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  "name": ""
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  {
   "cells": [
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "# Figure 2\n",
      "\n",
      "In this notebook, we analyze the accuracy of the diffusion tensor model (DTM). \n",
      "\n",
      "We start by importing the necessary modules: "
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "import nibabel as ni\n",
      "import osmosis.model.analysis as oza\n",
      "import osmosis.model.dti as dti\n",
      "import osmosis.viz.mpl as mpl"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 1
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "We set the path to point to where the data is installed: "
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "import os\n",
      "import osmosis as oz\n",
      "import osmosis.io as oio\n",
      "oio.data_path = os.path.join(oz.__path__[0], 'data')"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 2
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "We create strings that point to the data for this subject:"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "subject = 'SUB1'\n",
      "data_1k_1, data_1k_2 = oio.get_dwi_data(1000, subject)\n",
      "data_2k_1, data_2k_2 = oio.get_dwi_data(2000, subject)\n",
      "data_4k_1, data_4k_2 = oio.get_dwi_data(4000, subject)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 3
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "We will only analyze data within a white-matter masked region. Here, we load this mask and generate a masking array:"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "wm_mask = np.zeros(ni.load(data_1k_1[0]).shape[:3])\n",
      "wm_nifti = ni.load(oio.data_path + '/%s/%s_wm_mask.nii.gz'%(subject, subject)).get_data()\n",
      "wm_mask[np.where(wm_nifti==1)] = 1"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 4
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "We generate the model class instances, which will be used to analyze accuracy. Model parameters are not saved to file: "
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "TM_1k_1 = dti.TensorModel(*data_1k_1, mask=wm_mask, params_file='temp')\n",
      "TM_1k_2 = dti.TensorModel(*data_1k_2, mask=wm_mask, params_file='temp')\n",
      "TM_2k_1 = dti.TensorModel(*data_2k_1, mask=wm_mask, params_file='temp')\n",
      "TM_2k_2 = dti.TensorModel(*data_2k_2, mask=wm_mask, params_file='temp')\n",
      "TM_4k_1 = dti.TensorModel(*data_4k_1, mask=wm_mask, params_file='temp')\n",
      "TM_4k_2 = dti.TensorModel(*data_4k_2, mask=wm_mask, params_file='temp')"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "Loading from file: /home/arokem/usr/lib/python2.7/site-packages/osmosis/data/SUB1/SUB1_b1000_1.bvals\n",
        "Loading from file: /home/arokem/usr/lib/python2.7/site-packages/osmosis/data/SUB1/SUB1_b1000_1.bvecs\n",
        "Loading from file: /home/arokem/usr/lib/python2.7/site-packages/osmosis/data/SUB1/SUB1_b1000_2.bvals\n",
        "Loading from file: /home/arokem/usr/lib/python2.7/site-packages/osmosis/data/SUB1/SUB1_b1000_2.bvecs\n",
        "Loading from file: /home/arokem/usr/lib/python2.7/site-packages/osmosis/data/SUB1/SUB1_b2000_1.bvals\n",
        "Loading from file: /home/arokem/usr/lib/python2.7/site-packages/osmosis/data/SUB1/SUB1_b2000_1.bvecs\n",
        "Loading from file: /home/arokem/usr/lib/python2.7/site-packages/osmosis/data/SUB1/SUB1_b2000_2.bvals\n",
        "Loading from file: /home/arokem/usr/lib/python2.7/site-packages/osmosis/data/SUB1/SUB1_b2000_2.bvecs\n",
        "Loading from file: /home/arokem/usr/lib/python2.7/site-packages/osmosis/data/SUB1/SUB1_b4000_1.bvals\n",
        "Loading from file: /home/arokem/usr/lib/python2.7/site-packages/osmosis/data/SUB1/SUB1_b4000_1.bvecs\n",
        "Loading from file: /home/arokem/usr/lib/python2.7/site-packages/osmosis/data/SUB1/SUB1_b4000_2.bvals\n",
        "Loading from file: /home/arokem/usr/lib/python2.7/site-packages/osmosis/data/SUB1/SUB1_b4000_2.bvecs\n"
       ]
      }
     ],
     "prompt_number": 5
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "We calculate relative RMSE, based on average from cross-prediction between the models fit on each data-set in each b value:"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "rrmse_1k = oza.cross_predict(TM_1k_1, TM_1k_2)\n",
      "rrmse_2k = oza.cross_predict(TM_2k_1, TM_2k_2)\n",
      "rrmse_4k = oza.cross_predict(TM_4k_1, TM_4k_2)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "Loading from file: /home/arokem/usr/lib/python2.7/site-packages/osmosis/data/SUB1/SUB1_b1000_1.nii.gz\n",
        "Loading from file: /home/arokem/usr/lib/python2.7/site-packages/osmosis/data/SUB1/SUB1_b1000_2.nii.gz"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\n",
        "Predicting signal from TensorModel"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\n",
        "Fitting TensorModel params using dipy"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\n",
        "Predicting signal from TensorModel"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\n",
        "Fitting TensorModel params using dipy"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\n",
        "Loading from file: /home/arokem/usr/lib/python2.7/site-packages/osmosis/data/SUB1/SUB1_b2000_1.nii.gz"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\n",
        "Loading from file: /home/arokem/usr/lib/python2.7/site-packages/osmosis/data/SUB1/SUB1_b2000_2.nii.gz"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\n",
        "Predicting signal from TensorModel"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\n",
        "Fitting TensorModel params using dipy"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\n",
        "Predicting signal from TensorModel"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\n",
        "Fitting TensorModel params using dipy"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\n",
        "Loading from file: /home/arokem/usr/lib/python2.7/site-packages/osmosis/data/SUB1/SUB1_b4000_1.nii.gz"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\n",
        "Loading from file: /home/arokem/usr/lib/python2.7/site-packages/osmosis/data/SUB1/SUB1_b4000_2.nii.gz"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\n",
        "Predicting signal from TensorModel"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\n",
        "Fitting TensorModel params using dipy"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\n",
        "Predicting signal from TensorModel"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\n",
        "Fitting TensorModel params using dipy"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\n"
       ]
      }
     ],
     "prompt_number": 6
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "We generate a figure that shows the distribution of the rRMSE measure across the voxels in the white-matter:"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "# Gray-scale color choices, based on http://colorbrewer2.org\n",
      "fig = mpl.probability_hist(rrmse_1k[np.isfinite(rrmse_1k)], label='b=%s'%str(1000), color=[0.8, 0.8, 0.8])\n",
      "fig = mpl.probability_hist(rrmse_2k[np.isfinite(rrmse_2k)], fig=fig, label='b=%s'%str(2000), color=[0.59, 0.59, 0.59])\n",
      "fig = mpl.probability_hist(rrmse_4k[np.isfinite(rrmse_4k)], fig=fig, label='b=%s'%str(4000), color=[0.32, 0.32, 0.32])\n",
      "ax = fig.axes[0]\n",
      "ax.set_xlim([0.6, 1.4])\n",
      "fig.axes[0].plot([1,1], [ax.get_ylim()[0], ax.get_ylim()[1]], '--k')\n",
      "fig.axes[0].plot([1/np.sqrt(2),1/np.sqrt(2)], [ax.get_ylim()[0], ax.get_ylim()[1]], '--k')\n",
      "\n",
      "plt.legend()\n",
      "fig.savefig('figures/Figure2_histogram.svg')"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "display_data",
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xHSUs0EAkiUYxV7RHuhKJMQabzQapVAqz2RyRA5HA4OJRJSUlOHbsWFSsEzNR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\nsSUAAAAASUVORK5CYII=\n",
       "text": [
        "<matplotlib.figure.Figure at 0x4329050>"
       ]
      }
     ],
     "prompt_number": 7
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "We also print to the notebook the proportion of voxels with rRMSE that is adequate (smaller than 1):"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "for this in [rrmse_1k,rrmse_2k, rrmse_4k]:\n",
      "    isfin = this[np.isfinite(this)]\n",
      "    print \"The proportion of voxels with rRMSE<1.0 is %s\"%(100 * len(np.where(isfin<1)[0])/float(len(isfin)))"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "The proportion of voxels with rRMSE<1.0 is 97.9663434943\n",
        "The proportion of voxels with rRMSE<1.0 is 98.8645296532\n",
        "The proportion of voxels with rRMSE<1.0 is 97.568928873\n"
       ]
      }
     ],
     "prompt_number": 8
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "We examine a particular voxel. This is used to demonstrate how rRMSE is calculated: "
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "# Look at the same corpus callosum voxel as in Figure 1: \n",
      "vox_idx = (40, 73, 32)  # This doesn't make sense in HT's brain."
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 9
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "First, we scatter-plot data-to-data reliability in this voxel: "
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "fig, axes = plt.subplots(1,3,squeeze=True)\n",
      "axes[0].set_ylabel(r'$\\frac{S}{S_0}$')\n",
      "for ax, models in zip(axes,([TM_1k_1,TM_1k_2],[TM_2k_1, TM_2k_2],[TM_4k_1, TM_4k_2])):\n",
      "    ax.scatter(models[0].relative_signal[vox_idx], models[1].relative_signal[vox_idx], \n",
      "               color=[0.5, 0.5, 0.5])\n",
      "    ax.grid()\n",
      "    ax.set_xlim([0,1])\n",
      "    ax.set_ylim([0,1])\n",
      "    ax.set_aspect('equal')\n",
      "    ax.set_xlabel(r'$\\frac{S}{S_0}$')\n",
      "    \n",
      "fig.set_size_inches([10,10])\n",
      "\n",
      "fig.savefig('figures/Figure2_scatter_self.svg')"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stderr",
       "text": [
        "/home/arokem/usr/lib/python2.7/site-packages/osmosis/model/base.py:383: RuntimeWarning: divide by zero encountered in divide\n",
        "  signal_rel = self.signal/np.reshape(self.S0, (self.S0.shape + (1,)))\n",
        "/home/arokem/usr/lib/python2.7/site-packages/osmosis/model/base.py:383: RuntimeWarning: invalid value encountered in divide\n",
        "  signal_rel = self.signal/np.reshape(self.S0, (self.S0.shape + (1,)))\n"
       ]
      },
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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bt9DS0gKapiGTybBx40YcP34cVVVVoCgKNE3jtddeg4+Pz1P9fSqVCl988YXAuy2TybB2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\nTVMbAq0FrIcAAAAASUVORK5CYII=\n",
       "text": [
        "<matplotlib.figure.Figure at 0x432d350>"
       ]
      }
     ],
     "prompt_number": 10
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Next, we scatter plot the accuracy of model predictions from one data-set, relative to the data from the other data-set in each b value:"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "fig, axes = plt.subplots(1,3,squeeze=True)\n",
      "for ax, models in zip(axes,([TM_1k_1,TM_1k_2],[TM_2k_1, TM_2k_2],[TM_4k_1, TM_4k_2])):\n",
      "    ax.scatter(models[0].relative_signal[vox_idx], models[1].fit[vox_idx]/models[1].S0[vox_idx], \n",
      "               color=[0.5, 0.5, 0.5])\n",
      "    ax.grid()\n",
      "    ax.set_xlim([0,1])\n",
      "    ax.set_ylim([0,1])\n",
      "    ax.set_aspect('equal')\n",
      "    ax.set_xlabel(r'Measured $\\frac{S}{S_0}$')\n",
      "axes[0].set_ylabel(r'Predicted $\\frac{S}{S_0}$')    \n",
      "fig.set_size_inches([10,10])\n",
      "\n",
      "fig.savefig('figures/Figure2_scatter_cross.svg')\n",
      "print rrmse_1k[vox_idx],rrmse_2k[vox_idx], rrmse_4k[vox_idx]"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "Predicting signal from TensorModel\n",
        "Predicting signal from TensorModel"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\n",
        "Predicting signal from TensorModel"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\n",
        "0.768360258114"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        " 0.768733481783 0.86385518906\n"
       ]
      },
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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wsrLCE088gTt37nSpUPVAYnh7NrcMQUFBOHr0KNRqNRwcHPDCCy/A3d29x9dc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       "text": [
        "<matplotlib.figure.Figure at 0xcb7b1d0>"
       ]
      }
     ],
     "prompt_number": 11
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 11
    }
   ],
   "metadata": {}
  }
 ]
}