Fast and Accurate Inverse Blood Flow Modeling from Minimal Cuff-Pressure Data via PINNs

Abstract

Accurate assessment of central hemodynamics is essential for diagnosis and risk stratification, yet it still relies largely on invasive measurements or on indirect reconstructions built from population-averaged transfer functions. While conventional methods are valuable in clinical practice, they face limitations, particularly in personalized medicine. Physics-informed methods address these by integrating physical principles, reducing the need for extensive data. In this work, a fully noninvasive, patient-specific framework is developed that combines a validated 1-D model of the systemic arterial tree with physics-informed neural networks (PINNs). This model performs the inverse solution of the flow and pressure fields within the arterial network, given minimal noninvasive measurements of pressure from a cuff reading and trains in 4000 iterations, at least 10x faster than the current state-of-the-art models due to several model enhancements. We validate the model predictions against our 1-D solver, yielding a near perfect correlation, and perform additional tests on a clinical dataset for the identification of important central hemodynamic parameters of cardiac output $CO$ and central systolic blood pressure $cSBP$, with correlations of $r=0.847$ and $r=0.951$, respectively. Moreover, the model is able to tune the patient-specific coefficients of the terminal resistance $R_T$ and compliance $C_T$ while training, treating them as learnable parameters. The inverse PINN model is able to solve the entire tree of 8 arteries with a single network, costing 5-10 minutes of computational time. This significant performance boost compared to traditional iterative inverse methods holds promise towards applications of personalized cardiac output monitoring and hemodynamic assessment via noninvasive approaches like wearable devices.

Figures (7)

• Figure 1: Inverse solution framework: The 1-D arterial network is adjusted on a patient-specific basis, so that the geometry and arterial compliance are matched based on the age, height, gender and $cfPWV$. Then, an arterial subdomain is extracted from the reference tree with adjusted terminal resistance/compliance parameters. Finally, an inverse flow solution is performed by training the PINN model to match the cuff pressure measurements, while adjusting/learning the patient-specific $CO$ and Windkessel parameters.
• Figure 2: Temporal periodicity: In PINNs we can enforce periodicity in the time dimension (red dashes) by transforming the input coordinates using Fourier feature embeddings. This achieves a periodic solution without the need of simulating multiple cardiac cycles as in traditional numerical integration.
• Figure 3: Training convergence: The full training takes roughly 4000 iterations: Rprop is used to warm up training for 100 iterations, followed by 4000 iterations of SSBroyden2. Each run takes approximately 5-7 minutes on a 4090 GPU.
• Figure 4: PINN solution fields: Indicative velocity ($u$), pressure ($P$) and the conical area ($A$) fields obtained by the PINN model for the aorta and radial arteries. Multiple wave reflections are visible mainly within the smaller radial artery.
• Figure 5: Numerical validation dataset: The initial in silico dataset which was population-matched with the clinical Asklepios dataset, consisted of 620 patients. An LHS method was deployed to extract 50 representative patients for testing, showing good coverage for the indicative pair-wise parameter plots.