

Correspondence points for three subjects on the ground truth meshes (anterior view). Color denotes correspondence (see zoomed in boxes). The plot of left atrium volume over time shows the time points selected for display.

Fig. 3.. Modes of Variation

Anterior view of Left Atrium across the primary and secondary mode of variation. Heat maps show the distance from mean shape.

Fig. 4.. Full Sequence Reconstruction

The box plot shows the distribution of particle-wise reconstruction RMSE at each time point. Below the average particle RMSE over all time points is displayed as a heat maps on a representative mesh, illustrating regional accuracy. Note the heat maps are scaled differently to make local changes visible.

Fig. 5.. Partial Sequence Reconstruction

The box plot shows the distribution of error with various percentages of missing time points.

Fig. 6.. Specificity

The box plot shows the distribution of particle-wise RMSE between sampled and closest true particle sets at each time point.