PUNCH: Physics-informed Uncertainty-aware Network for Coronary Hemodynamics

TL;DR

A non-invasive, uncertainty-aware framework for estimating coronary flow reserve (CFR) directly from standard angiography, which integrates physics-informed neural networks with variational inference to infer coronary blood flow from first-principles models of contrast transport, without requiring ground-truth flow measurements.

Abstract

Coronary microvascular dysfunction (CMD) affects millions worldwide yet remains underdiagnosed because gold-standard physiological measurements are invasive and variably reproducible. We introduce a non-invasive, uncertainty-aware framework for estimating coronary flow reserve (CFR) directly from standard angiography. The system integrates physics-informed neural networks with variational inference to infer coronary blood flow from first-principles models of contrast transport, without requiring ground-truth flow measurements. The pipeline runs in approximately three minutes per patient on a single GPU, with no population-level training. Using 1{,}000 synthetic spatiotemporal intensity maps (kymographs) with controlled noise and artifacts, the framework reliably identifies degraded data and outputs appropriately inflated uncertainty estimates, showing strong correspondence between predictive uncertainty and error (Pearson $r = 0.997$, Spearman $ρ= 0.998$). Clinical validation in 12 patients shows strong agreement between PUNCH-derived CFR and invasive bolus thermodilution (Pearson $r = 0.90$, $p = 6.3 \times 10^{-5}$). We focus on the LAD, the artery most commonly assessed in routine CMD testing. Probabilistic CFR estimates have confidence intervals narrower than the variability of repeated invasive measurements. By transforming routine angiography into quantitative, uncertainty-aware assessment, this approach enables scalable, safer, and more reproducible evaluation of coronary microvascular function. Because standard angiography is widely available globally, the framework could expand access to CMD diagnosis and establish a new paradigm for physics-informed, patient-specific inference from clinical imaging.

Figures (6)

• Figure 1: PUNCH enables uncertainty-aware estimation of coronary flow reserve from standard angiography. Fluoroscopy images acquired at rest and hyperemia undergo vessel centerline tracking to generate spatiotemporal intensity maps (kymographs). These kymographs serve as input to a physics-informed neural network that jointly optimizes data fidelity ($\mathcal{L}_{Data}$), advection-diffusion physics constraints ($\mathcal{L}_{PDE}$), and variational inference regularization ($\mathcal{L}_{KL}$). The framework outputs posterior distributions of rest velocity, hyperemic velocity, and coronary flow reserve (CFR), providing probabilistic estimates with quantified uncertainty. The dual-branch architecture models both physiological states while sharing a common latent variable z to capture measurement uncertainty from noise, motion artifacts, and incomplete contrast filling.
• Figure 2: Kymograph construction from coronary angiography. Spatiotemporal representation of contrast transport enables velocity inference. (a) Sequential fluoroscopy frames show progressive contrast dye advancement through the left anterior descending (LAD) coronary artery. Vessel centerline tracking identifies corresponding anatomical positions across frames. (b) Stacking intensity profiles along the centerline over time constructs a kymograph where the x-axis represents distance along the vessel ($s$) and the y-axis represents time ($t$). Diagonal patterns in the kymograph reflect contrast propagation, with slope $\frac{\Delta s}{\Delta t}$ approximating local blood velocity $u$. This representation transforms the inverse problem of velocity estimation from fluoroscopy into a tractable physics-informed learning task governed by advection-diffusion dynamics.
• Figure 3: Physics-informed neural networks with variational inference enable joint rest-hyperemia modeling. The framework consists of three subnetworks per physiological state: intensity predictor $I(s,t)$, velocity predictor $u(s)$, and dispersion predictor $D(s,t)$. Rest (subscript R) and hyperemia (subscript H) branches share a common latent variable $z \in \mathbb{R}^{d_z}$ sampled from a learned variational posterior $q_\phi(z)$, ensuring coherent uncertainty propagation between states. Training optimizes a composite loss combining data fidelity to observed noisy kymographs ($\mathcal{L}_{\text{Data}}$), physics-based residuals enforcing the advection-diffusion PDE ($\mathcal{L}_{\text{PDE}}$), and Kullback--Leibler regularization ($\lambda_{\text{KL}} \cdot \text{KL}$). Automatic differentiation computes spatial and temporal derivatives for physics enforcement. At inference, Monte Carlo sampling from the posterior generates distributions over velocity fields and CFR, yielding probabilistic estimates with model-predicted confidence intervals.
• Figure 4: Numerical simulation enables systematic evaluation under known ground truth. The one-dimensional advection-dispersion equation is solved numerically with randomly generated velocity profiles $u(s)$ and dispersion coefficients $D(s,t)$ to produce noise-free synthetic kymographs. Realistic angiographic noise and artifacts are then applied, including Poisson shot noise, spatial blur, low-frequency intensity variations, vertical banding, localized intensity dropout, and temporal pixelation. This corruption pipeline generates 1,000 synthetic cases spanning mild to severe degradation, enabling quantitative assessment of model accuracy, uncertainty calibration, and robustness to image quality deterioration under controlled conditions where true flow parameters are known.
• Figure 5: PUNCH demonstrates strong agreement with invasive CFR assessment. (a) Input kymograph (blue) to PUNCH, output kymograph (yellow) and overlay of input and output kymograph (b) Correlation plot comparing PUNCH-derived CFR posterior means against invasive bolus thermodilution measurements in 12 patients shows strong linear association (Pearson $r = 0.90$, $p = 6.3\times10^{-5}$; Deming regression slope $= 1.01$, intercept $= -0.49$). Error bars represent PUNCH posterior standard deviations and invasive measurement variability across three repeated acquisitions. (c) Bland--Altman analysis reveals mean bias of $-0.45$ (SD $\pm0.75$) with 95% limits of agreement $[-1.91, 1.02]$, indicating modest systematic underestimation. All 12 cases fall within agreement bounds. (d) Individual patient predictions with 95% credible intervals (shaded regions) demonstrate consistency between predicted uncertainty and observed invasive values, with narrower PUNCH confidence intervals than intra-patient invasive variability, suggesting improved reproducibility.