Bayesian Vector Flow Mapping (B-VFM)

Abstract

Cardiovascular disease, the leading cause of death in the United States, underscores the need for improved diagnostic imaging tools. While current clinical assessments of heart function rely primarily on global metrics such as ejection fraction, chamber pressure, and flow rate, regional flow imaging offers complementary insight. Intracardiac flow properties such as vortex formation and blood residence time reveal physiologic patterns that are not captured by global measures alone and can provide predictive information on pathological remodeling and thrombus risk. Echocardiography, a non-invasive, non-ionizing, portable, and relatively inexpensive modality, is widely used in clinical practice. Color-Doppler echocardiography, in particular, provides flow information along the ultrasound beam direction and serves as the foundation for vector flow mapping (VFM), a technique to reconstruct two-dimensional velocity fields in the left ventricle. However, existing VFM methods remain limited: they are highly sensitive to noise, rely on heuristic hyperparameter selection, and treat reconstruction as a deterministic problem without quantifying measurement uncertainty. These limitations hinder the reliability of VFM in challenging clinical conditions where imaging data are imperfect. This thesis introduces Bayesian Vector Flow Mapping (B-VFM), a hierarchical probabilistic framework for reconstructing intracardiac velocity fields from color-Doppler data while explicitly modeling uncertainty. First, we perform a theoretical error analysis of ultrasound acquisition to characterize sources of variability in Doppler measurements and segmentation. These uncertainties are then propagated through the B-VFM formulation, which model priors as Gaussian distributions. Unlike traditional approaches, B-VFM optimizes for hyperparameters and outputs both velocity fields using a probabilistic approach, taking into account local measurement uncertainties. Validation on synthetic cardiovascular flows demonstrates reduced reconstruction errors compared to state-of-the-art, 'vanilla', VFM, and a patient case study highlights the potential of using reconstructed methods with their error maps for further patient analysis. Finally, we discuss the extensibility of this general Bayesian framework, including integration of multimodal imaging, incorporation of more complex priors, and future applications to three-dimensional flow reconstruction. Collectively, this work establishes a principled foundation for uncertainty-aware flow imaging, with the potential to enhance the clinical value of echocardiographic diagnostics in cardiovascular disease.