Jul 2026· IEEE Transactions on Image Processing· Vol 35, pp. 8354-8369· 0 citations· 59 references
Medicine
Abstract
Ultrafast ultrasound blood flow imaging is a state-of-the-art technique for depiction of complex blood flow dynamics in vivo through thousands of full-view image data (or, timestamps) acquired per second. Physics-informed Neural Network (PINN) is one of the most preeminent solvers of the Navier-Stokes equations, widely used as the governing equation of blood flow. However, the current approaches which implement time-dependent Navier-Stokes equations within the loss function are impractical for ultrafast ultrasound. We hereby propose an accelerated PINN training framework for solving the Navier-Stokes equations. It involves discretizing the time domain in Navier-Stokes equations and sequentially solving them with test-time adaptation. The novel training framework is coined as SeqPINN. Upon its success, we propose a parallel training scheme for all timestamps based on averaged constant stochastic gradient descent as initialization. Uncertainty estimation through Stochastic Weight Averaging Gaussian is then used as an indicator of generalizability of the initialization. This algorithm, named SP-PINN, further expedites PINN training while achieving comparable accuracy to SeqPINN. The performance of SeqPINN and SP-PINN was evaluated through finite-element simulations and in vitro phantoms of single-branch and trifurcate blood vessels. Results show that both algorithms were manyfold faster than the original design of PINN, while respectively achieving Root Mean Square Errors of 0.63 cm/s and 0.81 cm/s on the straight vessel and 1.07 cm/s and 1.41 cm/s on the trifurcate vessel when recovering blood flow velocities. The successful implementation of SeqPINN and SP-PINN opens the gate for real-time training of PINNs for Navier-Stokes equations and subsequently reliable imaging-based blood flow assessment in clinical practice.
Accurate, spatially resolved flow field measurements are essential for the reliable assessment of hemodynamic quantities in cardiovascular research and clinical practice. Experimental techniques, such as 4D flow MRI, PIV, or Doppler ultrasound, often yield data that are sparse, noisy, or under-resolved, particularly near vessel walls and in regions of complex flow. This limits the fidelity of distributed or derived hemodynamic indicators such as the wall shear stress and the clinical utility of such measurements. To address these challenges, we propose a physics-informed neural network (PINN) framework that integrates the incompressible Navier-Stokes equations with velocity measurements coming from experimental flow field data. By embedding physical laws into data, PINN enhances the reconstruction of velocity fields, enables the estimation of unmeasured quantities such as pressure and wall shear stress, and improves the spatial resolution of hemodynamic indicators. We show the effectiveness of our approach using both in silico and experimental data. First, we apply our method to the FDA nozzle benchmark, leveraging both control particle image velocimetry (PIV) measurements and computational fluid dynamics (CFD) simulations. Next, we apply our method to the more complex case of blood flow in an aneurysm model, exploiting in vitro 4D flow MRI data. In both cases, the synergy between data-driven learning and physics-based regularization yields results that align more closely with ground truth observations than standard CFD or pure data-driven approaches. Our findings highlight the potential of PINNs to improve the fidelity of under-resolved flow field measurements and yield spatially resolved hemodynamic indicators.
Irena Radivsi'c, Raffaele Tirotta, Alberto Zingaro et al.· 0 citations
Laser speckle imaging is essential for continuous hemodynamic monitoring, but emerging high-speed modalities such as rolling shutter speckle imaging (RSSI) are severely bottlenecked by intensive computational demands and high susceptibility to noise caused by statistical undersampling. To address these fundamental limitations, we introduce the Bifurcated Speckle Network (BiSNet), a hybrid deep learning architecture that merges empirical data training with analytical physical models to mitigate noise artifacts of undersampled speckle measurements in RSSI. To realize this hybrid training framework, BiSNet links localized architectural constraints with physics-guided optimization. By bounding the network's receptive field, the model is forced to evaluate flow dynamics based on localized speckle fluctuations. This prevents the network from memorizing the macroscopic, uniform structures of physical phantoms. Also, a physics-guided loss embeds the RSSI forward model directly into the training process, enabling the network to learn the governing physics. This approach improves data efficiency, allowing the model to generalize across diverse flow conditions without requiring an exhaustive library of experimental phantom datasets. Validated using controlled microfluidic setups and in vivo cranial window models, BiSNet delivers high-fidelity, real-time hemodynamic mapping. By effectively suppressing undersampling noise and bypassing the latency of traditional iterative solvers, our proposed framework accelerates accurate flow parameter estimation for continuous biological monitoring.
Sangjun Byun, Changyoon Yi, Donggeon Bae et al.· Journal of Physics: Photonic...· 0 citations
The results demonstrate that PINN achieves more accurate and stable full-field vibration reconstructions than conventional PINNs, particularly under conditions involving high-frequency modes, and highlights the potential of hybrid data-physics neural frameworks as an efficient and reliable approach for solving complex PDE-governed dynamical systems.
Hai-Long Liu, S. Hedayatrasa, Yunpeng Zhu et al.· e-Journal of Nondestructive...· 0 citations
Time-of-flight magnetic resonance angiography (TOF-MRA) is widely used for noninvasive visualization of arterial anatomy, but extracting hemodynamics like blood velocity typically requires supplementary phase-contrast scans, tagging or multi-TE images. This study proposes a novel, physics-informed computational framework to extract variable fluid velocity directly from standard TOF-MRA signal profiles. We analytically expand the approach-to-steady-state Bloch equations to include convective flow, establishing a mathematical relationship between the spatial decay of longitudinal magnetization and fluid velocity. The velocity derivation was further extended to pointwise estimation over a 1-D centerline, overcoming the limitations of constant-velocity assumptions. To validate and solve this problem, a MATLAB (R2025b) simulation framework was developed to model fluid flow in two variable-geometry flowing tube cases, i.e., continuous narrowing and focal stenosis, under synthetic scanner noise. A global inverse optimization approach utilizing Dual-Tikhonov regularization was applied to stably invert the ill-posed transit time integral, actively penalizing high-frequency numerical ringing while preserving structural curves. The computational simulations successfully recovered ground-truth point-wise velocities, tracking gradual hemodynamic accelerations and sharp stenotic jets. This theoretical framework and the example centerline TOF-MRA signal intensity provide a robust mathematical proof-of-concept that quantitative, localized functional hemodynamic metrics can be extracted from standard structural MRA imaging, establishing a foundation for advanced flow quantification without requiring additional scan time.
Abrar Faiyaz, Md Nasir Uddin, Giovanni Schifitto· Bioengineering· 0 citations
This work extends the previously proposed PINN framework with spatiotemporal implicit neural representations (INRs) to represent the MR signal as a continuous spatiotemporal function and to improve the accuracy, smoothness, and physical consistency of the PINN model.
Christos Tsepas, Chang Yan, M. Fuetterer et al.· 0 citations
We present a multi-domain physics-informed neural network (MDPINN) framework for reconstructing three-dimensional (3D) velocity fields from sparse two-dimensional concentration measurements in complex microfluidic flows. The approach is demonstrated in intersecting channels at a Reynolds number of 320, where strong 3D mixing occurs. Using planar concentration data obtained via confocal laser scanning microscopy (CLSM), the MDPINN infers the full 3D concentration and velocity fields by enforcing governing flow and transport equations. Using synchronized concentration–velocity data obtained from computational fluid dynamics (CFD) simulations, we first show that only nine optimally placed data planes (approximately 10% of total data) are sufficient to accurately reconstruct the full fields, achieving maximum absolute errors below 8% in concentration and 7% in velocity. A systematic analysis of data placement provides an optimized sampling strategy that includes near-wall measurements at z+ ≈ 1 and a normalized inter-plane spacing below 0.165. We then apply the validated MDPINN framework to experimental CLSM data, from which the inferred velocity fields differ from idealized CFD predictions, demonstrating the value of experimental data-based reconstruction in capturing realistic flow behavior. This study provides a practical tool that reconstructs difficult-to-measure velocity fields from easily accessible scalar data, which is applicable to a variety of fluidic systems.
N. Ohashi, Jingxuan Deng, Hantian Liu et al.· The Physics of Fluids· 0 citations
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