Learning Disease-Sensitive Latent Interaction Graphs From Noisy Cardiac Flow Measurements

Cardiac blood flow patterns contain rich information about disease severity and clinical interventions, yet current imaging and computational methods fail to capture underlying relational structures of coherent flow features. We propose a physics-informed, latent relational framework to model cardiac vortices as interacting nodes in a graph. Our model combines a neural relational inference architecture with physics-inspired interaction energy and birth-death dynamics, yielding a latent graph sensitive to disease severity and intervention level. We first apply this to computational fluid dynamics simulations of aortic coarctation. Learned latent graphs reveal that as the aortic radius narrows, vortex interactions become stronger and more frequent. This leads to a higher graph entropy, correlating monotonically with coarctation severity ($R^2=0.78$, Spearman $|ρ|=0.96$). We then extend this method to ultrasound datasets of left ventricles under varying levels of left ventricular assist device support. Again the latent graph representation captures the weakening of coherent vortical structures, thereby demonstrating cross-modal generalisation. Results show latent interaction graphs and entropy serve as robust and interpretable markers of cardiac disease and intervention.