arXiv subjects

Matías Courdurier

Publications and source records attributed to Matías Courdurier.

5 recordsLinked to original sources

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

Understanding the dynamics of the frequency bias in neural networks

Recent works have shown that traditional Neural Network (NN) architectures display a marked frequency bias in the learning process. Namely, the NN first learns the low-frequency features before learning the high-frequency ones. In this study, we rigorously develop a partial differential equation (PDE) that unravels the frequency dynamics of the error for a 2-layer NN in the Neural Tangent Kernel regime. Furthermore, using this insight, we explicitly demonstrate how an appropriate choice of distributions for the initialization weights can eliminate or control the frequency bias. We focus our study on the Fourier Features model, an NN where the first layer has sine and cosine activation functions, with frequencies sampled from a prescribed distribution. In this setup, we experimentally validate our theoretical results and compare the NN dynamics to the solution of the PDE using the finite element method. Finally, we empirically show that the same principle extends to multi-layer NNs.

cs.LG↗

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↗

arXiv2023

Unsupervised reconstruction of accelerated cardiac cine MRI using Neural Fields

Cardiac cine MRI is the gold standard for cardiac functional assessment, but the inherently slow acquisition process creates the necessity of reconstruction approaches for accelerated undersampled acquisitions. Several regularization approaches that exploit spatial-temporal redundancy have been proposed to reconstruct undersampled cardiac cine MRI. More recently, methods based on supervised deep learning have been also proposed to further accelerate acquisition and reconstruction. However, these techniques rely on usually large dataset for training, which are not always available. In this work, we propose an unsupervised approach based on implicit neural field representations for cardiac cine MRI (so called NF-cMRI). The proposed method was evaluated in in-vivo undersampled golden-angle radial multi-coil acquisitions for undersampling factors of 26x and 52x, achieving good image quality, and comparable spatial and improved temporal depiction than a state-of-the-art reconstruction technique.

eess.IV↗

arXiv2023

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↗