Left atrial flow and thrombosis risk from 4D CT contrast dynamics by physics-informed neural network and indicator dilution theory

Figures

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  Figure 1:. Patient-specific left atrial segmentations from computed tomography (CT) images depicting left atrium wall (in gray), left atrial appendage (in red), mitral valve plane (in green), and the pulmonary veins inlets (in blue). Top row shows the LAAT/TIA-negative cases (1-3) whereas the bottom row shows the LAAT/TIA-positive cases (4-6).

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  Figure 2:. Overview of the study. (A) Patient-specific pulmonary vein (PV) contrast inflow profiles from 4D contrast CT are modeled with gamma-variate fits. (B) Contrast concentration maps obtained from CFD simulations. (C) Physics-informed residual adaptive neural network (PirateNet) framework: spatiotemporal inputs are encoded with Fourier features and passed through four residual blocks to infer contrast concentration, velocity, pressure, and residence time. Each block consists of three multilayer perceptrons (MLPs) and an adaptive skip connection step with a trainable parameter α initialized at 0. Training minimizes a composite loss including data, residence time inflow conditions, Navier-Stokes, and transport equations. (D) Indicator dilution theory (IDT) framework: chamber transport is modeled through an impulse response inferred from the PV inflow profiles and simulated contrast maps. Both inflow and response curves are parameterized with gamma-variate models, and residence time is obtained from the closed-form integral of the corresponding survival function (a hypergeometric function).

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  Figure 3:. Contrast concentration (c) and residence time (TR) maps comparison of case 3 (top) and case 5 (bottom) between CFD, PirateNet, and IDT. Three 2D sections of the left atrium are shown at selected time instants. Contrast concentration snapshots are shown at tc/T = 12, 18, and 25, whereas residence time snapshots are shown at tc/T=12,18, and 25, whereas residence time snapshots are shown at tTR/T=2,8, and 15. Here tc is referenced to the contrast-training window (cycles 10–25), and tTR is referenced to the start of residence time integration. Contrast concentration is dimensionless, whereas residence time is given in seconds.

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  Figure 4:. Comparison of LAA TR by PirateNet and IDT with CFD ground-truth data. The top panels (A–F) display joint probability density functions of CFD residence times (x-axis) and IDT-inferred residence time (y-axis, filled black contours), p(TR,CFD, TR,IDT), or PirateNet-inferred residence time (y-axis, blue line contours), p(TR,CFD, TR,PirateNet). 15 cycles of residence time are pooled to display the joint pdfs. Panels (A) through (F) respectively represent cases 1 through 6. Each contour, from dark to light, contains 75%, 90%, 95%, and 99% of the data, respectively. The bottom right corner of each panel shows the correlation coefficients RPirateNet and RIDT. The bottom panels (G–I) are scatter plots of mean LAA TR from PirateNet and IDT vs. with mean TR from CFD, averaged within the LAA over three different cardiac cycles: G), 4T ≤ t ≤ 5T; H), 9T ≤ t ≤ 10T; I) 14T ≤ t ≤ 15T. Hollow and solid symbols respectively represent LAAT/TIA-negative and cases LAAT/TIA-positive cases.

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  Figure 5:. Comparison of volume-averaged LAA residence time TR inferred by the PirateNet (blue) and IDT (black) against CFD ground truth (red). Panels (A)–(F) correspond to cases 1–6. Insets show representative training contrast concentration time curves at inlet and chamber locations (lighter/darker shades indicate PVs/LAA). For the PINN, the LAA volume-averaged contrast and the cross-section–averaged contrast at each PV inlet are shown. For IDT, the LAA volume-averaged contrast and the cross-section–averaged contrast pooled across the four PV inlets are shown. In each inset, only the time interval used to train the corresponding method is shown.

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  Figure 6:. Instantaneous 3D velocity vector fields computed by CFD and inferred by contrast-trained PirateNet, together with normalized errors in PirateNet-inferred velocity magnitude (ϵM) and angular orientation (ϵO). Left panels (A,C,E) show case 3 (LAAT/TIA-negative, normal LA function), whereas right panels (B,D,F) show case 5 (LAAT/TIA-positive, impaired LA function). Each row represents one phases of the cardiac cycle: Top panels (A, B) represent atrial diastole; center panels (C, D) represent early LV filling; bottom panels (E, F) represent and atrial systole. As temporal reference, flow-rate waveforms through the pulmonary veins and mitral valve, together with LA and LAA volume traces, are shown alongside the vector fields; magenta dashed lines indicate the corresponding time instants. Vectors are colored by proximity to anatomical regions: right PVs (blue), left PVs (cyan), LAA (green), and MV (red). To facilitate visualization, the length of PINN-inferred velocity vectors are scaled by a factor of 2.0 in case 3 and 1.8 in case 5, respectively.