Revisiting the Hodgkin-Huxley and Fitzhugh-Nagumo models of action potential propagation (original) (raw)
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SIMULATION OF THE EFFECTS OF AXON COMPRESSION ON THE PROPAGATION OF THE ACTION POTENTIAL
The dynamics of the action potential in a myelinated nerve axon due to mechanical compression (as in the case of carpal tunnel syndrome) is simulated in 2D by an efficient numerical procedure coupling the Quasi-Static approximation of the Maxwell equations with the nonlinear differential equations describing the bioelectric behaviour of nerve structure. The solution of this multiphysics problem is obtained by using a commercial software allowing to implement a Finite Element Analysis. The value of synthetic electrical parameters (equivalent conductivity and permittivity) are derived from those of the various layers making up the myelin. The axial symmetry of the problem is exploited and a thin layer approximation of the axonal membrane is considered. The membrane is replaced by a discontinuity surface on which an appropriate condition between the internal and external domains is set allowing to accurately reproduce the saltatory propagation mechanisms of the action potential. The effects due to different compression extents of the median nerve between a pair of nodes of Ranvier are simulated. The obtained results are in good agreement with experimental findings available in the literature.
Neuroelectric potentials derived from an extended version of the Hodgkin-Huxley model
Journal of Theoretical Biology, 1966
In 1952, Hodgkin and Huxley and others generated a revolution in our concept of the axon membrane and how it propagates the action potential. In 1959, Bullock described another revolution, a "quiet revolution" in our concept of the functions performed by the remainder of the nerve cell. In this paper we have attempted to show a possible connection between these two revolutions. We have proposed that a single unifying concept, that of the Modem Ionic Hypothesis, can account for almost all of the diverse behavior described by Bullock. In addition, we have attempted to demonstrate the value of electronic analogs in the study of systems as complex as that of the neural membrane.
The Hodgkin-Huxley Nerve Axon Model
This technical note shows the use of the MLAB mathematical and statistical modelling system for solving the Hodgkin-Huxley differential equations for arbitrary initial conditions. The prevailing model of a nerve axon membrane is a pair of theories concerning the nature of the axon membrane with respect to active ("pumping") and passive (diffusion) steady-state transport of various ions across the membrane and with respect to time-dependent "gate" opening and closing which controls the active passage of ions through such "open gates". It is postulated that the membrane in a given state has a certain permeability for each given ion, and that this permeability is determined by the electrochemical potential across the membrane. The permeability, P C , of a membrane for a particular chemical species, C, is a measure of the ease of diffusion of C across the membrane in the presence of a concentration difference on either side of the membrane. In particular, u...
International Journal of Engineering Research and Technology (IJERT), 2020
https://www.ijert.org/the-hodgkin-huxley-model-analysis-of-dynamic-behavior-of-the-action-potential-in-the-giant-squid-axon https://www.ijert.org/research/the-hodgkin-huxley-model-analysis-of-dynamic-behavior-of-the-action-potential-in-the-giant-squid-axon-IJERTV9IS050731.pdf The main concern of modelling a biological neuron using any electronic circuit to create qualitive models. A nerve cell reacts to a stimulus with a voltage shift or an energy potential gap between the cell and its environment resulting in a spike in voltage. To generate action potential, different methods should be implemented. To improve the propagation of action potential, we use an accurate and efficient method i.e. Hodgkin- Huxley model. The Hodgkin-Huxley experiment is a quantitative description of the actual movement of the neuronal membrane across ion- selective channels, and demonstrated the underpinnings of cell physiology as one of the most revolutionary studies of the 20th century and beyond. Using simple, first-order, ordinary differential equations, Hodgkin and Huxley were able to explain their time behavior using potassium (K) and sodium (Na) streams of intracellular membrane potential and currents. This was done using parameters equipped with a voltage clamp test on the giant axon of the squid. MATLAB simulates the kinetics of ionic currents, effects of alteration of the component currents, and the analysis time step.
The Hodgkin and Huxley model of the action potential
This review will survey the historical development of cellular neurophysiology, centring onthe revelatory discoveries and formalism of the Hodgkin and Huxley model. In the first section, I will discuss the state of the field before Hodgkin and Huxley’spioneering research – in an attempt to elucidate the framing problems that led Hodgkin and Huxley into conducting their research. In the second section, I will discuss the influence of the voltage clamp, and how it was applied by Hodgkin and Huxley to the study of the action potential of the squid giant axon. The third section will focus on the key experimental observations of the squid giant axon experiments. In the fourth section I will discuss their assumptions, and then proceed to present an essentialised form of the mathematical model. Throughout, I will comment on modern confirmations of their predictions
A mathematical model for conduction of action potentials along bifurcating axons
The Journal of physiology, 1979
1. A mathematical model based on the Hodgkin-Huxley equations is derived to describe quantitatively the propagation of action potentials in a branching axon. 2. The model treats the case of a bifurcating axon with branches of different diameters. The solution takes into account the changes in space constant in the different regions. 3. The model allows for investigating parameters leading to preferential conduction of action potentials in one daughter branch as seen experimentally. 4. Assuming that the only difference between the various daughter branches is in their diameters, conduction blocks should occur simultaneously rather than differentially into all daughter branches when the geometrical ratio is greater than 10. 5. In order to obtain differential conduction into the two branches changes in ionic concentrations due to the repetitive action potentials had to be introduced into the equations. 6. We find that conditions which allow differential buildup of K concentration aroun...
Biophysics and Modeling of Mechanotransduction in Neurons: A Review
Mathematics, 2021
Mechanosensing is a key feature through which organisms can receive inputs from the environment and convert them into specific functional and behavioral outputs. Mechanosensation occurs in many cells and tissues, regulating a plethora of molecular processes based on the distribution of forces and stresses both at the cell membrane and at the intracellular organelles levels, through complex interactions between cells’ microstructures, cytoskeleton, and extracellular matrix. Although several primary and secondary mechanisms have been shown to contribute to mechanosensation, a fundamental pathway in simple organisms and mammals involves the presence of specialized sensory neurons and the presence of different types of mechanosensitive ion channels on the neuronal cell membrane. In this contribution, we present a review of the main ion channels which have been proven to be significantly involved in mechanotransduction in neurons. Further, we discuss recent studies focused on the biologi...
An electromechanical model of neuronal dynamics using Hamilton's principle
Frontiers in Cellular Neuroscience, 2015
Damage of the brain may be caused by mechanical loads such as penetration, blunt force, shock loading from blast, and by chemical imbalances due to neurological diseases and aging that trigger not only neuronal degeneration but also changes in the mechanical properties of brain tissue. An understanding of the interconnected nature of the electro-chemo-mechanical processes that result in brain damage and ultimately loss of functionality is currently lacking. While modern mathematical models that focus on how to link brain mechanics to its biochemistry are essential in enhancing our understanding of brain science, the lack of experimental data required by these models as well as the complexity of the corresponding computations render these models hard to use in clinical applications. In this paper we propose a unified variational framework for the modeling of neuronal electromechanics. We introduce a constrained Lagrangian formulation that takes into account Newton's law of motion of a linear viscoelastic Kelvin-Voigt solid-state neuron as well as the classic Hodgkin-Huxley equations of the electronic neuron. The system of differential equations describing neuronal electromechanics is obtained by applying Hamilton's principle. Numerical simulations of possible damage dynamics in neurons will be presented.
PROPAGATION OF ACTION POTENTIAL IN NEURON - A NEW APPROACH WITH MAGNETIC EFFECT OF CURRENT
IAEME PUBLICATION, 2021
The central nervous system CNS acquired the control of the human body by to and fro transformation of information. The information is transferred from one neuron, the basic element of CNS to another neuron as electrical signals, called action potential. The axon a part of neuron acts as the medium for this propagation. The magnitude and duration of action potential remains the same throughout the propagation path. The process of propagation is termed as saltatory transmission or hopping. (Saltare means jump in Greek). This can be termed as lossless transmission in electrical engineering terms. At present, neuron is modeled as resistance-capacitance (RC) circuit in Hodkin Huxley model. To explain the lossless transmission, the transmission channel is to be modelled as an LC (Inductance- capacitance) circuit or a compensated RLC (resistance-Inductance-Capacitance) circuit. The current model can be changed to this form by the addition of an inductance, which is equivalent to the self-induced inductance in the neuron due to the flow of current through the neuron.
Spike initiation and propagation on axons with slow inward currents
Biological Cybernetics, 1993
We investigate spike initiation and propagation in a model axon that has a slow regenerative conductance as well as the usual Hodgkin-Huxley type sodium and potassium conductances. We study the role of slow conductance in producing repetitive firing, compute the dispersion relation for an axon with an additional slow conductance, and show that under appropriate conditions such an axon can produce a traveling zone of secondary spike initiation. This study illustrates some of the complex dynamics shown by excitable membranes with fast and slow conductances.