Brain volume and number of fibres.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "%matplotlib inline\n",
    "import numpy as np\n",
    "import scipy as sp\n",
    "import pandas as pd\n",
    "import matplotlib.pyplot as plt"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 242,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "a = 1e-6\n",
    "l = 1\n",
    "Lmin = 0"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 243,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "def NfibForW2(W):\n",
    "    Lmax=np.power(W,1/3)\n",
    "    Ltot=W/a\n",
    "    x=np.linspace(Lmin,Lmax,100000)\n",
    "    y=np.exp(-l*x)\n",
    "    LtotTmp=np.dot(x,y)\n",
    "    adj = Ltot/LtotTmp\n",
    "    y=np.exp(-l*x)*adj\n",
    "    Nfib=np.sum(y)\n",
    "    return Nfib"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 269,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "def NfibForW(W):\n",
    "    Lmax=np.power(W,1/3)\n",
    "    Ltot=W/a\n",
    "    num = (1-np.exp(-l*Lmax))\n",
    "    den = (1-np.exp(-l*Lmax)*(l*Lmax+1))\n",
    "    Nfib = Ltot*l*num/den\n",
    "    print (Nfib,Ltot*l/2.0)\n",
    "    return Nfib"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 270,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "2392211.19118 500000.0\n",
      "W: 1 Nfib: 2392211.19118\n",
      "3991620.33907 1000000.0\n",
      "W: 2 Nfib: 3991620.33907\n",
      "5419947.21905 1500000.0\n",
      "W: 3 Nfib: 5419947.21905\n",
      "6756359.40981 2000000.0\n",
      "W: 4 Nfib: 6756359.40981\n",
      "8033106.41618 2500000.0\n",
      "W: 5 Nfib: 8033106.41618\n",
      "9267230.83256 3000000.0\n",
      "W: 6 Nfib: 9267230.83256\n",
      "10469063.0892 3500000.0\n",
      "W: 7 Nfib: 10469063.0892\n",
      "11645430.7348 4000000.0\n",
      "W: 8 Nfib: 11645430.7348\n",
      "12801125.1262 4500000.0\n",
      "W: 9 Nfib: 12801125.1262\n",
      "13939660.5931 5000000.0\n",
      "W: 10 Nfib: 13939660.5931\n",
      "104733059.745 50000000.0\n",
      "W: 100 Nfib: 104733059.745\n"
     ]
    }
   ],
   "source": [
    "Warr = [1,2,3,4,5,6,7,8,9,10,100]\n",
    "Nfibarr = []\n",
    "for W in Warr:\n",
    "    Nfib = NfibForW(W)\n",
    "    print('W:',W,'Nfib:',Nfib)\n",
    "    Nfibarr.append(Nfib)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 250,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x10dd07eb8>]"
      ]
     },
     "execution_count": 250,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
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bSN9/jJvH9GDWxEF6tS4iAUflXs3MeD05m4dWpNOiWRiLb05kfFwXr2OJiHwn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\nQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x10dcdfe80>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot(Warr,Nfibarr)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 208,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x10dc95240>]"
      ]
     },
     "execution_count": 208,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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iIo5xRblnHj7BpLe+obi0grcnD+XqXm2cjiQi4qigL/fNewu5d+FmGjVswAdT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\nM3z9yuxgpQAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x10dd45f60>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot(Warr,N2)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.6.3"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}