Can Microcoils Stimulate Neurons? - A Critique of Alzahrani & Roth (2024)

Title: Can Microcoils Stimulate Neurons?

Subtitle: A Critique of Alzahrani & Roth (2024)

Paper: The Difference between Traditional Magnetic Stimulation and Microcoil Stimulation: Threshold and the Electric Field Gradient

Authors: Mohammed Alzahrani and Bradley J. Roth

DOI: https://doi.org/10.3390/app14188349

Introduction

In this paper, Prof. Roth questions the validity of the neural activation threshold that has been conventionally used in microcoil-based neural magnetic stimulation research. His central argument is that directly applying the activating function threshold measured in transcranial magnetic stimulation (TMS) experiments — dEₓ/dx ≈ 1100 mV/cm² — to microcoil design is theoretically unjustified. The problem being raised is meaningful, and the cable equation analysis and Hodgkin-Huxley (HH) model simulations are logically sound. Nevertheless, this critique examines the paper’s limitations in terms of the biological plausibility of its model assumptions, the justification for key parameters, and its consistency with existing experimental findings.

Contributions of the Paper

Building on the interpretation that the neural membrane functions as a spatial low-pass filter, the paper shows that when spatial frequency k exceeds the inverse of the axon’s space constant λ (i.e., kλ >> 1), activation drops sharply.

$V_0 = \frac{S_0}{1 + k^2\lambda^2}$

From this expression, the paper quantitatively derives that the activation threshold for microcoils can be at least 300 times higher than that of TMS. A strength of the argument is that two independent analytical methods — cable equation-based analysis and HH model simulation — yield qualitatively consistent results. The paper further connects these findings to the strength-duration curve of electrical stimulation, offering an intuitive basis for understanding the results.

Critique

1. Biological Plausibility of the Model

Both analytical methods in this paper assume a long, straight, and uniform unmyelinated axon. However, the cortical neurons that microcoils actually target look nothing like this. Real cortical neurons have complex dendritic arbors extending in multiple directions, are often myelinated, and exhibit branching, curvature, and morphological heterogeneity.

Maccabee et al. (1993) experimentally confirmed that the activation mechanisms differ between straight and bent neurons, and Nagarajan et al. (1993) demonstrated that stimulation characteristics change in neurons with finite length and branching structure. Given this morphological complexity, it is difficult to assume that the authors’ theory applies directly to real neurons. This leaves open the question of how valid the paper’s central conclusion — a 300-fold increase in threshold — actually is under physiological conditions.

2. Lack of Justification for the Key Parameter b

The paper’s central claim that the microcoil threshold is approximately 300 times higher than that of TMS relies entirely on the electric field modeling constant b = 0.01 cm. Yet the paper acknowledges that this value was back-estimated by visually inspecting the dEₓ/dx graph in Lee et al. (2016), without providing a detailed account of the quantitative estimation process.

The uncertainty in estimating b has a direct impact on the reliability of the conclusions. It is therefore a methodological shortcoming that no sensitivity analysis was conducted to assess how the results change with different values of b.

3. Inconsistency with Experimental Results

A fundamental weakness of this paper is that it conflicts with the experimental demonstration by Lee et al. (2016) of successful neuron activation using microcoils, both in vitro and in vivo. The paper suggests that this experimental success may have been due to capacitive coupling rather than magnetic induction, but this is speculation without direct evidence or proof.

When theory and experiment conflict, experimental results conventionally take precedence in terms of credibility. As long as this gap remains unresolved, it is difficult to accept the paper’s conclusions as definitive.

Conclusion

This paper rigorously proves the proposition that, in an idealized axon model, the critical dEₓ/dx rises when the spatial extent of stimulation falls below λ. This proposition is theoretically sound and merits serious discussion in the design and interpretation of future experiments in this field.

However, the simplified axon assumptions, unverified parameter estimates, and inconsistency with existing experimental results make it difficult to fully accept the quantitative conclusions the paper puts forward. Rather than treating this paper as a definitive conclusion, it is more appropriate to regard it as the presentation of a theoretical hypothesis calling for more realistic neuron models and experimental validation.

References

• Roth, B.J., & Basser, P.J. (1990). A model of the stimulation of a nerve fiber by electromagnetic induction. IEEE Transactions on Biomedical Engineering, 37, 588-597.
• Lee, S.W., & Fried, S.I. (2016). Implantable microcoils for intracortical magnetic stimulation. Science Advances, 2(12), e1600889.
• Maccabee, P.J., et al. (1993). Magnetic coil stimulation of straight and bent amphibian and mammalian peripheral nerve in vitro. Journal of Physiology, 460, 201-219.
• Nagarajan, S.S., Durand, D.M., & Warman, E.N. (1993). Effects of induced electric fields on finite neuronal structures. IEEE Transactions on Biomedical Engineering, 40, 1175-1188.