3D velocity and pressure field reconstruction in the cardiac left ventricle via physics informed neural network from echocardiography guided by 3D color Doppler

Fluid dynamics of the heart chamber can provide critical biological cues for understanding cardiac health and disease and have the potential for supporting diagnosis and prognosis. However, directly acquiring fluid dynamics information from clinical imaging remains challenging, as they are often noisy and have limited resolution, preventing accurate detailed fluid dynamics analysis. Image-based flow simulations offer high detail but are typically difficult to align with clinical velocity measurements, and as a result, may not accurately depict true fluid dynamics. Inverse-computing velocity fields from images via intra-ventricular flow mapping (VFM) has been reported, but it can become inaccurate when faced with missing or noisy measurement data, which is common with modalities such as ultrasound. Here, we propose a physics-informed neural network (PINN) framework that can accurately reconstruct detailed 3D flow fields of the cardiac left ventricle within a localized time window, using supervision from color Doppler measurements, despite their low resolution and signal-tonoise ratio. This framework couples PINN solvers at consecutive time frames with discrete temporal numerical differentiation and is thus named the "Coupled Sequential Frame PINN" or CSF-PINN. We used image-based flow simulations of fetal and adult hearts to generate synthetic color Doppler velocity data at different spatial and temporal resolution for testing the framework. Results show that CSF-PINN can accurately predict high levels of fluid dynamics details, including flow patterns, intraventricular pressure gradients, vorticity structures, and energy losses. CSF-PINN outperforms vanilla PINN in both accuracy and computational efficiency, however, its accuracy is more limited for velocity-gradient-dependent parameters, such as vorticity and wall shear stress (WSS) magnitude. CSF-PINN's accuracy is maintained even when color Doppler velocity data are spatially and temporally sparse and noisy, and when complex motions of the mitral valve are modelled. These are scenarios in which previous methodologies, including image-based flow simulations and VFM, have struggled. Additionally, we propose a scheme for advancing fluid dynamics predictions to subsequent time windows by using training from the previous time window to initialize networks for the subsequent window, further minimizing errors.