{
 "metadata": {
  "name": "slice_timing_full"
 },
 "nbformat": 3,
 "nbformat_minor": 0,
 "worksheets": [
  {
   "cells": [
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "On the timing of slices"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "%pylab inline"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\n",
        "Welcome to pylab, a matplotlib-based Python environment [backend: module://IPython.kernel.zmq.pylab.backend_inline].\n",
        "For more information, type 'help(pylab)'.\n"
       ]
      }
     ],
     "prompt_number": 1
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "import numpy as np"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 2
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "import matplotlib.pylab as plt"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 3
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "import nibabel as nib"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 4
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "fname = 'bold.nii.gz'"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 5
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "img = nib.load(fname)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 6
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "We want to do slice timing.\n",
      "\n",
      "Do we have any interesting information in the scan header?"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "hdr = img.get_header()\n",
      "hdr"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "pyout",
       "prompt_number": 7,
       "text": [
        "<nibabel.nifti1.Nifti1Header at 0x4410210>"
       ]
      }
     ],
     "prompt_number": 7
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "print(hdr)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "<class 'nibabel.nifti1.Nifti1Header'> object, endian='<'\n",
        "sizeof_hdr      : 348\n",
        "data_type       : \n",
        "db_name         : \n",
        "extents         : 0\n",
        "session_error   : 0\n",
        "regular         : r\n",
        "dim_info        : 0\n",
        "dim             : [  4  64  64  35 165   1   1   1]\n",
        "intent_p1       : 0.0\n",
        "intent_p2       : 0.0\n",
        "intent_p3       : 0.0\n",
        "intent_code     : none\n",
        "datatype        : int16\n",
        "bitpix          : 16\n",
        "slice_start     : 0\n",
        "pixdim          : [ 1.  3.  3.  3.  3.  0.  0.  0.]\n",
        "vox_offset      : 352.0\n",
        "scl_slope       : 1.0\n",
        "scl_inter       : 0.0\n",
        "slice_end       : 0\n",
        "slice_code      : unknown\n",
        "xyzt_units      : 10\n",
        "cal_max         : 0.0\n",
        "cal_min         : 0.0\n",
        "slice_duration  : 0.0\n",
        "toffset         : 0.0\n",
        "glmax           : 0\n",
        "glmin           : 0\n",
        "descrip         : FSL4.0\n",
        "aux_file        : \n",
        "qform_code      : scanner\n",
        "sform_code      : scanner\n",
        "quatern_b       : 0.0\n",
        "quatern_c       : 0.0\n",
        "quatern_d       : 0.0\n",
        "qoffset_x       : -93.0\n",
        "qoffset_y       : -103.418151855\n",
        "qoffset_z       : -45.4796600342\n",
        "srow_x          : [  3.   0.   0. -93.]\n",
        "srow_y          : [   0.            3.            0.         -103.41815186]\n",
        "srow_z          : [  0.           0.           3.         -45.47966003]\n",
        "intent_name     : \n",
        "magic           : n+1\n"
       ]
      }
     ],
     "prompt_number": 8
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "The 'pixdim' field says that our volume is 3 x 3 x 3 x 3.  What's the fourth 3?"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "# hdr.get_slice_times()"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 9
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "We really need to know the slice order of this scan, and we can't afford to guess.\n",
      "\n",
      "What's your guess for this dataset?\n",
      "\n",
      "How would you check?"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Let's say the slices arrived in ascending interleaved order."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "slice_order = range(0, 35, 2) + range(1, 35, 2)\n",
      "slice_order = np.array(slice_order)\n",
      "slice_order"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "pyout",
       "prompt_number": 10,
       "text": [
        "array([ 0,  2,  4,  6,  8, 10, 12, 14, 16, 18, 20, 22, 24, 26, 28, 30, 32,\n",
        "       34,  1,  3,  5,  7,  9, 11, 13, 15, 17, 19, 21, 23, 25, 27, 29, 31,\n",
        "       33])"
       ]
      }
     ],
     "prompt_number": 10
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Revision - what does the 2 mean in the vector above?"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "What does this mean in terms of times that the slices arrived?"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "n_slices = img.shape[2]\n",
      "n_slices"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "pyout",
       "prompt_number": 11,
       "text": [
        "35"
       ]
      }
     ],
     "prompt_number": 11
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Get the TR information from the header, somehow?"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "TR = hdr['pixdim'][4]\n",
      "time_one_slice = TR / n_slices\n",
      "time_one_slice"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "pyout",
       "prompt_number": 12,
       "text": [
        "0.085714285714285715"
       ]
      }
     ],
     "prompt_number": 12
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "At the moment we have the order in which the slices arrived.  Now we want the times of each slice, where the first value will be the time of acquisition of the first slice in space, the second value will be the time of acquisition of the second slice in space."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "space_to_order = np.argsort(slice_order)\n",
      "space_to_order"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "pyout",
       "prompt_number": 13,
       "text": [
        "array([ 0, 18,  1, 19,  2, 20,  3, 21,  4, 22,  5, 23,  6, 24,  7, 25,  8,\n",
        "       26,  9, 27, 10, 28, 11, 29, 12, 30, 13, 31, 14, 32, 15, 33, 16, 34,\n",
        "       17])"
       ]
      }
     ],
     "prompt_number": 13
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "We're going to do some fancy indexing to clarify what space_to_order is"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "slice_order[space_to_order]"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "pyout",
       "prompt_number": 14,
       "text": [
        "array([ 0,  1,  2,  3,  4,  5,  6,  7,  8,  9, 10, 11, 12, 13, 14, 15, 16,\n",
        "       17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33,\n",
        "       34])"
       ]
      }
     ],
     "prompt_number": 14
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "slice_times = space_to_order * time_one_slice\n",
      "slice_times"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "pyout",
       "prompt_number": 15,
       "text": [
        "array([ 0.        ,  1.54285714,  0.08571429,  1.62857143,  0.17142857,\n",
        "        1.71428571,  0.25714286,  1.8       ,  0.34285714,  1.88571429,\n",
        "        0.42857143,  1.97142857,  0.51428571,  2.05714286,  0.6       ,\n",
        "        2.14285714,  0.68571429,  2.22857143,  0.77142857,  2.31428571,\n",
        "        0.85714286,  2.4       ,  0.94285714,  2.48571429,  1.02857143,\n",
        "        2.57142857,  1.11428571,  2.65714286,  1.2       ,  2.74285714,\n",
        "        1.28571429,  2.82857143,  1.37142857,  2.91428571,  1.45714286])"
       ]
      }
     ],
     "prompt_number": 15
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Any objections?\n",
      "\n",
      "Was the first slice really taken at time 0?\n"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "slice_times = space_to_order * time_one_slice + time_one_slice / 2.\n",
      "slice_times"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "pyout",
       "prompt_number": 16,
       "text": [
        "array([ 0.04285714,  1.58571429,  0.12857143,  1.67142857,  0.21428571,\n",
        "        1.75714286,  0.3       ,  1.84285714,  0.38571429,  1.92857143,\n",
        "        0.47142857,  2.01428571,  0.55714286,  2.1       ,  0.64285714,\n",
        "        2.18571429,  0.72857143,  2.27142857,  0.81428571,  2.35714286,\n",
        "        0.9       ,  2.44285714,  0.98571429,  2.52857143,  1.07142857,\n",
        "        2.61428571,  1.15714286,  2.7       ,  1.24285714,  2.78571429,\n",
        "        1.32857143,  2.87142857,  1.41428571,  2.95714286,  1.5       ])"
       ]
      }
     ],
     "prompt_number": 16
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "The first value corresponds to the first (0) slice in the volume, and gives the time that slice was aquired from the start of the volume.\n",
      "\n",
      "(To be explicit, we've taken the position that a slice is aquired in the middle of how long it took to aquire it)."
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Let's take a voxel time-course from the first slice.  You've seen this before."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "data = img.get_data()\n",
      "slice0_vol0 = data[:, :, 0, 0]\n",
      "plt.gray()\n",
      "plt.imshow(slice0_vol0)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "pyout",
       "prompt_number": 17,
       "text": [
        "<matplotlib.image.AxesImage at 0x4444ed0>"
       ]
      },
      {
       "output_type": "display_data",
       "png": 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W/Pl+v29mdSvGi0IUznt+JiMIfHipLlsjT1BKmCMFLVP31dLxB/TzajaPYZGX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\n",
       "text": [
        "<matplotlib.figure.Figure at 0x368e050>"
       ]
      }
     ],
     "prompt_number": 17
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "We take a voxel from the middle of the mid-brain, say row 32, column 25."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "slice0_time_course = data[32, 25, 0, :] # all points in time\n",
      "plt.plot(slice0_time_course)\n",
      "plt.xlabel('Scan number')"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "pyout",
       "prompt_number": 18,
       "text": [
        "<matplotlib.text.Text at 0x4410610>"
       ]
      },
      {
       "output_type": "display_data",
       "png": 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kz3de2QCtlWdP2+RvSp7seWUvghnZDwwwoheV/zXz7GWVPb9P2XIJRhunvt78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\nsBcRCQEFexGREFCwFxEJgW9bQOJRUM1uZAAAAABJRU5ErkJggg==\n",
       "text": [
        "<matplotlib.figure.Figure at 0x4427b50>"
       ]
      }
     ],
     "prompt_number": 18
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "What if I wanted to have 'time' instead of 'Scan number' as the values on the x-axis?"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "n_scans = img.shape[-1]\n",
      "scan_starts = np.arange(n_scans) * TR # times scans began\n",
      "scan_starts[:10]"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "pyout",
       "prompt_number": 19,
       "text": [
        "array([  0.,   3.,   6.,   9.,  12.,  15.,  18.,  21.,  24.,  27.])"
       ]
      }
     ],
     "prompt_number": 19
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "slice0_times = scan_starts + slice_times[0]\n",
      "slice0_times[:10]"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "pyout",
       "prompt_number": 20,
       "text": [
        "array([  0.04285714,   3.04285714,   6.04285714,   9.04285714,\n",
        "        12.04285714,  15.04285714,  18.04285714,  21.04285714,\n",
        "        24.04285714,  27.04285714])"
       ]
      }
     ],
     "prompt_number": 20
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "plt.plot(slice0_times, slice0_time_course)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "pyout",
       "prompt_number": 21,
       "text": [
        "[<matplotlib.lines.Line2D at 0x48af0d0>]"
       ]
      },
      {
       "output_type": "display_data",
       "png": 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rGdkPDzM76CMfAQ4cUFvfMNhDjMhe5VzwNs60aew82tXHUbVxolF3RRrdwJbs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\n",
       "text": [
        "<matplotlib.figure.Figure at 0x4429190>"
       ]
      }
     ],
     "prompt_number": 21
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "plt.plot(slice0_times[:10], slice0_time_course[:10], 'r:+')\n",
      "plt.xlabel('Time of acquisition')"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "pyout",
       "prompt_number": 22,
       "text": [
        "<matplotlib.text.Text at 0x48af990>"
       ]
      },
      {
       "output_type": "display_data",
       "png": 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4y4IFUFzs23384Q/wq1/5dh8SNFSiEfGX2lqIiPDtwiBHjsD+/TB6tO/2IZbo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\n",
       "text": [
        "<matplotlib.figure.Figure at 0x48a29d0>"
       ]
      }
     ],
     "prompt_number": 22
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Now let's take a time course from the middle of the TR."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "space_to_order"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "pyout",
       "prompt_number": 23,
       "text": [
        "array([ 0, 18,  1, 19,  2, 20,  3, 21,  4, 22,  5, 23,  6, 24,  7, 25,  8,\n",
        "       26,  9, 27, 10, 28, 11, 29, 12, 30, 13, 31, 14, 32, 15, 33, 16, 34,\n",
        "       17])"
       ]
      }
     ],
     "prompt_number": 23
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Because this is interleaved, in fact the second slice in space is about half way through the volume in time."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "slice1_time_course = data[32, 25, 1, :] # all points in time\n",
      "plt.plot(slice1_time_course)\n",
      "plt.xlabel('Scan number')"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "pyout",
       "prompt_number": 24,
       "text": [
        "<matplotlib.text.Text at 0x487fd10>"
       ]
      },
      {
       "output_type": "display_data",
       "png": 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6e945q4RPuvXaa9qr3Vt19u3t7OTkKzApYxxR7PlEdFpioFW2KT7Oo5zTp/3b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\nSUVORK5CYII=\n",
       "text": [
        "<matplotlib.figure.Figure at 0x7ff7e826b610>"
       ]
      }
     ],
     "prompt_number": 24
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "What times are these?"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "slice1_times = scan_starts + slice_times[1]\n",
      "slice1_times[:10]"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "pyout",
       "prompt_number": 25,
       "text": [
        "array([  1.58571429,   4.58571429,   7.58571429,  10.58571429,\n",
        "        13.58571429,  16.58571429,  19.58571429,  22.58571429,\n",
        "        25.58571429,  28.58571429])"
       ]
      }
     ],
     "prompt_number": 25
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "plt.plot(slice0_times[:10], slice0_time_course[:10], 'r:+', label='slice 0')\n",
      "plt.hold(True)\n",
      "plt.plot(slice1_times[:10], slice1_time_course[:10], 'b-o', label='slice 1')\n",
      "plt.xlabel('Time of acquisition')\n",
      "plt.legend()"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "pyout",
       "prompt_number": 26,
       "text": [
        "<matplotlib.legend.Legend at 0x4abb890>"
       ]
      },
      {
       "output_type": "display_data",
       "png": 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V950+vRgAKMgTk8rKAlavFroV+rH/FI1SCTQ02Ma0M6K3qKg3kZX1job7l2DHjmUCtIjY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\nQCGGMUU+vrE8gb3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zt3pt+K+1DQoN5cNkGm3ffmfFD7X67iZd8ek2m07PEO7nnzV3EIjV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\n",
       "text": [
        "<matplotlib.figure.Figure at 0x487dd50>"
       ]
      }
     ],
     "prompt_number": 26
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "What does slice timing do?"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "We want values from the blue line, sampled at the times of the red points.\n",
      "\n",
      "We have values for slice 1 at times `slice1_times`.  But we want to estimate what the values would have been, for slice 1, if slice 1 had arrived at `slice0_times`.  And so on for the other slices.\n",
      "\n",
      "This is *interpolation*."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "import scipy.interpolate as spi"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 27
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Let's investigate ``spi.interp1d``"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "x = slice1_times\n",
      "y = slice1_time_course\n",
      "interpolator = spi.interp1d(x, y, 'linear')\n",
      "interpolator"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "pyout",
       "prompt_number": 28,
       "text": [
        "<scipy.interpolate.interpolate.interp1d at 0x45a6490>"
       ]
      }
     ],
     "prompt_number": 28
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "# What happens here? \n",
      "# slice1_at_slice0 = interpolator(slice0_times)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 29
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "This is the problem of *extrapolation*.  What to do?"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "x = slice1_times\n",
      "y = slice1_time_course\n",
      "interpolator = spi.interp1d(x, y, 'linear', bounds_error=False, fill_value=0)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 30
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "slice1_at_slice0 = interpolator(slice0_times)\n",
      "plt.plot(slice0_times[:10], slice0_time_course[:10], 'r:+', label='slice 0')\n",
      "plt.hold(True)\n",
      "plt.plot(slice1_times[:10], slice1_time_course[:10], 'b-o', label='slice 1')\n",
      "plt.plot(slice0_times[:10], slice1_at_slice0[:10], 'kx', label='1 -> 0')\n",
      "plt.xlabel('Time of acquisition')\n",
      "plt.legend()"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "pyout",
       "prompt_number": 31,
       "text": [
        "<matplotlib.legend.Legend at 0x7ff7e860fcd0>"
       ]
      },
      {
       "output_type": "display_data",
       "png": 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BmDlzJtLS0qBWq1FYWAgAKCgogJubGwDAw8MDOTk5lmlzc3Ph4eFhc6GIiKj9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\nNwAAAABJRU5ErkJggg==\n",
       "text": [
        "<matplotlib.figure.Figure at 0x7ff7e85a3350>"
       ]
      }
     ],
     "prompt_number": 31
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "x = slice1_times\n",
      "y = slice1_time_course\n",
      "interpolator = spi.interp1d(x, y, 'linear', bounds_error=False, fill_value=np.mean(slice1_time_course))"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 32
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "slice1_at_slice0 = interpolator(slice0_times)\n",
      "plt.plot(slice0_times[:10], slice0_time_course[:10], 'r:+', label='slice 0')\n",
      "plt.hold(True)\n",
      "plt.plot(slice1_times[:10], slice1_time_course[:10], 'b-o', label='slice 1')\n",
      "plt.plot(slice0_times[:10], slice1_at_slice0[:10], 'kx', label='1 -> 0')\n",
      "plt.xlabel('Time of acquisition')\n",
      "plt.legend()"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "pyout",
       "prompt_number": 33,
       "text": [
        "<matplotlib.legend.Legend at 0x4fcae50>"
       ]
      },
      {
       "output_type": "display_data",
       "png": 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4CguB+/V6iOHV1nJD2Gj8u3Xjqz/eWrtnAEtN8P/6FzdFtZUmTpyo0uceFAQs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\nCZ4QQqwUJXhCCLFS/w8Dj4ZOyhbQXAAAAABJRU5ErkJggg==\n",
       "text": [
        "<matplotlib.figure.Figure at 0x7ff7e85f4610>"
       ]
      }
     ],
     "prompt_number": 33
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Is there a better way of doing the extrapolation?"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "n_scans"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "pyout",
       "prompt_number": 34,
       "text": [
        "165"
       ]
      }
     ],
     "prompt_number": 34
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "x_padded = np.zeros((n_scans + 2,))\n",
      "y_padded = np.zeros((n_scans + 2,))\n",
      "x_padded[1:-1] = slice1_times\n",
      "x_padded[0] = x[0] - TR\n",
      "x_padded[-1] = x[-1] + TR\n",
      "y_padded[1:-1] = slice1_time_course\n",
      "y_padded[0] = y[0]\n",
      "y_padded[-1] = y[-1]\n",
      "interpolator = spi.interp1d(x_padded, y_padded, 'linear')"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 35
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "slice1_at_slice0 = interpolator(slice0_times)\n",
      "plt.plot(slice0_times[:10], slice0_time_course[:10], 'r:+', label='slice 0')\n",
      "plt.hold(True)\n",
      "plt.plot(slice1_times[:10], slice1_time_course[:10], 'b-o', label='slice 1')\n",
      "plt.plot(slice0_times[:10], slice1_at_slice0[:10], 'kx', label='1 -> 0')\n",
      "plt.xlabel('Time of acquisition')\n",
      "plt.legend()"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "pyout",
       "prompt_number": 36,
       "text": [
        "<matplotlib.legend.Legend at 0x521d190>"
       ]
      },
      {
       "output_type": "display_data",
       "png": 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5pF88RUXA3Xo9zPCqq4UhbDz+3bqJ1R9vrd0zgKUm+H/9S5ii2kzjx49X6XMP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\n",
       "text": [
        "<matplotlib.figure.Figure at 0x7ff7e859de90>"
       ]
      }
     ],
     "prompt_number": 36
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "interpolator = spi.interp1d(x_padded, y_padded, 'cubic')"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 37
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "fine_time = np.linspace(x_padded[0], x_padded[9], 100)\n",
      "predicted_signal = interpolator(fine_time)\n",
      "plt.plot(fine_time, predicted_signal, ':', label='predicted')\n",
      "plt.plot(slice1_times[:10], slice1_time_course[:10], 'x', label='actual')\n",
      "plt.xlabel('Time of acquisition')\n",
      "plt.legend()"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "pyout",
       "prompt_number": 38,
       "text": [
        "<matplotlib.legend.Legend at 0x5462c90>"
       ]
      },
      {
       "output_type": "display_data",
       "png": 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FlVJ89NFHxMXFAZCWlkZcXByenp7o9XqCgoLIzMy0Y/gty1tvwZtv2r7d33+3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\nCyGEi/r/AS2yVrlWG8lvAAAAAElFTkSuQmCC\n",
       "text": [
        "<matplotlib.figure.Figure at 0x4fafa90>"
       ]
      }
     ],
     "prompt_number": 38
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "It looks like we're going to be doing a lot of padding over the last axis.  Let's make a function for that"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "def pad_ends(first, middle, last):\n",
      "    \"\"\" Pad array `middle` along last axis with `first` value and `last` value\n",
      "    \"\"\"\n",
      "    middle = np.array(middle) # Make sure middle is an array\n",
      "    pad_ax_len = middle.shape[-1] # Length of the axis we are padding\n",
      "    pad_shape = middle.shape[:-1] + (pad_ax_len + 2,) # Shape of the padded array\n",
      "    padded = np.empty(pad_shape, dtype=middle.dtype) # Padded array ready to fill\n",
      "    padded[..., 0] = first\n",
      "    padded[..., 1:-1] = middle\n",
      "    padded[..., -1] = last\n",
      "    return padded"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 39
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "assert np.all(pad_ends(0, [2, 3], 5) == [0, 2, 3, 5])\n",
      "a = np.zeros((2, 3))\n",
      "b = np.ones((2, 3, 4)) * 10\n",
      "c = np.ones((2, 3))\n",
      "assert np.all(pad_ends(a, b, c) == np.concatenate((a.reshape((2, 3, 1)), b, c.reshape((2, 3, 1))), axis=2))"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 40
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Can we interpolate a whole slice of data at a time?"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "slice1_all = data[:, :, 1, :]\n",
      "slice1_all.shape"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "pyout",
       "prompt_number": 41,
       "text": [
        "(64, 64, 165)"
       ]
      }
     ],
     "prompt_number": 41
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Can ``spi.interp1d`` interpolate this array for me?  Or do I have to do this one time course at a time?"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "x = slice1_times # as before\n",
      "y = slice1_all # as before\n",
      "interpolator = spi.interp1d(x, y, 'linear', axis=2, bounds_error=False, fill_value=0)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 42
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "How would I pack this array with a repeat of the first and last scans?"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "slice_dims = img.shape[:2]\n",
      "n_scans = img.shape[3]\n",
      "slice1_all_padded = pad_ends(slice1_all[:, :, 0], slice1_all, slice1_all[:, :, -1])"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 43
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "interpolator = spi.interp1d(x_padded, slice1_all_padded, 'linear')"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 44
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "slice1_all_at_slice0 = interpolator(slice0_times)\n",
      "slice1_at_slice0_again = slice1_all_at_slice0[32, 25, :]\n",
      "plt.plot(slice0_times[:10], slice0_time_course[:10], 'r:+', label='slice 0')\n",
      "plt.hold(True)\n",
      "plt.plot(slice1_times[:10], slice1_time_course[:10], 'b-o', label='slice 1')\n",
      "plt.plot(slice0_times[:10], slice1_at_slice0_again[:10], 'kx', label='1 -> 0')\n",
      "plt.xlabel('Time of acquisition')\n",
      "plt.legend()"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "pyout",
       "prompt_number": 45,
       "text": [
        "<matplotlib.legend.Legend at 0x56b2a90>"
       ]
      },
      {
       "output_type": "display_data",
       "png": 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5pF88RUXA3Xo9zPCqq4UhbDz+3bqJ1R9vrd0zgKUm+H/9S5ii2kzjx49X6XMP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\n",
       "text": [
        "<matplotlib.figure.Figure at 0x7ff7e8618090>"
       ]
      }
     ],
     "prompt_number": 45
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Make this into a function to interpolate a 3D slice at a time"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "def interp_slice(old_times, slice_nd, new_times, kind='linear'):\n",
      "    \"\"\" Interpolate a 3D slice `slice_nd` with times changing from `old_times` to `new_times`\n",
      "    \"\"\"\n",
      "    n_time = slice_nd.shape[-1]\n",
      "    assert n_time == len(old_times)\n",
      "    padded_times = pad_ends(old_times[0] - (old_times[1] - old_times[0]), \n",
      "                        old_times,\n",
      "                        old_times[-1] + (old_times[-1] - old_times[-2]))\n",
      "    to_interpolate = pad_ends(slice_nd[..., 0], slice_nd, slice_nd[..., -1])\n",
      "    interpolator = spi.interp1d(padded_times, to_interpolate, kind, axis=-1)\n",
      "    return interpolator(new_times)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 46
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Check we get the same from the function as we did from the manual way before"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "interpolated = interp_slice(slice1_times, slice1_all, slice0_times)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 47
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "assert np.allclose(interpolated, slice1_all_at_slice0)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 48
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Now we are ready for full slice-timing glory"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "data = img.get_data()"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 49
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "slice_times"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "pyout",
       "prompt_number": 50,
       "text": [
        "array([ 0.04285714,  1.58571429,  0.12857143,  1.67142857,  0.21428571,\n",
        "        1.75714286,  0.3       ,  1.84285714,  0.38571429,  1.92857143,\n",
        "        0.47142857,  2.01428571,  0.55714286,  2.1       ,  0.64285714,\n",
        "        2.18571429,  0.72857143,  2.27142857,  0.81428571,  2.35714286,\n",
        "        0.9       ,  2.44285714,  0.98571429,  2.52857143,  1.07142857,\n",
        "        2.61428571,  1.15714286,  2.7       ,  1.24285714,  2.78571429,\n",
        "        1.32857143,  2.87142857,  1.41428571,  2.95714286,  1.5       ])"
       ]
      }
     ],
     "prompt_number": 50
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "scan_starts"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "pyout",
       "prompt_number": 51,
       "text": [
        "array([   0.,    3.,    6.,    9.,   12.,   15.,   18.,   21.,   24.,\n",
        "         27.,   30.,   33.,   36.,   39.,   42.,   45.,   48.,   51.,\n",
        "         54.,   57.,   60.,   63.,   66.,   69.,   72.,   75.,   78.,\n",
        "         81.,   84.,   87.,   90.,   93.,   96.,   99.,  102.,  105.,\n",
        "        108.,  111.,  114.,  117.,  120.,  123.,  126.,  129.,  132.,\n",
        "        135.,  138.,  141.,  144.,  147.,  150.,  153.,  156.,  159.,\n",
        "        162.,  165.,  168.,  171.,  174.,  177.,  180.,  183.,  186.,\n",
        "        189.,  192.,  195.,  198.,  201.,  204.,  207.,  210.,  213.,\n",
        "        216.,  219.,  222.,  225.,  228.,  231.,  234.,  237.,  240.,\n",
        "        243.,  246.,  249.,  252.,  255.,  258.,  261.,  264.,  267.,\n",
        "        270.,  273.,  276.,  279.,  282.,  285.,  288.,  291.,  294.,\n",
        "        297.,  300.,  303.,  306.,  309.,  312.,  315.,  318.,  321.,\n",
        "        324.,  327.,  330.,  333.,  336.,  339.,  342.,  345.,  348.,\n",
        "        351.,  354.,  357.,  360.,  363.,  366.,  369.,  372.,  375.,\n",
        "        378.,  381.,  384.,  387.,  390.,  393.,  396.,  399.,  402.,\n",
        "        405.,  408.,  411.,  414.,  417.,  420.,  423.,  426.,  429.,\n",
        "        432.,  435.,  438.,  441.,  444.,  447.,  450.,  453.,  456.,\n",
        "        459.,  462.,  465.,  468.,  471.,  474.,  477.,  480.,  483.,\n",
        "        486.,  489.,  492.])"
       ]
      }
     ],
     "prompt_number": 51
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "interp_data = np.empty(data.shape)\n",
      "desired_times = scan_starts"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 52
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "for slice_no in range(data.shape[-2]):\n",
      "    these_times = slice_times[slice_no] + scan_starts\n",
      "    data_slice = data[:, :, slice_no, :]\n",
      "    interped = interp_slice(these_times, data_slice, desired_times, 'cubic')\n",
      "    interp_data[:, :, slice_no, :] = interped"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 53
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Check we get the same result as we would from doing this manually"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "one_tc = data[32, 32, 17, :]\n",
      "old_times = slice_times[17] + scan_starts\n",
      "n_scans = len(one_tc)\n",
      "one_tc_padded = pad_ends(one_tc[0], one_tc, one_tc[-1])\n",
      "old_times_padded = pad_ends(old_times[0] - TR, old_times, old_times[-1] + TR)\n",
      "interpolator = spi.interp1d(old_times_padded, one_tc_padded, 'cubic')\n",
      "tc = interpolator(desired_times)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 54
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "assert np.allclose(tc, interp_data[32, 32, 17, :])"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 55
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "How about a function to do slice timing on an image?"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "def slice_time_image(img, slice_times, TR, kind='cubic'):\n",
      "    \"\"\" Take nibabel image `img` and run slice timing correction using `slice_times`\n",
      "    \"\"\"\n",
      "    data = img.get_data()\n",
      "    assert len(slice_times) == img.shape[-2]\n",
      "    n_scans = img.shape[-1]\n",
      "    scan_starts = np.arange(n_scans) * TR\n",
      "    interp_data = np.empty(data.shape)\n",
      "    desired_times = scan_starts\n",
      "    for slice_no in range(data.shape[-2]):\n",
      "        these_times = slice_times[slice_no] + scan_starts\n",
      "        data_slice = data[:, :, slice_no, :]\n",
      "        interped = interp_slice(these_times, data_slice, desired_times, kind)\n",
      "        interp_data[:, :, slice_no, :] = interped\n",
      "    new_img = nib.Nifti1Image(interp_data, img.get_affine(), img.get_header())\n",
      "    return new_img"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 56
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "new_img = slice_time_image(img, slice_times, TR)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 57
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Check we get the same answer as last time"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "new_data = new_img.get_data()\n",
      "assert np.allclose(tc, new_data[32, 32, 17, :])"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 58
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Can we run this in a pipeline?"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "import os\n",
      "pth, fname = os.path.split(fname)\n",
      "pth, fname"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "pyout",
       "prompt_number": 59,
       "text": [
        "('', 'bold.nii.gz')"
       ]
      }
     ],
     "prompt_number": 59
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "new_fname = os.path.join(pth, 'a' + fname)\n",
      "new_fname"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "pyout",
       "prompt_number": 60,
       "text": [
        "'abold.nii.gz'"
       ]
      }
     ],
     "prompt_number": 60
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "raw_img = nib.load(fname)\n",
      "interp_img = slice_time_image(raw_img, slice_times, TR)\n",
      "nib.save(interp_img, new_fname)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 61
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "How about a function that takes the filename and the slice times, and the TR, and writes out a new filename?"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "def slice_time_file(fname, slice_times, TR, kind='cubic'):\n",
      "    pth, fname = os.path.split(fname)\n",
      "    new_fname = os.path.join(pth, 'a' + fname)\n",
      "    raw_img = nib.load(fname)\n",
      "    interp_img = slice_time_image(raw_img, slice_times, TR, kind)\n",
      "    nib.save(interp_img, new_fname)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 62
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "slice_time_file(fname, slice_times, TR, 'cubic')"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 63
    }
   ],
   "metadata": {}
  }
 ]
}