{
"cells": [
{
"cell_type": "markdown",
"id": "warming-county",
"metadata": {},
"source": [
"# Diffusion Encoding Gradients Example"
]
},
{
"cell_type": "code",
"execution_count": 1,
"id": "hearing-laundry",
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"Building GrOpt . . .\n"
]
},
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"data": {
"text/html": [
" \n",
" "
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"source": [
"import os\n",
"\n",
"os.chdir(\"./python/\")\n",
"\n",
"import build_gropt\n",
"build_gropt.build_gropt()\n",
"import gropt\n",
"\n",
"from helper_utils import *\n",
"from interactive_plots import plot_waveform_interactive\n",
"from plotly.offline import download_plotlyjs, init_notebook_mode, plot, iplot\n",
"from IPython.core.display import display, HTML\n",
"init_notebook_mode(connected = True)\n",
"config={'showLink': False, 'displayModeBar': False}\n",
"from timeit import default_timer as timer\n",
"\n",
"%matplotlib inline"
]
},
{
"cell_type": "markdown",
"id": "official-gallery",
"metadata": {},
"source": [
"## Constraints on:\n",
"- Maximum gradient amplitude: params['gmax']\n",
"- Maximum slew rate: params['smax']\n",
"- Zero gradient moment = 0 (mT*ms)/m\n",
"- Add objective function to maximize b-value\n",
"- Add constraint to turn gradients off during excitation RF (T_90), refocusing RF (T_180), and ADC readout (T_redout)"
]
},
{
"cell_type": "code",
"execution_count": 2,
"id": "democratic-brass",
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"Minimum TE = 69.06 ms\n"
]
},
{
"data": {
"text/html": [
"\n",
"\n",
"\n",
" \n",
"\n",
""
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"source": [
"params = {}\n",
"params['mode'] = 'diff_bval' # Objective function that maximizes b-value\n",
"params['gmax'] = 50 # Maximum gradient amplitude, mT/m\n",
"params['smax'] = 100 # Maximum slew rate, mT/m/ms\n",
"params['MMT'] = 0 # Nulling M0\n",
"params['T_readout'] = 20 # Time from start to center of readout, ms\n",
"params['T_90'] = 3 # Duration of excitation RF pulse, ms\n",
"params['T_180'] = 5 # Duration of refocusing RF pulse, ms\n",
"params['b'] = 1000 # Diffusion b-value, s/mm^2\n",
"params['dt'] = 400e-6 # Raster time of the gradient waveform being optimized\n",
"\n",
"# Convex Optimized Diffusion Encoding (CODE)\n",
"G_min, T_min = get_min_TE(params, bval=params['b'], min_TE = 40, max_TE = 120)\n",
"print('Minimum TE =', round(T_min,2), 'ms')\n",
"\n",
"fig = plot_waveform_interactive(-1*G_min, params, width=585, height=430)\n",
"plot(fig, filename = 'fig.html', config = config)\n",
"display(HTML('fig.html'))"
]
},
{
"cell_type": "markdown",
"id": "manual-dining",
"metadata": {},
"source": [
"## M0 Nulled CODE\n",
"\n",
"Generate a waveform with $M_0 = 0$, other parameters as listed in the code.\n",
"\n",
"TE was manually selected (44.4 ms) to hit b-value = 600"
]
},
{
"cell_type": "code",
"execution_count": 3,
"id": "cooked-applicant",
"metadata": {},
"outputs": [
{
"data": {
"text/html": [
"\n",
"\n",
"\n",
" \n",
"\n",
""
],
"text/plain": [
""
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"params = {}\n",
"# Maximize b-value for diffusion waveforms\n",
"params['mode'] = 'diff_bval'\n",
"\n",
"# Hardware constraints\n",
"params['gmax'] = 50.0 # Max Gradient Amplitude [mT/m], you can use T/m here too\n",
"params['smax'] = 50.0 # Max Slewrate [mT/m/ms]\n",
"\n",
"# Moment nulling\n",
"params['MMT'] = 0\n",
"\n",
"# Sequence TE and dt of output [ms]\n",
"params['TE'] = 60\n",
"params['dt'] = 400e-6\n",
"\n",
"# Time from end of diffusion waveform to TE [ms]\n",
"params['T_readout'] = 16.0\n",
"# Time of excitation 90 [ms]\n",
"params['T_90'] = 4.0\n",
"# Time for 180 flip [ms]\n",
"params['T_180'] = 6.0\n",
"\n",
"# Run optimization\n",
"G, dd = gropt.gropt(params, verbose=1)\n",
"fig = plot_waveform_interactive(G, params, width=585, height=430)\n",
"plot(fig, filename = 'fig.html', config = config)\n",
"display(HTML('fig.html')) "
]
},
{
"cell_type": "markdown",
"id": "compact-reservoir",
"metadata": {},
"source": [
"## M0+M1 Nulled CODE\n",
"\n",
"Generate a waveform with $M_0 = 0$ and $M_1 = 0$, other parameters as listed in the code.\n",
"\n",
"TE was manually selected (82 ms) to hit b-value = 600"
]
},
{
"cell_type": "code",
"execution_count": 4,
"id": "enhanced-proportion",
"metadata": {},
"outputs": [
{
"data": {
"text/html": [
"\n",
"\n",
"\n",
" \n",
"\n",
""
],
"text/plain": [
""
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"params = {}\n",
"params['mode'] = 'diff_bval'\n",
"params['gmax'] = 0.05\n",
"params['smax'] = 50.0\n",
"params['MMT'] = 1\n",
"params['TE'] = 82.0\n",
"params['T_readout'] = 16.0\n",
"params['T_90'] = 4.0\n",
"params['T_180'] = 6.0\n",
"params['dt'] = 200e-6\n",
"\n",
"G, dd = gropt.gropt(params, verbose=1)\n",
"\n",
"fig = plot_waveform_interactive(G, params, width=585, height=430)\n",
"plot(fig, filename = 'fig.html', config = config)\n",
"display(HTML('fig.html'))"
]
},
{
"cell_type": "markdown",
"id": "frequent-paris",
"metadata": {},
"source": [
"Constraining $M_0 = M_1 = 0$ for conventional and optimized diffusion encoding methods mitigate signal losses, due to constant moving tissue"
]
},
{
"cell_type": "markdown",
"id": "occupied-ghost",
"metadata": {},
"source": [
"## M0+M1+M2 Nulled CODE\n",
"\n",
"Generate a waveform with $M_0 = 0$, $M_1 = 0$ and $M_2 = 0$, other parameters as listed in the code.\n",
"\n",
"TE was manually selected (97 ms) to hit b-value = 600"
]
},
{
"cell_type": "code",
"execution_count": 5,
"id": "egyptian-edwards",
"metadata": {},
"outputs": [
{
"data": {
"text/html": [
"\n",
"\n",
"\n",
" \n",
"\n",
""
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"text/plain": [
""
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"metadata": {},
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"source": [
"params = {}\n",
"params['mode'] = 'diff_bval'\n",
"params['gmax'] = 0.05\n",
"params['smax'] = 50.0\n",
"params['MMT'] = 2\n",
"params['TE'] = 97.0\n",
"params['T_readout'] = 16.0\n",
"params['T_90'] = 4.0\n",
"params['T_180'] = 6.0\n",
"params['dt'] = 200e-6\n",
"\n",
"G, dd = gropt.gropt(params, verbose=1)\n",
"\n",
"fig = plot_waveform_interactive(G, params, width=585, height=430)\n",
"plot(fig, filename = 'fig.html', config = config)\n",
"display(HTML('fig.html'))"
]
},
{
"cell_type": "markdown",
"id": "convenient-paris",
"metadata": {},
"source": [
"Constraining $M_0 = M_1 = M_2 = 0$ for conventional and optimized diffusion encoding methods mitigate signal losses, due to constant moving **and** accelerating tissue"
]
},
{
"cell_type": "markdown",
"id": "novel-relative",
"metadata": {},
"source": [
"#### We constrain to null for a specific eddy current time constants (lambda) to null diffusion incuded eddy current"
]
},
{
"cell_type": "code",
"execution_count": 6,
"id": "adapted-binary",
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"Minimum TE = 88.2 ms\n"
]
},
{
"data": {
"text/html": [
"\n",
"\n",
"\n",
" \n",
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