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Clinical investigations of anatomy's structural changes over time couldgreatly benefit from population-level quantification of shape, orspatiotemporal statistic shape modeling (SSM). Such a tool enablescharacterizing patient organ cycles or disease progression in relation to acohort of interest. Constructing shape models requires establishing aquantitative shape representation (e.g., corresponding landmarks).Particle-based shape modeling (PSM) is a data-driven SSM approach that capturespopulation-level shape variations by optimizing landmark placement. However, itassumes cross-sectional study designs and hence has limited statistical powerin representing shape changes over time. Existing methods for modelingspatiotemporal or longitudinal shape changes require predefined shape atlasesand pre-built shape models that are typically constructed cross-sectionally.This paper proposes a data-driven approach inspired by the PSM method to learnpopulation-level spatiotemporal shape changes directly from shape data. Weintroduce a novel SSM optimization scheme that produces landmarks that are incorrespondence both across the population (inter-subject) and acrosstime-series (intra-subject). We apply the proposed method to 4D cardiac datafrom atrial-fibrillation patients and demonstrate its efficacy in representingthe dynamic change of the left atrium. Furthermore, we show that our methodoutperforms an image-based approach for spatiotemporal SSM with respect to agenerative time-series model, the Linear Dynamical System (LDS). LDS fit usinga spatiotemporal shape model optimized via our approach provides bettergeneralization and specificity, indicating it accurately captures theunderlying time-dependency.

Spatiotemporal Cardiac Statistical Shape Modeling: A Data-Driven Approach