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 τWK=R2C, and the characteristic-impedance coordinate κ=R1C. Across 945499 intraoperative windows from 2562 patients, HIPNO predicts τwave, 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.
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.
Owing to the recent advancements in wearable devices for health care, the importance of BP estimation without cuffs increases. Cuff technologies are inappropriate for continuous BP measurement due to their inconvenient usage, invasive character, necessity of calibration, large size, and inability to perform long-term monitoring. Normally, the algorithm used for cuffless BP prediction employs machine learning models that operate according to the data-driven approach. However, although they show high numerical accuracy, ML models do not provide any interpretability, resulting in poor physiological validity and clinical applicability. We propose a combination of Windkessel and ML models that incorporates the physical aspects into the latter one. It is performed by reformulating Windkessel into a form that will allow employing ML models. The result is a system of ODEs which can be used in the neural network. Thus, the inclusion of physical constraints improves the data-driven approach by making models consistent with physics, understandable, and robust. For illustration, we apply the described technique using a publicly available MIMIC-II database that we obtain from the UCI Machine Learning Repository.
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.
Adrián Robles Arques, Martín Ruiz Fernandez, Javier Sanchis +2