clean up hodgkin-huxley

2 files changed, 113 insertions, 19 deletions

diff --git a/examples/hodgkin_huxley/model.modelica b/examples/hodgkin_huxley/model.modelica
index 782cb20..7e44547 100644
--- a/examples/hodgkin_huxley/model.modelica
+++ b/examples/hodgkin_huxley/model.modelica
@@ -1,24 +1,32 @@
 model HodgkinHuxley
-    "Predator-Prey Model"
-    parameter Real G_Na =120        "conductance";
-    parameter Real G_K  =36         "conductance";
-    parameter Real G_lk =0.3        "conductance";
-    parameter Real C    =1.0        "membrane capacitance";
+    "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    "leakage";
-    Real n;
-    Real alpha_n;
-    Real beta_n;
-    Real m;
-    Real alpha_m;
-    Real beta_m;
-    Real h;
-    Real alpha_h;
-    Real beta_h;
+    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 * der(V_m) = - G_Na * (Vm - E_Na) - G_K * (V_m - E_K) - G_lk * (V_m - V_lk);
-    der(n) = - (alpha_n + beta_n) * n + alpha_n;
-    der(m) = - (alpha_m + beta_m) * m + alpha_m;
-    der(h) = - (alpha_h + beta_h) * h + alpha_h;
+    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
index e69de29..4598c97 100644
--- a/examples/hodgkin_huxley/page.md
+++ b/examples/hodgkin_huxley/page.md
@@ -0,0 +1,86 @@
+
+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)