Estimation of the Motor Threshold for Near-Rectangular Stimuli Using the Hodgkin-Huxley Model

Abstract

The motor threshold measurement is a standard in preintervention probing in TMS experiments. We aim to predict the motor threshold for near-rectangular stimuli to efficiently determine the motor threshold size before any experiments take place. Estimating the behavior of large-scale networks requires dynamically accurate and efficient modeling. We utilized a Hodgkin-Huxley (HH) type model to evaluate motor threshold values and computationally validated its function with known true threshold data from 50 participants trials from state-of-the-art published datasets. For monophasic, bidirectional, and unidirectional rectangular stimuli in posterior-anterior or anterior-posterior directions as generated by the cTMS device, computational modeling of the HH model captured the experimentally measured population-averaged motor threshold values at high precision (maximum error ≤ 8%). The convergence of our biophysically based modeling study with experimental data in humans reveals that the effect of the stimulus shape is strongly correlated with the activation kinetics of the voltage-gated ion channels. The proposed method can reliably predict motor threshold size using the conductance-based neuronal models and could therefore be embedded in new generation neurostimulators. Advancements in neural modeling will make it possible to enhance treatment procedures by reducing the number of delivered magnetic stimuli to participants.

Figure 1

FEM simulation of E-field norm distributions for different distances from the coil surface. (a) Placing figure-8 coil on the skull and the generated E-field. (b) E-filed 5 mm under the coil surface. (c) E-filed 10 mm under the coil surface. (d) E-field 15 mm under the coil surface. For this model, a 70 mm figure-8 coil is connected to 1 kV. The E-field norm means the amplitude of the electric field ($\sqrt{E_x^2+E_y^2+E_z^2}$).

Figure 2

cTMS device pulses as monophasic, unidirectional, and bidirectional waveforms, normalized to unity amplitude which have been tested in different human experiments. (a) Monophasic pulses with positive pulse widths of 30, 60, and 120 μs in [5, 27] with initial PA direction. (b) Unidirectional pulses for negative pulse widths of 40, 80, and 120 μs in [8] with initial AP direction. (c) Three different unidirectional and bidirectional waveforms in [28]; RB : Rectangular bidirectional (m = 1). RU-N : Rectangular unidirectional with initial AP direction (m = 0.2). RU-R : Rectangular unidirectional with initial PA direction. (d) Unidirectional pulses for positive pulse widths of 60 μs and the minimum threshold pulse width (ThPW) in [29] with initial AP direction (m = 0.2). The ratio of the peak of the negative phase to the positive phase is called the m ratio. Generally, the stimulus intensity is proportional to the E-field, (a derivative of the B-field), i.e., the current density in the brain and input to the HH model.

Figure 3

The effect of different pulse shapes on the MT (mean ± standard deviation). Strength-duration curves for (a) RMT measurement results and (b) AMT measurement results for monophasic pulses in [5, 27] (n = 10), which are compared to the simulation results of the HH model, (c) RMT measurement results for unidirectional pulses in [8] (n = 15). (d) Resting motor thresholds for RB, RU-N, and RU-R pulses in [28] (n = 13), in comparison with the modeling results. The stimulus intensity reflects the MT as a percentage of the maximum stimulator output. The maximum voltage of the cTMS device is 2800 V which is equivalent to 100% stimulus intensity. The filled red area shows the standard deviation of the mean, according to the experimental results. All estimated MT values are inside or very close to the area of the standard deviation.

Figure 4

Results of human experiments [29] and HH modeling results of (a) the threshold intensity for a 60 μs unidirectional pulse, according to the #1RMT protocol and (b) the minimum threshold pulse width (ThPW), according to the #2RMT protocol. The amplitude of each estimated pulse indicates the minimum intensity required to stimulate the neuron and to generate an action potential in the HH model (continuous lines). The amplitude of each tested pulse indicates the minimum intensity required to elicit minimal MEPs in the experimental trials (dashed lines).

Figure 5

Sensitivity analysis results for the parameters of the HH equations. The MT changes, depending on (a) membrane capacitance changes from 0.6 to 1.4 μF/cm², (b) sodium channel conductance changes from 10 to 90 mS/cm², (c) slow potassium channel conductance changes from 0.0325 to 0.52 mS/cm², (d) TMS-induced current density changes from 21.5 to 32.5 (A/m²). MT sizes are normalized with the experimentally measured MT for the RU-N stimuli. The ∗ marker represents the standard values utilized in this study to estimate the MT.