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

Viraj Patel; Marko Grujic; Philipp Aigner; Theodor Abart; Marcus Granegger; Deblina Bhattacharjee; Katharine Fraser

cs.LGFeb 26, 2026

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

Authors: Viraj Patel, Marko Grujic, Philipp Aigner, Theodor Abart, Marcus Granegger, Deblina Bhattacharjee, Katharine Fraser

Organizations: Department of Computer Science, University of Bath, Bath, UK · Christian Doppler Laboratory for Mechanical Circulatory Support, Department of Cardiac and Thoracic Aortic Surgery, Medical University of Vienna, Vienna, Austria · Department of Mechanical Engineering, University of Bath, Bath, UK

Abstract

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 develop the method using computational fluid dynamics simulations of aortic coarctation, where learned interaction graphs reveal increasingly structured vortex interactions as vessel narrowing progresses. The resulting graph entropy exhibits a strong monotonic relationship with coarctation severity ( $R^2=0.78$ , Spearman $|ρ|=0.96$ ). We then evaluate the framework on fluid-structure interaction simulations of intracranial aneurysms using multiple geometric severity descriptors. Among these, aneurysm volume produces the most informative latent representation, with non-interaction graph entropy demonstrating a strong monotonic relationship with severity (Spearman $|ρ| = 0.91$ ) and generalising to several alternative morphological measures. Finally, we apply the approach to ultrasound-derived flow fields of a left ventricle under varying levels of left ventricular assist device support, where the latent graph captures the progressive loss of coherent vortex interactions under mechanical assistance, demonstrating cross-modal generalisation to imaging data. Across all datasets, latent interaction graphs and graph entropy provide interpretable markers of disease severity and intervention, linking haemodynamic organisation to clinically relevant physiological changes.

Figures & tables

Figure 1: NRI architecture, with modifications compared with ( Kipf et al. 2018 ) in orange. The encoder, which used a disease severity conditioned physics head, and decoder, are alternating MLPs and message passing layers. Solid blocks represent node-level embeddings and multi-coloured blocks represent edge-level embeddings.

Severity Measure	$\rho$	$p$ -value	$R^{2}$	Monotonicity	No. Signficant Runs /5
Volume	-0.9053	$\mathbf{1.7275\times 10^{-7}}$	0.0875	0.8705	5
Diameter	-0.4758	0.0955	0.2531	0.6733	3
Sac Height	-0.4696	0.0740	0.3216	0.6743	3
Neck Width	0.1229	0.6209	0.0711	0.4619	0
Aspect Ratio	-0.1005	0.4092	0.1015	0.5362	1
Lobulation Index	0.0086	0.4725	0.0985	0.4886	1

Table 1: Performance of models conditioned on different aneurysm severity measures, averaged over five random seeds.

Figure 2: Cross-evaluation of conditioned models against alternative aneurysm severity measures. The entry in each cell represents the number of statistically significant Spearman correlations ( $p<0.05$ ) between graph entropy and the corresponding severity measure across five random seeds.

Ablation	Existence Accuracy	MAE	MSE	$\rho$	$p$ -value	$R^{2}$	Monotonicity
None	$\mathbf{0.840}$	$\mathbf{0.013}$	$0.015$	$\mathbf{-0.988}$	$\mathbf{4.26\times 10^{-6}}$	$\mathbf{0.915}$	$\mathbf{1.00}$
No ordering	$0.605$	$0.014$	$0.015$	$-0.691$	$0.058$	$0.845$	$0.800$
No physics gating	$0.778$	$0.014$	$0.016$	$-0.167$	$0.693$	$0.000$	$0.640$
No severity conditioning	$0.704$	$0.013$	$\mathbf{0.011}$	$0.518$	$0.188$	$0.418$	$0.308$
Original NRI	$0.617$	$0.016$	$0.019$	$0.458$	$0.254$	$0.210$	$0.308$

Table 2: Ablations on NRI model applied to CoA dataset.

Figure 3: Change in graph entropy for perturbations of $\pm 10$ to severity for the CoA dataset. $\Delta H$ was largest at severe coarctation and lowest in healthier regimes.

Panel of Figure 4 — Figure 4: Aortic coarctation: (a) the distribution of edge probability and (b) the entropy of the latent interaction graph changes with coarctation level. Intracranial aneurysm: (c) the distribution of edge probability for binned aneurysm volumes (no interaction) and (d) the entropy of the latent graph changes with aneurysm volume. LVAD support: (e) the distribution of edge probability (for no interaction) and (f) the entropy of the latent interaction graph changes with LVAD support level. Decreasing % of aorta radius corresponds to increasing disease severity. LVAD support levels: 0.0 = no support, 0.5 = partial support, and 1.0 = full support.

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Abstract

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