A model-driven bilevel optimization framework that couples SENSE-based image reconstruction with SPIRiT-based k-space calibration through shared CSMs, and introduces a deep-prior-guided regularization strategy that preserves the structure of classical linear regularizers while adaptively learning spatially varying regularization weights from denoised intermediate reconstructions.
Quantifying myocardial perfusion from cardiac magnetic resonance (CMR) can be achieved by fitting tracer-kinetic models to the dynamic contrast-enhanced MR data. However, fitting the observed data with multi-compartment exchange models, which describe the evolution of the contrast agent in the tissue, to estimate perfusion parameters is a challenging inverse problem that is sensitive to noise and acquisition variability. Previously, physics-informed neural networks (PINNs) have been proposed as an alternative to conventional non-linear least squares fitting methods with promising results for quantitative perfusion CMR. In this work, we extend 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. In realistic simulated CMR datasets, our proposed PINN with INRs demonstrates improved robustness and parameter estimation accuracy over the previously established methods. The code is available at https://github.com/q-cardIA/pinn-inr.
This study addresses the computational challenges of estimating two-dimensional electric field (EF) distributions within heterogeneous breast tissue models, a critical task in medical applications such as microwave imaging and hyperthermia. Traditional numerical simulation methods are accurate but computationally expensive, often requiring minutes of processing time. To overcome this limitation, we propose a deep learning approach that predicts EF distributions directly from dielectric property maps, specifically electrical conductivity and permittivity, significantly reducing inference time to a matter of seconds. Two convolutional neural network architectures are evaluated: a U-Net model with a ResNeXt50 encoder (R50-UNet) and a standard ResNeXt50 model (R50). Additionally, we introduce a masking-based loss function that emphasizes learning in regions of highest relevance within the domain. Quantitative evaluation demonstrates that the R50-UNet model outperforms the standard R50 model, achieving up to a 14.66 dB improvement in signal-to-noise ratio (SNR). The application of the masking method further enhances performance, with an additional gain of up to 3.24 dB in SNR. Data efficiency analysis reveals that while the R50 model reaches performance saturation with only 25% of the available training data, the R50-UNet architecture combined with masked loss continues to improve as more data are utilized. These findings support the feasibility of using deep learning for fast and accurate EF prediction in biomedical scenarios where computation time and spatial precision are critical.
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.
We introduce Simulation-Based Imaging (SBI), a framework for non-destructive acoustic imaging in which machine learning models trained entirely on simulated data serve as real-time solvers for the acoustic inverse problem. A high-fidelity nodal Discontinuous Galerkin forward solver generates large training datasets by randomizing inclusion geometry within a unit-cube domain; a 2D convolutional neural network then learns a direct mapping from boundary pressure measurements to a 32 by 32 by 32 voxel reconstruction of the interior. The trained model reliably recovers inclusion position and size from 144 boundary sensors with no prior knowledge of inclusion count or geometry. Reconstruction error degrades by only 13% under 5% additive measurement noise, and just 17% of the sensor array (24 of 144 sensors) suffices for quality within 4% of full coverage. These results establish SBI as a viable proof-of-concept imaging device whose complexity resides in software rather than hardware, opening a path toward cheap, portable, deployable imaging systems.
PURPOSE To evaluate whether deep learning improves the robustness of voxelwise kinetic parameter estimation from hyperpolarized (HP) 13C MRI compared with nonlinear least-squares (NLLS) fitting. METHODS A hybrid neural network (NN) was trained on synthetic pyruvate/lactate time courses generated from an open-system two-compartment HP 13C signal model to estimate the pyruvate-to-lactate conversion rate ( k PL ), vascular-extravascular exchange rate ( k VE ), and vascular volume fraction ( v B ). NN performance was compared with NLLS across flip-angle schemes, SNR levels, perturbations in acquisition parameters, and in vivo. Matched-ratio simulations tested whether model-estimated ( k PL ) retained information beyond the Lac/Pyr area-under-the-curve ratio, AUC Lac / Pyr = AUC Lac / AUC Pyr . RESULTS In simulations, NLLS and NN performance were comparable for k PL estimation at high SNR, whereas the NN outperformed NLLS at low SNR and for the weakly identifiable parameters k VE and v B . In vivo, NN maps were more spatially coherent than NLLS maps: k PL corresponded with AUC Lac / Pyr , while k VE and v B corresponded with pyruvate AUC. In matched-ratio simulations, NLLS-derived k PL discriminated the metabolic classes better than NN-derived k PL , although both model-based estimates retained discriminatory information. CONCLUSION NLLS is effective for k PL estimation under ideal model-matched conditions, whereas the NN provides more stable voxelwise maps, especially for weakly identifiable parameters and under low-SNR or in vivo conditions. Prospective biological or repeatability validation is needed to establish quantitative accuracy.