Investigating molecular transport in the human brain from MRI with physics-informed neural networks

Multi-modal fusion and feature enhancement U-Net coupling with stem cell niches proximity estimation for voxel-wise GBM recurrence prediction. Phys Med Biol 2024;69:10.1088/1361-6560/ad64b8. [PMID: 39019073 PMCID: PMC11308744 DOI: 10.1088/1361-6560/ad64b8] [Citation(s) in RCA: 0] [Impact Index Per Article: 0]

Objective.We aim to develop a Multi-modal Fusion and Feature Enhancement U-Net (MFFE U-Net) coupling with stem cell niche proximity estimation to improve voxel-wise Glioblastoma (GBM) recurrence prediction.Approach.57 patients with pre- and post-surgery magnetic resonance (MR) scans were retrospectively solicited from 4 databases. Post-surgery MR scans included two months before the clinical diagnosis of recurrence and the day of the radiologicaly confirmed recurrence. The recurrences were manually annotated on the T1ce. The high-risk recurrence region was first determined. Then, a sparse multi-modal feature fusion U-Net was developed. The 50 patients from 3 databases were divided into 70% training, 10% validation, and 20% testing. 7 patients from the 4th institution were used as external testing with transfer learning. Model performance was evaluated by recall, precision, F1-score, and Hausdorff Distance at the 95% percentile (HD95). The proposed MFFE U-Net was compared to the support vector machine (SVM) model and two state-of-the-art neural networks. An ablation study was performed.Main results.The MFFE U-Net achieved a precision of 0.79 ± 0.08, a recall of 0.85 ± 0.11, and an F1-score of 0.82 ± 0.09. Statistically significant improvement was observed when comparing MFFE U-Net with proximity estimation couple SVM (SVMPE), mU-Net, and Deeplabv3. The HD95 was 2.75 ± 0.44 mm and 3.91 ± 0.83 mm for the 10 patients used in the model construction and 7 patients used for external testing, respectively. The ablation test showed that all five MR sequences contributed to the performance of the final model, with T1ce contributing the most. Convergence analysis, time efficiency analysis, and visualization of the intermediate results further discovered the characteristics of the proposed method.Significance. We present an advanced MFFE learning framework, MFFE U-Net, for effective voxel-wise GBM recurrence prediction. MFFE U-Net performs significantly better than the state-of-the-art networks and can potentially guide early RT intervention of the disease recurrence.

Physics informed contour selection for rapid image segmentation

Effective training of deep image segmentation models is challenging due to the need for abundant, high-quality annotations. To facilitate image annotation, we introduce Physics Informed Contour Selection (PICS)-an interpretable, physics-informed algorithm for rapid image segmentation without relying on labeled data. PICS draws inspiration from physics-informed neural networks (PINNs) and an active contour model called snake. It is fast and computationally lightweight because it employs cubic splines instead of a deep neural network as a basis function. Its training parameters are physically interpretable because they directly represent control knots of the segmentation curve. Traditional snakes involve minimization of the edge-based loss functionals by deriving the Euler-Lagrange equation followed by its numerical solution. However, PICS directly minimizes the loss functional, bypassing the Euler Lagrange equations. It is the first snake variant to minimize a region-based loss function instead of traditional edge-based loss functions. PICS uniquely models the three-dimensional (3D) segmentation process with an unsteady partial differential equation (PDE), which allows accelerated segmentation via transfer learning. To demonstrate its effectiveness, we apply PICS for 3D segmentation of the left ventricle on a publicly available cardiac dataset. We also demonstrate PICS's capacity to encode the prior shape information as a loss term by proposing a new convexity-preserving loss term for left ventricle. Overall, PICS presents several novelties in network architecture, transfer learning, and physics-inspired losses for image segmentation, thereby showing promising outcomes and potential for further refinement.

Quantitative analysis of molecular transport in the extracellular space using physics-informed neural network

The brain extracellular space (ECS), an irregular, extremely tortuous nanoscale space located between cells or between cells and blood vessels, is crucial for nerve cell survival. It plays a pivotal role in high-level brain functions such as memory, emotion, and sensation. However, the specific form of molecular transport within the ECS remain elusive. To address this challenge, this paper proposes a novel approach to quantitatively analyze the molecular transport within the ECS by solving an inverse problem derived from the advection-diffusion equation (ADE) using a physics-informed neural network (PINN). PINN provides a streamlined solution to the ADE without the need for intricate mathematical formulations or grid settings. Additionally, the optimization of PINN facilitates the automatic computation of the diffusion coefficient governing long-term molecule transport and the velocity of molecules driven by advection. Consequently, the proposed method allows for the quantitative analysis and identification of the specific pattern of molecular transport within the ECS through the calculation of the Péclet number. Experimental validation on two datasets of magnetic resonance images (MRIs) captured at different time points showcases the effectiveness of the proposed method. Notably, our simulations reveal identical molecular transport patterns between datasets representing rats with tracer injected into the same brain region. These findings highlight the potential of PINN as a promising tool for comprehensively exploring molecular transport within the ECS.

Exploring the potential of Physics-Informed Neural Networks to extract vascularization data from DCE-MRI in the presence of diffusion

Dynamic contrast-enhanced magnetic resonance imaging (DCE-MRI) is widely used to assess tissue vascularization, particularly in oncological applications. However, the most widely used pharmacokinetic (PK) models do not account for contrast agent (CA) diffusion between neighboring voxels, which can limit the accuracy of the results, especially in cases of heterogeneous tumors. To address this issue, previous works have proposed algorithms that incorporate diffusion phenomena into the formulation. However, these algorithms often face convergence problems due to the ill-posed nature of the problem. In this work, we present a new approach to fitting DCE-MRI data that incorporates CA diffusion by using Physics-Informed Neural Networks (PINNs). PINNs can be trained to fit measured data obtained from DCE-MRI while ensuring the mass conservation equation from the PK model. We compare the performance of PINNs to previous algorithms on different 1D cases inspired by previous works from literature. Results show that PINNs retrieve vascularization parameters more accurately from diffusion-corrected tracer-kinetic models. Furthermore, we demonstrate the robustness of PINNs compared to other traditional algorithms when faced with noisy or incomplete data. Overall, our results suggest that PINNs can be a valuable tool for improving the accuracy of DCE-MRI data analysis, particularly in cases where CA diffusion plays a significant role.

SIMPLEX: Multiple phase-cycled bSSFP quantitative magnetization transfer imaging with physic-guided simulation learning of neural network

Most quantitative magnetization transfer (qMT) imaging methods require acquiring additional quantitative maps (such as T1) for data fitting. A method based on multiple phase-cycled bSSFP was recently proposed to enable high-resolution 3D qMT imaging based on least square fitting without any extra acquisition, and thus has high potential for simplifying the qMT procedure. However, the quantification of qMT parameters with this method was suboptimal, limiting its potential for clinical application despite its simpler protocol and higher spatial resolution. To improve the fitting of qMT data obtained with multiple phase-cycled bSSFP, we propose SIMulation-based Physics-guided Learning of neural network for qMT parameters EXtraction, or SIMPLEX. In contrast to previous deep learning supervised approaches for quantitative MR that require the acquisition of input data and corresponding ground truth for training, we leveraged the MR signal model to generate training samples without expensive data curation. The network was trained exclusively with simulation data by predicting the simulation parameters. The same network was applied directly to in-vivo data without additional training. The approach was verified with both simulation and in-vivo data. SIMPLEX showed a decrease in fitting mean squared error for all simulation data compared to the existing least-square fitting method. The in-vivo experiment revealed that the network performed well with the real in vivo data unseen during training. For all experiments, we observed that SIMPLEX consistently improved the quantification quality of the qMT parameters whilst being more robust to noise compared to the prior technique. The proposed SIMPLEX will expedite the routine clinical application of qMT by providing qMT parameters (exchange rate, pool fraction) as well as T1, T2, and ΔB0 maps simultaneously with high spatial resolution, better reliability, and reduced processing time.

Topological data analysis for revealing dynamic brain reconfiguration in MEG data

In recent years, the focus of the functional connectivity community has shifted from stationary approaches to the ones that include temporal dynamics. Especially, non-invasive electrophysiological data (magnetoencephalography/electroencephalography (MEG/EEG)) with high temporal resolution and good spatial coverage have made it possible to measure the fast alterations in the neural activity in the brain during ongoing cognition. In this article, we analyze dynamic brain reconfiguration using MEG images collected from subjects during the rest and the cognitive tasks. Our proposed topological data analysis method, called Mapper, produces biomarkers that differentiate cognitive tasks without prior spatial and temporal collapse of the data. The suggested method provides an interactive visualization of the rapid fluctuations in electrophysiological data during motor and cognitive tasks; hence, it has the potential to extract clinically relevant information at an individual level without temporal and spatial collapse.