Hierarchical Geodesic Polynomial Model for Multilevel Analysis of Longitudinal Shape

Ye Han, Jared Vicory, Guido Gerig, Patricia Sabin, Hannah Dewey, Silvani Amin, Ana Sulentic, Christian Hertz, Matthew Jolley, Beatriz Paniagua, James Fishbaugh

Research output: Chapter in Book/Report/Conference proceedingConference contribution


Longitudinal analysis is a core aspect of many medical applications for understanding the relationship between an anatomical subject’s function and its trajectory of shape change over time. Whereas mixed-effects (or hierarchical) modeling is the statistical method of choice for analysis of longitudinal data, we here propose its extension as hierarchical geodesic polynomial model (HGPM) for multilevel analyses of longitudinal shape data. 3D shapes are transformed to a non-Euclidean shape space for regression analysis using geodesics on a high dimensional Riemannian manifold. At the subject-wise level, each individual trajectory of shape change is represented by a univariate geodesic polynomial model on timestamps. At the population level, multivariate polynomial expansion is applied to uni/multivariate geodesic polynomial models for both anchor points and tangent vectors. As such, the trajectory of an individual subject’s shape changes over time can be modeled accurately with a reduced number of parameters, and population-level effects from multiple covariates on trajectories can be well captured. The implemented HGPM is validated on synthetic examples of points on a unit 3D sphere. Further tests on clinical 4D right ventricular data show that HGPM is capable of capturing observable effects on shapes attributed to changes in covariates, which are consistent with qualitative clinical evaluations. HGPM demonstrates its effectiveness in modeling shape changes at both subject-wise and population levels, which is promising for future studies of the relationship between shape changes over time and the level of dysfunction severity on anatomical objects associated with disease.

Original languageEnglish (US)
Title of host publicationInformation Processing in Medical Imaging - 28th International Conference, IPMI 2023, Proceedings
EditorsAlejandro Frangi, Marleen de Bruijne, Demian Wassermann, Nassir Navab
PublisherSpringer Science and Business Media Deutschland GmbH
Number of pages12
ISBN (Print)9783031340475
StatePublished - 2023
Event28th International Conference on Information Processing in Medical Imaging, IPMI 2023 - San Carlos de Bariloche, Argentina
Duration: Jun 18 2023Jun 23 2023

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume13939 LNCS
ISSN (Print)0302-9743
ISSN (Electronic)1611-3349


Conference28th International Conference on Information Processing in Medical Imaging, IPMI 2023
CitySan Carlos de Bariloche


  • geodesic regression
  • hierarchical modeling
  • longitudinal data
  • statistical shape analysis

ASJC Scopus subject areas

  • Theoretical Computer Science
  • General Computer Science


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