Abstract Transcranial temporal interference stimulation (tTIS) is a promising non-invasive brain stimulation technique that has the potential to selectively modulate deep brain regions by delivering two high-frequency alternating currents that interfere to produce a low-frequency amplitude-modulated envelope at the target. A key challenge in deploying tTIS is finding electrode current patterns that are simultaneously effective, focal, and safe. This is a fundamentally non-convex optimization problem for which a number of methods have recently been proposed. However, no systematic comparison of these methods across a large and diverse set of brain targets has been performed, leaving practitioners without clear guidance on how best to optimize for a particular experimental setting. In this work, we present a comprehensive benchmarking study comparing seven tTIS optimization methods that have appeared in the literature in recent years: exhaustive search, genetic algorithm, multi-objective evolutionary algorithm (MOVEA), min-max optimization, convex TI (CVXTI), non-convex optimization with convex relaxations, and an unsupervised neural network. All methods were evaluated across 250 brain targets spanning cortical and subcortical gray matter and white matter regions in five finite element head models. Each method was evaluated on two key metrics: mean electric field strength within the target region of interest, and off-target stimulated brain volume. Results were stratified by tissue type and target depth to identify systematic performance differences. Based on these results, we provide practical evidence-based recommendations for optimization method selection among these seven methods depending on target location, tissue type, and available computation time. Moreover we provide the code base that will allow other investigators to use these methods for their own applications. Our goal is to provide researchers and clinicians with a clear, evidence-based framework for choosing a tTIS optimization method suited to their specific target and application.

BACKGROUND:Many neurological and psychiatric disorders involve dysregulation of subcortical structures. Transcranial temporal interference stimulation (tTIS) is a novel, non-invasive method developed to selectively modulate deep brain regions and associated neural circuits. METHODS:A systematic review was conducted to evaluate human applications of tTIS (PROSPERO ID: CRD42024559678). MEDLINE, Embase, APA PsycINFO, CENTRAL, ClinicalTrials.gov, and WHO ICTRP were searched up to December 12, 2024. Studies involving human applications of tTIS were eligible. Methodological quality was appraised using the National Institutes of Health and modified Oxford Centre for Evidence-Based Medicine tools. RESULTS:Forty-eight records were reviewed (20 published studies, 28 ongoing trials). Of published studies, 16 single-session and 4 multi-session studies assessed safety, mechanistic outcomes, or therapeutic effects of tTIS in 820 participants. Stimulation was most commonly delivered at beta (20 Hz) or gamma (30-130 Hz) envelope frequencies. Neuroimaging studies support target engagement of the motor cortex, basal ganglia, and hippocampus in humans, particularly when stimulation is paired with behavioural tasks. Preliminary clinical findings in small samples demonstrated acute symptom improvements in bradykinesia and tremor within 60 min following a single tTIS session in Parkinson's disease and essential tremor. Reported adverse events across studies were mild (e.g., tingling, itching). Emerging trials increasingly utilize multi-session protocols (2-40 sessions) and are extending tTIS to patients with neurological and psychiatric disorders, particularly epilepsy and depression. CONCLUSIONS:Phase 1 studies demonstrate that tTIS is safe, well-tolerated, and capable of engaging deep brain targets in humans. Well-controlled Phase 2 trials are needed to assess its therapeutic potential in patient populations.

Transcranial alternating current stimulation (tACS) and transcranial temporal interference stimulation (tTIS) are non-invasive brain stimulation techniques used to probe causal relationships between brain oscillations and behavior. The ability of tACS to entrain brain oscillations has been previously tested by phase-locking transcranial magnetic stimulation (TMS) to the tACS signal in order to observe tACS-phase dependency of the motor evoked response. Prior investigations using this technique have been limited by suboptimal accuracy in triggering of TMS to a specific phase of the tACS signal. Furthermore, these approaches cannot be applied to more complex waveforms such as those utilized in tTIS. This paper introduces a real-time, optimization-based method for phase-specific triggering compatible with tACS and tTIS. Our approach uses waveform fitting to estimate phase in real-time on the deterministic Real-Time eXperimental Interface (RTXI) platform. Across multiple frequencies of tACS and tTIS (5-80 Hz), results show high accuracy and low variability in phase targeting (1 degree) in all tested conditions. Limitations of the approach and generalizability of the platform to other closed-loop neurostimulation techniques are given in the discussion.

This paper proposes a method to learn approximations of missing Ordinary Differential Equations (ODEs) and states in physiological models where knowledge of the system's relevant states and dynamics is incomplete. The proposed method augments known ODEs with neural networks (NN), then trains the hybrid ODE-NN model on a subset of available physiological measurements (i.e., states) to learn the NN parameters that approximate the unknown ODEs. Thus, this method can model an approximation of the original partially specified system subject to the constraints of known biophysics. This method also addresses the challenge of jointly estimating physiological states, NN parameters, and unknown initial conditions during training using recursive Bayesian estimation. We validate this method using two simulated physiological systems, where subsets of the ODEs are assumed to be unknown during the training and test processes. The proposed method almost perfectly tracks the ground truth in the case of a single missing ODE and state and performs well in other cases where more ODEs and states are missing. This performance is robust to input signal perturbations and noisy measurements. A critical advantage of the proposed hybrid methodology over purely data-driven methods is the incorporation of the ODE structure in the model, which allows one to infer unobserved physiological states. The ability to flexibly approximate missing or inaccurate components in ODE models improves a significant modeling bottleneck without sacrificing interpretability.

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Transcranial magnetic stimulation (TMS) is often applied to the motor cortex to stimulate a collection of motor evoked potentials (MEPs) in groups of peripheral muscles. The causal interface between TMS and MEP is the selective activation of neurons in the motor cortex; moving around the TMS ‘spot’ over the motor cortex causes different MEP responses. A question of interest is whether a collection of MEP responses can be used to identify the stimulated locations on the cortex, which could potentially be used to then place the TMS coil to produce chosen sets of MEPs. In this work we leverage our previous report on a 3D convolutional neural network (CNN) architecture that predicted MEPs from the induced electric field, to tackle an inverse imaging task in which we start with the MEPs and estimate the stimulated regions on the motor cortex. We present and evaluate five different inverse imaging CNN architectures, both conventional and generative, in terms of several measures of reconstruction accuracy. We found that one architecture, which we propose as M2M-InvNet, consistently achieved the best performance.

BackgroundTranscranial temporal interference stimulation (tTIS) is a new, emerging neurostimulation technology that utilizes two or more electric fields at specific frequencies to modulate the oscillations of neurons at a desired spatial location in the brain. The physics of tTIS offers the advantage of modulating deep brain structures in a non-invasive fashion and with minimal stimulation of the overlying cortex outside of a selected target. As such, tTIS can be effectively employed in the context of therapeutics for the psychiatric disease of disrupted brain connectivity, such as major depressive disorder (MDD). The subgenual anterior cingulate cortex (sgACC), a key brain center that regulates human emotions and influences negative emotional states, is a plausible target for tTIS in MDD based on reports of its successful neuromodulation with invasive deep brain stimulation.MethodsThis pilot, single-site, double-blind, randomized, sham-controlled interventional clinical trial will be conducted at St. Michael’s Hospital – Unity Health Toronto in Toronto, ON, Canada. The primary objective is to demonstrate target engagement of the sgACC with 130 Hz tTIS using resting-state magnetic resonance imaging (MRI) techniques. The secondary objective is to estimate the therapeutic potential of tTIS for MDD by evaluating the change in clinical characteristics of participants and electrophysiological outcomes and providing feasibility and tolerability estimates for a large-scale efficacy trial. Thirty participants (18–65 years) with unipolar, non-psychotic MDD will be recruited and randomized to receive 10 sessions of 130 Hz tTIS or sham stimulation (n = 15 per arm). The trial includes a pre- vs. post-treatment 3T MRI scan of the brain, clinical evaluation, and electroencephalography (EEG) acquisition at rest and during the auditory mismatch negativity (MMN) paradigm.DiscussionThis study is one of the first-ever clinical trials among patients with psychiatric disorders examining the therapeutic potential of repetitive tTIS and its neurobiological mechanisms. Data obtained from this trial will be used to optimize the tTIS approach and design a large-scale efficacy trial. Research in this area has the potential to provide a novel treatment option for individuals with MDD and circuitry-related disorders and may contribute to the process of obtaining regulatory approval for therapeutic applications of tTIS.Clinical Trial RegistrationClinicalTrials.gov, identifier NCT05295888.

BackgroundRepetitive transcranial magnetic stimulation (rTMS) is widely used in both research and clinical settings to modulate human brain function and behavior through the engagement of the mechanisms of plasticity. Based upon experiments using single-pulse TMS as a probe, the physiologic mechanism of these effects is often assumed to be via changes in cortical excitability, with 10 Hz rTMS increasing and 1 Hz rTMS decreasing the excitability of the stimulated region. However, the reliability and reproducibility of these rTMS protocols on cortical excitability across and within individual subjects, particularly in comparison to robust sham stimulation, have not been systematically examined.ObjectivesIn a cohort of 28 subjects (39 ± 16 years), we report the first comprehensive study to (1) assess the neuromodulatory effects of traditional 1 Hz and 10 Hz rTMS on corticospinal excitability against both a robust sham control, and two other widely used patterned rTMS protocols (intermittent theta burst stimulation, iTBS; and continuous theta burst stimulation, cTBS), and (2) determine the reproducibility of all rTMS protocols across identical repeat sessions.ResultsAt the group level, neither 1 Hz nor 10 Hz rTMS significantly modulated corticospinal excitability. 1 Hz and 10 Hz rTMS were also not significantly different from sham and both TBS protocols. Reproducibility was poor for all rTMS protocols except for sham. Importantly, none of the real rTMS and TBS protocols demonstrated greater neuromodulatory effects or reproducibility after controlling for potential experimental factors including baseline corticospinal excitability, TMS coil deviation and the number of individual MEP trials.ConclusionsThese results call into question the effectiveness and reproducibility of widely used rTMS techniques for modulating corticospinal excitability, and suggest the need for a fundamental rethinking regarding the potential mechanisms by which rTMS affects brain function and behavior in humans.

Increasing the intensity of tumor treating fields (TTF) within a tumor bed improves clinical efficacy, but reaching sufficiently high field intensities to achieve growth arrest remains challenging due in part to the insulating nature of the cranium. Using MRI-derived finite element models (FEMs) and simulations, we optimized an exhaustive set of intracranial electrode locations to obtain maximum TTF intensities in three clinically challenging high-grade glioma (HGG) cases (i.e., thalamic, left temporal, brainstem). Electric field strengths were converted into therapeutic enhancement ratios (TER) to evaluate the predicted impact of stimulation on tumor growth. Concurrently, conventional transcranial configurations were simulated/optimized for comparison. Optimized intracranial TTF were able to achieve field strengths that have previously been shown capable of inducing complete growth arrest, in 98–100% of the tumor volumes using only 0.54–0.64 A current. The reconceptualization of TTF as a targeted, intracranial therapy has the potential to provide a meaningful survival benefit to patients with HGG and other brain tumors, including those in surgically challenging, deep, or anatomically eloquent locations which may preclude surgical resection. Accordingly, such an approach may ultimately represent a paradigm shift in the use of TTFs for the treatment of brain cancer.

Background: Repetitive transcranial magnetic stimulation (rTMS) is widely used in both research and clinical settings to modulate human brain function and behavior through engagement of the mechanisms of plasticity. Based upon experiments using single-pulse TMS as a probe, the physiologic mechanism of these effects is often assumed to be via changes in cortical excitability, with 10 Hz rTMS increasing and 1 Hz rTMS decreasing the excitability of the stimulated region. However, the reliability and reproducibility of traditional rTMS protocols on cortical excitability across and within individual subjects, particularly in comparison to robust sham stimulation, have not been systematically examined.Objectives: In a cohort of 28 subjects (39 [[EQUATION]] 16 years), we report the first comprehensive study to (1) assess the neuromodulatory effects of traditional 1 Hz and 10 Hz rTMS on corticospinal excitability against both a robust sham control, and two other widely used patterned rTMS protocols (intermittent theta burst stimulation, iTBS; and continuous theta burst stimulation, cTBS), and (2) determine the reproducibility of all rTMS protocols across identical repeat sessions.Results: At the group level, neither 1 Hz nor 10 Hz rTMS significantly modulated corticospinal excitability. 1 Hz and 10 Hz rTMS were also not significantly different from sham and both TBS protocols. Reproducibility was poor for all rTMS protocols except for sham. Importantly, none of the real rTMS and TBS protocols demonstrated greater neuromodulatory effects or reproducibility after controlling for potential experimental factors including baseline corticospinal excitability, TMS coil deviation and number of individual MEP trials.Conclusions: These results call into question the effectiveness and reproducibility of widely used rTMS techniques for modulating corticospinal excitability, and suggest the need for a fundamental rethinking regarding the potential mechanisms by which rTMS affects brain function and behavior in humans.

Background: Computational biomedical simulations frequently contain parameters that model physical fea -tures, material coefficients, and physiological effects, whose values are typically assumed known a priori. Understanding the effect of variability in those assumed values is currently a topic of great interest. A general-purpose software tool that quantifies how variation in these parameters affects model outputs is not broadly available in biomedicine. For this reason, we developed the 'UncertainSCI' uncertainty quantification software suite to facilitate analysis of uncertainty due to parametric variability.Methods: We developed and distributed a new open-source Python-based software tool, UncertainSCI, which employs advanced parameter sampling techniques to build polynomial chaos (PC) emulators that can be used to predict model outputs for general parameter values. Uncertainty of model outputs is studied by modeling parameters as random variables, and model output statistics and sensitivities are then easily computed from the emulator. Our approaches utilize modern, near-optimal techniques for sampling and PC construction based on weighted Fekete points constructed by subsampling from a suitably randomized candidate set.Results: Concentrating on two test cases-modeling bioelectric potentials in the heart and electric stimulation in the brain-we illustrate the use of UncertainSCI to estimate variability, statistics, and sensitivities associated with multiple parameters in these models.Conclusion: UncertainSCI is a powerful yet lightweight tool enabling sophisticated probing of parametric variability and uncertainty in biomedical simulations. Its non-intrusive pipeline allows users to leverage existing software libraries and suites to accurately ascertain parametric uncertainty in a variety of applications.

Tate et al., (2023). UncertainSCI: A Python Package for Noninvasive Parametric Uncertainty Quantification of Simulation Pipelines. Journal of Open Source Software, 8(90), 4249, https://doi.org/10.21105/joss.04249

Department of Neurosurgery, University of California, San Francisco, California, USA (D.J.S.); Department of Neurosurgery, Brigham and Women’s Hospital, Harvard Medical School, Boston, Massachusetts, USA (J.D.B., W.L.B., O.A., E.A.C.); Department of Neurosurgery, Boston Children’s Hospital, Harvard Medical School, Boston, MA, USA (J.D.B.); David H. Koch Institute for Integrative Cancer Research, Massachusetts Institute of Technology, Cambridge, Massachusetts, USA (J.D.B.); Department of Physics, University of Massachusetts, Boston, Massachusetts, USA (S.R.); Department of Electrical and Computer Engineering, Northeastern University, Boston, Massachusetts, USA (S.R.); Department of Pediatrics, University of Alabama at Birmingham, Birmingham, Alabama, USA (G.K.F.)

Direct electrocortical stimulation (DECS) with electrocorticography electrodes is an established therapy for epilepsy and an emerging application for stroke rehabilitation and brain-computer interfaces. However, the electrophysiological mechanisms that result in a therapeutic effect remain unclear. Patient-specific computational models are promising tools to predict the voltages in the brain and better understand the neural and clinical response to DECS, but the accuracy of such models has not been directly validated in humans. A key hurdle to modeling DECS is accurately locating the electrodes on the cortical surface due to brain shift after electrode implantation. Despite the inherent uncertainty introduced by brain shift, the effects of electrode localization parameters have not been investigated. The goal of this study was to validate patient-specific computational models of DECS against in vivo voltage recordings obtained during DECS and quantify the effects of electrode localization parameters on simulated voltages on the cortical surface. We measured intracranial voltages in six epilepsy patients during DECS and investigated the following electrode localization parameters: principal axis, Hermes, and Dykstra electrode projection methods combined with 0, 1, and 2 mm of cerebral spinal fluid (CSF) below the electrodes. Greater CSF depth between the electrode and cortical surface increased model errors and decreased predicted voltage accuracy. The electrode localization parameters that best estimated the recorded voltages across six patients with varying amounts of brain shift were the Hermes projection method and a CSF depth of 0 mm (r = 0.92 and linear regression slope = 1.21). These results are the first to quantify the effects of electrode localization parameters with in vivo intracranial recordings and may serve as the basis for future studies investigating the neuronal and clinical effects of DECS for epilepsy, stroke, and other emerging closed-loop applications.

Transcranial current stimulation (tCS) has been used extensively to noninvasively investigate and influence brain function in both healthy volunteers and clinical populations. Though positive results have been obtained with current methods, accurate targeting, high focality and deep stimulation are yet to be achieved. Transcranial temporal interference stimulation (tTIS) offers a potential solution to these issues by combining two alternating currents to create an amplitude-modulated electric field that can peak deep in the brain (Fig. 1A). Simulations of electric field in human models indicated the potential of tTIS for subthreshold neuromodulation similar to tACS, but with maximal effects in deep brain areas and greater focality. For tTIS to become practical, optimization methods are needed that can selectively stimulate a region of interest (ROI) while meeting safety constraints. Because conventional tCS presents a linear optimization problem, existing optimization methods for tCS cannot be used for tTIS. Previously proposed solutions for tTIS optimization included exhaustive search (Rampersad et al., 2019) and reformulations of existing tCS methods (Huang et al., 2020). These methods take hours to complete, making them inefficient for practical use in research or in the clinic. As an alternative we posed tTIS targeting as a non-convex optimization problem and exploit its associated mathematical model using convex relaxations and tailored heuristics. We tested our algorithm on multiple realistic human head models with 88 electrodes for a large set of ROIs spread throughout the brain (Fig. 1B). Our method was able to find current patterns that deliver maximal tTIS fields to any ROI in seconds. We combined this method with Pareto optimization, which allowed maximizing focality in addition to ROI effects, but significantly increases the runtime. Optimization outcomes were evaluated on ROI effects, focality and efficiency, and compared to the two previously proposed methods (Fig. 1C), demonstrating a tradeoff dependent on ROI location. Keywords: temporal interference, transcranial stimulation, optimization, simulation

Modeling biological dynamical systems is challenging due to the interdependence of different system components, some of which are not fully understood. To fill existing gaps in our ability to mechanistically model physiological systems, we propose to combine neural networks with physics-based models. Specifically, we demonstrate how we can approximate missing ordinary differential equations (ODEs) coupled with known ODEs using Bayesian filtering techniques to train the model parameters and simultaneously estimate dynamic state variables. As a study case we leverage a well-understood model for blood circulation in the human retina and replace one of its core ODEs with a neural network approximation, representing the case where we have incomplete knowledge of the physiological state dynamics. Results demonstrate that state dynamics corresponding to the missing ODEs can be approximated well using a neural network trained using a recursive Bayesian filtering approach in a fashion coupled with the known state dynamic differential equations. This demonstrates that dynamics and impact of missing state variables can be captured through joint state estimation and model parameter estimation within a recursive Bayesian state estimation (RBSE) framework. Results also indicate that this RBSE approach to training the NN parameters yields better outcomes (measurement/state estimation accuracy) than training the neural network with backpropagation through time in the same setting.