CardiacFlow: Cardiac Blood Flow Modeling

• CardiacFlow is a framework that reconstructs, simulates, and analyzes cardiac blood flow using acquisition-aware, patient-specific CFD and surrogate methods.
• It employs advanced techniques such as diffeomorphic mesh propagation, valve morphing, and physics-constrained PINNs to capture coupled chamber-valve dynamics with high-fidelity results.
• The approach identifies biomarkers and flow patterns—like vortex formation and energy dissipation—that inform clinical assessments of cardiac function.

CardiacFlow can be understood as a class of acquisition-aware frameworks for reconstructing, simulating, and analyzing cardiac blood flow from medical data. Its central object is the coupled dynamics of cardiac chambers, valve motion, and circulation, with the aim of recovering spatiotemporally resolved hemodynamics that routine imaging only partially observes. In its most complete form, CardiacFlow denotes patient-specific whole-heart computational fluid dynamics in deforming domains with realistic valve surrogates and circulation coupling; in a broader sense, it also includes Doppler-, CT-, and CMR-based methods that estimate flow fields, flow-related surrogates, or motion-flow-consistent kinematics when full intracardiac CFD is impractical (Kong et al., 10 May 2026).

1. Physiological object and observability gap

Intracardiac flow is organized by the coupled motion of chambers and valves, and clinically important structures include jets, vortex rings, recirculation zones, shunting patterns, pressure gradients, and energy losses. A central physiological motif is diastolic vortex formation, which helps redirect inflow toward the outflow tract, preserve momentum, and reduce energy dissipation. Abnormal wall motion, chamber remodeling, or valvular dysfunction can disrupt this organization, and flow topology and energetics have been linked to heart failure, myocardial infarction, valvular disease, and cardiomyopathy (Kong et al., 10 May 2026).

The principal measurement problem is that routine imaging is incomplete. The whole-heart CFD literature repeatedly frames simulation as complementary to 4D-Flow MRI because clinical flow imaging remains constrained by long acquisition times, patient cooperation requirements, limited spatial and temporal resolution, noise, reconstruction artifacts, smoothing and partial-volume effects, and difficulty resolving vortices, wall shear stress, and high-speed jets. These issues are amplified in pediatric congenital heart disease, where anatomy is small, heart rates are high, abnormal jets can exceed MRI velocity-encoding assumptions, and flow quantification can vary substantially across nearby planes (Kong et al., 10 May 2026).

A second complication is that intracardiac flow is not necessarily well described as uniformly laminar. Patient-specific large-eddy simulation of the left heart has shown intermittent, transitional behavior, with turbulent spots in the left atrium and left ventricle correlated with flow deceleration, especially in the upper atrium and near the ventricular apex in the second half of diastole after E-wave vortex-ring impact. In the reported case, the maximum Reynolds number at the mitral valve during diastole and at the aortic valve during systole was of order $Re \sim 5000$, which supports the view that transition sensitivity is a modeling issue rather than a numerical curiosity (Chnafa et al., 2013).

2. Whole-heart image-based CFD architecture

The most explicit CardiacFlow formulation is an end-to-end whole-heart pipeline that reconstructs moving cardiac anatomy from time-resolved images, solves CFD in deforming domains, and represents all four valves by resistive immersed surfaces with physiologically realistic opening and closing dynamics. The framework is intentionally positioned between fully coupled electromechanics/FSI digital twins, which are physiologically rich but expensive and difficult to tune, and simplified single-chamber or valve-free image-based flow models, which are computationally cheaper but incomplete (Kong et al., 10 May 2026).

In the reported healthy adult case, the imaging input was ECG-gated CTA with 10 phases over the cardiac cycle, sampled every 10% of the RR interval, image size $512\times512\times213$, and voxel resolution $0.39\times0.39\times0.7\ \text{mm}^3$. In the pediatric CHD case, the input was cardiac MRI with 4D-Flow MRI, with 30 reconstructed time frames over a 487 ms cardiac cycle and additional catheterization pressures and quantitative flow data. The CHD anatomy included congenitally corrected transposition of the great arteries $(S,L,L)$, a large outlet perimembranous VSD, ASD, and pulmonary valve obstruction / pulmonary stenosis. Segmentation used a previously developed ML framework in the healthy case and a pretrained residual U-Net, fine-tuned on five manually segmented representative frames, in the MRI-based CHD case (Kong et al., 10 May 2026).

From segmentation masks, surface meshes are generated by Marching Cubes and tetrahedral volume meshes are built for CFD. The fluid domain includes ventricles, left atrium plus pulmonary veins, right atrium plus SVC/IVC, aorta, and pulmonary arteries, with truncation at pulmonary veins, vena cava, the aorta before the arch, and pulmonary arteries just distal to branch PA origins. A key enabling component is diffeomorphic mesh propagation with a neural ODE, adapted from SDF4CHD, so that a baseline mesh is transported smoothly across the cardiac cycle while preserving topology: $$\frac{\partial \phi(\mathbf{p}, t)}{\partial t} = \mathbf{v}_\theta(\phi(\mathbf{p}, t), t), \qquad \phi(\mathbf{p}, 0) = \mathbf{p}_{T_0},$$

$$\mathbf{p}_{T_i} = \phi(\mathbf{p}, T_i) = \mathbf{p}_{T_0} + \int_0^{T_i} \mathbf{v}_\theta(\phi(\mathbf{p}, t), t)\, dt.$$

The implementation uses forward Euler on normalized time $t\in[0,1]$, composes four successive diffeomorphic deformation modules, and trains with point matching, normal consistency, and ARAP regularization using $\lambda_{\text{point}}=0.3$, $\lambda_{\text{normal}}=0.4$, and $\lambda_{\text{arap}}=0.3$ (Kong et al., 10 May 2026).

Because patient-specific valve leaflets are difficult to reconstruct from CTA or MRI, all four valves are generated by morphing templates for the aortic, pulmonary, mitral, and tricuspid valves, with manual affine placement followed by thin-plate spline morphing to annular or root landmarks. In the healthy subject, the resulting simulations reproduced physiologic pressure-volume behavior, valve timing, and ventricular vortex formation. In the CHD subject, simulated chamber and vessel pressures agreed with cardiac catheterization measurements, simulated flow fields were qualitatively consistent with 4D-Flow MRI while providing higher-resolution visualization of flow structures obscured by imaging artifacts, and the comparison with the healthy case revealed altered diastolic flow organization and elevated normalized viscous dissipation (Kong et al., 10 May 2026).

3. Acquisition-aware estimation beyond full CFD

Whole-heart CFD is only one branch of CardiacFlow. A parallel branch reconstructs velocity, pressure, or flow-related surrogates directly from acquisition-specific measurements, often by embedding modality physics into the inference problem.

Framework	Primary output	Main constraint
Dynamic 4DCT LAA analysis	$512\times512\times213$0, $512\times512\times213$1, $512\times512\times213$2, $512\times512\times213$3, $512\times512\times213$4 maps	Contrast-kinetic surrogate, not true velocity (Severance et al., 4 Feb 2025)
SinoFlow	$512\times512\times213$5 from CT	Sinogram-domain PINN; 2D vessel simulation study (Guo et al., 5 Nov 2025)
Physics-constrained iVFM	2-D LV vector flow in apical three-chamber view	Planar continuity and free-slip boundary constraints (Vixège et al., 2021)
Automated 2D PC-CMR analysis	Peak, net, forward, backward flow in Ao and PA	View selection, QC, and segmentation from full CMR exams (Chan et al., 2022)

In 4DCT of the left atrial appendage, CT does not directly measure velocity vectors or volumetric flow rates, but dynamic contrast enhancement can be fit voxelwise with a gamma-variate model to produce maps of peak enhancement $512\times512\times213$6, time-to-peak $512\times512\times213$7, bolus-shape parameter $512\times512\times213$8, early arrival time $512\times512\times213$9, and residence time $0.39\times0.39\times0.7\ \text{mm}^3$0. The emphasized descriptor is

$0.39\times0.39\times0.7\ \text{mm}^3$1

the first temporal moment of the fitted enhancement curve divided by its zeroth moment. In this setting, CardiacFlow is explicitly not direct flow quantification; it is a framework for contrast-kinetic biomarkers of slow flow, delayed filling, and stasis in AF (Severance et al., 4 Feb 2025).

CT-based inverse hemodynamics has also been formulated as a scanner-aware PINN problem. In the SinoFlow study, the network predicts concentration $0.39\times0.39\times0.7\ \text{mm}^3$2, velocity components $0.39\times0.39\times0.7\ \text{mm}^3$3, and pressure $0.39\times0.39\times0.7\ \text{mm}^3$4 from dynamic CT data while enforcing advection and incompressible Navier–Stokes residuals. The key distinction is supervision in the sinogram domain rather than on filtered-backprojection images, which avoids propagating motion artifacts caused by contrast evolution during gantry rotation. In a 2D Y-shaped bifurcation with $0.39\times0.39\times0.7\ \text{mm}^3$5, SinoFlow outperformed image-domain training across gantry speeds and noise levels; for example, concentration RMSE at 4 Hz was $0.39\times0.39\times0.7\ \text{mm}^3$6 versus $0.39\times0.39\times0.7\ \text{mm}^3$7, and inlet velocity RMSE at 1 Hz was $0.39\times0.39\times0.7\ \text{mm}^3$8 versus $0.39\times0.39\times0.7\ \text{mm}^3$9 (Guo et al., 5 Nov 2025).

In echocardiography, physics-constrained intraventricular vector flow mapping reconstructs a 2-D velocity field from one-component color Doppler in the probe-centered polar system by minimizing a Doppler residual subject to planar mass conservation and free-slip wall constraints: $(S,L,L)$0 Validated against patient-specific CFD, the reported relative errors ranged from $(S,L,L)$1 to $(S,L,L)$2, with excellent agreement for mean vorticity and mean stream function, and the method resolved the rapid-filling vortex in vivo in routine apical three-chamber data (Vixège et al., 2021).

For CMR, automated 2D phase-contrast analysis extends CardiacFlow from model building to workflow automation. A sequential AlexNet/VGG-11/nnU-Net pipeline performs view selection, quality control, and Ao/PA segmentation from full clinical scans, reaching internal accuracy values of $(S,L,L)$3 for view classification and $(S,L,L)$4 for QC, with Dice scores $(S,L,L)$5 and strong agreement between manual and automatic flow parameters (Chan et al., 2022).

A further infrastructure layer is now available in beamspace echocardiography. EchoXFlow preserves 37,125 recordings from 666 routine-care examinations as separable 1D, 2D, and 3D streams with multiple Doppler modalities and synchronized ECG, enabling benchmark tasks such as B-mode $(S,L,L)$6 tissue Doppler and B-mode $(S,L,L)$7 color Doppler velocity, power, and local variation. This suggests that acquisition-domain, cross-modal supervision is becoming a distinct CardiacFlow paradigm rather than merely a data-preprocessing choice (Stenhede et al., 6 May 2026).

Flow compatibility can also regulate motion reconstruction itself. In right-ventricular MRI, a variational framework combines cine-derived boundary kinematics with measured valve-plane flux $(S,L,L)$8 and optional hemodynamic force $(S,L,L)$9, using global mass and momentum constraints to correct endocardial motion. In the reported corrected case, the mass-constrained solution reduced systolic artifacts while differing from the anatomy-only reconstruction by a mean Euclidean distance of $$\frac{\partial \phi(\mathbf{p}, t)}{\partial t} = \mathbf{v}_\theta(\phi(\mathbf{p}, t), t), \qquad \phi(\mathbf{p}, 0) = \mathbf{p}_{T_0},$$0 mm and a Hausdorff distance of $$\frac{\partial \phi(\mathbf{p}, t)}{\partial t} = \mathbf{v}_\theta(\phi(\mathbf{p}, t), t), \qquad \phi(\mathbf{p}, 0) = \mathbf{p}_{T_0},$$1 mm at peak systole (Capuano et al., 16 Apr 2025).

4. Multiscale numerics, valves, and motion models

CardiacFlow frameworks differ sharply in how they treat moving walls, valve dynamics, and the surrounding circulation. A representative multiscale left-heart model solves incompressible Navier–Stokes in an ALE formulation on a moving left-heart domain, models the mitral and aortic valves with the Resistive Immersed Implicit Surface method, prescribes LV wall motion from a 3D electromechanical model, extends that motion to the left atrium and ascending aorta through harmonic preprocessing plus a 0D atrial-volume model, and couples the 3D CFD to a closed-loop 0D circulation through pressure and flow continuity. In the healthy simulation, this framework reproduced physiologically meaningful LV stroke volume $$\frac{\partial \phi(\mathbf{p}, t)}{\partial t} = \mathbf{v}_\theta(\phi(\mathbf{p}, t), t), \qquad \phi(\mathbf{p}, 0) = \mathbf{p}_{T_0},$$2 ml, ejection fraction $$\frac{\partial \phi(\mathbf{p}, t)}{\partial t} = \mathbf{v}_\theta(\phi(\mathbf{p}, t), t), \qquad \phi(\mathbf{p}, 0) = \mathbf{p}_{T_0},$$3, peak AV flow rate $$\frac{\partial \phi(\mathbf{p}, t)}{\partial t} = \mathbf{v}_\theta(\phi(\mathbf{p}, t), t), \qquad \phi(\mathbf{p}, 0) = \mathbf{p}_{T_0},$$4, LV peak pressure $$\frac{\partial \phi(\mathbf{p}, t)}{\partial t} = \mathbf{v}_\theta(\phi(\mathbf{p}, t), t), \qquad \phi(\mathbf{p}, 0) = \mathbf{p}_{T_0},$$5, peak E-wave velocity $$\frac{\partial \phi(\mathbf{p}, t)}{\partial t} = \mathbf{v}_\theta(\phi(\mathbf{p}, t), t), \qquad \phi(\mathbf{p}, 0) = \mathbf{p}_{T_0},$$6, peak A-wave velocity $$\frac{\partial \phi(\mathbf{p}, t)}{\partial t} = \mathbf{v}_\theta(\phi(\mathbf{p}, t), t), \qquad \phi(\mathbf{p}, 0) = \mathbf{p}_{T_0},$$7, and $$\frac{\partial \phi(\mathbf{p}, t)}{\partial t} = \mathbf{v}_\theta(\phi(\mathbf{p}, t), t), \qquad \phi(\mathbf{p}, 0) = \mathbf{p}_{T_0},$$8 ratio $$\frac{\partial \phi(\mathbf{p}, t)}{\partial t} = \mathbf{v}_\theta(\phi(\mathbf{p}, t), t), \qquad \phi(\mathbf{p}, 0) = \mathbf{p}_{T_0},$$9 (Zingaro et al., 2021).

At the higher-fidelity end, large-eddy simulation of a realistic left heart from the pulmonary veins to the aortic root used an unstructured grid of $$\mathbf{p}_{T_i} = \phi(\mathbf{p}, T_i) = \mathbf{p}_{T_0} + \int_0^{T_i} \mathbf{v}_\theta(\phi(\mathbf{p}, t), t)\, dt.$$0 tetrahedral cells with typical grid size $$\mathbf{p}_{T_i} = \phi(\mathbf{p}, T_i) = \mathbf{p}_{T_0} + \int_0^{T_i} \mathbf{v}_\theta(\phi(\mathbf{p}, t), t)\, dt.$$1 mm, simulated 25 heart cycles, and phase-averaged over 15 cycles. The solver, YALES2BIO, employed a non-dissipative 4th-order finite-volume scheme. The physical conclusion was not full turbulence throughout the chambers, but transitional, intermittent turbulence localized in specific regions and phases, which implies that numerical dissipation and cycle averaging materially affect what a CardiacFlow simulation can resolve (Chnafa et al., 2013).

An equally consequential modeling choice is anatomical detail. In a porcine LV study comparing a detailed endocardial surface with papillary muscles and trabeculae against a smoothed version, the simplified geometry preserved gross temporal trends in flow rate and maximum opening velocity, but materially altered diastolic vortex topology. The complex model produced a two-vortex filling structure with apical circulation, whereas the smoothed model produced one dominant vortex that did not cover the apex. Quantitatively, the smoothed model showed a $$\mathbf{p}_{T_i} = \phi(\mathbf{p}, T_i) = \mathbf{p}_{T_0} + \int_0^{T_i} \mathbf{v}_\theta(\phi(\mathbf{p}, t), t)\, dt.$$2 smaller filling flow rate after middle diastole and, at middle systole, a $$\mathbf{p}_{T_i} = \phi(\mathbf{p}, T_i) = \mathbf{p}_{T_0} + \int_0^{T_i} \mathbf{v}_\theta(\phi(\mathbf{p}, t), t)\, dt.$$3 smaller maximum velocity at the aortic opening, a $$\mathbf{p}_{T_i} = \phi(\mathbf{p}, T_i) = \mathbf{p}_{T_0} + \int_0^{T_i} \mathbf{v}_\theta(\phi(\mathbf{p}, t), t)\, dt.$$4 smaller aortic flow rate, and a $$\mathbf{p}_{T_i} = \phi(\mathbf{p}, T_i) = \mathbf{p}_{T_0} + \int_0^{T_i} \mathbf{v}_\theta(\phi(\mathbf{p}, t), t)\, dt.$$5 smaller apex-to-aortic pressure drop (Kong et al., 2019).

Valve fidelity is similarly decisive in echo-derived ventricular CFD. A hybrid echocardiography–CFD framework that reconstructs the mitral valve, aortic valve, and a superior closing wall from routine 2D echo showed that the mitral valve changes where the diastolic vortex ring forms, how deeply it propagates, and how much circulation develops. With the mitral valve included, peak inflow velocity near the annulus was $$\mathbf{p}_{T_i} = \phi(\mathbf{p}, T_i) = \mathbf{p}_{T_0} + \int_0^{T_i} \mathbf{v}_\theta(\phi(\mathbf{p}, t), t)\, dt.$$6 versus $$\mathbf{p}_{T_i} = \phi(\mathbf{p}, T_i) = \mathbf{p}_{T_0} + \int_0^{T_i} \mathbf{v}_\theta(\phi(\mathbf{p}, t), t)\, dt.$$7 without the valve, counter-clockwise circulation increased from $$\mathbf{p}_{T_i} = \phi(\mathbf{p}, T_i) = \mathbf{p}_{T_0} + \int_0^{T_i} \mathbf{v}_\theta(\phi(\mathbf{p}, t), t)\, dt.$$8 to $$\mathbf{p}_{T_i} = \phi(\mathbf{p}, T_i) = \mathbf{p}_{T_0} + \int_0^{T_i} \mathbf{v}_\theta(\phi(\mathbf{p}, t), t)\, dt.$$9, and normalized energy loss in the unhealthy AMI ventricle reached $t\in[0,1]$0 compared with $t\in[0,1]$1 in the healthy VSWMA case (Hedayat et al., 2019).

5. Biomarkers, disease signatures, and latent flow structure

A defining feature of CardiacFlow is that it seeks biomarkers from structure and organization, not only from instantaneous velocity magnitude. In the whole-heart CFD framework, the healthy case reproduced physiologic pressure-volume behavior, valve timing, and ventricular vortex formation, whereas the pediatric CHD case showed catheterization-consistent pressures, 4D-Flow-MRI-consistent flow topology, altered diastolic flow organization, and elevated normalized viscous dissipation. This shifts disease interpretation from chamber geometry alone to chamber–valve–flow coupling (Kong et al., 10 May 2026).

Contrast-kinetic CT provides another class of biomarkers. In the LAA, $t\in[0,1]$2 reflects early bolus arrival, $t\in[0,1]$3 reflects filling delay, $t\in[0,1]$4 reflects local contrast accumulation, and $t\in[0,1]$5 reflects delayed, broadened, or prolonged enhancement. The paper’s examples distinguish a relatively homogeneous appendage, where proximal, middle, and distal voxels have similar fitted curves and similar $t\in[0,1]$6, from a delayed-filling appendage, where middle and distal regions show later, lower enhancement and increased $t\in[0,1]$7. A plausible implication is that CardiacFlow biomarkers need not be restricted to physically explicit velocity fields if the target question is residence, wash-in, or stasis (Severance et al., 4 Feb 2025).

Doppler-based CardiacFlow can also produce hemodynamic descriptors rather than only reconstructed vectors. In physics-constrained iVFM, mean vorticity peaked around the end of early filling with a value about $t\in[0,1]$8, and the concordance with CFD was strong, with $t\in[0,1]$9 for mean vorticity and $\lambda_{\text{point}}=0.3$0 for mean absolute stream function. The method therefore supports vortex-centric interpretation of diastolic function from routine echocardiography (Vixège et al., 2021).

A newer abstraction is to treat vortices as interacting entities. A latent relational framework models vortices as graph nodes with features including center coordinates, radius, orientation, existence, and vorticity, and infers directed interactions using a modified neural relational inference model with physics-inspired interaction energy

$\lambda_{\text{point}}=0.3$1

In aortic coarctation CFD, graph entropy increased monotonically with severity, with Spearman coefficient $\lambda_{\text{point}}=0.3$2, $\lambda_{\text{point}}=0.3$3, and $\lambda_{\text{point}}=0.3$4. In LVAD-supported ventricular Echo-PIV, the entropy of the non-interaction graph decreased monotonically with increasing support, with monotonicity score $\lambda_{\text{point}}=0.3$5, Spearman coefficient $\lambda_{\text{point}}=0.3$6, and $\lambda_{\text{point}}=0.3$7. This suggests that CardiacFlow is increasingly concerned with relational organization of coherent structures, not just field reconstruction (Patel et al., 26 Feb 2026).

6. Limits, misconceptions, and emerging directions

A common misconception is that CardiacFlow is primarily about generating higher-resolution flow pictures. The literature instead frames it as a balance among physiological realism, computational cost, and modeling effort. Whole-heart image-based CFD explicitly aims for a clinically plausible middle ground between monolithic electromechanics/FSI digital twins and simplified valve-free or single-chamber models, because neither extreme is currently satisfactory for broad clinical translation (Kong et al., 10 May 2026).

Another misconception is that all CardiacFlow outputs are direct physical flow fields. Several important branches are explicitly surrogate-based or dimension-reduced. Dynamic 4DCT in AF maps contrast kinetics rather than true velocities; physics-constrained iVFM reconstructs only a planar 2-D field under quasi-symmetry and free-slip assumptions; SinoFlow is presently a 2D, simulation-only vessel study; and automated PC-CMR pipelines quantify Ao/PA flow only after explicit quality control because artifacts, off-axis prescription, arrhythmia, and breathing can corrupt net-flow estimates (Severance et al., 4 Feb 2025, Vixège et al., 2021, Guo et al., 5 Nov 2025, Chan et al., 2022).

Boundary-condition uncertainty is another persistent bottleneck. FalconBC addresses this upstream problem by treating clinical targets, inflow features, and point-cloud anatomy embeddings as conditioning variables or jointly estimated latent quantities in amortized probabilistic inference. Demonstrated on an aorto-iliac bifurcation with varying stenosis and on a coronary arterial tree, it is not a cardiac chamber-flow solver, but it suggests that CardiacFlow will increasingly depend on learned posterior inference for physiologic loading rather than repeated manual or MCMC-based calibration (Choi et al., 18 Mar 2026).

Two emerging directions extend CardiacFlow beyond forward CFD. One is acquisition-domain multimodal learning, for which EchoXFlow supplies a beamspace testbed with synchronized B-mode, Doppler, and ECG. The other is population-scale generative modeling of 3D+t anatomy: Cardiac Mesh Flow uses flow matching to generate multi-scale free-form deformation fields that warp a template mesh into a four-chamber sequence with anatomical correspondence, temporal coherence, periodic consistency, and optional conditioning on cardiac chamber volumes. A plausible implication is that future CardiacFlow systems will combine acquisition-aware supervision, flow-compatible motion priors, amortized boundary-condition inference, and whole-heart CFD within a single multiscale ecosystem rather than treating these as separate methodological families (Stenhede et al., 6 May 2026, Ma et al., 3 May 2026).