Computation of transcranial magnetic stimulation electric fields using self-supervised deep learning

Real-time estimation of the optimal coil placement in transcranial magnetic stimulation using multi-task deep learning

Transcranial magnetic stimulation (TMS) has emerged as a promising neuromodulation technique with both therapeutic and diagnostic applications. As accurate coil placement is known to be essential for focal stimulation, computational models have been established to help find the optimal coil positioning by maximizing electric fields at the cortical target. While these numerical simulations provide realistic and subject-specific field distributions, they are computationally demanding, precluding their use in real-time applications. In this paper, we developed a novel multi-task deep neural network which simultaneously predicts the optimal coil placement for a given cortical target as well as the associated TMS-induced electric field. Trained on large amounts of preceding numerical optimizations, the Attention U-Net-based neural surrogate provided accurate coil optimizations in only 35 ms, a fraction of time compared to the state-of-the-art numerical framework. The mean errors on the position estimates were below 2 mm, i.e., smaller than previously reported manual coil positioning errors. The predicted electric fields were also highly correlated (r> 0.97) with their numerical references. In addition to healthy subjects, we validated our approach also in glioblastoma patients. We first statistically underlined the importance of using realistic heterogeneous tumor conductivities instead of simply adopting values from the surrounding healthy tissue. Second, applying the trained neural surrogate to tumor patients yielded similar accurate positioning and electric field estimates as in healthy subjects. Our findings provide a promising framework for future real-time electric field-optimized TMS applications.

Prediction of hippocampal electric field in time series induced by TI-DMS with temporal convolutional network

Temporal interference deep-brain magnetic stimulation (TI-DMS) induces rhythmic electric field (EF) in the hippocampus to normalize cognitive function. The rhythmic time series of the hippocampal EF is essential for the assessment of TI-DMS. However, the finite element method (FEM) takes several hours to obtain the time series of EF. In order to reduce the time cost, the temporal convolutional network (TCN) model is adopted to predict the time series of hippocampal EF induced by TI-DMS. It takes coil configuration and loaded current as input and predicts the time series of maximum and mean values of the left and right hippocampal EF. The prediction takes only a few seconds. The model parameter combination of kernel size and layers is selected optimally by cross-validation method. The experimental results for multiple subjects show that the R2 of all the time series predicted by the model exceed 0.98. And the prediction accuracy is even higher as the input parameters approach the training set. These results demonstrate that the adopted model can quickly predict the time series of hippocampal EF induced by TI-DMS with relatively high accuracy, which is beneficial for future clinical applications.

Individual Prediction of Electric Field Induced by Deep-Brain Magnetic Stimulation With CNN-Transformer

Deep-brain Magnetic Stimulation (DMS) can improve the symptoms caused by Alzheimer's disease by inducing rhythmic electric field in the deep brain, and the induced electric field is rhythm-dependent. However, calculating the induced electric field requires building a voxel model of the brain for the stimulated object, which usually takes several hours. In order to obtain the rhythm-dependent electric field induced by DMS in real time, we adopt a CNN-Transformer model to predict it. A data set with a sample size of 7350 is established for the training and testing of the model. 10-fold cross validation is used to determine the optimal hyperparameters for training CNN-Transformer. The combination of 5-layer CNN and 6-layer Transformer is verified as the optimal combination of CNN-Transformer model. The experimental results show that the CNN-Transformer model can complete the prediction in 0.731s (CPU) or 0.042s (GPU), and the overall performance metrics of prediction can reach: MAE =0.0269, RMSE =0.0420, MAPE =4.61% and R2=0.9627. The prediction performance of the CNN-Transformer model for the hippocampal electric field is better than that of the brain grey matter electric field, and the stimulation rhythm has less influence on the model performance than the coil configuration. Taking the same dataset to train and test the separate CNN model and Transformer model, it is found that CNN-Transformer has better prediction performance than the separate CNN model and Transformer model in the task of predicting electric field induced by DMS.

A review of algorithms and software for real-time electric field modeling techniques for transcranial magnetic stimulation

Transcranial magnetic stimulation (TMS) is a device-based neuromodulation technique increasingly used to treat brain diseases. Electric field (E-field) modeling is an important technique in several TMS clinical applications, including the precision stimulation of brain targets with accurate stimulation density for the treatment of mental disorders and the localization of brain function areas for neurosurgical planning. Classical methods for E-field modeling usually take a long computation time. Fast algorithms are usually developed with significantly lower spatial resolutions that reduce the prediction accuracy and limit their usage in real-time or near real-time TMS applications. This review paper discusses several modern algorithms for real-time or near real-time TMS E-field modeling and their advantages and limitations. The reviewed methods include techniques such as basis representation techniques and deep neural-network-based methods. This paper also provides a review of software tools that can integrate E-field modeling with navigated TMS, including a recent software for real-time navigated E-field mapping based on deep neural-network models.

Electric Field Modeling in Personalizing Transcranial Magnetic Stimulation Interventions

The modeling of transcranial magnetic stimulation (TMS)-induced electric fields (E-fields) is a versatile technique for evaluating and refining brain targeting and dosing strategies, while also providing insights into dose-response relationships in the brain. This review outlines the methodologies employed to derive E-field estimations, covering TMS physics, modeling assumptions, and aspects of subject-specific head tissue and coil modeling. We also summarize various numerical methods for solving the E-field and their suitability for various applications. Modeling methodologies have been optimized to efficiently execute numerous TMS simulations across diverse scalp coil configurations, facilitating the identification of optimal setups or rapid cortical E-field visualization for specific brain targets. These brain targets are extrapolated from neurophysiological measurements and neuroimaging, enabling precise and individualized E-field dosing in experimental and clinical applications. This necessitates the quantification of E-field estimates using metrics that enable the comparison of brain target engagement, functional localization, and TMS intensity adjustments across subjects. The integration of E-field modeling with empirical data has the potential to uncover pivotal insights into the aspects of E-fields responsible for stimulating and modulating brain function and states, enhancing behavioral task performance, and impacting the clinical outcomes of personalized TMS interventions.

ViTab Transformer Framework for Predicting Induced Electric Field and Focality in Transcranial Magnetic Stimulation

Transcranial magnetic stimulation is an electromagnetic induction-based non-invasive therapeutic technique for neurological diseases. For finding new clinical applications and enhancing the efficacy of TMS in existing neurological disorders, the current study focuses on a deep learning-based prediction model as an alternative to time-consuming electromagnetic (EM) simulation software. The main bottleneck of the existing prediction models is to consider very few input parameters of a standard coil such as coil type and coil position for predicting an output of electric field value. To overcome this limitation, a transformer-based prediction model titled as ViTab transformer is developed in this work to predict electric field (E-max), focality or area of stmulation (S-half), and volume of stimulation (V-half) by considering several input parameters such as sources of MRI images, types of coils, coil position, rate of change of current, brain tissues conductivity, and coil distance from the scalp. The proposed framework consists of a vision and a tab transformer to handle both image and tabular-type data. The prediction performance of the offered model is evaluated in terms of coefficient determination, R2 score, for E-max, V-half, and S-half in the testing phase. The obtained result in terms of R2 score for E-max, V-half, and S-half are found 0.97, 0.87, and 0.90 respectively. The results indicate that the suggested ViTab transformer model can predict electric field as well as focality more accurately than the current state-of-the-art methods. The reduced computational time, as well as efficient prediction accuracy, resembles that ViTab transformer can assist the neuroscientist and neurosurgeon prior to providing superior TMS treatment in near future.

In-vivoverified anatomically aware deep learning for real-time electric field simulation

Objective.Transcranial magnetic stimulation (TMS) has emerged as a prominent non-invasive technique for modulating brain function and treating mental disorders. By generating a high-precision magnetically evoked electric field (E-field) using a TMS coil, it enables targeted stimulation of specific brain regions. However, current computational methods employed for E-field simulations necessitate extensive preprocessing and simulation time, limiting their fast applications in the determining the optimal coil placement.Approach.We present an attentional deep learning network to simulate E-fields. This network takes individual magnetic resonance images and coil configurations as inputs, firstly transforming the images into explicit brain tissues and subsequently generating the local E-field distribution near the target brain region. Main results. Relative to the previous deep-learning simulation method, the presented method reduced the mean relative error in simulated E-field strength of gray matter by 21.1%, and increased the correlation between regional E-field strengths and corresponding electrophysiological responses by 35.0% when applied into another dataset.In-vivoTMS experiments further revealed that the optimal coil placements derived from presented method exhibit comparable stimulation performance on motor evoked potentials to those obtained using computational methods. The simplified preprocessing and increased simulation efficiency result in a significant reduction in the overall time cost of traditional TMS coil placement optimization, from several hours to mere minutes.Significance.The precision and efficiency of presented simulation method hold promise for its application in determining individualized coil placements in clinical practice, paving the way for personalized TMS treatments.

Real-Time Acoustic Simulation Framework for tFUS: A Feasibility Study Using Navigation System

Transcranial focused ultrasound (tFUS), in which acoustic energy is focused on a small region in the brain through the skull, is a non-invasive therapeutic method with high spatial resolution and depth penetration. Image-guided navigation has been widely utilized to visualize the location of acoustic focus in the cranial cavity. However, this system is often inaccurate because of the significant aberrations caused by the skull. Therefore, acoustic simulations using a numerical solver have been widely adopted to compensate for this inaccuracy. Although the simulation can predict the intracranial acoustic pressure field, real-time application during tFUS treatment is almost impossible due to the high computational cost. In this study, we propose a neural network-based real-time acoustic simulation framework and test its feasibility by implementing a simulation-guided navigation (SGN) system. Real-time acoustic simulation is performed using a 3D conditional generative adversarial network (3D-cGAN) model featuring residual blocks and multiple loss functions. This network was trained by the conventional numerical acoustic simulation program (i.e., k-Wave). The SGN system is then implemented by integrating real-time acoustic simulation with a conventional image-guided navigation system. The proposed system can provide simulation results with a frame rate of 5 Hz (i.e., about 0.2 s), including all processing times. In numerical validation (3D-cGAN vs. k-Wave), the average peak intracranial pressure error was 6.8 ± 5.5%, and the average acoustic focus position error was 5.3 ± 7.7 mm. In experimental validation using a skull phantom (3D-cGAN vs. actual measurement), the average peak intracranial pressure error was 4.5%, and the average acoustic focus position error was 6.6 mm. These results demonstrate that the SGN system can predict the intracranial acoustic field according to transducer placement in real-time.

Real-Time Computation of Brain E-Field for Enhanced Transcranial Magnetic Stimulation Neuronavigation and Optimization

Transcranial Magnetic Stimulation (TMS) coil placement and pulse waveform current are often chosen to achieve a specified E-field dose on targeted brain regions. TMS neuronavigation could be improved by including real-time accurate distributions of the E-field dose on the cortex. We introduce a method and develop software for computing brain E-field distributions in real-time enabling easy integration into neuronavigation and with the same accuracy as 1st -order finite element method (FEM) solvers. Initially, a spanning basis set (< 400) of E-fields generated by white noise magnetic currents on a surface separating the head and permissible coil placements are orthogonalized to generate the modes. Subsequently, Reciprocity and Huygens' principles are utilized to compute fields induced by the modes on a surface separating the head and coil by FEM, which are used in conjunction with online (real-time) computed primary fields on the separating surface to evaluate the mode expansion. We conducted a comparative analysis of E-fields computed by FEM and in real-time for eight subjects, utilizing two head model types (SimNIBS's 'headreco' and 'mri2mesh' pipeline), three coil types (circular, double-cone, and Figure-8), and 1000 coil placements (48,000 simulations). The real-time computation for any coil placement is within 4 milliseconds (ms), for 400 modes, and requires less than 4 GB of memory on a GPU. Our solver is capable of computing E-fields within 4 ms, making it a practical approach for integrating E-field information into the neuronavigation systems without imposing a significant overhead on frame generation (20 and 50 frames per second within 50 and 20 ms, respectively).

A Review of Formulations, Boundary Value Problems and Solutions for Numerical Computation of Transcranial Magnetic Stimulation Fields

Since the inception of the transcranial magnetic stimulation (TMS) technique, it has become imperative to numerically compute the distribution of the electric field induced in the brain. Various models of the coil-brain system have been proposed for this purpose. These models yield a set of formulations and boundary conditions that can be employed to calculate the induced electric field. However, the literature on TMS simulation presents several of these formulations, leading to potential confusion regarding the interpretation and contribution of each source of electric field. The present study undertakes an extensive compilation of widely utilized formulations, boundary value problems and numerical solutions employed in TMS fields simulations, analyzing the advantages and disadvantages associated with each used formulation and numerical method. Additionally, it explores the implementation strategies employed for their numerical computation. Furthermore, this work provides numerical expressions that can be utilized for the numerical computation of TMS fields using the finite difference and finite element methods. Notably, some of these expressions are deduced within the present study. Finally, an overview of some of the most significant results obtained from numerical computation of TMS fields is presented. The aim of this work is to serve as a guide for future research endeavors concerning the numerical simulation of TMS.

Rapid estimation of cortical neuron activation thresholds by transcranial magnetic stimulation using convolutional neural networks

BACKGROUND

Transcranial magnetic stimulation (TMS) can modulate neural activity by evoking action potentials in cortical neurons. TMS neural activation can be predicted by coupling subject-specific head models of the TMS-induced electric field (E-field) to populations of biophysically realistic neuron models; however, the significant computational cost associated with these models limits their utility and eventual translation to clinically relevant applications.

OBJECTIVE

To develop computationally efficient estimators of the activation thresholds of multi-compartmental cortical neuron models in response to TMS-induced E-field distributions.

METHODS

Multi-scale models combining anatomically accurate finite element method (FEM) simulations of the TMS E-field with layer-specific representations of cortical neurons were used to generate a large dataset of activation thresholds. 3D convolutional neural networks (CNNs) were trained on these data to predict thresholds of model neurons given their local E-field distribution. The CNN estimator was compared to an approach using the uniform E-field approximation to estimate thresholds in the non-uniform TMS-induced E-field.

RESULTS

The 3D CNNs estimated thresholds with mean absolute percent error (MAPE) on the test dataset below 2.5% and strong correlation between the CNN predicted and actual thresholds for all cell types (R2 > 0.96). The CNNs estimated thresholds with a 2-4 orders of magnitude reduction in the computational cost of the multi-compartmental neuron models. The CNNs were also trained to predict the median threshold of populations of neurons, speeding up computation further.

CONCLUSION

3D CNNs can estimate rapidly and accurately the TMS activation thresholds of biophysically realistic neuron models using sparse samples of the local E-field, enabling simulating responses of large neuron populations or parameter space exploration on a personal computer.

A Systematic Review and Large-Scale tES and TMS Electric Field Modeling Study Reveals How Outcome Measure Selection Alters Results in a Person- and Montage-Specific Manner

Background

Electric field (E-field) modeling is a potent tool to examine the cortical effects of transcranial magnetic and electrical stimulation (TMS and tES, respectively) and to address the high variability in efficacy observed in the literature. However, outcome measures used to report E-field magnitude vary considerably and have not yet been compared in detail.

Objectives

The goal of this two-part study, encompassing a systematic review and modeling experiment, was to provide an overview of the different outcome measures used to report the magnitude of tES and TMS E-fields, and to conduct a direct comparison of these measures across different stimulation montages.

Methods

Three electronic databases were searched for tES and/or TMS studies reporting E-field magnitude. We extracted and discussed outcome measures in studies meeting the inclusion criteria. Additionally, outcome measures were compared via models of four common tES and two TMS modalities in 100 healthy younger adults.

Results

In the systematic review, we included 118 studies using 151 outcome measures related to E-field magnitude. Structural and spherical regions of interest (ROI) analyses and percentile-based whole-brain analyses were used most often. In the modeling analyses, we found that there was an average of only 6% overlap between ROI and percentile-based whole-brain analyses in the investigated volumes within the same person. The overlap between ROI and whole-brain percentiles was montage- and person-specific, with more focal montages such as 4Ã-1 and APPS-tES, and figure-of-eight TMS showing up to 73%, 60%, and 52% overlap between ROI and percentile approaches respectively. However, even in these cases, 27% or more of the analyzed volume still differed between outcome measures in every analyses.

Conclusions

The choice of outcome measures meaningfully alters the interpretation of tES and TMS E-field models. Well-considered outcome measure selection is imperative for accurate interpretation of results, valid between-study comparisons, and depends on stimulation focality and study goals. We formulated four recommendations to increase the quality and rigor of E-field modeling outcome measures. With these data and recommendations, we hope to guide future studies towards informed outcome measure selection, and improve the comparability of studies.