Physics-Informed Neural Networks for Brain Hemodynamic Predictions Using Medical Imaging

Reconstructing blood flow in data-poor regimes: a vasculature network kernel for Gaussian process regression

Blood flow reconstruction in the vasculature is important for many clinical applications. However, in clinical settings, the available data are often quite limited. For instance, transcranial Doppler ultrasound is a non-invasive clinical tool that is commonly used in clinical settings to measure blood velocity waveforms at several locations. This amount of data is grossly insufficient for training machine learning surrogate models, such as deep neural networks or Gaussian process regression. In this work, we propose a Gaussian process regression approach based on empirical kernels constructed by data generated from physics-based simulations-enabling near-real-time reconstruction of blood flow in data-poor regimes. We introduce a novel methodology to reconstruct the kernel within the vascular network. The proposed kernel encodes both spatiotemporal and vessel-to-vessel correlations, thus enabling blood flow reconstruction in vessels that lack direct measurements. We demonstrate that any prediction made with the proposed kernel satisfies the conservation of mass principle. The kernel is constructed by running stochastic one-dimensional blood flow simulations, where the stochasticity captures the epistemic uncertainties, such as lack of knowledge about boundary conditions and uncertainties in vasculature geometries. We demonstrate the performance of the model on three test cases, namely, a simple Y-shaped bifurcation, abdominal aorta and the circle of Willis in the brain.

Aggregated Pattern Classification Method for improving neural disorder stage detection

BACKGROUND

Neurological disorders pose a significant health challenge, and their early detection is critical for effective treatment planning and prognosis. Traditional classification of neural disorders based on causes, symptoms, developmental stage, severity, and nervous system effects has limitations. Leveraging artificial intelligence (AI) and machine learning (ML) for pattern recognition provides a potent solution to address these challenges. Therefore, this study focuses on proposing an innovative approach-the Aggregated Pattern Classification Method (APCM)-for precise identification of neural disorder stages.

METHOD

The APCM was introduced to address prevalent issues in neural disorder detection, such as overfitting, robustness, and interoperability. This method utilizes aggregative patterns and classification learning functions to mitigate these challenges and enhance overall recognition accuracy, even in imbalanced data. The analysis involves neural images using observations from healthy individuals as a reference. Action response patterns from diverse inputs are mapped to identify similar features, establishing the disorder ratio. The stages are correlated based on available responses and associated neural data, with a preference for classification learning. This classification necessitates image and labeled data to prevent additional flaws in pattern recognition. Recognition and classification occur through multiple iterations, incorporating similar and diverse neural features. The learning process is finely tuned for minute classifications using labeled and unlabeled input data.

RESULTS

The proposed APCM demonstrates notable achievements, with high pattern recognition (15.03%) and controlled classification errors (CEs) (10.61% less). The method effectively addresses overfitting, robustness, and interoperability issues, showcasing its potential as a powerful tool for detecting neural disorders at different stages. The ability to handle imbalanced data contributes to the overall success of the algorithm.

CONCLUSION

The APCM emerges as a promising and effective approach for identifying precise neural disorder stages. By leveraging AI and ML, the method successfully resolves key challenges in pattern recognition. The high pattern recognition and reduced CEs underscore the method's potential for clinical applications. However, it is essential to acknowledge the reliance on high-quality neural image data, which may limit the generalizability of the approach. The proposed method allows future research to refine further and enhance its interpretability, providing valuable insights into neural disorder progression and underlying biological mechanisms.

Imaging of Intracranial Aneurysms: A Review of Standard and Advanced Imaging Techniques

The treatment of intracranial aneurysms is dictated by its risk of rupture in the future. Several clinical and radiological risk factors for aneurysm rupture have been described and incorporated into prediction models. Despite the recent technological advancements in aneurysm imaging, linear length and visible irregularity with a bleb are the only radiological measure used in clinical prediction models. The purpose of this article is to summarize both the standard imaging techniques, including their limitations, and the advanced techniques being used experimentally to image aneurysms. It is expected that as our understanding of advanced techniques improves, and their ability to predict clinical events is demonstrated, they become an increasingly routine part of aneurysm assessment. It is important that neurovascular specialists understand the spectrum of imaging techniques available.

Hemodynamic factors of spontaneous vertebral artery dissecting aneurysms assessed with numerical and deep learning algorithms: Role of blood pressure and asymmetry

BACKGROUND AND OBJECTIVES

The pathophysiology of spontaneous vertebral artery dissecting aneurysms (SVADA) is poorly understood. Our goal is to investigate the hemodynamic factors contributing to their formation using computational fluid dynamics (CFD) and deep learning algorithms.

METHODS

We have developed software that can use patient imagery as input to recreate the vertebrobasilar arterial system, both with and without SVADA, which we used in a series of three patients. To obtain the kinematic blood flow data before and after the aneurysm forms, we utilized numerical methods to solve the complex Navier-Stokes partial differential equations. This was accomplished through the application of a finite volume solver (OpenFoam/Helyx OS). Additionally, we trained a neural ordinary differential equation (NODE) to learn and replicate the dynamical streamlines obtained from the computational fluid dynamics (CFD) simulations.

RESULTS

In all three cases, we observed that the equilibrium of blood pressure distributions across the VAs, at a specific vertical level, accurately predicted the future SVADA location. In the two cases where there was a dominant VA, the dissection occurred on the dominant artery where blood pressure was lower compared to the contralateral side. The SVADA sac was characterized by reduced wall shear stress (WSS) and decreased velocity magnitude related to increased turbulence. The presence of a high WSS gradient at the boundary of the SVADA may explain its extension. Streamlines generated by CFD were learned with a neural ordinary differential equation (NODE) capable of capturing the system's dynamics to output meaningful predictions of the flow vector field upon aneurysm formation.

CONCLUSION

In our series, asymmetry in the vertebrobasilar blood pressure distributions at and proximal to the site of the future SVADA accurately predicted its location in all patients. Deep learning algorithms can be trained to model blood flow patterns within biological systems, offering an alternative to the computationally intensive CFD. This technology has the potential to find practical applications in clinical settings.

Performance of Fourier-based activation function in physics-informed neural networks for patient-specific cardiovascular flows

BACKGROUND AND OBJECTIVES

Physics-informed neural networks (PINNs) can be used to inversely model complex physical systems by encoding the governing partial differential equations and training data into the neural network. However, neural networks are known to be biased towards learning less complex functions, called spectral bias. This has important implications in modeling cardiovascular flows, where spatial frequencies can vary substantially across anatomies and pathologies (e.g., aneurysms or stenoses). Recent evidence suggests that Fourier-based activation functions have desirable properties, and can potentially reduce spectral bias; however, the performance and adequacy of such Fourier activation functions have not yet been evaluated in patient-specific cardiovascular flow applications.

METHODS

The performance of sine activation function was evaluated against tanh and swish activation functions in a 1D advection-diffusion problem, an eccentric 2D stenosis model (Re=5000), and a patient-specific 3D aortic model (Re=823) under pulsatile flow conditions. CFD simulations were performed at high spatio-temporal resolution and data points were extracted for training the neural network. The number of training data points were normalized by L/D. The performance of the PINNs framework was evaluated with increasing number of training data points and across all three activation functions.

RESULTS

Our results demonstrate that sine activation function presents desirable characteristics, such as monotonic reduction in errors, relatively faster convergence, and accurate eigen spectra at higher modes, compared to tanh and swish activation functions. Interestingly, for all activation functions, the domain-averaged errors tended to asymptote at ≈15-20% despite substantial increase in training point density. For 2D eccentric stenosis, errors asymptoted at a sensor point density of 40L/D. For 3D patient-specific aorta, this asymptote was achieved at 180L/D for all three activation functions with an error of ≈15% although sine activation function demonstrated relatively faster convergence.

CONCLUSIONS

We have demonstrated that Fourier-based activation functions have higher performance in terms of accuracy and convergence properties for cardiovascular flow applications; however, inherent challenges of neural networks (e.g., spectral bias) can limit the accuracy to ≈15% under physiological, 3D patient-specific blood flow conditions.

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.

Accelerated simulation methodologies for computational vascular flow modelling

Vascular flow modelling can improve our understanding of vascular pathologies and aid in developing safe and effective medical devices. Vascular flow models typically involve solving the nonlinear Navier-Stokes equations in complex anatomies and using physiological boundary conditions, often presenting a multi-physics and multi-scale computational problem to be solved. This leads to highly complex and expensive models that require excessive computational time. This review explores accelerated simulation methodologies, specifically focusing on computational vascular flow modelling. We review reduced order modelling (ROM) techniques like zero-/one-dimensional and modal decomposition-based ROMs and machine learning (ML) methods including ML-augmented ROMs, ML-based ROMs and physics-informed ML models. We discuss the applicability of each method to vascular flow acceleration and the effectiveness of the method in addressing domain-specific challenges. When available, we provide statistics on accuracy and speed-up factors for various applications related to vascular flow simulation acceleration. Our findings indicate that each type of model has strengths and limitations depending on the context. To accelerate real-world vascular flow problems, we propose future research on developing multi-scale acceleration methods capable of handling the significant geometric variability inherent to such problems.

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.

Hyper-acute effects of sub-concussive soccer headers on brain function and hemodynamics

Introduction

Sub-concussive head impacts in soccer are drawing increasing research attention regarding their acute and long-term effects as players may experience thousands of headers in a single season. During these impacts, the head experiences rapid acceleration similar to what occurs during a concussion, but without the clinical implications. The physical mechanism and response to repetitive impacts are not completely understood. The objective of this work was to examine the immediate functional outcomes of sub-concussive level impacts from soccer heading in a natural, non-laboratory environment.

Methods

Twenty university level soccer athletes were instrumented with sensor-mounted bite bars to record impacts from 10 consecutive soccer headers. Pre- and post-header measurements were collected to determine hyper-acute changes, i.e., within minutes after exposure. This included measuring blood flow velocity using transcranial Doppler (TCD) ultrasound, oxyhemoglobin concentration using functional near infrared spectroscopy imaging (fNIRS), and upper extremity dual-task (UEF) neurocognitive testing.

Results

On average, the athletes experienced 30.7 ± 8.9 g peak linear acceleration and 7.2 ± 3.1 rad/s peak angular velocity, respectively. Results from fNIRS measurements showed an increase in the brain oxygenation for the left prefrontal cortex (PC) (p = 0.002), and the left motor cortex (MC) (p = 0.007) following the soccer headers. Additional analysis of the fNIRS time series demonstrates increased sample entropy of the signal after the headers in the right PC (p = 0.02), right MC (p = 0.004), and left MC (p = 0.04).

Discussion

These combined results reveal some variations in brain oxygenation immediately detected after repetitive headers. Significant changes in balance and neurocognitive function were not observed in this study, indicating a mild level of head impacts. This is the first study to observe hemodynamic changes immediately after sub-concussive impacts using non-invasive portable imaging technology. In combination with head kinematic measurements, this information can give new insights and a framework for immediate monitoring of sub-concussive impacts on the head.

Physics-informed neural networks (PINNs) for 4D hemodynamics prediction: An investigation of optimal framework based on vascular morphology

Hemodynamic parameters are of great significance in the clinical diagnosis and treatment of cardiovascular diseases. However, noninvasive, real-time and accurate acquisition of hemodynamics remains a challenge for current invasive detection and simulation algorithms. Here, we integrate computational fluid dynamics with our customized analysis framework based on a multi-attribute point cloud dataset and physics-informed neural networks (PINNs)-aided deep learning modules. This combination is implemented by our workflow that generates flow field datasets within two types of patient personalized models - aorta with fine coronary branches and abdominal aorta. Deep learning modules with or without an antecedent hierarchical structure model the flow field development and complete the mapping from spatial and temporal dimensions to 4D hemodynamics. 88,000 cases on 4 randomized partitions in 16 controlled trials reveal the hemodynamic landscape of spatio-temporal anisotropy within two types of personalized models, which demonstrates the effectiveness of PINN in predicting the space-time behavior of flow fields and gives the optimal deep learning framework for different blood vessels in terms of balancing the training cost and accuracy dimensions. The proposed framework shows intentional performance in computational cost, accuracy and visualization compared to currently prevalent methods, and has the potential for generalization to model flow fields and corresponding clinical metrics within vessels at different locations. We expect our framework to push the 4D hemodynamic predictions to the real-time level, and in statistically significant fashion, applicable to morphologically variable vessels.

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.

Elasticity imaging using physics-informed neural networks: Spatial discovery of elastic modulus and Poisson's ratio

Elasticity imaging is a technique that discovers the spatial distribution of mechanical properties of tissue using deformation and force measurements under various loading conditions. Given the complexity of this discovery, most existing methods approximate only one material parameter while assuming homogeneous distributions for the others. We employ physics-informed neural networks (PINN) in linear elasticity problems to discover the space-dependent distribution of both elastic modulus (E) and Poisson's ratio (ν) simultaneously, using strain data, normal stress boundary conditions, and the governing physics. We validated our model on three examples. First, we experimentally loaded hydrogel samples with embedded stiff inclusions, representing tumorous tissue, and compared the approximations against ground truth determined through tensile tests. Next, using data from finite element simulation of a rectangular domain containing a stiff circular inclusion, the PINN model accurately localized the inclusion and estimated both E and ν. We observed that in a heterogeneous domain, assuming a homogeneous ν distribution increases estimation error for stiffness as well as the area of the stiff inclusion, which could have clinical importance when determining size and stiffness of tumorous tissue. Finally, our model accurately captured spatial distribution of mechanical properties and the tissue interfaces on data from another computational model, simulating uniaxial loading of a rectangular hydrogel sample containing a human brain slice with distinct gray matter and white matter regions and complex geometrical features. This elasticity imaging implementation has the potential to be used in clinical imaging scenarios to reliably discover the spatial distribution of mechanical parameters and identify material interfaces such as tumors. STATEMENT OF SIGNIFICANCE: Our work is the first implementation of physics-informed neural networks to reconstruct both material parameters - Young's modulus and Poisson's ratio - and stress distributions for isotropic linear elastic materials by having deformation and force measurements. We comprehensively validate our model using experimental measurements and synthetic data generated using finite element modeling. Our method can be implemented in clinical elasticity imaging scenarios to improve diagnosis of tumors and for mechanical characterization of biomaterials and biological tissues in a minimally invasive manner.

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.