  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.
