content/Signal_Measurement.ipynb

{
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   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Signal Generation\n",
    "*by Luke Chang*\n",
    "\n",
    "Measuring in-vivo brain activity from humans is an extraordinary feat. How do scanners work? and what exactly are we measuring? In this course, we will be learning how to analyze functional magnetic resonance imaging (fMRI) data. Before we dive in the analysis methods, it's important to have a basic understanding of what we are measuring. This course primarily focuses on Blood Oxygenated Level Dependent (BOLD) fMRI signals. In this section, we will watch a few short videos by Martin Lindquist and Tor Wager to gain a very high level understanding of (1) magnetic resonance physics, (2) how images are formed from these signals, (3) the relationship between k-space and image space, and (4) BOLD physiology. Gaining a deep understanding of the MR physics and physiological basis for the BOLD fMRI signal is beyond the scope of this course and we refer the interested reader to the excellent [Huettel, Song, & McCarthy (2004) Functional magnetic resonance imaging textbook](https://www.amazon.com/Functional-Magnetic-Resonance-Imaging-Huettel/dp/0878936270/ref=pd_sbs_14_1/144-9493364-1935804?_encoding=UTF8&pd_rd_i=0878936270&pd_rd_r=ac61b1df-17bf-47c5-8db5-25dfa36bcd16&pd_rd_w=J61zv&pd_rd_wg=d1O2i&pf_rd_p=703f3758-d945-4136-8df6-a43d19d750d1&pf_rd_r=PCEXDFT3TQQ4JW7FD8HF&psc=1&refRID=PCEXDFT3TQQ4JW7FD8HF) for a more in depth conceptual and quantitative overview.\n",
    "\n",
    "The lecture for this section can be viewed {download}`here <../images/lectures/Measurement_Signal.pdf>`."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Basic MR Physics"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2020-09-17T01:11:00.153682Z",
     "start_time": "2020-09-17T01:11:00.040122Z"
    }
   },
   "outputs": [
    {
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\n",
      "text/html": [
       "\n",
       "        <iframe\n",
       "            width=\"400\"\n",
       "            height=\"300\"\n",
       "            src=\"https://www.youtube.com/embed/XsDXxgjEJVY\"\n",
       "            frameborder=\"0\"\n",
       "            allowfullscreen\n",
       "        ></iframe>\n",
       "        "
      ],
      "text/plain": [
       "<IPython.lib.display.YouTubeVideo at 0x7f92503ee990>"
      ]
     },
     "execution_count": 1,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "from IPython.display import YouTubeVideo\n",
    "\n",
    "YouTubeVideo('XsDXxgjEJVY')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Image Formation"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2020-09-17T01:32:48.407361Z",
     "start_time": "2020-09-17T01:32:48.297811Z"
    }
   },
   "outputs": [
    {
     "data": {
      "image/jpeg": 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\n",
      "text/html": [
       "\n",
       "        <iframe\n",
       "            width=\"400\"\n",
       "            height=\"300\"\n",
       "            src=\"https://www.youtube.com/embed/PxqDjhO9FUs\"\n",
       "            frameborder=\"0\"\n",
       "            allowfullscreen\n",
       "        ></iframe>\n",
       "        "
      ],
      "text/plain": [
       "<IPython.lib.display.YouTubeVideo at 0x7f92207ec350>"
      ]
     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "YouTubeVideo('PxqDjhO9FUs')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## K-Space"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2020-09-17T01:34:24.689879Z",
     "start_time": "2020-09-17T01:34:24.608734Z"
    }
   },
   "outputs": [
    {
     "data": {
      "image/jpeg": 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\n",
      "text/html": [
       "\n",
       "        <iframe\n",
       "            width=\"400\"\n",
       "            height=\"300\"\n",
       "            src=\"https://www.youtube.com/embed/FI5frNsRTI4\"\n",
       "            frameborder=\"0\"\n",
       "            allowfullscreen\n",
       "        ></iframe>\n",
       "        "
      ],
      "text/plain": [
       "<IPython.lib.display.YouTubeVideo at 0x7f92207ecf90>"
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "YouTubeVideo('FI5frNsRTI4')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## fMRI Signal & BOLD Physiology"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2020-09-17T01:45:44.889253Z",
     "start_time": "2020-09-17T01:45:44.811833Z"
    }
   },
   "outputs": [
    {
     "data": {
      "image/jpeg": 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     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
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  }
 ],
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   "display_name": "Python 3.7.7 64-bit ('base': conda)",
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 },
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