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  "signature": "sha256:4b6d2054d49910b09e67d31973142bb4fc916f9dc2dcc2eac5f460e6701bbf96"
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  {
   "cells": [
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "## Setup"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "# Compatibility with Python 3\n",
      "from __future__ import print_function  # print('me') instead of print 'me'\n",
      "from __future__ import division  # 1/2 == 0.5, not 0"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 1
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "# Show figures inside the notebook\n",
      "%matplotlib inline"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 2
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "import numpy as np  # the Python array package\n",
      "import matplotlib.pyplot as plt  # the Python plotting package"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 3
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "There is a four-dimensional (X, Y, Z, t) BOLD image in the same directory as this notebook, called `ds107_sub012_t1r2.nii`.   Import the `nibabel` module, and load the image with nibabel to create an image object.  Turn off memory mapping with the load command."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "# Load image object using nibabel, turning off memory mapping.\n",
      "fname = 'ds107_sub012_t1r2.nii'\n",
      "import nibabel as nib\n",
      "img = nib.load(fname, mmap=False)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 4
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "In the usual way get the array data from this image and show the image shape."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "# Get image array data from image object\n",
      "data = img.get_data()"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 5
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Select the 10th volume (time index 9) from 4D image data array, by slicing over the last dimension.  What shape is it?"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "# Get the 10th volume and show shape\n",
      "tenth_vol = data[..., 9]\n",
      "tenth_vol.shape"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 6,
       "text": [
        "(64, 64, 35)"
       ]
      }
     ],
     "prompt_number": 6
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Get the standard deviation across all voxels in this 3D volume:"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "# Standard deviation across all voxels for 10th volume\n",
      "np.std(tenth_vol)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 7,
       "text": [
        "387.19281139947577"
       ]
      }
     ],
     "prompt_number": 7
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Loop over all volumes in the 4D image and store the standard deviation for each volume in a list.  Plot these to see if there are any volumes with particularly unusual standard deviation."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "# Get standard deviation for each volume; then plot the values\n",
      "stds = []\n",
      "for i in range(data.shape[-1]):\n",
      "    vol = data[..., i]\n",
      "    stds.append(np.std(vol))\n",
      "plt.plot(stds)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 8,
       "text": [
        "[<matplotlib.lines.Line2D at 0x109f57990>]"
       ]
      },
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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kpFAvekfk5ysvEGELTwdonbFxAM+sHEnsLTN7V6s9GO/hyMbp3Nn5vvvuItX0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\nAAAAAElFTkSuQmCC\n",
       "text": [
        "<matplotlib.figure.Figure at 0x107029790>"
       ]
      }
     ],
     "prompt_number": 8
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "SPM uses a measure called \"global signal\" to give a very rough estimate of the average signal value within the brain.  The idea is that you need a threshold to select voxels with signal high enough to be inside the brain, and not in the air around the brain, which has very low (near 0) signal.\n",
      "\n",
      "The algorithm goes like this.\n",
      "\n",
      "* Get a single 3D volume V;\n",
      "* Calculate the mean signal of the voxels in V; call that M;\n",
      "* Make a threshold T where T = M / 8.\n",
      "* Select all voxel values in V that are greater than T; call these values W;\n",
      "* Return the mean of all values in W.\n",
      "\n",
      "See [SPM global image signal](http://imaging.mrc-cbu.cam.ac.uk/imaging/PrinciplesStatistics#Global_image_signal).\n",
      "\n",
      "In the SPM code, the algorithm is implemented in a MATLAB function called `spm_global`.  "
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "I used the MATLAB script `get_global_signals.m` (in this directory) to run the `spm_global` MATLAB function on the volumes of `ds107_sub012_t1r2.nii`.  The script saved the SPM global values to a text file `global_signals.txt` in this directory.   The first four lines of the `global_signals.txt` file look like this:\n",
      "\n",
      "```\n",
      "376.53\n",
      "375.75\n",
      "375.26\n",
      "376.01\n",
      "```\n",
      "\n",
      "Read these global values calculated by SPM into a list, and plot the values."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "# Read global signal values calculated by SPM, and plot\n",
      "global_signals = np.loadtxt('global_signals.txt')\n",
      "plt.plot(global_signals)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 9,
       "text": [
        "[<matplotlib.lines.Line2D at 0x10a0bfc50>]"
       ]
      },
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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KsbfykLfYEvtZs+gGumIFib1sHWaXkN8wf/ELumn9+td0c5Sstblz6eY6dSrd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\nYII=\n",
       "text": [
        "<matplotlib.figure.Figure at 0x1070294d0>"
       ]
      }
     ],
     "prompt_number": 9
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Now implement the algorithm above to recalculate the SPM global signal for the first volume (volume index zero).  Hint: you will likely need to index using a boolean (mask) array.  Remember, the steps are:\n",
      "\n",
      "* Get a single 3D volume V;\n",
      "* Calculate the mean signal of the voxels in V; call that M;\n",
      "* Make a threshold T where T = M / 8.\n",
      "* Select all voxel values in V that are greater than T; call these values W;\n",
      "* Get the mean of all values in W.\n",
      "\n",
      "You should get the same value as SPM - the first value you read from `global_signals.txt`."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "# Apply algorithm for SPM global calculation to first volume\n",
      "vol = data[..., 0]\n",
      "T = np.mean(vol)/ 8\n",
      "msk = vol > T\n",
      "W = vol[msk]\n",
      "np.mean(W)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 10,
       "text": [
        "376.53382753187225"
       ]
      }
     ],
     "prompt_number": 10
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Make a function called `spm_global` that accepts a 3D array as input, and returns the global signal using the SPM algorithm.  Call that function on the first volume to show that it is working (as in `print(spm_global(data[:, :, :, 0]))`)."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "# Make a `spm_global` function that accepts a 3D array as input,\n",
      "# and returns the global mean for the volume according to the SPM algorithm\n",
      "def spm_global(vol):\n",
      "    T = np.mean(vol) / 8\n",
      "    return np.mean(vol[vol > T])\n",
      "\n",
      "print(spm_global(data[:, :, :, 0]))"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "376.533827532\n"
       ]
      }
     ],
     "prompt_number": 11
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Make a function called `get_spm_globals` that accepts an image filename as an argument.  The function will load the image, get the array data for the image, use your new `spm_global` function calculate the global value for each volume, and return these values as a list.  Finally, show this is working by plotting the values for the `ds107_sub012_t1r2.nii` image with something like: \n",
      "\n",
      "```\n",
      "all_globals = get_spm_globals('ds107_sub012_t1r2.nii')\n",
      "plt.plot(all_globals)\n",
      "```"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "# Write a function `get_spm_globals` that returns the global values \n",
      "# for each volume\n",
      "def get_spm_globals(fname):\n",
      "    img = nib.load(fname)\n",
      "    data = img.get_data()\n",
      "    spm_vals = []\n",
      "    for i in range(data.shape[-1]):\n",
      "        vol = data[..., i]\n",
      "        spm_vals.append(spm_global(vol))\n",
      "    return spm_vals\n",
      "\n",
      "all_globals = get_spm_globals('ds107_sub012_t1r2.nii')\n",
      "plt.plot(all_globals)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 12,
       "text": [
        "[<matplotlib.lines.Line2D at 0x10a479cd0>]"
       ]
      },
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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w9L0C5szeno3TtSvZaBZ5XavgSOxTUsya4WySF8YxLh9QI27dxnU6HQwGA7pb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\nfx6ZmZmtGnhL01KT+rYkzY3pgQeAF15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       "text": [
        "<matplotlib.figure.Figure at 0x10a0dacd0>"
       ]
      }
     ],
     "prompt_number": 12
    }
   ],
   "metadata": {}
  }
 ]
}