Physics-informed neural networks for myocardial perfusion MRI quantification

Personalized predictions of Glioblastoma infiltration: Mathematical models, Physics-Informed Neural Networks and multimodal scans

Predicting the infiltration of Glioblastoma (GBM) from medical MRI scans is crucial for understanding tumor growth dynamics and designing personalized radiotherapy treatment plans. Mathematical models of GBM growth can complement the data in the prediction of spatial distributions of tumor cells. However, this requires estimating patient-specific parameters of the model from clinical data, which is a challenging inverse problem due to limited temporal data and the limited time between imaging and diagnosis. This work proposes a method that uses Physics-Informed Neural Networks (PINNs) to estimate patient-specific parameters of a reaction-diffusion partial differential equation (PDE) model of GBM growth from a single 3D structural MRI snapshot. PINNs embed both the data and the PDE into a loss function, thus integrating theory and data. Key innovations include the identification and estimation of characteristic non-dimensional parameters, a pre-training step that utilizes the non-dimensional parameters and a fine-tuning step to determine the patient specific parameters. Additionally, the diffuse-domain method is employed to handle the complex brain geometry within the PINN framework. The method is validated on both synthetic and patient datasets, showing promise for personalized GBM treatment through parametric inference within clinically relevant timeframes.

A Novel Self-Supervised Learning-Based Method for Dynamic CT Brain Perfusion Imaging

Dynamic computed tomography (CT)-based brain perfusion imaging is a non-invasive technique that can provide quantitative measurements of cerebral blood flow (CBF), cerebral blood volume (CBV), and mean transit time (MTT). However, due to high radiation dose, dynamic CT scan with a low tube voltage and current protocol is commonly used. Because of this reason, the increased noise degrades the quality and reliability of perfusion maps. In this study, we aim to propose and investigate the feasibility of utilizing a convolutional neural network and a bi-directional long short-term memory model with an attention mechanism to self-supervisedly yield the impulse residue function (IRF) from dynamic CT images. Then, the predicted IRF can be used to compute the perfusion parameters. We evaluated the performance of the proposed method using both simulated and real brain perfusion data and compared the results with those obtained from two existing methods: singular value decomposition and tensor total-variation. The simulation results showed that the overall performance of parameter estimation obtained from the proposed method was superior to that obtained from the other two methods. The experimental results showed that the perfusion maps calculated from the three studied methods were visually similar, but small and significant differences in perfusion parameters between the proposed method and the other two methods were found. We also observed that there were several low-CBF and low-CBV lesions (i.e., suspected infarct core) found by all comparing methods, but only the proposed method revealed longer MTT. The proposed method has the potential to self-supervisedly yield reliable perfusion maps from dynamic CT images.

A physics-informed deep learning framework for dynamic susceptibility contrast perfusion MRI

BACKGROUND

Perfusion magnetic resonance imaging (MRI)s plays a central role in the diagnosis and monitoring of neurovascular or neurooncological disease. However, conventional processing techniques are limited in their ability to capture relevant characteristics of the perfusion dynamics and suffer from a lack of standardization.

PURPOSE

We propose a physics-informed deep learning framework which is capable of analyzing dynamic susceptibility contrast perfusion MRI data and recovering the dynamic tissue response with high accuracy.

METHODS

The framework uses physics-informed neural networks (PINNs) to learn the voxel-wise TRF, which represents the dynamic response of the local vascular network to the contrast agent bolus. The network output is stabilized by total variation and elastic net regularization. Parameter maps of normalized cerebral blood flow (nCBF) and volume (nCBV) are then calculated from the predicted residue functions. The results are validated using extensive comparisons to values derived by conventional Tikhonov-regularized singular value decomposition (TiSVD), in silico simulations and an in vivo dataset of perfusion MRI exams of patients with high-grade gliomas.

RESULTS

The simulation results demonstrate that PINN-derived residue functions show a high concordance with the true functions and that the calculated values of nCBF and nCBV converge towards the true values for higher contrast-to-noise ratios. In the in vivo dataset, we find high correlations between conventionally derived and PINN-predicted perfusion parameters (Pearson's rho for nCBF:0.84 ± 0.03 $0.84 \pm 0.03$ and nCBV:0.92 ± 0.03 $0.92 \pm 0.03$ ) and very high indices of image similarity (structural similarity index for nCBF:0.91 ± 0.03 $0.91 \pm 0.03$ and for nCBV:0.98 ± 0.00 $0.98 \pm 0.00$ ).

CONCLUSIONS

PINNs can be used to analyze perfusion MRI data and stably recover the response functions of the local vasculature with high accuracy.

Deep learning-based segmentation of left ventricular myocardium on dynamic contrast-enhanced MRI: a comprehensive evaluation across temporal frames

PURPOSE

Cardiac perfusion MRI is vital for disease diagnosis, treatment planning, and risk stratification, with anomalies serving as markers of underlying ischemic pathologies. AI-assisted methods and tools enable accurate and efficient left ventricular (LV) myocardium segmentation on all DCE-MRI timeframes, offering a solution to the challenges posed by the multidimensional nature of the data. This study aims to develop and assess an automated method for LV myocardial segmentation on DCE-MRI data of a local hospital.

METHODS

The study consists of retrospective DCE-MRI data from 55 subjects acquired at the local hospital using a 1.5 T MRI scanner. The dataset included subjects with and without cardiac abnormalities. The timepoint for the reference frame (post-contrast LV myocardium) was identified using standard deviation across the temporal sequences. Iterative image registration of other temporal images with respect to this reference image was performed using Maxwell's demons algorithm. The registered stack was fed to the model built using the U-Net framework for predicting the LV myocardium at all timeframes of DCE-MRI.

RESULTS

The mean and standard deviation of the dice similarity coefficient (DSC) for myocardial segmentation using pre-trained network Net_cine is 0.78 ± 0.04, and for the fine-tuned network Net_dyn which predicts mask on all timeframes individually, it is 0.78 ± 0.03. The DSC for Net_dyn ranged from 0.71 to 0.93. The average DSC achieved for the reference frame is 0.82 ± 0.06.

CONCLUSION

The study proposed a fast and fully automated AI-assisted method to segment LV myocardium on all timeframes of DCE-MRI data. The method is robust, and its performance is independent of the intra-temporal sequence registration and can easily accommodate timeframes with potential registration errors.

Model discovery approach enables noninvasive measurement of intra-tumoral fluid transport in dynamic MRI

Dynamic contrast-enhanced magnetic resonance imaging (DCE-MRI) is a routine method to noninvasively quantify perfusion dynamics in tissues. The standard practice for analyzing DCE-MRI data is to fit an ordinary differential equation to each voxel. Recent advances in data science provide an opportunity to move beyond existing methods to obtain more accurate measurements of fluid properties. Here, we developed a localized convolutional function regression that enables simultaneous measurement of interstitial fluid velocity, diffusion, and perfusion in 3D. We validated the method computationally and experimentally, demonstrating accurate measurement of fluid dynamics in situ and in vivo. Applying the method to human MRIs, we observed tissue-specific differences in fluid dynamics, with an increased fluid velocity in breast cancer as compared to brain cancer. Overall, our method represents an improved strategy for studying interstitial flows and interstitial transport in tumors and patients. We expect that our method will contribute to the better understanding of cancer progression and therapeutic response.

Learning Traveling Solitary Waves Using Separable Gaussian Neural Networks

In this paper, we apply a machine-learning approach to learn traveling solitary waves across various physical systems that are described by families of partial differential equations (PDEs). Our approach integrates a novel interpretable neural network (NN) architecture, called Separable Gaussian Neural Networks (SGNN) into the framework of Physics-Informed Neural Networks (PINNs). Unlike the traditional PINNs that treat spatial and temporal data as independent inputs, the present method leverages wave characteristics to transform data into the so-called co-traveling wave frame. This reformulation effectively addresses the issue of propagation failure in PINNs when applied to large computational domains. Here, the SGNN architecture demonstrates robust approximation capabilities for single-peakon, multi-peakon, and stationary solutions (known as "leftons") within the (1+1)-dimensional, b-family of PDEs. In addition, we expand our investigations, and explore not only peakon solutions in the ab-family but also compacton solutions in (2+1)-dimensional, Rosenau-Hyman family of PDEs. A comparative analysis with multi-layer perceptron (MLP) reveals that SGNN achieves comparable accuracy with fewer than a tenth of the neurons, underscoring its efficiency and potential for broader application in solving complex nonlinear PDEs.

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.

High-resolution quantification of stress perfusion defects by cardiac magnetic resonance

Aims

Quantitative stress perfusion cardiac magnetic resonance (CMR) is becoming more widely available, but it is still unclear how to integrate this information into clinical decision-making. Typically, pixel-wise perfusion maps are generated, but diagnostic and prognostic studies have summarized perfusion as just one value per patient or in 16 myocardial segments. In this study, the reporting of quantitative perfusion maps is extended from the standard 16 segments to a high-resolution bullseye. Cut-off thresholds are established for the high-resolution bullseye, and the identified perfusion defects are compared with visual assessment.

Methods and results

Thirty-four patients with known or suspected coronary artery disease were retrospectively analysed. Visual perfusion defects were contoured on the CMR images and pixel-wise quantitative perfusion maps were generated. Cut-off values were established on the high-resolution bullseye consisting of 1800 points and compared with the per-segment, per-coronary, and per-patient resolution thresholds. Quantitative stress perfusion was significantly lower in visually abnormal pixels, 1.11 (0.75-1.57) vs. 2.35 (1.82-2.9) mL/min/g (Mann-Whitney U test P < 0.001), with an optimal cut-off of 1.72 mL/min/g. This was lower than the segment-wise optimal threshold of 1.92 mL/min/g. The Bland-Altman analysis showed that visual assessment underestimated large perfusion defects compared with the quantification with good agreement for smaller defect burdens. A Dice overlap of 0.68 (0.57-0.78) was found.

Conclusion

This study introduces a high-resolution bullseye consisting of 1800 points, rather than 16, per patient for reporting quantitative stress perfusion, which may improve sensitivity. Using this representation, the threshold required to identify areas of reduced perfusion is lower than for segmental analysis.

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.

Spatio-temporal physics-informed learning: A novel approach to CT perfusion analysis in acute ischemic stroke

CT perfusion imaging is important in the imaging workup of acute ischemic stroke for evaluating affected cerebral tissue. CT perfusion analysis software produces cerebral perfusion maps from commonly noisy spatio-temporal CT perfusion data. High levels of noise can influence the results of CT perfusion analysis, necessitating software tuning. This work proposes a novel approach for CT perfusion analysis that uses physics-informed learning, an optimization framework that is robust to noise. In particular, we propose SPPINN: Spatio-temporal Perfusion Physics-Informed Neural Network and research spatio-temporal physics-informed learning. SPPINN learns implicit neural representations of contrast attenuation in CT perfusion scans using the spatio-temporal coordinates of the data and employs these representations to estimate a continuous representation of the cerebral perfusion parameters. We validate the approach on simulated data to quantify perfusion parameter estimation performance. Furthermore, we apply the method to in-house patient data and the public Ischemic Stroke Lesion Segmentation 2018 benchmark data to assess the correspondence between the perfusion maps and reference standard infarct core segmentations. Our method achieves accurate perfusion parameter estimates even with high noise levels and differentiates healthy tissue from infarcted tissue. Moreover, SPPINN perfusion maps accurately correspond with reference standard infarct core segmentations. Hence, we show that using spatio-temporal physics-informed learning for cerebral perfusion estimation is accurate, even in noisy CT perfusion data. The code for this work is available at https://github.com/lucasdevries/SPPINN.

Unified Bayesian network for uncertainty quantification of physiological parameters in dynamic contrast enhanced (DCE) MRI of the liver

Objective. Physiological parameter estimation is affected by intrinsic ambiguity in the data such as noise and model inaccuracies. The aim of this work is to provide a deep learning framework for accurate parameter and uncertainty estimates for DCE-MRI in the liver.Approach. Concentration time curves are simulated to train a Bayesian neural network (BNN). Training of the BNN involves minimization of a loss function that jointly minimizes the aleatoric and epistemic uncertainties. Uncertainty estimation is evaluated for different noise levels and for different out of distribution (OD) cases, i.e. where the data during inference differs strongly to the data during training. The accuracy of parameter estimates are compared to a nonlinear least squares (NLLS) fitting in numerical simulations andin vivodata of a patient suffering from hepatic tumor lesions.Main results. BNN achieved lower root-mean-squared-errors (RMSE) than the NLLS for the simulated data. RMSE of BNN was on overage of all noise levels lower by 33% ± 1.9% forktrans, 22% ± 6% forveand 89% ± 5% forvpthan the NLLS. The aleatoric uncertainties of the parameters increased with increasing noise level, whereas the epistemic uncertainty increased when a BNN was evaluated with OD data. For thein vivodata, more robust parameter estimations were obtained by the BNN than the NLLS fit. In addition, the differences between estimated parameters for healthy and tumor regions-of-interest were significant (p< 0.0001).Significance. The proposed framework allowed for accurate parameter estimates for quantitative DCE-MRI. In addition, the BNN provided uncertainty estimates which highlighted cases of high noise and in which the training data did not match the data during inference. This is important for clinical application because it would indicate cases in which the trained model is inadequate and additional training with an adapted training data set is required.

AI-AIF: artificial intelligence-based arterial input function for quantitative stress perfusion cardiac magnetic resonance

Aims

One of the major challenges in the quantification of myocardial blood flow (MBF) from stress perfusion cardiac magnetic resonance (CMR) is the estimation of the arterial input function (AIF). This is due to the non-linear relationship between the concentration of gadolinium and the MR signal, which leads to signal saturation. In this work, we show that a deep learning model can be trained to predict the unsaturated AIF from standard images, using the reference dual-sequence acquisition AIFs (DS-AIFs) for training.

Methods and results

A 1D U-Net was trained, to take the saturated AIF from the standard images as input and predict the unsaturated AIF, using the data from 201 patients from centre 1 and a test set comprised of both an independent cohort of consecutive patients from centre 1 and an external cohort of patients from centre 2 (n = 44). Fully-automated MBF was compared between the DS-AIF and AI-AIF methods using the Mann-Whitney U test and Bland-Altman analysis. There was no statistical difference between the MBF quantified with the DS-AIF [2.77 mL/min/g (1.08)] and predicted with the AI-AIF (2.79 mL/min/g (1.08), P = 0.33. Bland-Altman analysis shows minimal bias between the DS-AIF and AI-AIF methods for quantitative MBF (bias of -0.11 mL/min/g). Additionally, the MBF diagnosis classification of the AI-AIF matched the DS-AIF in 669/704 (95%) of myocardial segments.

Conclusion

Quantification of stress perfusion CMR is feasible with a single-sequence acquisition and a single contrast injection using an AI-based correction of the AIF.

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

In recent years, a plethora of methods combining neural networks and partial differential equations have been developed. A widely known example are physics-informed neural networks, which solve problems involving partial differential equations by training a neural network. We apply physics-informed neural networks and the finite element method to estimate the diffusion coefficient governing the long term spread of molecules in the human brain from magnetic resonance images. Synthetic testcases are created to demonstrate that the standard formulation of the physics-informed neural network faces challenges with noisy measurements in our application. Our numerical results demonstrate that the residual of the partial differential equation after training needs to be small for accurate parameter recovery. To achieve this, we tune the weights and the norms used in the loss function and use residual based adaptive refinement of training points. We find that the diffusion coefficient estimated from magnetic resonance images with physics-informed neural networks becomes consistent with results from a finite element based approach when the residuum after training becomes small. The observations presented here are an important first step towards solving inverse problems on cohorts of patients in a semi-automated fashion with physics-informed neural networks.