Physics-Guided Neural Networks for Intraventricular Vector Flow Mapping

TL;DR

This work investigates physics-guided learning approaches for intraventricular vector flow mapping from color Doppler, introducing two PINN variants (RB-PINNs and AL-PINNs) and a physics-guided nnU-Net. By incorporating mass conservation and boundary conditions as physics losses, the authors demonstrate that PINNs can match the traditional iVFM performance, while the nnU-Net approach achieves quasi-real-time inference and superior robustness on sparse or truncated data. The dual-stage PINN optimization and pre-optimized weight initialization substantially reduce training time, whereas the nnU-Net benefits from physics-aware regularization and augmented training data, including iVFM-derived labels. Overall, the study highlights the complementary strengths of physics-informed and supervised neural approaches for clinical vector flow mapping, with nnU-Net offering the most practical path toward real-time deployment and potential biomarker discovery.

Abstract

Intraventricular vector flow mapping (iVFM) seeks to enhance and quantify color Doppler in cardiac imaging. In this study, we propose novel alternatives to the traditional iVFM optimization scheme by utilizing physics-informed neural networks (PINNs) and a physics-guided nnU-Net-based supervised approach. When evaluated on simulated color Doppler images derived from a patient-specific computational fluid dynamics model and in vivo Doppler acquisitions, both approaches demonstrate comparable reconstruction performance to the original iVFM algorithm. The efficiency of PINNs is boosted through dual-stage optimization and pre-optimized weights. On the other hand, the nnU-Net method excels in generalizability and real-time capabilities. Notably, nnU-Net shows superior robustness on sparse and truncated Doppler data while maintaining independence from explicit boundary conditions. Overall, our results highlight the effectiveness of these methods in reconstructing intraventricular vector blood flow. The study also suggests potential applications of PINNs in ultrafast color Doppler imaging and the incorporation of fluid dynamics equations to derive biomarkers for cardiovascular diseases based on blood flow.

Figures (8)

• Figure 1: Architectures of PINNs and physics-guided nnU-Net. A.D. refers to automatic differentiation. In \ref{['fig:pinns']}, the 2D input of PINNs has a shape of ($B \times 2$), where $B$ is the batch size. $r$ and $\theta$ denote radial and angular coordinates. In \ref{['fig:nnunet']}, nnU-Net takes a 4D input of shape ($B \times 5 \times 192 \times 40$), which is the concatenation of sign-inverted dealiased Doppler velocity $V_\textnormal{D}$, weight matrix $W$, left ventricular segmentation $S$, radial coordinate array $R$, and angular coordinate array $\Theta$.
• Figure 2: Simulated color Doppler image during early filling derived from patient-specific CFD heart models with four variants of mitral valves. CFD #1-3 represent cases following mitral valve replacement with a bioprosthetic valve, while CFD #4 is a normal case.
• Figure 3: Dual-stage (AdamW + L-BFGS) versus single-stage (AdamW only) optimization using RB-PINNs initialized with pre-optimized weights. T refers to the total amount of time required for dual-stage optimization. In this example, 3.5 $\times$ more time is needed for single-stage optimization (top right) to converge to a similar solution given by dual-stage optimization (bottom right).
• Figure 4: Top row: time-varying squared correlation between CFD-based velocities and reconstructed velocities by each method; mid and bottom rows: CFD-based velocities versus estimated velocities derived from various methods. For mid and bottom rows, velocity data from 100 simulated color Doppler images were pooled. The binned scatter plots show the number of velocity occurrences.
• Figure 5: Normalized root-mean-square errors (nRMSE) between CFD-based and estimated velocity vectors by different techniques.