Computed Tomography (CT)-derived Cardiovascular Flow Estimation Using Physics-Informed Neural Networks Improves with Sinogram-based Training: A Simulation Study

TL;DR

This simulation study investigates CT-based, non-invasive blood-flow estimation using physics-informed neural networks (PINNs) and introduces SinoFlow, a sinogram-based PINN framework that embeds CT acquisition physics via a time-dependent Radon transform. Compared to an image-domain baseline (ImageFlow) trained on filtered backprojection reconstructions, SinoFlow demonstrates substantially improved accuracy for both concentration and velocity fields across a range of gantry rotation speeds, noise levels, and pulsed-mode CT parameters. Key findings show SinoFlow’s robustness to motion artifacts and imaging noise, with accurate outlet-flow ratios and compatibility with pulsed-mode acquisition, highlighting its potential to enable reliable CT-based hemodynamics in practice. The work provides a foundation for extending PINN-based CT flow estimation to more realistic 3D anatomies and advanced CT modalities such as dual-energy or photon-counting systems.

Abstract

Background: Non-invasive imaging-based assessment of blood flow plays a critical role in evaluating heart function and structure. Computed Tomography (CT) is a widely-used imaging modality that can robustly evaluate cardiovascular anatomy and function, but direct methods to estimate blood flow velocity from movies of contrast evolution have not been developed. Purpose: This study evaluates the impact of CT imaging on Physics-Informed Neural Networks (PINN)-based flow estimation and proposes an improved framework, SinoFlow, which uses sinogram data directly to estimate blood flow. Methods: We generated pulsatile flow fields in an idealized 2D vessel bifurcation using computational fluid dynamics and simulated CT scans with varying gantry rotation speeds, tube currents, and pulse mode imaging settings. We compared the performance of PINN-based flow estimation using reconstructed images (ImageFlow) to SinoFlow. Results: SinoFlow significantly improved flow estimation performance by avoiding propagating errors introduced by filtered backprojection. SinoFlow was robust across all tested gantry rotation speeds and consistently produced lower mean squared error and velocity errors than ImageFlow. Additionally, SinoFlow was compatible with pulsed-mode imaging and maintained higher accuracy with shorter pulse widths. Conclusions: This study demonstrates the potential of SinoFlow for CT-based flow estimation, providing a more promising approach for non-invasive blood flow assessment. The findings aim to inform future applications of PINNs to CT images and provide a solution for image-based estimation, with reasonable acquisition parameters yielding accurate flow estimates.

Figures (8)

• Figure 1: Flow Simulation Geometry, Velocity Analysis, and Concentration ProfileA) The Y-shaped tube geometry, where a clot obstructs flow in one of the outlets. Black lines mark the inlet and outlet cross-sections used for velocity and concentration measurements. B) Velocity profile at the inlet, with the black curve representing the ground truth and the green curve showing the PINN prediction. The yellow-shaded area between the two curves indicates the root mean square error (RMSE). High-velocity and low-velocity errors are computed from the upper and lower 10% of the values, respectively, while the peak-to-peak error corresponds to the difference between the 10% high and low velocities in both the ground truth and predicted profiles. C) Concentration profile prescribed at the inlet.
• Figure 2: PINN-based Flow Estimation Approaches In both ImageFlow and SinoFlow, the same image domain PINN is used to predict concentration and flow field movies. However, SinoFlow includes the forward rendering process in the pipeline to generate a predicted sinogram $g_{pred}$ and therefore calculates a sinogram loss as the data loss, while ImageFlow compares generated concentrations $c_{pred}$ to FBP-reconstructed concentration values.
• Figure 3: FBP and PINN-predicted concentration scenes and boxplots of ImageFlow and SinoFlow results at different GRS. A) The FBP, ImageFlow predicted and SinoFlow predicted concentration scenes and their differences compared with the ground truth at 1, 2, 3, 4, 6, 8, and 10 Hz GRS. B) ImageFlow (blue) and SinoFlow (red) predicted concentration and flow velocity results at the inlet, using boxplots (each box contains 6 data points from the 6 tested gantry starting angle), including concentration RMSE, velocity RMSE, high velocity error, low velocity error, velocity range error and outlet velocity ratio across GRS. FBP concentration errors are shown in green. The grey dashed line in the outlet velocity ratio boxplot indicates the ratio of 1 (equal flow between the two outlets), and the black line the ground truth ratio. For statistical analysis, black asterisks indicates significant difference found between ImageFlow and SinoFlow results while blue asterisks compares FBP and ImageFlow and red asterisks compares FBP and SinoFlow.
• Figure 4: FBP and PINN-predicted concentration scenes and boxplots of ImageFlow and SinoFlow results at different CNR.A) FBP, ImageFlow predicted and SinoFlow predicted concentration scenes and their differences compared with the ground truth at 4 Hz GRS and 12, 24, 34, 46, 60 71 and 75 CNR. B) Concentration and flow velocity results at the inlet at 4 Hz GRS and varying CNR. FBP results are shown in green while ImageFlow are in blue and SinoFlow results are in red. Black lines for the four velocity error panels are the mean noise-free SinoFlow results at 4 Hz. The black line for the outlet ratio is the ground truth ratio. For statistical analysis, black asterisks indicates significant difference found between ImageFlow and SinoFlow results while blue asterisks compares FBP and ImageFlow and red asterisks compares FBP and SinoFlow.
• Figure 5: Pulse Mode Imaging Sinograms and Performance of SinoFlow at different duty cycles and pulse widths.A) Visualization of pulse mode imaging sinogram at 100%, 75% and 50% duty cycle (grey areas on the sinogram were skipped in PINN solving) at 4 Hz GRS and CNR=60. The last row uses a smaller pulse width, causing a shorter on and off period. B) SinoFlow predicted concentration and flow velocity results at the inlet at 15%, 25%, 50% and 75% duty cycle. 10-view (blue) and 50-view (orange) pulse widths were evaluated. Black lines for the four velocity error panels are the mean SinoFlow results at 4 Hz GRS and 60 CNR. The black line for the outlet ratio is the ground truth ratio. For statistical analysis, black asterisks indicates significant difference found between between 10-view and 50-view pulse width results.