Analysis of Flow Curves from CMR42

Reading XML Reports of Flows From CMR42.ipynb

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  {
   "cells": [
    {
     "cell_type": "heading",
     "level": 1,
     "metadata": {},
     "source": [
      "Cardiac Flows Exported From CMR42"
     ]
    },
    {
     "cell_type": "heading",
     "level": 3,
     "metadata": {},
     "source": [
      "Reading the XML Files"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "CMR42 can export reports either in text or in xml format. Unfortunately, the text form rounds the output and is anyway rather irregular and would require some munging. It seems better to try and parse the xml files.\n",
      "\n",
      "Python has several modules for this, but the most common interface seems to be the `etree` parser available in the standard library or in `lmxml`.\n",
      "\n",
      "We have a suitable test file in `flows.xml`."
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "First a little boiler plate"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "from __future__ import division\n",
      "from __future__ import print_function\n",
      "import json\n",
      "import matplotlib as mpl\n",
      "mpl.rcParams.update(json.load(open('styles/bmh_matplotlibrc.json')))"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 1
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "This is the file to read:"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "cmr42_flows_file = 'flows.xml'"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 2
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "We'll try using the `lxml` xml library on the test file."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "from lxml import etree\n",
      "\n",
      "root = etree.parse(cmr42_flows_file).getroot()\n",
      "\n",
      "patinfo   = root.find('Patient')\n",
      "studyinfo = root.find('Study')\n",
      "\n",
      "# This seems to the analysis\n",
      "cfreport = root.find('FlowComparisonReport')"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 3
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Within a `FlowComparisonReport` we have sections `FLOW1` and `FLOW2`. Within each of these we have a `FlowReport->Analysis->ROI`. Within the `ROI` there are multiple `Phase` records of the following form, one for each time point:\n",
      "```\n",
      "<Phase nb=\"1\">\n",
      "    <TriggerTime val=\"0\" unit=\"msec\"/>\n",
      "    <Area val=\"785.33\" unit=\"sqmm\"/>\n",
      "    <Velocity mean=\"-1.04144\" sd=\"10.1143\" sum=\"-294.434\" min=\"-33.9844\" max=\"26.5137\" unit=\"cm/s\"/>\n",
      "    <Flow val=\"-8.17871\" unit=\"ml/s\"/>\n",
      "</Phase>\n",
      "```\n",
      "The attribute `nb` seems to just an index for the record. `TriggerTime`, `Area` and `Flow` are accessible via `val` attributes. Velocity statistics ar separate attributes if the `Velocity` tag (`mean`, `sd`, `sum`, `min` and `max`). "
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "flow1 = cfreport.find('FLOW1')\n",
      "flow2 = cfreport.find('FLOW2')"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 4
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "#\n",
      "# The flow curve data\n",
      "#\n",
      "\n",
      "roi1 = flow1.find('FlowReport').find('Analysis').find('ROI')\n",
      "roi2 = flow2.find('FlowReport').find('Analysis').find('ROI')\n",
      "\n",
      "import pandas as pd\n",
      "def roi_stats(roi):\n",
      "    '''\n",
      "    '''\n",
      "    time_, area, vmean, vsd, vsum, vmin, vmax, flow  = zip(*[(\n",
      "        float(f.find('TriggerTime').get('val')),\n",
      "        float(f.find('Area').get('val')),\n",
      "        float(f.find('Velocity').get('mean')),\n",
      "        float(f.find('Velocity').get('sd')), \n",
      "        float(f.find('Velocity').get('sum')), \n",
      "        float(f.find('Velocity').get('min')), \n",
      "        float(f.find('Velocity').get('max')),         \n",
      "        float(f.find('Flow').get('val')),        \n",
      "        )                                               \n",
      "        for f in roi.findall('Phase')]\n",
      "    )\n",
      "    df = pd.DataFrame.from_items(\n",
      "        zip(\n",
      "            ['time', 'area', 'vmean', 'vsd', 'vsum', 'vmin', 'vmax', 'flow'],\n",
      "            [time_,    area,   vmean,   vsd,   vsum,   vmin,   vmax, flow]\n",
      "        )\n",
      "    )\n",
      "    return df\n",
      "\n",
      "\n",
      "roidf1 = roi_stats(roi1)\n",
      "roidf2 = roi_stats(roi2)\n",
      "\n",
      "time_units = roi1.find('Phase').find('TriggerTime').get('unit')\n",
      "flow_units = roi1.find('Phase').find('Flow').get('unit')\n",
      "area_units = roi1.find('Phase').find('Area').get('unit')\n",
      "velo_units = roi1.find('Phase').find('Velocity').get('unit')\n",
      "\n",
      "# The R to R interval in milliseconds (assuming heart rate in beats/min)\n",
      "r_to_r = 60000 / float(flow1.find('FlowReport').find('Series').find('HeartRate').get('val'))\n",
      "assert flow1.find('FlowReport').find('Series').find('HeartRate').get('unit') == '1/min'\n",
      "patient_name = patinfo.find('DicomPatientName').get('val')\n"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 5
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Take a quick look at the tables."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "display(roidf1.head())\n",
      "display(roidf2.head())"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "html": [
        "<div style=\"max-height:1000px;max-width:1500px;overflow:auto;\">\n",
        "<table border=\"1\" class=\"dataframe\">\n",
        "  <thead>\n",
        "    <tr style=\"text-align: right;\">\n",
        "      <th></th>\n",
        "      <th>time</th>\n",
        "      <th>area</th>\n",
        "      <th>vmean</th>\n",
        "      <th>vsd</th>\n",
        "      <th>vsum</th>\n",
        "      <th>vmin</th>\n",
        "      <th>vmax</th>\n",
        "      <th>flow</th>\n",
        "    </tr>\n",
        "  </thead>\n",
        "  <tbody>\n",
        "    <tr>\n",
        "      <th>0</th>\n",
        "      <td>   0.00</td>\n",
        "      <td> 785.330</td>\n",
        "      <td> -1.04144</td>\n",
        "      <td> 10.1143</td>\n",
        "      <td>  -294.434</td>\n",
        "      <td>-33.9844</td>\n",
        "      <td>  26.5137</td>\n",
        "      <td>  -8.17871</td>\n",
        "    </tr>\n",
        "    <tr>\n",
        "      <th>1</th>\n",
        "      <td>  41.05</td>\n",
        "      <td> 873.003</td>\n",
        "      <td> 10.11540</td>\n",
        "      <td> 13.2224</td>\n",
        "      <td>  3179.100</td>\n",
        "      <td>-37.2803</td>\n",
        "      <td>  46.8750</td>\n",
        "      <td>  88.30820</td>\n",
        "    </tr>\n",
        "    <tr>\n",
        "      <th>2</th>\n",
        "      <td>  82.10</td>\n",
        "      <td> 932.726</td>\n",
        "      <td> 44.42660</td>\n",
        "      <td> 12.0250</td>\n",
        "      <td> 14917.600</td>\n",
        "      <td>  9.8877</td>\n",
        "      <td>  71.3379</td>\n",
        "      <td> 414.37800</td>\n",
        "    </tr>\n",
        "    <tr>\n",
        "      <th>3</th>\n",
        "      <td> 123.15</td>\n",
        "      <td> 967.882</td>\n",
        "      <td> 55.83220</td>\n",
        "      <td> 29.2069</td>\n",
        "      <td> 19454.000</td>\n",
        "      <td>-42.6270</td>\n",
        "      <td>  94.7754</td>\n",
        "      <td> 540.39000</td>\n",
        "    </tr>\n",
        "    <tr>\n",
        "      <th>4</th>\n",
        "      <td> 164.20</td>\n",
        "      <td> 998.958</td>\n",
        "      <td> 50.37310</td>\n",
        "      <td> 57.0117</td>\n",
        "      <td> 18115.400</td>\n",
        "      <td>-77.7832</td>\n",
        "      <td> 128.9060</td>\n",
        "      <td> 503.20600</td>\n",
        "    </tr>\n",
        "  </tbody>\n",
        "</table>\n",
        "<p>5 rows \u00d7 8 columns</p>\n",
        "</div>"
       ],
       "metadata": {},
       "output_type": "display_data",
       "text": [
        "     time     area     vmean      vsd       vsum     vmin      vmax       flow\n",
        "0    0.00  785.330  -1.04144  10.1143   -294.434 -33.9844   26.5137   -8.17871\n",
        "1   41.05  873.003  10.11540  13.2224   3179.100 -37.2803   46.8750   88.30820\n",
        "2   82.10  932.726  44.42660  12.0250  14917.600   9.8877   71.3379  414.37800\n",
        "3  123.15  967.882  55.83220  29.2069  19454.000 -42.6270   94.7754  540.39000\n",
        "4  164.20  998.958  50.37310  57.0117  18115.400 -77.7832  128.9060  503.20600\n",
        "\n",
        "[5 rows x 8 columns]"
       ]
      },
      {
       "html": [
        "<div style=\"max-height:1000px;max-width:1500px;overflow:auto;\">\n",
        "<table border=\"1\" class=\"dataframe\">\n",
        "  <thead>\n",
        "    <tr style=\"text-align: right;\">\n",
        "      <th></th>\n",
        "      <th>time</th>\n",
        "      <th>area</th>\n",
        "      <th>vmean</th>\n",
        "      <th>vsd</th>\n",
        "      <th>vsum</th>\n",
        "      <th>vmin</th>\n",
        "      <th>vmax</th>\n",
        "      <th>flow</th>\n",
        "    </tr>\n",
        "  </thead>\n",
        "  <tbody>\n",
        "    <tr>\n",
        "      <th>0</th>\n",
        "      <td>   0.00</td>\n",
        "      <td> 512.240</td>\n",
        "      <td>  3.44161</td>\n",
        "      <td>  9.76552</td>\n",
        "      <td>   634.655</td>\n",
        "      <td>-32.4463</td>\n",
        "      <td> 28.4912</td>\n",
        "      <td>  17.6293</td>\n",
        "    </tr>\n",
        "    <tr>\n",
        "      <th>1</th>\n",
        "      <td>  41.05</td>\n",
        "      <td> 484.201</td>\n",
        "      <td>  6.69766</td>\n",
        "      <td> 10.30920</td>\n",
        "      <td>  1167.490</td>\n",
        "      <td>-19.8486</td>\n",
        "      <td> 30.9082</td>\n",
        "      <td>  32.4301</td>\n",
        "    </tr>\n",
        "    <tr>\n",
        "      <th>2</th>\n",
        "      <td>  82.10</td>\n",
        "      <td> 546.094</td>\n",
        "      <td> 39.32220</td>\n",
        "      <td> 10.59310</td>\n",
        "      <td>  7730.500</td>\n",
        "      <td> 25.0488</td>\n",
        "      <td> 57.0557</td>\n",
        "      <td> 214.7360</td>\n",
        "    </tr>\n",
        "    <tr>\n",
        "      <th>3</th>\n",
        "      <td> 123.15</td>\n",
        "      <td> 577.083</td>\n",
        "      <td> 60.67430</td>\n",
        "      <td>  9.67872</td>\n",
        "      <td> 12605.100</td>\n",
        "      <td> 46.7285</td>\n",
        "      <td> 78.0029</td>\n",
        "      <td> 350.1410</td>\n",
        "    </tr>\n",
        "    <tr>\n",
        "      <th>4</th>\n",
        "      <td> 164.20</td>\n",
        "      <td> 585.417</td>\n",
        "      <td> 62.70280</td>\n",
        "      <td> 11.11790</td>\n",
        "      <td> 13214.600</td>\n",
        "      <td> 39.2578</td>\n",
        "      <td> 79.3213</td>\n",
        "      <td> 367.0730</td>\n",
        "    </tr>\n",
        "  </tbody>\n",
        "</table>\n",
        "<p>5 rows \u00d7 8 columns</p>\n",
        "</div>"
       ],
       "metadata": {},
       "output_type": "display_data",
       "text": [
        "     time     area     vmean       vsd       vsum     vmin     vmax      flow\n",
        "0    0.00  512.240   3.44161   9.76552    634.655 -32.4463  28.4912   17.6293\n",
        "1   41.05  484.201   6.69766  10.30920   1167.490 -19.8486  30.9082   32.4301\n",
        "2   82.10  546.094  39.32220  10.59310   7730.500  25.0488  57.0557  214.7360\n",
        "3  123.15  577.083  60.67430   9.67872  12605.100  46.7285  78.0029  350.1410\n",
        "4  164.20  585.417  62.70280  11.11790  13214.600  39.2578  79.3213  367.0730\n",
        "\n",
        "[5 rows x 8 columns]"
       ]
      }
     ],
     "prompt_number": 6
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "and plot the curves."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "# Temporal resoltion\n",
      "dts = np.diff(roidf1.time)\n",
      "assert np.sum(np.abs(dts-dts[0])) < 0.1\n",
      "dt = np.mean(dts)\n",
      "\n",
      "plot(roidf1.time, roidf1.flow, '-', label=roi1.get('roi_id'))\n",
      "plot(roidf2.time, roidf2.flow, '-', label=roi2.get('roi_id'))\n",
      "grid(True)\n",
      "legend()\n",
      "xlabel('Delay from Trigger (%s)' % time_units)\n",
      "ylabel('Flow (%s)' % flow_units)\n",
      "text(500, 100, 'R-R Interval  = %3.0f ms\\nTemporal Res. = %3.0f ms' % (r_to_r, dt))\n",
      "#text(500, 150, 'Temporal Res. = %3.0f ms' % dt)\n",
      "title('%s (Flow)' % (patient_name));"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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RpqIFLt+8w6XsYsa5te1sxM1hbaLPKJcO4mlFEIQmE4VKG4m4mIO3kxm2prX7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\nqfz0009wd3fHlStXMGXKFEyaNAkA4O/vj+joaPj7+2PSpEnYtm0bE7B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9s+Qe/9vf/gaR\nSARPT0+MHz++xd2YiYkJfvzxR+zcuRO2trbYt28fpk6dytSHh4fjf//7H95++23Y2dnB29sb3377\n7TNd/4033sC+ffueqP9J59u7dy88PT1hbW2Nr776ijlXR9oAgM1m49ixY/j9998hFovh7u6OQ4cO\nMec8cOAA3nzzzU6/Bor+oEm6KEbJ4sWL4ebmhn/84x/6ltLtfPnllzh06BAuXLjQbn1kZCSWL1+O\nhQsX6uya8+bNQ3R0tEEsgDx27Bj27duHAwcO6FsKpRNQU6EYHdnZ2QgNDUVqamqLQfbeQnFxMR48\neIDBgwcjMzMTU6dOxTvvvIN3330XAJCQkAAfHx/Y29tj3759WL58OR4+fPhM40AUSndBu78oRsUn\nn3yCoKAg/OUvf+mVhgI0LPJcunQpBAIBxowZgxkzZmD58uVMfUZGBrOA8LPPPsP3339PDYViMNA7\nFQqFQqHoDHqnQqFQKBSdQU2FQqFQKDqDmgqFQqFQdAY1FQqFQqHoDGoqFAqFQtEZ1FQoFAqFojP+\nH0WVQ7iOKesYAAAAAElFTkSuQmCC\n",
       "text": [
        "<matplotlib.figure.Figure at 0x2c7f990>"
       ]
      }
     ],
     "prompt_number": 7
    }
   ],
   "metadata": {}
  }
 ]
}