Physics-Informed Hemodynamic Modeling for Data-Free Prediction and Sparse-Data Assimilation

Continuous hemodynamic monitoring guides treatment decisions in surgery and intensive care. However, gold-standard signals are only measured in severe cases due to risks associated with invasive measurement. In this work, we introduce HIPNO (Hemodynamic Inference via Physics-informed Neural Operators) to recover hemodynamic state from ubiquitous, non-invasive signals and expand access to advanced monitoring. HIPNO addresses a problem of scale symmetry in physics-informed hemodynamic inference, where different combinations of flow, resistance, and compliance can generate the same observed pressure. We identify the symmetry group of the observation model and parameterize the network in its quotient space. For the 3-element Windkessel model, the quotient coordinates are the compliance-normalized flow $U=Q/C$, the decay time constant $τ_{WK}=R_2 C$, and the characteristic-impedance coordinate $κ=R_1 C$. Across 945499 intraoperative windows from 2562 patients, HIPNO predicts $τ_{wave}$, a proxy for vascular decay derived from pressure, with 32% lower error on the log scale than a population baseline while preserving mean arterial pressure accuracy. Because vascular decay and flow drive occupy separate coordinates, counterfactual perturbations produce the expected directional responses in at least 90% of windows in almost all prespecified scenarios, a separation unavailable to pressure-only baselines. The coordinates are also used as inputs to a calibration model for monitored cardiac output. Finally, the formulation identifies the external compliance or flow reference required to recover absolute physical scale.

We present the development and application of a three-dimensional Physics-Informed Neural Network (PINN) framework for the investigation of haemodynamic behaviour in the human aorta. The model incorporates a time-resolved simulation of pulsatile blood flow over a two-minute interval, enabling the extraction of pressure and velocity fields with high temporal fidelity. The mechanical stress exerted on the aortic wall was quantified through Laplace's law, with temporal averaging applied to derive representative stress distributions. This approach circumvents the computational overhead associated with conventional computational fluid dynamics (CFD) methods by eliminating mesh generation and exploiting the automatic differentiation capabilities inherent to neural networks. The proposed methodology demonstrates that PINNs can serve as an efficient and accurate alternative for modelling complex vascular flow phenomena, offering significant advantages in scalability and computational cost reduction while maintaining physical consistency.

Accurate correspondence matching across multiple angiographic views is the prerequisite for 3D coronary reconstruction and interventional guidance. However, the development of robust deep learning models for this task has been stifled by a fundamental data bottleneck. Obtaining ground truth for matching tasks in angiography pairs is prohibitively expensive and hard to scale. To overcome this barrier, we introduce a physically-grounded data generation framework that synthesizes high-fidelity Digital Reconstructed Radiographs (DRRs) from 3D Coronary CT Angiography (CCTA) volumes. Our framework generates dense, highly accurate 3D-to-2D projection labels by simulating realistic C-arm acquisition geometry on patient anatomy at zero human cost. Leveraging this dense supervision, we propose a Geometry-Informed Matching Module (GIMM) that integrates global feature and anatomical structure into correspondence learning. Unlike real angiography where assessment relies on subjective human annotation, our dataset provides 2D correspondence labels with paired images, allowing human-free evaluation. We comprehensively evaluate our method on the proposed CT-derived DRR dataset and demonstrate improvements over other matching baseline models.