Transcranial Magnetic Stimulation (TMS)

• TMS is a non-invasive neurostimulation technique that uses time-varying magnetic fields to induce electric currents in targeted brain regions.
• Advanced coil designs and pulse optimization improve stimulation focality, energy efficiency, and reduce coil heating.
• Integration of real-time neuronavigation and robotics enables precise, personalized treatment planning and enhanced reproducibility.

Transcranial Magnetic Stimulation (TMS) is a non-invasive neurostimulation technique that utilizes time-varying magnetic fields to induce electric fields in the cerebral cortex, enabling activation or modulation of neural circuits for research, diagnostic, and therapeutic purposes. TMS is governed by Maxwell’s equations under the quasi-static approximation and can be delivered via various coil designs and pulse waveforms to target distinct brain regions and effect neuroplasticity. Continuous advances in biophysical modeling, hardware, algorithmic optimization, and workflow integration have transformed TMS from a basic mapping tool to a precision neuromodulation modality.

1. Electromagnetic Principles and Modeling Foundations

TMS relies on Faraday’s law of induction: a pulsed current $I(t)$ in a coil (typically figure‐eight or circular) generates a rapidly changing magnetic flux density $B(\mathbf{r},t)$ in adjacent tissue. The induced electric field $E(\mathbf{r},t)$ satisfies

$$\nabla \times E(\mathbf{r}, t) = -\frac{\partial B(\mathbf{r}, t)}{\partial t}, \quad \nabla \cdot [\sigma(\mathbf{r}) E(\mathbf{r}, t)] = 0,$$

where $\sigma(\mathbf{r})$ is the conductivity, typically piecewise constant or anisotropic in white matter (Gomez-Tames et al., 2020, Franke et al., 2023). The vector potential formulation introduces $A(\mathbf{r}, t)$ such that $B = \nabla \times A$, and

$$E(\mathbf{r}, t) = -\frac{\partial A(\mathbf{r}, t)}{\partial t} - \nabla \phi(\mathbf{r}, t),$$

where $-\partial A/\partial t$ describes the anatomy-independent primary field, and $-\nabla \phi$ enforces current continuity at tissue boundaries.

Computational dosimetry employs finite element (FEM), boundary element (BEM), or finite difference (FDM) solvers on MRI-derived head meshes, integrating precise segmentation of scalp, skull, CSF, gray and white matter. These solvers yield $E(\mathbf{r}, t)$ distributions critical for patient-specific treatment planning and dose optimization (Gomez-Tames et al., 2020). Quantitative metrics such as peak field strength $E_\text{max}$, focality (spread $S_{1/2}$), half-depth $d_{1/2}$, and pulse energy $W$ are standardized.

2. Coil Design, Pulse Optimization, and Energy Efficiency

Coil geometry and winding pattern dictate stimulation focality, depth, and energy efficiency. Figure-eight coils produce a focal “hot spot” at the intersection of the two loops, whereas circular or double-cone coils facilitate deeper, less focal stimulation (Heidarpanah, 2022, Gomez-Tames et al., 2020). Recent advances introduce mathematically rigorous, anatomy-independent coil optimization methods using Hilbert space projections, spanning continuous current densities $j(\mathbf{r})$ on arbitrary closed surfaces, and exploiting modal basis expansions, Gram matrix solutions, and streamline discretization for manufacturability (Koehler et al., 2023, Koehler et al., 6 Jan 2026). This approach yields real coil windings matching prescribed field distributions with error typically <4%, and reduces pulse energy by 40–60% compared to legacy designs.

Pulse shape control is equally central. The modular pulse synthesizer (MPS) enables user-defined E-field waveforms, including arbitrary monophasic, biphasic, asymmetric, and burst pulses, using cascaded low-voltage, high-speed modules (Li et al., 2022). Convex optimization of monophasic asymmetric pulses under neuron-model activation constraints achieves up to 92% reduction in coil heating for comparable neural selectivity, as evidenced by AP/PA motor threshold and MEP latency preservation in human experiments (Ma et al., 11 Oct 2025). Magnetic-core coil architectures—especially Fe-based powder cores with high $B_\text{sat}$—can further halve pulse energy and losses, but require careful management of saturation margins and acceptable mass (Koehler et al., 2 Nov 2025).

A comparative table of advanced coil/pulse technologies is shown below:

Approach	Field Match (%)	Energy Reduction (%)	Key Limitation
Anatomy-independent Hilbert Space (Koehler et al., 2023)	96–99.4	40–56	Manufacturing complexity, acoustic noise
Modular Pulse Synthesizer (Li et al., 2022)	Arbitrary waveform	up to 90	Electronics cost, waveform fidelity
Fe-powder core (Koehler et al., 2 Nov 2025)	~95	37–53	Weight (>1–6 kg), saturation margin

3. Workflow, Neuronavigation, and Robotics Integration

Personalized TMS requires precise coil placement relative to individual cortical geometry, estimated from MRI. Real-time neuronavigation systems such as SlicerTMS integrate deep-learning E-field surrogates, probabilistic conductivity from diffusion MRI, and interactive 3D visualization interfaces (Franke et al., 2023). The operator can explore “what-if” scenarios, adjust coil pose (6-DOF), and immediately review changes in E-field on mesh, MRI volume, or tractography—all with sub-0.2 s latency.

Robotics-based platforms further reduce operator variability and enhance reproducibility. KUKA-based image-guided systems utilize rigid and ICP registration of patient anatomy to plan deterministic coil poses in “true zero” alignment with local cortical geometry, thereby halving translational error and enhancing rotational accuracy by two orders of magnitude compared to manual methods (Liu et al., 2024). These augmentations propagate directly to greater consistency in induced fields, as measured by magnetic field sensors and phantoms.

Robo-TMS systems extend this paradigm, providing hardware, calibration, and closed-loop control architectures for high-throughput, multi-site stimulation, with future prospects for marker-less vision alignment, learning-based E-field prediction, and individualized MRI synthesis (Bai et al., 6 Jul 2025).

4. Biophysical Mechanisms, Network Effects, and Biomarker Extraction

Single-pulse and repetitive TMS drives a cascade of neurophysiological events: direct depolarization at axon bends or initial segments, network transmission via glutamatergic and GABAergic circuits, homeostatic shifts in synaptic efficacy (LTP/LTD), and large-scale reorganization of functional connectivity (Heidarpanah, 2022, Gomez-Tames et al., 2020, Murphy et al., 2022). Animal models confirm multiphasic local firing—excitation followed by prolonged inhibition and rebound—whose temporal balance determines net BOLD response (Rafiei et al., 2021).

Predictive models coupling regional TMS-induced activity ($\Delta A$) and structural context network (SCN) features (fiber density, core-periphery structure) accurately forecast downstream changes in functional connectivity (FC) between anatomically distributed systems, e.g., FPS and DMS (Murphy et al., 2022). Dense SCN core overlap enables maximal $\Delta$FC, offering a quantitative roadmap for targeting network hubs in psychiatric protocols.

Emerging TMS-EEG biomarkers (TEPs) probe both cortical excitability and network connectivity. Reliability metrics—ICC (relative reliability), SEM/SDC (absolute reliability), and CV—must meet rigorous statistical standards before clinical adoption. Late TEP components (N100, P200) demonstrate moderate to substantial ICC and acceptable SDC; spatial-temporal reliability portraits facilitate robust biomarker extraction (Bertazzoli et al., 2024).

5. Closed-Loop Control, Digital Twins, and Artifact Management

Adaptive TMS strategies now leverage closed-loop feedback from real-time EEG (and MMG/EMG), using fractional-order model predictive control (FOS-MPC) frameworks to suppress pathologic oscillations (e.g., seizure mitigation) while enforcing energy and safety constraints (Romero et al., 2019). Digital-twin-style models of motor-evoked potentials, integrating spatial, orientation, and recruitment variability calibrated from empirical distributions, support large-scale simulation and benchmarking of closed-loop thresholding, amplitude tracking, and spatial targeting algorithms (Farahmandrad et al., 4 Jul 2025).

Artifact rejection remains a core challenge in TMS-EEG. Conventional ICA and PCA-based methods often fail to reconstruct the true EEG signal within 20 ms post-TMS, due to complex overlap of artifact and neural response. Local gap-filling algorithms, based on state-space embedding and nearest-neighbor prediction, provide superior reconstruction under additive, stationary conditions and preserve critical diagnostic information for closed-loop operation (Vafeidis et al., 2018).

6. Clinical Translation and Future Directions

High-frequency rTMS (≥ 5 Hz) to prefrontal or motor targets is established as safe and moderately efficacious for mood and cognitive disorders, including Alzheimer’s disease; protocols frequently employ sessions of 10–20 trains at 90–100% rMT, sometimes augmented by cognitive training (Heidarpanah, 2022). Safety is well characterized—transient discomfort, rare seizure risk <0.01%—yet optimization of pulse shape, coil placement, and interindividual parameter tuning remains outstanding.

Integration of adaptive stimulation, real-time biomarker extraction, anatomy-independent coil matching, and precision robotics will be pivotal. Prospective extensions include closed-loop control driven by concurrent EEG or MMG, multi-locus electronic steering, and manufacturable optimized coil geometries via open-source toolchains (Koehler et al., 2023, Koehler et al., 6 Jan 2026). Quantitative, robust mechanistic modeling will ensure that TMS continues to evolve as a rigorously engineered modality for personalized, network-guided neuromodulation.