ilumr 1D MRI Lesson.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Demo lesson for [ilumr](https://www.ilumr.com)\n",
    "### Prerequisites\n",
    "- Magnetic Field and Homogeneity\n",
    "- Larmor Precession Frequency\n",
    "- Fourier Transform\n",
    "- FID and RF Pulses\n",
    "- Spin Echo and the concept of Pulse Sequences\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import ipywidgets as widgets\n",
    "import asyncio\n",
    "from bokeh.io import show\n",
    "from bokeh.layouts import row\n",
    "import bokeh.plotting as bokplt\n",
    "from microspec_api.program import Program, list_programs\n",
    "from microspec_api import jupyterplot as jp\n",
    "GR_init = 1.0\n",
    "MRI = Program('2D_SLICE_MRI')\n",
    "MRI.load_par('example_pars/2D_SLICE_MRI.yaml')\n",
    "MRI.load_par('auto_pars/shims.yaml')\n",
    "MRI.load_par('auto_pars/frequency.yaml')\n",
    "MRI.load_par('auto_pars/hardpulse_90.yaml')\n",
    "MRI.load_par('auto_pars/hardpulse_180.yaml')\n",
    "MRI.set_par('read_GZ', int(30000*GR_init))\n",
    "await MRI.run()"
   ]
  },
  {
   "attachments": {
    "phantom1D.jpg": {
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"
    }
   },
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# 1D Magnetic Resonance Imaging\n",
    "\n",
    "This module introduces magnetic field gradients and shows how they can be added to a pulse sequence to perform a simple imaging experiment: one dimensional projection.\n",
    "\n",
    "*Load the **Z1D** phantom from the ilumr phantom kit for the experiments in this module:*\n",
    "\n",
    "![phantom1D.jpg](attachment:phantom1D.jpg)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Magnetic Field Gradients\n",
    "\n",
    "So far we have assumed that the magnetic field is homogeneous, the precession frequency is the same throughout the sample and there is no way to determine how much signal came from a specific region of the sample. The key to separating the NMR signal from spins in different locations is to modify the precession frequency of the spins in way that varies with their position. Generally this can be accomplished with a magnetic field gradient: we take our homogenous field where the precession frequency is the same everywhere and purposely distort it with electromagnetic coils in such a way that the field is stronger on one side of the sample, weaker on the other, and varies linearly inbetween. This varying field strength is called a *magnetic field gradient*, and the coils *gradient coils*. The amount of current in these coils can be controlled to switch the gradient on/off or vary its strength."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "jupyter": {
     "source_hidden": true
    }
   },
   "outputs": [
    {
     "data": {
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     "metadata": {},
     "output_type": "display_data"
    },
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   "source": [
    "# TODO: need diagram, maybe vector plot of field with gradient\n",
    "# import holoviews as hv\n",
    "# def disable_logo(plot, element):\n",
    "#     plot.state.toolbar.logo = None\n",
    "# print(hv.__version__)\n",
    "# hv.extension('bokeh', logo=False)\n",
    "# hv.plotting.bokeh.ElementPlot.finalize_hooks.append(disable_logo)\n",
    "\n",
    "x,y  = np.mgrid[-5:6,-5:6] * 0.2\n",
    "angles = np.pi/2+0*y\n",
    "lengths = (x+3)/25\n",
    "stem_x0 = x.flatten()\n",
    "stem_y0 = y.flatten()\n",
    "stem_x1 = stem_x0 + (lengths * np.cos(angles)).flatten()\n",
    "stem_y1 = stem_y0 + (lengths * np.sin(angles)).flatten()\n",
    "headl_x1 = stem_x1 + (0.25*lengths * np.cos(angles+np.pi*0.85)).flatten()\n",
    "headl_y1 = stem_y1 + (0.25*lengths * np.sin(angles+np.pi*0.85)).flatten()\n",
    "headr_x1 = stem_x1 + (0.25*lengths * np.cos(angles-np.pi*0.85)).flatten()\n",
    "headr_y1 = stem_y1 + (0.25*lengths * np.sin(angles-np.pi*0.85)).flatten()\n",
    "\n",
    "cm = np.array([\"#C7E9B4\", \"#7FCDBB\", \"#41B6C4\", \"#1D91C0\", \"#225EA8\", \"#0C2C84\"])\n",
    "ix = ((lengths-lengths.min())/(lengths.max()-lengths.min())*5).astype('int')\n",
    "colors = cm[ix]\n",
    "\n",
    "#vectorfield = hv.VectorField((x, y, angles, magnitudes))\n",
    "#watercells = hv.Rectangles([(-1,-2,1,-1)])\n",
    "freq = np.linspace(-1,1,256)\n",
    "specmag = np.zeros(len(freq))\n",
    "for i,f in enumerate(freq):\n",
    "    if (f>-0.75 and f<-0.25) or (f>0.25 and f<0.75):\n",
    "        specmag[i] = 1\n",
    "gaussian = np.exp(-0.5*np.linspace(-3,3,32)**2)\n",
    "specmag = np.convolve(specmag, gaussian, mode='same')\n",
    "specmag/=specmag.max()\n",
    "#spectrum = hv.Area((freq, specmag), vdims=['magnitude'])\n",
    "#vec_spec_plt = (vectorfield.opts(magnitude='Magnitude', height=300, responsive=True) + spectrum.opts(height=300, responsive=True)).opts(sizing_mode='stretch_width')\n",
    "#vec_spec_plt\n",
    "\n",
    "colors = 'red'\n",
    "water_color = '#0080FF'\n",
    "\n",
    "pvec = bokplt.figure(title='Sample in Magnetic Field with Gradient', x_axis_label='Z Position (Vertical)', sizing_mode=\"stretch_width\", height=300, toolbar_location=None)\n",
    "pvec.segment(stem_x0, stem_y0, stem_x1, stem_y1, color=colors)#, color=colors.flatten())\n",
    "pvec.segment(stem_x1, stem_y1, headl_x1, headl_y1, color=colors)\n",
    "pvec.segment(stem_x1, stem_y1, headr_x1, headr_y1, color=colors)\n",
    "pvec.rect(-0.5, 0.0, 0.5, 1.5, color=water_color, fill_alpha=0.25)\n",
    "pvec.rect(0.5, 0.0, 0.5, 1.5, color=water_color, fill_alpha=0.25)\n",
    "pvec.yaxis.visible=False\n",
    "pvec.xaxis.major_label_text_alpha=0\n",
    "pvec.grid.visible=False\n",
    "pvec.title.align = 'center'\n",
    "pvec.title.text_font_style = 'normal'\n",
    "pspec = bokplt.figure(title='NMR Spectrum', x_axis_label='Precession Frequency', sizing_mode=\"stretch_width\", height=300, toolbar_location=None)\n",
    "pspec.line(freq, specmag, color=water_color)\n",
    "pspec.varea(x=freq, y1=0, y2=specmag, color=water_color, fill_alpha=0.25)\n",
    "pspec.yaxis.visible=False\n",
    "pspec.xaxis.major_label_text_alpha=0\n",
    "pspec.grid.visible=False\n",
    "pspec.title.align = 'center'\n",
    "pspec.title.text_font_style = 'normal'\n",
    "show(bokplt.Row(pvec, pspec))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The figure above shows how two water cells at different vertical locations in a magnetic field with a vertical gradient will experience different field strengths and therefore emit NMR signals at two distinct frequencies."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Pulse Sequence with Gradient\n",
    "\n",
    "With an inhomogeneous magnetic field, the spins will no longer precess all at the same frequency, and will quickly go out of phase. To observe this signal more easily we will use a *spin echo* pulse sequence with a gradient added, shown below. The gradient will be pulsed for efficiency, for the full duration of acquisition and for half that duration between the 90° and 180° RF pulses, but a constantly enabled gradient would produce similar results."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "jupyter": {
     "source_hidden": true
    }
   },
   "outputs": [
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   "source": [
    "# NOTE: could actually just do constant gradient experiment first for simplicity\n",
    "# all times in ns\n",
    "samples = MRI.get_scaled_par('samples')\n",
    "dw = MRI.get_scaled_par('dwell_time')*10 # convert to ns\n",
    "echo_time = MRI.get_scaled_par('echo_time')\n",
    "ignore_samples = MRI.config_get('derived_parameters.ignore_samples.value')\n",
    "Tsample = (samples+7)*dw\n",
    "T90 = MRI.get_scaled_par('width_90')\n",
    "A90 = MRI.get_scaled_par('amp_90')\n",
    "T180 = MRI.get_scaled_par('width_180')\n",
    "A180 = MRI.get_scaled_par('amp_180')\n",
    "Tunslice = MRI.config_get('derived_parameters.unslice_time.value')\n",
    "T1 = MRI.config_get('derived_parameters.T1.value')\n",
    "T2 = MRI.config_get('derived_parameters.T2.value')\n",
    "T3 = MRI.config_get('derived_parameters.T3.value')\n",
    "\n",
    "GR = 1.0\n",
    "spin_echo_sequence = [\n",
    "    (T90, A90, 0, 0),\n",
    "    (Tunslice, 0, 0, 0),\n",
    "    (T1, 0, GR, 0),\n",
    "    (T2, 0, 0, 0),\n",
    "    (T180, A180, 0, 0),\n",
    "    (T3, 0, 0, 0),\n",
    "    (Tsample, 0, GR, 1)\n",
    "]\n",
    "\n",
    "padding = 1000*1000\n",
    "spin_echo_sequence.append((padding, 0, 0, 0))\n",
    "t = [-padding, 0]\n",
    "RF = [0, 0]\n",
    "GZ = [0, 0]\n",
    "Acq = [0, 0]\n",
    "for dt, A, G, S in spin_echo_sequence:\n",
    "    t.append(t[-1])\n",
    "    RF.append(A)\n",
    "    GZ.append(G)\n",
    "    Acq.append(S)\n",
    "    t.append(t[-1]+dt)\n",
    "    RF.append(A)\n",
    "    GZ.append(G)\n",
    "    Acq.append(S)\n",
    "\n",
    "t = np.array(t)/1e6\n",
    "RF = np.array(RF) + 2\n",
    "GZ = np.array(GZ)\n",
    "Acq = np.array(Acq) - 2\n",
    "pseq = bokplt.figure(x_axis_label='time (ms)', sizing_mode=\"stretch_width\", height=200)\n",
    "pseq.toolbar.logo = None\n",
    "pseq.line(t, RF, line_color=jp.PLOT_COLORS[0], legend_label='RF Pulse')\n",
    "pseq.line(t, GZ, line_color=jp.PLOT_COLORS[1], legend_label='Gradient')\n",
    "pseq.line(t, Acq, line_color=jp.PLOT_COLORS[2], legend_label='Acquisition')\n",
    "pseq.yaxis.visible=False\n",
    "show(pseq)"
   ]
  },
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   "source": [
    "## Experiment: Spin Echo with Gradient\n",
    "\n",
    "The pulse sequence above can be run below, with an adjustable gradient strength. A gradient strength of 0 should reproduce the standard spin echo result, and increasing the gradient will show the effect of the gradient field on the spin echo signal."
   ]
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   "source": [
    "GR = GR_init\n",
    "run_button = widgets.Button(description=\"Run\")\n",
    "grad_slider = widgets.FloatSlider(value=GR, min=0.0, max=1.0, description='Gradient')\n",
    "progress = jp.Progress(hold=True)\n",
    "controls_row = widgets.HBox([run_button, grad_slider, progress._progressbar])\n",
    "display(controls_row)\n",
    "plot_1 = jp.Plot(\n",
    "    MRI,\n",
    "    title=\"NMR Complex Signal\",\n",
    "    xlabel=\"time (μs)\",\n",
    "    ylabel=\"signal (μV)\",\n",
    "    pipeline=[jp.complex_autophase, jp.complex_to_plot],\n",
    "    height=300\n",
    ")  # displays plot automatically\n",
    "\n",
    "async def run():\n",
    "    MRI.load_par('example_pars/2D_SLICE_MRI.yaml')\n",
    "    MRI.load_par('auto_pars/shims.yaml')\n",
    "    MRI.load_par('auto_pars/frequency.yaml')\n",
    "    MRI.load_par('auto_pars/hardpulse_90.yaml')\n",
    "    MRI.load_par('auto_pars/hardpulse_180.yaml')\n",
    "    MRI.set_par('read_GZ', int(30000*GR))\n",
    "    await MRI.run(progress_handler=jp.multi_update(progress.update, plot_1.update))\n",
    "\n",
    "def on_run_button_clicked(b):\n",
    "    asyncio.ensure_future(run())\n",
    "\n",
    "def on_grad_slider_value_change(change):\n",
    "    global GR\n",
    "    GR = change['new']\n",
    "\n",
    "grad_slider.observe(on_grad_slider_value_change, names='value')\n",
    "run_button.on_click(on_run_button_clicked)"
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   "source": [
    "## Frequency Encoding\n",
    "\n",
    "The information we want to extract is the density of water at any particular location (let's call this $D(z)$), and with that information we can build an image. As mentioned before, introducing a linear gradient in the field has caused the precession frequency to vary linearly with position in one dimension (in this case the vertical, or Z direction). If the magnetic field with no gradient is $B_0$ (Tesla), the gradient strength is $G_z$ (Tesla/meter), and $z=0$ is defined as the centre of the sample, where the gradient has no effect, then we can calculate the precession frequency at any z position:\n",
    "\n",
    "$$ f(z) = \\frac{\\gamma}{2\\pi} \\cdot (B_0 + G_z \\cdot z) $$\n",
    "\n",
    "When we apply the fourier transform to the NMR signal $g(t)$ we obtain a spectrum $G(f)$. The magnitude of the spectrum is proportional to the amount of spins with a particular precession frequency, which is determined by the density of water in the sample, so:\n",
    "\n",
    "$$ D(z) \\propto \\left| G(f(z)) \\right| $$\n",
    "\n",
    "Because $f(z)$ is linear, it shifts and rescales the z axis to become the frequency axis, therefore the magnitude spectrum plot is also a one dimensional image of the water in the sample, just with shifted/rescaled axes."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Experiment: 1D Imaging\n",
    "\n",
    "The same pulse sequence again, but this time with the magnitude spectrum also plotted. There should be two distinct peaks in the spectrum corresponding to the two water cells in the phantom."
   ]
  },
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       "  var render_items = [{\"docid\":\"ca5e8512-fc79-4554-bc50-3ed4eb1ba221\",\"notebook_comms_target\":\"1791\",\"roots\":{\"1723\":\"c6a859ac-c8e7-4cfd-8683-cdcdda0829b4\"}}];\n",
       "  root.Bokeh.embed.embed_items_notebook(docs_json, render_items);\n",
       "\n",
       "  }\n",
       "  if (root.Bokeh !== undefined) {\n",
       "    embed_document(root);\n",
       "  } else {\n",
       "    var attempts = 0;\n",
       "    var timer = setInterval(function(root) {\n",
       "      if (root.Bokeh !== undefined) {\n",
       "        clearInterval(timer);\n",
       "        embed_document(root);\n",
       "      } else {\n",
       "        attempts++;\n",
       "        if (attempts > 100) {\n",
       "          clearInterval(timer);\n",
       "          console.log(\"Bokeh: ERROR: Unable to run BokehJS code because BokehJS library is missing\");\n",
       "        }\n",
       "      }\n",
       "    }, 10, root)\n",
       "  }\n",
       "})(window);"
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      "application/vnd.bokehjs_exec.v0+json": ""
     },
     "metadata": {
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     "output_type": "display_data"
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   ],
   "source": [
    "# NOTE: 1DMRI experiment, plots: Raw + FT magnitude.\n",
    "GR2 = GR_init\n",
    "button2 = widgets.Button(description=\"Run\")\n",
    "grad_slider2 = widgets.FloatSlider(value=GR2, min=0.0, max=1.0, description='Gradient')\n",
    "progress2 = jp.Progress(hold=True)\n",
    "display(widgets.HBox([button2, grad_slider2, progress2._progressbar]))\n",
    "p2a = jp.Plot(MRI,\n",
    "              title=\"Time Domain Complex Signal\",\n",
    "              xlabel=\"time (μs)\",\n",
    "              ylabel=\"signal (μV)\",\n",
    "              pipeline=[jp.complex_autophase, jp.complex_to_plot],\n",
    "              hold=True,\n",
    "              height=300,\n",
    "              toolbar_location='above')\n",
    "p2b = jp.Plot(MRI,\n",
    "              title=\"Frequency Spectrum Magnitude\",\n",
    "              xlabel=\"relative frequency (kHz)\",\n",
    "              ylabel=\"spectral density (μV/kHz)\",\n",
    "              pipeline=[jp.fft, jp.spectrum_mag_plot],\n",
    "              hold=True,\n",
    "              height=300,\n",
    "              toolbar_location='above')\n",
    "notebook_handle = show(row(p2a._figure, p2b._figure), notebook_handle=True)\n",
    "p2a._notebook_handle = notebook_handle\n",
    "p2b._notebook_handle = notebook_handle\n",
    "\n",
    "async def run2():\n",
    "    MRI.load_par('example_pars/2D_SLICE_MRI.yaml')\n",
    "    MRI.load_par('auto_pars/shims.yaml')\n",
    "    MRI.load_par('auto_pars/frequency.yaml')\n",
    "    MRI.load_par('auto_pars/hardpulse_90.yaml')\n",
    "    MRI.load_par('auto_pars/hardpulse_180.yaml')\n",
    "    MRI.set_par('read_GZ', int(30000*GR2))\n",
    "    await MRI.run(progress_handler=jp.multi_update(progress2.update, p2a.update, p2b.update))\n",
    "\n",
    "def on_button_clicked2(b):\n",
    "    asyncio.ensure_future(run2())\n",
    "\n",
    "def on_value_change2(change):\n",
    "    global GR2\n",
    "    GR2 = change['new']\n",
    "\n",
    "grad_slider2.observe(on_value_change2, names='value')\n",
    "button2.on_click(on_button_clicked2)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Review Questions\n",
    "- How does the height of the phantom in the 1D image (above right) change with gradient strength? How does this affect signal-to-noise ratio (SNR)?\n",
    "- How does the spectral width (in kHz) of the phantom in the 1D image change with gradient strength? How does this affect field-of-view (FOV) and spatial resolution?"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "5+5"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
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