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Transcranial Magnetic Stimulation: Principles and Applications

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Neural Engineering

Abstract

Transcranial magnetic stimulation (TMS) is a noninvasive method for focal brain stimulation, with applications in research, diagnostics, and treatment. In basic research, TMS can help establish a causal link between a brain circuit and a behavior. Clinically, repetitive TMS can alter the long-term excitability of specific brain regions to treat psychiatric and neurological disorders. This chapter aims to support engineers and researchers to understand and innovate TMS technology. It introduces the basics of TMS spanning engineering, physics, biophysics, paradigms, and applications. First, the principles of TMS devices are explained including the electrical circuit topologies and efficiency of the pulse generator as well as the design of the stimulation coil. Ancillary effects such as heating, electromagnetic forces, and interactions with other devices are considered. Then, the underlying physics and its modeling are presented, including the magnetic field of the coil and the impact of the subject’s head on the induced electric field. This is followed by a description of the biophysics of neuronal activation due to TMS, including the cable equation, leaky integrate-and-fire neural membrane dynamics, and morphologically realistic neuron models. Various methods to measure the responses to TMS are summarized, spanning observations of behavior, electromyography, epidural recordings, electroencephalography, functional near-infrared spectroscopy, functional magnetic resonance imaging, and positron emission tomography. The chapter concludes with an overview of stimulation paradigms encompassing single-pulse, paired-pulse, and repetitive TMS, along with their applications in basic research and the clinic. The chapter includes ten problems that cover the presented material.

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Authors and Affiliations

  1. Department of Psychiatry & Behavioral Sciences, Duke University, Durham, NC, USA

    Lari M. Koponen & Angel V. Peterchev

  2. Department of Biomedical Engineering, Duke University, Durham, NC, USA

    Angel V. Peterchev

  3. Department of Electrical & Computer Engineering, Duke University, Durham, NC, USA

    Angel V. Peterchev

  4. Department of Neurosurgery, Duke University, Durham, NC, USA

    Angel V. Peterchev

Authors
  1. Lari M. Koponen
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  2. Angel V. Peterchev
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Correspondence to Angel V. Peterchev .

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Editors and Affiliations

  1. Department of Biomedical Engineering, Carnegie Mellon University, Pittsburgh, PA, USA

    Bin He

Homework

Homework

Some of the problems require the use of physics equations, parameters values, and computer programs that are not covered in this chapter. Therefore, like a real-world engineer, the student may need to consult other resources. Problems 3, 5, and 7 involve integrals that can be evaluated numerically. These problems can be solved analytically as well for an extra challenge and deeper understanding of the underlying scaling laws. Problems with increased difficulty are denoted by an asterisk (∗).

  1. 1.

    The peak magnetic field of a TMS pulse is about 1 tesla. Verify this claim by computing the maximum magnetic field of a circular TMS coil.

    1. (a)

      The coil has 13 turns, with a mean diameter of 90 mm, and is driven with a peak coil current of 5000 A. You may further assume that the peak B-field is in the center of the coil.

    2. (b)

      (∗) Each turn in the coil windings is 7-mm-tall and 2-mm-wide (i.e., inner winding diameter is 64, and outer winding diameter 116 mm). The current density in the wire is uniform due to the use of litz wire. The windings are surrounded from all sides by 3 mm of nonmagnetic plastic. Compute the maximum B-field at the surface of the coil. Were the approximations made in part (a) reasonable?

  2. 2.

    Electrical safety implications of TMS:

    1. (a)

      A monophasic TMS device has a maximum capacitor voltage of 2800 V and a 185 μF capacitor. Compute the amount of energy stored in such a system. Compare this energy to (1) the battery in your smartphone and (2) the energy stored in a men’s Olympic javelin (mass of 800 g) thrown at 100 km/h. What implications does such energy storage system have for safety?

    2. (b)

      Compute the dielectric breakdown distance for such a voltage (in air). Consider the high-voltage breakdown of typical insulation materials (e.g., polyethylene film); does a 0.18-mm-thick polyethylene electrical tape provide adequate insulation at TMS voltages?

  3. 3.

    Compute the required power level to sustain biphasic rTMS at 10 Hz when the required coil voltage is 800 V. The coil has an inductance of 16 μH, the stimulator has an energy storage capacitance of 185 μF, and the total series resistance of the pulse generator and coil is 50 mΩ. You can assume that the high-voltage power supply used to recharge the capacitor is 80% efficient and that it can be operated at all times (even during the pulses). Hint: Evaluate the W loss integral of Eq. 7.7.

  4. 4.

    A person has a deep brain stimulator (DBS) to control the motor symptoms of Parkinson’s Disease. The DBS electrode in the subthalamic nucleus and the implanted pulse generator (IPG) in the chest are connected with a lead that is coiled between the scalp and the skull, forming three loops of 5 cm diameter. The impedance through the person’s body between the DBS electrode contact and the IPG can be approximated as a 1 kΩ resistor. Other impedances in the DBS circuit are negligible, unless otherwise indicated. The person needs to receive rTMS treatment for depression. For the coil placement used for this treatment and at maximum device output, each DBS lead loop encircles a uniform magnetic flux density of 0.5 T. The magnetic pulse is sine shaped with a period of 300 μs.

    1. (a)

      Assume that during the TMS procedure, the IPG is turned off but can still conduct current. Calculate the current induced by TMS through the electrode contacts at maximum device output. How does this compare to the typical DBS electrode current of 1 mA.

    2. (b)

      Repeat part (a) under the assumption that the IPG does not conduct any current until the voltage across it reaches 5 V.

    3. (c)

      What can the neurosurgeon implanting the DBS system do to reduce the current induced by the TMS pulse in the DBS electrode?

  5. 5.

    Reusable solid silver EEG cup electrodes are considered for a TMS–EEG study. Each electrode is approximately a disk of 10 mm diameter and 0.5 mm thickness. In the center of the disk, there is a circular hole of 2 mm diameter. (In reality, such cup electrodes are dome-shaped with a height of about 3 mm, but for this problem such details can be omitted.) The TMS protocol delivers a peak magnetic field of 0.5 T perpendicular to the electrode. The magnetic pulse is sine shaped with a period of 300 μs. These pulses are delivered at 1 Hz for a total of 1000 pulses.

    1. (a)

      Calculate the worst case peak current density induced in the EEG electrodes.

    2. (b)

      (∗) Calculate the corresponding average power dissipation in the EEG electrode during the TMS pulse train.

    3. (c)

      (∗) Calculate the increase in temperature of the EEG electrode by the end of the TMS pulse train.

    4. (d)

      Would the electrode temperature exceed 41 °C which is considered the safety limit?

    5. (e)

      Suggest ways to mitigate the electrode heating.

  6. 6.

    The circular coil of Problem 1 is placed inside a 3 T MRI device. Compute the worst-case torque that the coil undergoes during a TMS pulse. Hint: The TMS coil orientation in the MRI magnet affects the torque.

  7. 7.

    A TMS device designer aims to increase the device efficiency. The existing device uses a 185 μF energy storage capacitor with a peak voltage of 1600 V and a 16 μH coil with 18 turns. The neural membrane time constant is assumed to be 200 μs.

    1. (a)

      The designer evaluates an alternative approach in which the inductance of the coil is reduced to about 10 μH, while the shape and size of the coil are preserved. What is the new number of turns in the coil? Assuming the same capacitor, how should its voltage be changed to maintain the original range of stimulation strength relative to the neural activation threshold? What would be the relative energy savings resulting from this design change? For this part you can ignore the resistance of the pulse generator and coil and assume a purely sinusoidal pulse waveform.

    2. (b)

      (∗) Keeping the original 16 μH coil that has resistance of 50 mΩ, the designer decides to reduce the capacitance to 100 μF. How should the capacitor voltage be changed to maintain the original range of stimulation strength relative to the neural activation threshold? What would be the relative energy savings resulting from this design change? How does this change the resistive losses in the coil, ignoring eddy current effects? Compute also the numbers for an idealized coil with zero resistance (similar to part (a)), and compare the results. Where does the additional efficiency come from, and what other changes would you suggest as a designer for the next coil?

  8. 8.

    (∗) The cable equation (Eq. 7.30) indicates that, for straight nerve fibers, the site of maximum membrane depolarization is where the E-field gradient, rather than the E-field magnitude, is maximum. This is relevant for magnetic stimulation of long straight nerves in the periphery but not for TMS. To see why this is the case, compare (1) the peak E-field gradient in the cortex and (2) the peak effective E-field gradient along an axon due to a rounded bend of the axon. Hints: In Fig. 7.5, the E-field drops to 70% in 1.5–2.5 cm depending on direction. In Fig. 7.8, the bend in axon must fit inside a gyrus that is about 1 cm wide.

  9. 9.

    The action potential conduction velocity of the myelinated nerve fibers in the corticospinal tract is approximately 7 cm/ms. Considering the latency between the time a TMS pulse is applied to the primary motor cortex and an MEP is detected in a finger muscle, what difference do you expect between a subject who is 190 cm tall compared to one who is 155 cm tall?

  10. 10.

    A researcher wants to optimize the depression treatment protocol illustrated in Fig. 7.12. Considering the TMS safety guidelines for a Class 2 study [61], how much should the following rTMS pulse train parameters be decreased from their default values (given in parentheses) so that the stimulation is still considered safe?

    1. (a)

      Duration of each short train (4 s) when increasing intensity from 120% of resting motor threshold (RMT) to 130% RMT.

    2. (b)

      Number of pulses per short trains (40 pulses) when increasing pulse repetition rate from 10 Hz to 20 Hz.

    3. (c)

      Intensity and total number of trains (120% RMT and 75 trains) when decreasing the interval between short trains from 26 s to 5 s.

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Koponen, L.M., Peterchev, A.V. (2020). Transcranial Magnetic Stimulation: Principles and Applications. In: He, B. (eds) Neural Engineering. Springer, Cham. https://doi.org/10.1007/978-3-030-43395-6_7

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