Coil design considerations for deep transcranial magnetic stimulation

Abstract

Objectives: To explore the field characteristics and design tradeoffs of coils for deep transcranial magnetic stimulation (dTMS).

Methods: We simulated parametrically two dTMS coil designs on a spherical head model using the finite element method, and compare them with five commercial TMS coils, including two that are FDA approved for the treatment of depression (ferromagnetic-core figure-8 and H1 coil).

Results: Smaller coils have a focality advantage over larger coils; however, this advantage diminishes with increasing target depth. Smaller coils have the disadvantage of producing stronger field in the superficial cortex and requiring more energy. When the coil dimensions are large relative to the head size, the electric field decay in depth becomes linear, indicating that, at best, the electric field attenuation is directly proportional to the depth of the target. Ferromagnetic cores improve electrical efficiency for targeting superficial brain areas; however magnetic saturation reduces the effectiveness of the core for deeper targets, especially for highly focal coils. Distancing winding segments from the head, as in the H1 coil, increases the required stimulation energy.

Conclusions: Among standard commercial coils, the double cone coil offers high energy efficiency and balance between stimulated volume and superficial field strength. Direct TMS of targets at depths of ~4 cm or more results in superficial stimulation strength that exceeds the upper limit in current rTMS safety guidelines. Approaching depths of ~6 cm is almost certainly unsafe considering the excessive superficial stimulation strength and activated brain volume.

Significance: Coil design limitations and tradeoffs are important for rational and safe exploration of dTMS.

Keywords: Deep transcranial magnetic stimulation; Electric field; Energy; Focality; Model.

Figure 1

Cutaway views of the (a) crown and (b) C-core coil models. The direction of coil current flow is indicated with arrows. Plots (c) and (d) show the electric field attenuation in depth relative to the field strength at the head surface of the crown coil and the C-core coil (h = w = 7 cm) for various opening angles. The spherical head model has radius of 8.5 cm.

Figure 2

Simulation models of seven TMS coil configurations and the corresponding electric field distribution in the brain: (a) Magstim 90 mm circular coil, (b) Brainsway H1 coil, (c) crown coil (α = 65°, β = 40°; Figure 1(a)), (d) Magstim 70 mm figure-8 coil, (e) Neuronetics iron core figure-8 coil, (f) Magstim double cone coil, (g) stretched C-core coil (γ = 140°, h = w = 7 cm; Figure 1(b)). A quarter of the brain sphere is removed to visualize the electric field in depth. The electric field magnitude is normalized to the peak electric field on the cortical surface, max(∣E_{1.5 cm}∣).

Figure 3

Maximum direct stimulation depth versus stimulation strength in superficial cortex relative to motor threshold. The stimulation depth is estimated with equation (2) which assumes a large dTMS coil with linear electric field decay with distance, and thus represents the deepest possible direct stimulation for any coil. Note that in this extreme case the stimulation is also most nonfocal. The target area for conventional motor threshold determination is assumed to be at 2 cm depth.

Figure 4

Crown and C-core coil performance as a function of target depth (dashed line: 4 cm, solid line: 6 cm) and coil size parametrized by angles α and γ (see Figure 1 for angle definitions). Left column: angle β of the crown coil is fixed at 40° while α is varied from 20°–90°. Varying angle β in the crown coil while holding α fixed at 90° results in similar trends (see Supplementary Figure S1). Right column: γ of the C-core coil is varied from 10°–180°. Evaluated metrics are: (a–b) maximum electric field strength in the cortex relative to neural activation threshold, max(∣E_{2 cm}∣)/E_th, (c–d) directly activated brain volume, V_A, and (e–f) energy delivered to the coil assuming E_th = 1 V cm⁻¹, W.

Figure 5

Relative performance of crown (left column) and C-core (right column) coils of various sizes for stimulation of targets at depths of 2–6 cm: (a–b) maximum electric field strength in the superficial cortex, max(∣E_{2 cm}∣); (c–d) directly activated brain volume, V_A; and (e–f) energy delivered to the coil, W. The metrics are normalized to those of the nominal crown coil (α = 65°, β = 40°) and C-core coil (γ = 140°, h = w = 7 cm) shown in Figure 2(c) and (g), respectively.

Figure 6

Performance metrics of the seven TMS coil configurations shown in Figure 2 for stimulation target depths of 2–6 cm: (a) maximum electric field in the superficial cortex relative to neural activation threshold, max(∣E_{2 cm}∣)/E_th; (b) directly activated brain volume, V_A; and (c) energy delivered to the coil assuming E_th = 1 V cm⁻¹, W. The curves for coils with circular and double loop electric field patterns are shown in red and black, respectively.