arXiv subjects

Leonel E. Medina

Publications and source records attributed to Leonel E. Medina.

4 recordsLinked to original sources

arXiv2025

Transcutaneous Interference Spinal Cord Stimulation: Leadfield-Based Pareto Optimization of Electrode Montages for Improved Focality

Purpose: This study investigates the feasibility of transcutaneous interferential spinal cord stimulation (tISCS), a novel non-invasive neuromodulation method, using temporal interference to enhance focality and comfort in spinal cord stimulation. The central research question is whether tISCS can achieve targeted activation of spinal cord circuits while reducing unwanted stimulation of skin and muscle tissues, which are common limitations of conventional transcutaneous spinal cord stimulation (tSCS). Methods: A finite element model of the lower thorax was developed to simulate electric field distributions for various skin electrode montages. To address the computational bottleneck associated with high-resolution modeling and montage optimization, we implemented a leadfield-based Pareto optimization strategy to identify the electrode configuration that maximizes the electric field in the spinal cord and minimizes it in off-target tissues. tISCS montages were compared with tSCS montages in terms of focality and stimulation efficiency. Results: Optimized tISCS configurations significantly reduced electric field intensity in the skin by over 20-fold compared to tSCS. The ratio of spinal cord to skin electric fields increased by at least 10-fold, indicating enhanced focality. The injection current efficiency in tISCS can be leveraged to increase spinal cord electric fields by at least 5-fold while keeping skin exposure below the levels observed with tSCS. Conclusion: tISCS enables deeper and more selective spinal cord stimulation compared to tSCS, with substantially reduced off-target effects. This is the first computational demonstration of tISCS feasibility. Leadfield-guided Pareto optimization enables efficient montage selection, providing a foundation for future experimental applications.

physics.med-ph↗

arXiv2025

Approximation and stability results for the parabolic FitzHugh-Nagumo system with combined rapidly oscillating sources

The use of high-frequency currents in neurostimulation has received increased attention in recent years due to its varied effects on tissues and cells. Nonlinear differential equations are commonly used as models for Neurons, and averaging methods are suitable for addressing questions like stability when considering single-frequency sources. A recent strategy called temporal interference stimulation uses electrodes to deliver sinusoidal signals of slightly different frequencies. Thus, classical averaging cannot be directly applied. This paper considers the one-dimensional FitzHugh-Nagumo system under the effects of a source composed of two sinusoidal terms in time and decaying in space. We develop a new averaging strategy to show that the solution of the system can be approximated by an explicit highly-oscillatory term plus the solution of a simpler, non-autonomous system. One of the main novelties is an extension of the contracting rectangles method to the case of parabolic equations with space and time-depending coefficients.

math.AP↗

arXiv2025

Analysis of Neural Activation in Time-dependent Membrane Capacitance Models

Most models of neurons incorporate a capacitor to account for the marked capacitive behavior exhibited by the cell membrane. However, such capacitance is widely considered constant, thereby neglecting the possible effects of time-dependent membrane capacitance on neural excitability. This study presents a modified formulation of a neuron model with time-dependent membrane capacitance and shows that action potentials can be elicited for certain capacitance dynamics. Our main results can be summarized as: (a) it is necessary to have significant and abrupt variations in the capacitance to generate action potentials; (b) certain simple and explicitly constructed capacitance profiles with strong variations do generate action potentials; (c) forcing abrupt changes in the capacitance too frequently may result in no action potentials. These findings can have great implications for the design of ultrasound-based or other neuromodulation strategies acting through transiently altering the membrane capacitance of neurons.

q-bio.NC↗

arXiv2024

The impact of high frequency-based stability on the onset of action potentials in neuron models

This paper studies the phenomenon of conduction block in model neurons using high-frequency biphasic stimulation (HFBS). The focus is investigating the triggering of undesired onset action potentials when the HFBS is turned on. The approach analyzes the transient behavior of an averaged system corresponding to the FitzHugh-Nagumo neuron model using Lyapunov and quasi-static methods. The first result provides a more comprehensive understanding of the onset activation through a mathematical proof of how to avoid it using a ramp in the amplitude of the oscillatory source. The second result tests the response of the blocked system to a piecewise linear stimulus, providing a quantitative description of how the HFBS strength translates into conduction block robustness. The results of this work can provide insights for the design of electrical neurostimulation therapies.

q-bio.NC↗