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Signed-off-by: Vasilis Vryniotis <bbriniotis@datumbox.com>
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datumbox committed Oct 20, 2013
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105 changes: 105 additions & 0 deletions HodgkinHuxleyNeuron.php
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<?php
/**
* Hodgkin-Huxley Neuron Model
* http://www.datumbox.com/
*
* Copyright 2013, Vasilis Vryniotis
* Licensed under MIT or GPLv3
*/

/**
* This class simulates the Hodgkin-Huxley neuron model by using the Runge-Kutta numerical optimization method.
* Moreover it assumes a resting potential of 0mV as described on the original paper "A quantitative description of membrane current and its application to conduction and excitation in nerve" by Hodgkin and Huxley:
* http://www.sfn.org/~/media/SfN/Documents/ClassicPapers/ActionPotentials/hodgkin5.ashx
*/
class HodgkinHuxleyNeuron {

const gNa = 120; //maximum conductance Na
const ENa=115; //voltage measured in mV

const gK=36; //maximum conductance gK
const EK=-12; //voltage measured in mV

const gL=0.3; //voltage-independent conductance
const EL=10.6; //voltage measured in mV

const C=1; //Capacity of neuron

/**
* Runs the Hodgkin Huxley Neuron Model by sending a constant current T for a time period of Tmax
*
* @param float $I
* @param float $Tmax
*/
public function run($I = 10,$Tmax = 100) {
$m=0;
$n=0;
$h=0;

$dt=0.05;

$v = array('0'=>-10);

for($t=$dt; $t<=$Tmax; $t=$t+$dt) {

/*
//Uses Euler's method. (this method requires very small step size and thus is inefficient)
$v_previous=end($v);
$dm_dt=((2.5-0.1*$v_previous)/(exp(2.5-0.1*$v_previous)-1)) *(1-$m) - +4*exp(-$v_previous/18) *$m;
$m=$m+$dt*$dm_dt;
$dn_dt=((0.1-0.01*$v_previous)/(exp(1-0.1*$v_previous)-1)) *(1-$n) - 0.125*exp(-$v_previous/80) *$n;
$n=$n+$dt*$dn_dt;
$dh_dt=(0.07*exp(-$v_previous/20)) *(1-$h) - 1/(exp(3-0.1*$v_previous)+1) *$h;
$h=$h+$dt*$dh_dt;
$SumI=self::gNa*pow($m,3)*$h*($v_previous-self::ENa)+self::gK*pow($n,4)*($v_previous-self::EK)+self::gL*($v_previous-self::EL);
$dv_dt=(-$SumI+ $I)/self::C;
$v[(string)round($t,2)]=$v_previous+$dt*$dv_dt;
*/

//uses Runge-Kutta Method to calculate the parameters of the model.
$v_previous=end($v); //previous value at v(t)


$dm_dt=((2.5-0.1*$v_previous)/(exp(2.5-0.1*$v_previous)-1)) *(1-$m) - +4*exp(-$v_previous/18) *$m; //derivative dm/dt
//Runge-Kutta Method to calculate the parameter
$k1 = $dm_dt;
$k2 = $dm_dt + 1/2*$dt*$k1;
$k3 = $dm_dt + 1/2*$dt*$k2;
$k4 = $dm_dt + 1/2*$dt*$k3;
$m=$m+ 1/6*$dt*($k1+2*$k2+2*$k3+$k4); //estimating the new value of m

$dn_dt=((0.1-0.01*$v_previous)/(exp(1-0.1*$v_previous)-1)) *(1-$n) - 0.125*exp(-$v_previous/80) *$n; //derivative dn/dt
//Runge-Kutta Method to calculate the parameter
$k1 = $dn_dt;
$k2 = $dn_dt + 1/2*$dt*$k1;
$k3 = $dn_dt + 1/2*$dt*$k2;
$k4 = $dn_dt + 1/2*$dt*$k3;
$n=$n+ 1/6*$dt*($k1+2*$k2+2*$k3+$k4); //estimating the new value of n

$dh_dt=(0.07*exp(-$v_previous/20)) *(1-$h) - 1/(exp(3-0.1*$v_previous)+1) *$h; //derivative dh/dt
//Runge-Kutta Method to calculate the parameter
$k1 = $dh_dt;
$k2 = $dh_dt + 1/2*$dt*$k1;
$k3 = $dh_dt + 1/2*$dt*$k2;
$k4 = $dh_dt + 1/2*$dt*$k3;
$h=$h+ 1/6*$dt*($k1+2*$k2+2*$k3+$k4); //estimating the new value of h

$SumI=self::gNa*pow($m,3)*$h*($v_previous-self::ENa)+self::gK*pow($n,4)*($v_previous-self::EK)+self::gL*($v_previous-self::EL); //sum all the currents

$dv_dt=(-$SumI+ $I)/self::C; //derivative dv/dt
//Runge-Kutta Method to calculate the parameter
$k1 = $dv_dt;
$k2 = $dv_dt + 1/2*$dt*$k1;
$k3 = $dv_dt + 1/2*$dt*$k2;
$k4 = $dv_dt + 1/2*$dt*$k3;
$v[(string)round($t,2)]=$v_previous+1/6*$dt*($k1+2*$k2+2*$k3+$k4); //estimating the new value of v

}

return $v;
}
}
16 changes: 15 additions & 1 deletion README.md
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Hodgkin-Huxley-Neuron
=====================

Hodgkin-Huxley-Neuron
This class simulates the Hodgkin-Huxley neuron model by using the Runge-Kutta numerical optimization method.

Moreover it assumes a resting potential of 0mV as described on the original paper "A quantitative description of membrane current and its application to conduction and excitation in nerve" by Hodgkin and Huxley.

To read more about how it works check out the original blog post:
http://blog.datumbox.com/coding-brain-neurons-by-using-hodgkin-huxley-model/

Useful Links
============

Original Paper: http://www.sfn.org/~/media/SfN/Documents/ClassicPapers/ActionPotentials/hodgkin5.ashx

Datumbox: https://www.datumbox.com/

Machine Learning Blog: https://blog.datumbox.com/
47 changes: 47 additions & 0 deletions example.php
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<?php
require_once('./HodgkinHuxleyNeuron.php');

$HodgkinHuxleyNeuron = new HodgkinHuxleyNeuron();

$I=10;
$Tmax=100;
$data=$HodgkinHuxleyNeuron->run($I,$Tmax);

?>

<html>
<head>
<script type="text/javascript" src="https://www.google.com/jsapi"></script>
<script type="text/javascript">
// <![CDATA[
google.load("visualization", "1", {packages:["corechart"]});
google.setOnLoadCallback(drawChart);
function drawChart() {
var data = google.visualization.arrayToDataTable([
['T', 'mV'],
<?php
$str='';
foreach($data as $k=>$v) {
$str.='['.$k.','.$v.'],';
}
echo trim($str,',');
?>
]);

var options = {
title: 'Hodgkin-Huxley Neuron',
legend: 'none',
hAxis: {title: 'Time (ms)'},
vAxis: {title: 'Membrane potential (mV)'}
};

var chart = new google.visualization.LineChart(document.getElementById('chart_div'));
chart.draw(data, options);
}
// ]]>
</script>
</head>
<body>
<div id="chart_div" style="width:100%;min-width: 900px; height: 500px;"></div>
</body>
</html>

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