Probabilistic Spatio-Temporal Modeling of Cardiac Deformation using Gaussian Primitives

Swiss Data Science Center (SDSC) & Biomedical Informatics Group (ETHZ)
Earliest start date: January 2026

Background

Accurately estimating cardiac motion from cardiac Magnetic Resonance Imaging (MRI) data is a crucial step to evaluating cardiac function and detecting dysfunctions such as cardiomyopathy and infarction. The UK Biobank [1] offers an extensive dataset of cardiac MRI image volumes covering the ventricles of approximately 80,000 patients. These images are provided as temporal sequences (3D + T) that cover one heartbeat, enabling detailed tracking and modeling of myocardial tissue deformation. Previous work [2] has used a two-step pipeline consisting of landmark localization and shape registration to model myocardial motion, which is very expensive and constrained to predefined anatomical priors.

Figure 1: Deformation fields of myocardial walls. Source: [2]

The primary objective of this project is to develop a probabilistic, spatio-temporal model of cardiac deformation that combines Gaussian primitives [3] with state-space Gaussian process (GP) dynamics. The aim is to achieve a physically interpretable, data-efficient, and uncertaintyaware description of myocardial motion throughout the cardiac cycle, directly from 3D + T MRI sequences.

Specific Objectives

  1. Represent myocardial tissue with Gaussian primitives. Each Gaussian primitive will describe a local tissue parcel in 3D space by a mean position, covariance shape, and intensity. This compact representation provides a continuous and differentiable description of myocardial geometry and texture.
  2. Model temporal deformations with state-space Gaussian processes. The temporal evolution of each primitive’s degrees of freedom—translation, rotation (via angular velocity), and local stretch—will be modeled using Markovian GP priors in state-space form. This approach allows the deformation field to be expressed as a system of stochastic differential equations (SDEs), enabling Kalman filtering and smoothing for efficient inference across time while maintaining continuity and temporal smoothness.
  3. Enhancing flexibility and lowering dimensionality using a latent GP. Directly modeling the primitives’ parameters with a GP can limit model expressiveness and increase computational cost. To overcome these challenges, a promising approach is to employ a latent GP that adaptively encodes memory, efficiently integrating information from previous views. This strategy is inspired by the method presented in [4].
  4. Validate on dynamic cardiac MRI. The resulting model will be evaluated on 3D + T cardiac MRI datasets, assessing its ability to capture realistic and smooth deformation patterns.

Additional Information

  • What will you learn? The project will allow the student to gain hands-on experience with Gaussian splatting, spatio-temporal Gaussian processes, and probabilistic modelling in general.
  • Requirements: Basic knowledge of Gaussian processes, good Python and PyTorch skills.
  • Supervisors: – David Brüggemann ([email protected]) – Quentin Duchemin ([email protected]) – Olga Demler ([email protected])
  • Publication? Possible if the project goes well.
  • Interested? Contact us via email.

References

[1] Petersen, S.E., Matthews, P.M., Francis, J.M., Robson, M.D., et al.: Uk biobank’s cardiovascular magnetic resonance protocol. Journal of cardiovascular magnetic resonance 18, 8 (2016)

[2] Bello, G.A., Dawes, T.J., Duan, J., Biffi, C., et al.: Deep-learning cardiac motion analysis for human survival prediction. Nature machine intelligence 1, 95–104 (2019)

[3] Kerbl, B., Kopanas, G., Leimk¨uhler, T., Drettakis, G.: 3d gaussian splatting for real-time radiance field rendering. ACM Trans Graph 42, 139–1 (2023)

[4] Hou, Y., Kannala, J., Solin, A.: Multi-view stereo by temporal nonparametric fusion. In: Proceedings of the IEEE/CVF International Conference on Computer Vision, 2651–2660 (2019)