Browsing by Author "Courdurier Bettancourt, Matias Alejandro"

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    Analysis of neural activation in time-dependent membrane capacitance models
    (Springer Nature, 2025) Courdurier Bettancourt, Matias Alejandro; Medina, Leonel E.; Paduro Williamson, Esteban Andrés
    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.
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    Direct inversion of the Longitudinal Ray Transform for 2D residual elastic strain fields
    (2024) Wensrich, C.M.; Holman, S.; Courdurier Bettancourt, Matias Alejandro; Lionheart, W.R.B.; Polyalova, A. P; Svetov, I. E
    We examine the problem of Bragg-edge elastic strain tomography from energy resolved neutron transmission imaging. A new approach is developed for two-dimensional plane-stress and plane-strain systems whereby elastic strain can be reconstructed from its Longitudinal Ray Transform (LRT) as two parts of a Helmholtz decomposition based on the concept of an Airy stress potential. The solenoidal component of this decomposition is reconstructed using an inversion formula based on a tensor filtered back projection algorithm whereas the potential part can be recovered using either Hooke's law or a finite element model of the elastic system. The technique is demonstrated for two-dimensional plane-stress systems in both simulation, and on real experimental data. We also demonstrate that application of the standard scalar filtered back projection algorithm to the LRT in these systems recovers the trace of the solenoidal component of strain and we provide physical meaning for this quantity in the case of 2D plane-stress and plane-strain systems.