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diff --git a/examples/hodgkin_huxley/model.modelica b/examples/hodgkin_huxley/model.modelica deleted file mode 100644 index 7e44547..0000000 --- a/examples/hodgkin_huxley/model.modelica +++ /dev/null @@ -1,32 +0,0 @@ -model HodgkinHuxley - "Model of action potential in squid neurons (1952)" - parameter Real C_m =1.0 "membrane capacitance"; - parameter Real g_Na =120 "conductance"; - parameter Real g_K =36 "conductance"; - parameter Real g_L =0.3 "conductance"; - parameter Real V_Na =115 "potential"; - parameter Real V_K =-12 "potential"; - parameter Real V_lk =-49.387 "leak reveral potential"; - parameter Real E_Na =-190 "equilibrium potential"; - parameter Real E_K =-63 "equilibrium potential"; - parameter Real E_lk =-85.613 "equilibrium potential"; - parameter Real n =0.31768 "dimensionless; 0 to 1"; - parameter Real m =0.05293 "dimensionless; 0 to 1"; - parameter Real h =0.59612 "dimensionless; 0 to 1"; - Real V_m "membrane voltage potential"; - Real I =1.0 "membrane current"; - Real alpha_n, alpha_m, alpha_h "rate constants"; - Real beta_n, beta_m, beta_h "rate constants"; -equation - C_m * der(V_m) = I - g_Na * m^3 * h * (V_m - E_Na) - g_K * n^4 * (V_m - E_K) - G_lk * (V_m - E_lk); - der(n) = alpha_n - n * (alpha_n + beta_n); - der(m) = alpha_m - m * (alpha_m + beta_m); - der(h) = alpha_h - h * (alpha_h + beta_h); - - alpha_n = 0.01 * (V_m + 10) / (e^((V_m + 10)/10) - 1); - alpha_m = 0.1 * (V_m + 25) / (e^((V_m + 25)/10) - 1); - alpha_h = 0.07 * e^(V_m / 20); - beta_n = 0.125 * e^(V_m / 80); - beta_m = 4*e^(V_m/18); - beta_h = 1 / (e^((V_m + 30)/10) + 1); -end HodgkinHuxley; diff --git a/examples/hodgkin_huxley/page.md b/examples/hodgkin_huxley/page.md deleted file mode 100644 index 4598c97..0000000 --- a/examples/hodgkin_huxley/page.md +++ /dev/null @@ -1,86 +0,0 @@ - -The Hodgkin–Huxley model, or conductance-based model, is a mathematical model -that describes how action potentials in neurons are initiated and propagated. -It is a set of nonlinear differential equations that approximates the -electrical characteristics of excitable cells such as neurons and cardiac -myocytes, and hence it is a continuous time model, unlike the Rulkov map for -example. - -Alan Lloyd Hodgkin and Andrew Fielding Huxley described the model in 1952 to -explain the ionic mechanisms underlying the initiation and propagation of -action potentials in the squid giant axon. They received the 1963 Nobel Prize -in Physiology or Medicine for this work. - -## Mathematical properties - -The Hodgkin–Huxley model can be thought of as a differential equation with four -state variables, v(t), m(t), n(t), and h(t), that change with respect to time -t. The system is difficult to study because it is a nonlinear system and cannot -be solved analytically. However, there are many numeric methods available to -analyze the system. Certain properties and general behaviors, such as limit -cycles, can be proven to exist. - -## Alternative Models - -The Hodgkin–Huxley model is regarded as one of the great achievements of 20th-century biophysics. Nevertheless, modern Hodgkin–Huxley-type models have been extended in several important ways: - -* Additional ion channel populations have been incorporated based on experimental data. - -* The Hodgkin–Huxley model has been modified to incorporate transition state - theory and produce thermodynamic Hodgkin–Huxley models. - -* Models often incorporate highly complex geometries of dendrites and axons, - often based on microscopy data. - -* Stochastic models of ion-channel behavior, leading to stochastic hybrid - systems - -Several simplified neuronal models have also been developed (such as the -FitzHugh–Nagumo model), facilitating efficient large-scale simulation of groups -of neurons, as well as mathematical insight into dynamics of action potential -generation. - - -## References - -The body of this page is from Wikipedia (see below). - -#### Papers - -"The dual effect of membrane potential on sodium conductance in the giant axon -of Loligo". *The Journal of Physiology*. **116** (4): 497–506. April 1952. -doi:10.1113/jphysiol.1952.sp004719. - -"Currents carried by sodium and potassium ions through the membrane of the -giant axon of Loligo". *The Journal of Physiology*. **116** (4): 449–72. April 1952. -doi:10.1113/jphysiol.1952.sp004717. - -"The components of membrane conductance in the giant axon of Loligo". *The -Journal of Physiology*. **116** (4): 473–96. April 1952. -doi:10.1113/jphysiol.1952.sp004718. - -"The dual effect of membrane potential on sodium conductance in the giant axon -of Loligo". *The Journal of Physiology*. **116** (4): 497–506. April 1952. -doi:10.1113/jphysiol.1952.sp004719. - -"A quantitative description of membrane current and its application to -conduction and excitation in nerve". *The Journal of Physiology*. **117** (4): -500–44. August 1952. doi:10.1113/jphysiol.1952.sp004764. - -#### Interactive Models on the Web - -* ModelDB: [Squid axon (Hodgkin, Huxley 1952)](https://senselab.med.yale.edu/ModelDB/ShowModel.cshtml?model=5426) -* Wolfram Demonstrations: - [Interactive Hodgkin-Huxley](http://demonstrations.wolfram.com/HodgkinHuxleyActionPotentialModel/) - by Shimon Marom and - [Neural Impulses: The Action Potential in Action](http://www.demonstrations.wolfram.com/NeuralImpulsesTheActionPotentialInAction/) - by Garrett Neske -* [Hodgkin-Huxley Simulation with Javascript](http://myselph.de/hodgkinHuxley.html) - by Hubert Eichner, which creates static plots in the browser. -* BioModels database: [](http://www.ebi.ac.uk/biomodels-main/BIOMD0000000020) - -#### Other Links - -* Wikipedia: [Hodgkin–Huxley model](https://en.wikipedia.org/wiki/Hodgkin%E2%80%93Huxley_model) -* [Summary of the Hodgkin-Huxley model](http://ecee.colorado.edu/~ecen4831/HHsumWWW/HHsum.html) -* [Hodgkin-Huxley model in R](http://www.magesblog.com/2012/06/hodgkin-huxley-model-in-r.html) |