Predicting blood clot growth from sparse post-onset measurements with latent neural differential equations
Authors: Lennon J. Shikhman, Ying Qian, He Li
Organizations: School of Interactive Computing, Georgia Institute of Technology, Atlanta, GA 30332 · Department of Mathematics and Systems Engineering, Florida Institute of Technology, Melbourne, FL 32901 · School of Chemical, Materials and Biomedical Engineering, University of Georgia, Athens, GA 30605
Computational models of blood clotting improve understanding of thrombus formation, but their clinical application remains limited because many model inputs are difficult to measure and patient-specific data are often sparse. We present a computational framework based on latent neural differential equations that infers unknown model parameters from sparse measurements and forecasts thrombosis progression. We demonstrate the framework using data generated from a multiphysics blood-clotting model in which clot growth is governed by the coagulation cascade and diffusion. Four known biochemical inputs (fibrinogen and factors IX, VIII, and V), together with sparse early clot-size observations, are used to infer the tissue-factor parameter and predict subsequent clot growth. We compare seven probabilistic methods: stochastic neural ordinary differential equations (SNODE), stochastic neural functional differential equations (SNFDE), a latent neural-process baseline, a monotone probabilistic deep ensemble, empirical trajectory retrieval, PCA-ridge Gaussian posterior, and Gompertz-curve retrieval. SNODE achieved the best performance in inferring the unknown input and forecasting future clot-growth trajectories. SNFDE performed similarly and consistently outperformed the other non-differential models. Prediction accuracy improved as more observations became available, whereas longer forecasting horizons increased uncertainty and decreased accuracy. Latent neural differential equations thus effectively combine parameter inference and clot-growth forecasting from sparse measurements, providing a promising foundation for personalized thrombosis modeling.
Forecasting the future anatomy of slow-evolving neurodegenerative diseases could enable earlier, more targeted intervention and improve clinical trial design, but it remains challenging because true progression signals are subtle in longitudinal MRI. In this low-signal regime, transferring modern generative sequence models directly is unreliable: training is dominated by stable baseline anatomy and confounded by dense, sample-specific nuisance variation. We first provide a theoretical analysis that explains these failures through two modes. Identity collapse occurs when optimization is driven toward reproducing the current anatomy, which prevents the model from learning faint temporal change. The continuous interpolation trap arises when standard smooth networks cannot separate localized biological drift from pervasive noise, which leads to spurious changes that diffuse across the volume. To address both issues, we propose Latent Drift, a progressive generative framework that learns change in a compressed semantic representation rather than synthesizing full-resolution anatomy. This design removes pixel-level identity from the prediction target and concentrates model capacity on progression-relevant dynamics. We further apply Finite Scalar Quantization to the learned change representation, which suppresses small, high-frequency nuisance fluctuations while preserving consistent structural drift. Experiments on longitudinal 3D brain MRI show that Latent Drift improves patient-specific neuro-forecasting over diffusion and autoregressive transformer baselines across generative fidelity and clinically relevant evaluation metrics. Project page: \href{https://cutepkq.github.io/latent-drift}{https://cutepkq.github.io/latent-drift}.
Neural Controlled Differential Equations (NCDE) provide a powerful continuous-time framework for forecasting time series, but standard graph-based extensions typically learn spatial structure purely from data, even in settings where a directed graph structure is known a priori. We introduce Informed Neural controlled Differential EQuationS (INDEQS), a graph-based NCDE forecasting method that incorporates prior knowledge of a directed graph at distinct architectural positions. INDEQS separates inner mixing of hidden states across graph nodes from outer mixing between vector field and control, and offers both a lightweight graph-constrained variant and a more expressive variant, learning additional graph connections from data via adaptive graph convolutions. To systematically study when graph informedness is beneficial in forecasting, we devise a continuous advection simulation on directed graphs, yielding synthetic spatio-temporal datasets with known ground-truth flow structure. We then evaluate INDEQS on two real-world tasks: river discharge forecasting on a hydrological network and traffic flow prediction on PeMS08. Across these synthetic and real-world benchmarks, outer informedness consistently improves mean absolute error over an uninformed NCDE with comparable parameter count, particularly on larger graphs, while inner informedness offers a more parameter-efficient alternative when strict adherence to a known adjacency is desired. A comparison of discrete convolutional and continuous-time decoders further shows that continuous decoders yield better accuracy and greater temporal flexibility on real-world tasks. An implementation of INDEQS and the advection simulation is available at https://github.com/Mitchi1/indeqs.
Michael Detzel, Gabriel Nobis, Kristiyan Blagov +3
Clinical decision-making for coronary intervention relies mainly on angiography and fractional flow reserve (FFR). However, angiography is two-dimensional and lacks depth information for 3D lesion characterization, while FFR provides only a single functional index, offering limited hemodynamic insight. Among existing methods, numerical analysis is computationally expensive, whereas learning-based approaches require extensive supervision and often lack physical consistency. To address these limitations, we propose physics-informed hemodynamic modeling, an integrated deep learning framework for 3D coronary blood flow analysis from dual-view angiography. First, an attention-enhanced CNN reconstructs coronary geometry from angiography. The resulting point clouds are then mapped to a reference domain and Fourier-encoded for joint representation. A decoupled network separately predicts velocity and pressure fields, with embedded physical priors enabling efficient transfer across physiological conditions. Across 32 clinical patients evaluated under four flow conditions, the trans-stenotic pressure-drop mean absolute percentage error was 2.02%, while the velocity and pressure relative-L2 errors were 0.054 and 0.023, respectively. Validation against hospital-measured FFR further achieved 93.8% diagnostic accuracy (30/32; exact 95% CI, 79.2%-99.2%). The framework also supports illustrative revascularization comparisons and sparse-data assimilation, with the full angiography-to-hemodynamics pipeline completed within 20 minutes per patient.