Estimating pressure of pulmonary vasculature by combining patient-specific CFD simulations and physiological variables using PINN approach.

Introduction: The pulmonary artery (PA) tree transports blood from the right ventricle to the lungs for oxygenation. Accurate pressure measurements in this network are crucial for assessing both cardiac and pulmonary health [1]. Elevated pressure may indicate pulmonary hypertension, making it essential to evaluate the pressure gradient to understand blood flow dynamics. Clinicians have traditionally employed both invasive and non-invasive methods for pressure assessment. The insertion of a catheter into the PA for direct measurement is considered the gold standard [2]. However, echocardiography and cardiac magnetic resonance (CMR) imaging, while non-invasive, do not provide comprehensive insights into the entire pulmonary vasculature [3]. Computational fluid dynamics (CFD) simulations and lumped parameter models offer a non-invasive alternative for estimating hemodynamic metrics throughout the PA tree, yet they are not without the drawback of being time-consuming for individual patient analysis [4]. In response to these challenges, our research introduces a deep-learning approach to estimate pressures across the entire pulmonary vasculature by utilizing patient-specific CFD simulations and their physiological variables.

Materials and

Methods: In this study, we employed FE models generated from static CT scans specific to each patient (n=20) (Fig. 1). We performed CFD simulations on these models, where we applied the incompressible Navier–Stokes equations using an arbitrary Lagrangian-Eulerian formulation. Additionally, we incorporated a three-element Windkessel model, comprising Z, R, and C components representing PA impedance, peripheral resistance, and total arterial compliance, respectively, to characterize pulmonary vasculature properties (Fig. 2). To simulate blood flow within the pulmonary vasculature accurately, patient-specific inlet velocities were provided as input to the simulations. At the distal end of the vasculature, a boundary condition of zero pressure was imposed. This approach allowed us to estimate pressure distributions throughout the pulmonary vasculature accurately. Instead of laborious CFD simulations for each patient, we employed a physics-informed neural network (PINN) to get pressure prediction within one second. We leveraged boundary conditions of CFD simulations along with additional physiological variables such as age, gender, BMI, blood oxygen levels, etc., obtained from the Aylward open-access repository for training the PINN model. The PINN was trained by minimizing the difference between simulated velocity data and observed values as a data-driven loss function at distal points. Moreover, physics-based loss function was employed as a residual to minimize differences between simulated and PINN-estimated pressures as well (Fig. 3). This integrated approach allowed for robust estimation of pressure distributions in the pulmonary vasculature, combining both computational simulations and physiological data within a unified framework.

Results, Conclusions, and Discussions: Results and

Discussion: Our study demonstrated significant findings in terms of finding pressure at distal points of PA using CFD simulations. Furthermore, our PINN-based approach will successfully predict the pressures in pulmonary vasculature due to its enhanced capability to minimize the error between actual and predicted values by adding the residual loss function. This model promises enhanced accuracy and consistency when compared to both traditional CFD methods and feed-forward neural networks. Unlike the latter, which typically requires hundreds of training data for accurate predictions, our model achieves reliable results with less data.

Conclusions: In conclusion, this study underscores the potential of deep learning, through the PINN approach, in estimating PA pressures with a limited sample size of patients (n=20). The methodology demonstrates the improved accuracy of estimating pressure due to the training with both CFD simulations and the physiological variables, which can significantly enhance the evaluation of pulmonary vasculature in a variety of cardiac conditions.

References:
[1] Clephas, P. R. D., et al. "Pulmonary artery pressure monitoring in chronic heart failure: effects across clinically relevant subgroups in the MONITOR-HF trial." European Heart Journal (2024): ehae323.
[2] Bootsma, I. T., et al. "The contemporary pulmonary artery catheter. Part 2: measurements, limitations, and clinical applications." Journal of clinical monitoring and computing (2022): 1-15.
[3] Roeleveld, Roald J., et al. "A comparison of noninvasive MRI‐based methods of estimating pulmonary artery pressure in pulmonary hypertension." Journal of Magnetic Resonance Imaging: An Official Journal of the International Society for Magnetic Resonance in Medicine 22.1 (2005): 67-72.
[4] Dake, Prithvi G., et al. "Computational Fluid Dynamics in Cardiovascular Engineering: A Comprehensive Review." Transactions of the Indian National Academy of Engineering (2024): 1-28.

Acknowledgements (Optional): RA was supported by the NIH, under grant No. R00HL138288.