From noisy flow images, blood flow and vessel-wall motion come back together: PirateNets alternation cuts aortic velocity error to 0.0372
Synopsis
Starting from noisy velocity images, unsteady three-dimensional blood flow and elastic vessel-wall motion can be reconstructed together without a prescribed inlet waveform or initial velocity. The solver alternates a fluid update, in which a physics-informed network fits the observations while enforcing the incompressible Navier–Stokes equations on the moving domain, with a geometry update, in which registration plus interface traction continuity and an elastic momentum residual constrain wall displacement. On a converging channel and a patient-like aorta, the PirateNets version reaches velocity relative errors of 0.0243 and 0.0372, below the 0.1066 and 0.1305 of a standard PINN of the same depth and width.
Interpretation
The blood velocity field and the vessel-wall interface motion are reconstructed jointly inside one inverse problem whose only input is noisy time-dependent velocity images. Earlier time-dependent inverse methods recover flow from velocity data but do not jointly infer elastic wall motion and evolving geometry, while inverse fluid–structure interaction methods model wall deformation but mainly estimate material or boundary parameters on a prescribed reference geometry. On two unsteady three-dimensional geometries, a converging channel and a patient-like aorta, the PirateNets version gives velocity relative errors of 0.0243 and 0.0372 against 0.1066 and 0.1305 for a standard PINN of the same depth and width.
The solve splits the problem into a fluid subproblem and a geometry subproblem and updates them in a Gauss–Seidel-type alternation until the two sides agree. The geometry update runs in two steps: a static correction of the reference domain, then a deformation registration over each time window, with the registration map acting like a shape-gradient step. Both the fluid and geometry networks evaluate fields and physical residuals at sampled space–time points; the reference-domain mesh only generates those points, and the moving domain is never remeshed.
Wall displacement is regularized by physics rather than by image registration overlap alone. Letting the domain deform freely raises domain Dice to 94.2875, yet pointwise wall-displacement relative error stays at 1.1342, so good lumen overlap does not determine the motion of wall material points. With structure regularization, wall-displacement relative error falls to 0.3468 at one weight and 0.2193 at another, while Dice stays near 98.
Perspective
The demonstrated scope is two synthetic unsteady three-dimensional geometries, a converging channel and a patient-like aorta segmented from MRI, with observations generated from known ground truth plus Gaussian noise; the intended readers are computational and imaging researchers working on blood-flow inversion and physics-informed learning.
The wall elastic moduli are set below typical in vivo arterial values, which the authors say makes wall motion clearly visible in the synthetic tests; pointwise wall displacement is harder to recover than lumen shape, and its relative error rises from 0.2193 to the 0.3 to 0.8 range under coefficient perturbations.