A new systematic review has charted how physics-informed neural networks are being used to simulate blood moving through narrowed arteries, highlighting both the promise of artificial intelligence for cardiovascular modeling and the obstacles that still stand between laboratory algorithms and clinical tools. The review examines research published from 2019 through November 2025 on simplified two-dimensional artery models containing localized stenosis, the technical term for a constriction caused by the buildup or deformation of material within a blood vessel. Such narrowed regions can accelerate flow, alter pressure, generate recirculation zones and expose vessel walls to abnormal mechanical forces. By embedding the governing laws of fluid mechanics directly into the training of neural networks, researchers are attempting to reproduce these changes with less computational cost than conventional numerical simulation. The review, published in Neural Computing and Applications, identifies a rapidly expanding field in which machine learning is being combined with computational fluid dynamics rather than simply replacing it.

The study by Sunday Akinwamide, Farhan Mohamed, Mohd Shahrizal Sunar and colleagues follows the Preferred Reporting Items for Systematic Reviews and Meta-Analyses, or PRISMA 2020, framework. The authors searched eight databases and initially identified 324 records. After screening and applying their inclusion criteria, 32 studies remained for detailed analysis. The selected papers focused specifically on blood-flow modeling in simplified two-dimensional stenosed arteries using synthetic datasets, allowing the review team to compare how different investigators formulated their equations, represented artery geometry, imposed boundary conditions, generated training data and evaluated model performance. This narrow scope was deliberate. Although physics-informed neural networks are now being applied to aneurysms, deformable vessels, brain circulation and three-dimensional vascular trees, simple two-dimensional channels provide a controlled test bed. They make it easier to determine whether an algorithm is learning the underlying physics or merely fitting a particular set of simulated examples.

Traditional computational fluid dynamics remains the reference method for many blood-flow simulations. In a typical CFD calculation, the artery is divided into a mesh of small elements, and numerical solvers approximate the Navier–Stokes equations throughout that domain. These equations express conservation of momentum, while the continuity equation enforces conservation of mass. For an incompressible fluid, continuity requires the velocity field to have zero divergence, meaning that fluid cannot mysteriously appear or disappear inside the vessel. The momentum equations account for pressure, viscosity and inertial effects. Blood is often approximated as a Newtonian fluid in basic models, although its real rheology is more complicated: it contains cells, changes viscosity with shear rate and can behave as a non-Newtonian fluid under some conditions. CFD can resolve these details with high accuracy, but the result may depend strongly on mesh quality. A constriction creates steep velocity and pressure gradients, requiring fine meshes and substantial computing time.

A PINN approaches the same problem differently. Instead of relying entirely on a mesh, it uses a neural network to represent unknown quantities such as velocity and pressure as continuous functions of spatial coordinates and, when needed, time. During training, the network is penalized not only when its predictions disagree with available data but also when those predictions violate physical laws. A typical loss function may combine residuals from the continuity equation and momentum equations with errors at the inlet, outlet and vessel walls. Automatic differentiation calculates the derivatives needed for these residuals directly from the network, allowing the model to evaluate whether its predicted velocity and pressure fields satisfy the equations at selected points throughout the artery. Boundary conditions can specify an inlet velocity or pressure waveform, an outlet condition and a no-slip wall, in which fluid immediately adjacent to a stationary vessel wall has zero relative velocity. The network therefore learns a solution constrained by both data and mechanics.

This design can be especially useful when measurements are sparse. In a clinical setting, imaging may reveal the shape of an artery while providing limited information about the full velocity field or pressure distribution. A purely data-driven model could produce plausible-looking results while violating conservation laws or predicting physically impossible flow. A PINN can use the available observations together with governing equations to fill in missing information. In principle, the same framework can be used for forward problems, in which flow is predicted from known vessel geometry and conditions, and inverse problems, in which unknown quantities such as pressure, viscosity or boundary parameters are inferred from partial observations. The review describes this data-efficient and potentially generalizable character as one of the main reasons PINNs have attracted interest in hemodynamics. However, data efficiency does not mean that training is automatically easy or that sparse input guarantees clinical accuracy.

The reviewed studies reveal several recurring patterns in how researchers have adapted PINNs to stenosed arteries. Many use synthetic datasets produced by analytical solutions or established CFD solvers. These datasets allow researchers to know the “correct” velocity and pressure fields against which neural-network predictions can be compared. Others use hybrid PINN–CFD frameworks, in which conventional numerical methods supply high-quality information while the neural network accelerates repeated calculations, reconstructs fields or handles selected parts of the solution. The review reports a steady rise in such hybrid approaches. This trend reflects a practical shift in the field: rather than presenting artificial intelligence as a wholesale substitute for physics-based simulation, researchers are using it as a surrogate, correction model or computational companion. Mesh-free formulations are also becoming more prominent because they can avoid some of the difficulties associated with generating and refining meshes around irregular or sharply narrowed geometries.

The geometry of stenosis is a critical source of complexity. In a straight two-dimensional artery, a localized narrowing reduces the cross-sectional area available to the fluid. For a given volumetric flow rate, the average velocity must increase through the constricted section. The pressure field responds to the changing geometry, and downstream flow may separate from the wall, creating regions of recirculation. These effects can be described using quantities such as the Reynolds number, which compares inertial and viscous forces, and wall shear stress, or WSS, which measures the tangential force exerted by flowing blood on the vessel wall. WSS is calculated from the near-wall velocity gradient and blood viscosity. It is biologically important because endothelial cells respond to mechanical stimuli, and disturbed or oscillatory flow has been associated with vascular disease processes. Yet the review identifies WSS estimation as one of the most persistent weaknesses in current PINN studies. Small errors in velocity gradients near the wall can produce much larger errors in calculated shear stress, even when the overall flow field appears accurate.

Another challenge is the enforcement of boundary conditions. The performance of a PINN depends on how the loss function balances the interior physics equations against constraints at the inlet, outlet and walls. If the network focuses too heavily on matching boundary data, it may leave substantial equation residuals inside the domain. If it prioritizes the governing equations, it may satisfy them while producing inaccurate inlet or wall behavior. The problem becomes more difficult for pulsatile blood flow, where the inlet condition changes over time, and for models that attempt to represent elastic arterial walls or fluid–structure interaction. The review notes that researchers have experimented with adaptive weighting, progressive boundary complexity and other training strategies to address these imbalances. The neural network’s architecture, the location and density of collocation points, the choice of activation functions and the optimization schedule can all influence convergence. These are not minor implementation details: two models using the same physical equations can produce very different results if their training procedures sample the domain or weight the loss terms differently.

Scalability remains a central concern. PINNs can reduce the cost of evaluating a trained surrogate, but training may itself be computationally demanding, particularly when the model must represent sharp gradients, multiple flow regimes or many combinations of geometry and boundary conditions. A network trained for one stenosis shape may not generalize reliably to another, and a model designed for steady laminar flow may struggle with pulsatile or turbulent-like conditions. The review also finds that studies do not yet use consistent benchmarks. Researchers may report different error metrics, sample different regions of the artery or compare their networks with different CFD references. Without standardized geometries, physical parameters, boundary conditions and evaluation protocols, it is difficult to determine whether one method is genuinely more accurate or simply tested under more favorable circumstances. The authors argue that reproducible benchmarking is essential if the field is to progress from promising demonstrations to dependable hemodynamic analysis.

The review’s broader conclusion is cautiously optimistic. PINNs provide a framework for linking computational physics, biomedical engineering and machine learning, and they may eventually support faster simulations, parameter estimation and personalized vascular modeling. Their ability to incorporate physical laws could be valuable when patient-specific measurements are incomplete, while hybrid systems may preserve the reliability of CFD and reduce the burden of repeated calculations. But the evidence does not justify treating these models as ready-made diagnostic instruments. The studies considered in the review largely rely on simplified two-dimensional geometries and synthetic data rather than the full anatomical complexity and measurement uncertainty found in patients. Before clinical translation, researchers will need stronger validation against experiments, medical imaging and established numerical solvers; more reliable near-wall predictions; clearer treatment of blood’s non-Newtonian behavior and vessel elasticity; and common standards for reporting error and uncertainty. For now, the significance of the work is less that an artificial neural network has solved blood flow than that the field is beginning to define the conditions under which such a solution can be trusted.