diff --git a/README.md b/README.md index 97e88c8..3c05804 100644 --- a/README.md +++ b/README.md @@ -21,6 +21,7 @@ Created 28 September 2020 - Signal models: spoiled gradient echo - Water exchange models: FXL, NXL, NXL_be - T1 fitting using variable flip angle method, IR-SPGR and DESPOT1-HIFI +- T2(*) fitting for multi-TE acquisitions ### Not yet implemented/limitations: - Additional pharmacokinetic models (add by inheriting from PkModel class) diff --git a/demo/T2s_data/mag4D.nii b/demo/T2s_data/mag4D.nii new file mode 100644 index 0000000..6651356 Binary files /dev/null and b/demo/T2s_data/mag4D.nii differ diff --git a/demo/demo_fit_dce.ipynb b/demo/demo_fit_dce.ipynb index 3f59d90..114eac8 100644 --- a/demo/demo_fit_dce.ipynb +++ b/demo/demo_fit_dce.ipynb @@ -603,4 +603,4 @@ }, "nbformat": 4, "nbformat_minor": 5 -} +} \ No newline at end of file diff --git a/demo/demo_fit_t1.ipynb b/demo/demo_fit_t1.ipynb index abd1125..3ca7b88 100644 --- a/demo/demo_fit_t1.ipynb +++ b/demo/demo_fit_t1.ipynb @@ -3,7 +3,11 @@ { "cell_type": "markdown", "id": "b276d3b1-a112-4af7-97aa-994466f62f4a", - "metadata": {}, + "metadata": { + "pycharm": { + "name": "#%% md\n" + } + }, "source": [ "## T1 Fitting\n", "The t1_fit module contains classes for estimating T1. Both these and the classes in dce_fit are subclasses of Fitter, which means they can be used to fit a single T1 value (using the proc method) or an entire image (using the proc_image method)." @@ -13,7 +17,11 @@ "cell_type": "code", "execution_count": 1, "id": "affected-indonesia", - "metadata": {}, + "metadata": { + "pycharm": { + "name": "#%%\n" + } + }, "outputs": [], "source": [ "import os, sys\n", @@ -28,24 +36,30 @@ { "cell_type": "markdown", "id": "a426b25f-88e1-4a32-a627-675243e26cef", - "metadata": {}, + "metadata": { + "pycharm": { + "name": "#%% md\n" + } + }, "source": [ - "## T1 estimation methods (one value)\n", + "## T1 estimation methods (single value)\n", "The variable flip angle method estimates T1, using the relationship between flip angle, T1 and SPGR signal:" ] }, { "cell_type": "code", - "execution_count": 18, + "execution_count": 2, "id": "8b7c6e63-f4d1-4ea5-bbb8-a932d4862063", - "metadata": {}, + "metadata": { + "pycharm": { + "name": "#%%\n" + } + }, "outputs": 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\n", 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\n" }, "metadata": { "needs_background": "light" @@ -67,7 +81,11 @@ { "cell_type": "markdown", "id": "8cc53336-53ef-4cc3-aad3-0d4ef3c8784f", - "metadata": {}, + "metadata": { + "pycharm": { + "name": "#%% md\n" + } + }, "source": [ "#### Variable flip angle mapping (2 x flip angles)\n", "The simplest approach is to estimate T1 from two SPGR acquisitions with different flip angles. This is fastest but least precise method:" @@ -75,9 +93,13 @@ }, { "cell_type": "code", - "execution_count": 19, + "execution_count": 3, "id": "193be578-c800-49f2-839d-43466d273ff4", - "metadata": {}, + "metadata": { + "pycharm": { + "name": "#%%\n" + } + }, "outputs": [ { "name": "stdout", @@ -89,10 +111,8 @@ }, { "data": { - "image/png": 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\n", 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\n" }, "metadata": { "needs_background": "light" @@ -119,7 +139,11 @@ { "cell_type": "markdown", "id": "991c0e6c-56c1-4169-94d1-82d787ae5a62", - "metadata": {}, + "metadata": { + "pycharm": { + "name": "#%% md\n" + } + }, "source": [ "#### Variable flip angle (based on 3 x flip angles)\n", "Fit multiple acquisitions using the **linear regression** method (moderately fast, moderately accurate):" @@ -127,24 +151,26 @@ }, { "cell_type": "code", - "execution_count": 20, + "execution_count": 4, "id": "9af5810a-3cc9-4f2f-8350-5f8c182dd148", - "metadata": {}, + "metadata": { + "pycharm": { + "name": "#%%\n" + } + }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ - "Wall time: 959 µs\n", + "Wall time: 0 ns\n", "Fitted values: s0 = 13531.9, t1 = 1.326 s\n" ] }, { "data": { - "image/png": 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\n", 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\n" }, "metadata": { "needs_background": "light" @@ -171,31 +197,37 @@ { "cell_type": "markdown", "id": "433727e1-0f92-41c9-b49b-88f11358c704", - "metadata": {}, + "metadata": { + "pycharm": { + "name": "#%% md\n" + } + }, "source": [ "Now fit using the **non-linear** method (slowest, most accurate):" ] }, { "cell_type": "code", - "execution_count": 21, + "execution_count": 5, "id": "04a39172-427f-4b0e-ba85-e0870d0a2e3d", - "metadata": {}, + "metadata": { + "pycharm": { + "name": "#%%\n" + } + }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ - "Wall time: 1.99 ms\n", + "Wall time: 0 ns\n", "Fitted values: s0 = 13482.2, t1 = 1.323 s\n" ] }, { "data": { - "image/png": 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\n", 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\n" }, "metadata": { "needs_background": "light" @@ -222,7 +254,11 @@ { "cell_type": "markdown", "id": "a00eb683-0158-4fa1-b62d-ee4b14004235", - "metadata": {}, + "metadata": { + "pycharm": { + "name": "#%% md\n" + } + }, "source": [ "#### DESPOT1-HIFI method\n", "T1 can be estimated using a combination of SPGR (FLASH) and IR-SPGR (MP-RAGE) acquisitions. This technique also estimates the relative flip angle k_fa (nominal/actual FA). Now add 2 x IR-SPGR acquisitions to the previous 3 x SPGR scans. We now have 5 x acquisitions. All parameters are specified for each acquisition." @@ -230,24 +266,26 @@ }, { "cell_type": "code", - "execution_count": 22, + "execution_count": 6, "id": "5ac0739a-72e7-476b-aa69-f1bebf7cc32b", - "metadata": {}, + "metadata": { + "pycharm": { + "name": "#%%\n" + } + }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ - "Wall time: 2.91 ms\n", + "Wall time: 15.6 ms\n", "Fitted values: s0 = 11856.2, t1 = 1.022 s, k_fa = 1.138\n" ] }, { "data": { - "image/png": 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\n", 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\n" }, "metadata": { "needs_background": "light" @@ -280,7 +318,11 @@ { "cell_type": "markdown", "id": "480d8d69-def2-47cf-a364-6ab5fe7e2b64", - "metadata": {}, + "metadata": { + "pycharm": { + "name": "#%% md\n" + } + }, "source": [ "### Reference values\n", "Obtained from fitting DESPOT1-HIFI signal in Matlab:\n", @@ -294,7 +336,10 @@ "cell_type": "markdown", "id": "546d8b07-8a1d-4953-899f-6c9cd93aef0e", "metadata": { - "tags": [] + "tags": [], + "pycharm": { + "name": "#%% md\n" + } }, "source": [ "---\n", @@ -312,9 +357,13 @@ }, { "cell_type": "code", - "execution_count": 20, + "execution_count": 7, "id": "5eeef16b-f46d-4fca-87c9-d11f10912e7c", - "metadata": {}, + "metadata": { + "pycharm": { + "name": "#%%\n" + } + }, "outputs": [], "source": [ "vfa_fitter = t1_fit.VFALinear(fa=[2, 5, 12], tr=5.4e-3)" @@ -323,16 +372,24 @@ { "cell_type": "markdown", "id": "b6c7d146-c613-4a54-b933-17e26e0052b8", - "metadata": {}, + "metadata": { + "pycharm": { + "name": "#%% md\n" + } + }, "source": [ "Now use the proc_image method to fit every voxel and generate output images:" ] }, { "cell_type": "code", - "execution_count": 22, + "execution_count": 8, "id": "36b6e9cd-81c7-498d-91b9-d6df2e472963", - "metadata": {}, + "metadata": { + "pycharm": { + "name": "#%%\n" + } + }, "outputs": [], "source": [ "images = [os.path.join('.', 'T1_data', img) for img in ['FA2.nii.gz', 'FA5.nii.gz', 'FA12.nii.gz']]\n", @@ -342,16 +399,18 @@ }, { "cell_type": "code", - "execution_count": 24, + "execution_count": 10, "id": "a416a658-a7cf-4aa1-b90b-86b978ad7c3d", - "metadata": {}, + "metadata": { + "pycharm": { + "name": "#%%\n" + } + }, "outputs": [ { "data": { - "image/png": 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\n", 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\n" }, "metadata": { "needs_background": "light" @@ -361,14 +420,18 @@ ], "source": [ "fig, ax = plt.subplots(1,2)\n", - "ax[0].imshow(s0[78,:,:], cmap=\"gray\", origin=\"lower\", vmin=0, vmax=3000)\n", - "ax[1].imshow(t1[78,:,:], cmap=\"gray\", origin=\"lower\", vmin=0, vmax=2);" + "ax[0].imshow(s0[78,:,:], cmap=\"gray_r\", origin=\"lower\", vmin=0, vmax=3000)\n", + "ax[1].imshow(t1[78,:,:], cmap=\"gray_r\", origin=\"lower\", vmin=0, vmax=2);" ] }, { "cell_type": "markdown", "id": "878fb9fb-aca8-49af-88fb-bae3c32c6284", - "metadata": {}, + "metadata": { + "pycharm": { + "name": "#%% md\n" + } + }, "source": [ "### DESPOT1-HIFI\n", "Now fit all 5 scans using the DESPOT1-HIFI method." @@ -376,9 +439,13 @@ }, { "cell_type": "code", - "execution_count": 25, + "execution_count": 11, "id": "8ea99231-2eb7-467d-bdf5-3bd41df917d4", - "metadata": {}, + "metadata": { + "pycharm": { + "name": "#%%\n" + } + }, "outputs": [], "source": [ "hifi_fitter = t1_fit.HIFI(esp = np.array([5.4e-3, 5.4e-3, 5.4e-3, 5.4e-3, 5.4e-3]),\n", @@ -392,16 +459,24 @@ { "cell_type": "markdown", "id": "4187ebad-4a54-4a35-9516-7347ad6f3b2c", - "metadata": {}, + "metadata": { + "pycharm": { + "name": "#%% md\n" + } + }, "source": [ "To save time, use multple cores and supply a mask image to process a subset of voxels:" ] }, { "cell_type": "code", - "execution_count": 26, + "execution_count": 12, "id": "1d0efe83-3a94-4592-b201-b31eec8e512c", - "metadata": {}, + "metadata": { + "pycharm": { + "name": "#%%\n" + } + }, "outputs": [], "source": [ "images = [os.path.join('.', 'T1_data', img) for img in ['TI_168ms.nii.gz', 'TI_1068ms.nii.gz', 'FA2.nii.gz', 'FA5.nii.gz', 'FA12.nii.gz']]\n", @@ -416,16 +491,18 @@ }, { "cell_type": "code", - "execution_count": 46, + "execution_count": 13, "id": "83d0b631-c849-4a7d-b086-850a9583dba5", - "metadata": {}, + "metadata": { + "pycharm": { + "name": "#%%\n" + } + }, "outputs": [ { "data": { - "image/png": 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\n", 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\n" }, "metadata": { "needs_background": "light" @@ -435,9 +512,9 @@ ], "source": [ "fig, ax = plt.subplots(1,3)\n", - "ax[0].imshow(s0[78,:,:], cmap=\"gray\", origin=\"lower\", vmin=0, vmax=3000)\n", - "ax[1].imshow(t1[78,:,:], cmap=\"gray\", origin=\"lower\", vmin=0, vmax=2)\n", - "ax[2].imshow(k_fa[78,:,:], cmap=\"gray\", origin=\"lower\", vmin=0, vmax=1.5);" + "ax[0].imshow(s0[78,:,:], cmap=\"gray_r\", origin=\"lower\", vmin=0, vmax=3000)\n", + "ax[1].imshow(t1[78,:,:], cmap=\"gray_r\", origin=\"lower\", vmin=0, vmax=2)\n", + "ax[2].imshow(k_fa[78,:,:], cmap=\"gray_r\", origin=\"lower\", vmin=0, vmax=1.5);" ] } ], @@ -462,4 +539,4 @@ }, "nbformat": 4, "nbformat_minor": 5 -} +} \ No newline at end of file diff --git a/demo/demo_fit_t2s.ipynb b/demo/demo_fit_t2s.ipynb new file mode 100644 index 0000000..0d99620 --- /dev/null +++ b/demo/demo_fit_t2s.ipynb @@ -0,0 +1,232 @@ +{ + "cells": [ + { + "cell_type": "markdown", + "source": [ + "## T2* Fitting\n", + "The t2star_fit module contains classes for estimating T2* or T2. Both these and the classes in dce_fit are subclasses of Fitter, which means they can be used to fit a single T2* value (using the proc method) or an entire image (using the proc_image method)." + ], + "metadata": { + "collapsed": false, + "pycharm": { + "name": "#%% md\n" + } + } + }, + { + "cell_type": "code", + "execution_count": 1, + "outputs": [], + "source": [ + "import os, sys\n", + "import numpy as np\n", + "import matplotlib.pyplot as plt\n", + "sys.path.append('../src')\n", + "import t2star_fit\n", + "%load_ext autoreload\n", + "%autoreload 2" + ], + "metadata": { + "collapsed": false, + "pycharm": { + "name": "#%%\n" + } + } + }, + { + "cell_type": "markdown", + "source": [ + "## T2* estimation methods\n", + "The method estimates T2*, using the exponential relationship between echo time and signal:" + ], + "metadata": { + "collapsed": false, + "pycharm": { + "name": "#%% md\n" + } + } + }, + { + "cell_type": "code", + "execution_count": 2, + "outputs": [ + { + "data": { + "text/plain": "
", + "image/png": 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\n" + }, + "metadata": { + "needs_background": "light" + }, + "output_type": "display_data" + } + ], + "source": [ + "te_range = np.linspace(0, 100e-3, 50)\n", + "s_range_1 = t2star_fit.multiecho_signal(s0=100, t2s=10e-3, te=te_range)\n", + "s_range_2 = t2star_fit.multiecho_signal(s0=100, t2s=20e-3, te=te_range)\n", + "plt.plot(te_range, s_range_1, '-', label='s0=100, t2s=0.01 s')\n", + "plt.plot(te_range, s_range_2, '-', label='s0=100, t2s=0.02 s')\n", + "plt.xlabel('TE (s)')\n", + "plt.ylabel('signal');\n", + "plt.legend();" + ], + "metadata": { + "collapsed": false, + "pycharm": { + "name": "#%%\n" + } + } + }, + { + "cell_type": "markdown", + "source": [ + "### T2* fitting: single voxel" + ], + "metadata": { + "collapsed": false, + "pycharm": { + "name": "#%% md\n" + } + } + }, + { + "cell_type": "code", + "execution_count": 35, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Wall time: 0 ns\n", + "Fitted values (linear): s0 = 61.4, t2s = 0.0091 s\n", + "Wall time: 10.1 ms\n", + "Fitted values (non-linear): s0 = 97.6, t2s = 0.0080 s\n" + ] + }, + { + "data": { + "text/plain": "
", + "image/png": 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\n" + }, + "metadata": { + "needs_background": "light" + }, + "output_type": "display_data" + } + ], + "source": [ + "# Generate test data:\n", + "s0, t2s = 100, 8e-3\n", + "te = np.linspace(10e-3, 50e-3, 10)\n", + "te_plot_range = np.linspace(min(te), max(te), 100)\n", + "\n", + "s = np.abs(s0 * np.exp(-te/t2s) + 1 * np.random.randn(*te.shape))\n", + "\n", + "# Fit test data\n", + "min_signal = 0 # ignore echoes with signal lower than this\n", + "\n", + "%time s0_est_lin, t2s_est_lin = t2star_fit.MultiEchoT2sLinear(te, min_signal).proc(s)\n", + "print(f\"Fitted values (linear): s0 = {s0_est_lin:.1f}, t2s = {t2s_est_lin:.4f} s\")\n", + "%time s0_est_nonlin, t2s_est_nonlin = t2star_fit.MultiEchoT2sNonLinear(te, min_signal).proc(s)\n", + "print(f\"Fitted values (non-linear): s0 = {s0_est_nonlin:.1f}, t2s = {t2s_est_nonlin:.4f} s\")\n", + "\n", + "# Plot data:\n", + "plt.plot(te_plot_range, t2star_fit.multiecho_signal(s0_est_lin, t2s_est_lin, te_plot_range), '-', label='linear model')\n", + "plt.plot(te_plot_range, t2star_fit.multiecho_signal(s0_est_nonlin, t2s_est_nonlin, te_plot_range), '-', label='non-linear model')\n", + "plt.plot(te, s, 'o', label='signal')\n", + "plt.xlabel('TE (s)')\n", + "plt.ylabel('signal');\n", + "plt.legend();" + ], + "metadata": { + "collapsed": false, + "pycharm": { + "name": "#%%\n" + } + } + }, + { + "cell_type": "markdown", + "source": [ + "### T2* fitting: fit 4D phantom data to generate a T2* map" + ], + "metadata": { + "collapsed": false, + "pycharm": { + "name": "#%% md\n" + } + } + }, + { + "cell_type": "code", + "execution_count": 4, + "outputs": [], + "source": [ + "# create T2* fitter object (non-linear method) as before\n", + "te = np.array((0.0030, 0.0085, 0.0140, 0.0195, 0.0250, 0.0305, 0.0360, 0.0415))\n", + "t2star_fitter = t2star_fit.MultiEchoT2sLinear(te, min_signal=50)\n", + "\n", + "# use the proc_image to loop through all voxels in image\n", + "s0_map, t2s_map = t2star_fitter.proc_image('./T2s_data/mag4D.nii', threshold=200, dir='.', suffix='_linear', n_procs=3);" + ], + "metadata": { + "collapsed": false, + "pycharm": { + "name": "#%%\n" + } + } + }, + { + "cell_type": "code", + "execution_count": 34, + "outputs": [ + { + "data": { + "text/plain": "
", + "image/png": 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\n" + }, + "metadata": { + "needs_background": "light" + }, + "output_type": "display_data" + } + ], + "source": [ + "fig, ax = plt.subplots(1,2)\n", + "ax[0].imshow(s0_map[:,:,36], cmap=\"gray_r\", origin=\"lower\", vmin=0, vmax=2000)\n", + "ax[0].set_title('s0')\n", + "cax = ax[1].imshow(t2s_map[:,:,36], cmap=\"gray_r\", origin=\"lower\", vmin=0, vmax=0.2)\n", + "ax[1].set_title('T2*')\n", + "fig.colorbar(cax);" + ], + "metadata": { + "collapsed": false, + "pycharm": { + "name": "#%%\n" + } + } + } + ], + "metadata": { + "kernelspec": { + "display_name": "Python 3", + "language": "python", + "name": "python3" + }, + "language_info": { + "codemirror_mode": { + "name": "ipython", + "version": 2 + }, + "file_extension": ".py", + "mimetype": "text/x-python", + "name": "python", + "nbconvert_exporter": "python", + "pygments_lexer": "ipython2", + "version": "2.7.6" + } + }, + "nbformat": 4, + "nbformat_minor": 0 +} \ No newline at end of file diff --git a/demo/demo_imaging_utilities.ipynb b/demo/demo_imaging_utilities.ipynb new file mode 100644 index 0000000..b8f7fcf --- /dev/null +++ b/demo/demo_imaging_utilities.ipynb @@ -0,0 +1,118 @@ +{ + "cells": [ + { + "cell_type": "markdown", + "source": [ + "## ROI measure\n", + "Simple functions to read and write images, and extract numbers from images using ROI masks." + ], + "metadata": { + "collapsed": false, + "pycharm": { + "name": "#%% md\n" + } + } + }, + { + "cell_type": "code", + "execution_count": 2, + "outputs": [], + "source": [ + "import os, sys\n", + "import numpy as np\n", + "import matplotlib.pyplot as plt\n", + "sys.path.append('../src')\n", + "from utils.imaging import read_images, write_image, roi_measure\n", + "%load_ext autoreload\n", + "%autoreload 2" + ], + "metadata": { + "collapsed": false, + "pycharm": { + "name": "#%%\n" + } + } + }, + { + "cell_type": "markdown", + "source": [ + "### *roi_measure*\n", + "Use a mask image to extract the VIF signal from a 4D DCE-MRI image.\n", + "Image and mask can be nii images or numpy arrays.\n", + "If the image has the same shape as the mask, a single set of statistics is returned.\n", + "If the image has one additional dimension (e.g. time series) then a series of values are returned corresponding to locations in the last dimension.\n", + "Time-series images can also be provided as a *list* of images, e.g. 1 image for each time frame." + ], + "metadata": { + "collapsed": false, + "pycharm": { + "name": "#%% md\n" + } + } + }, + { + "cell_type": "code", + "execution_count": 15, + "outputs": [ + { + "data": { + "text/plain": "
", + "image/png": 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\n" + }, + "metadata": { + "needs_background": "light" + }, + "output_type": "display_data" + } + ], + "source": [ + "roi_stats = roi_measure(image=r'C:\\TEMP\\rDCE.nii', mask_image=r'C:\\TEMP\\VIF.nii')\n", + "plt.plot(roi_stats['mean'], label='mean')\n", + "plt.plot(roi_stats['median'], label='median')\n", + "plt.plot(roi_stats['sd'], label='standard deviation')\n", + "plt.legend();" + ], + "metadata": { + "collapsed": false, + "pycharm": { + "name": "#%%\n" + } + } + }, + { + "cell_type": "markdown", + "source": [ + "### *read_images* and *write_image*\n", + "These are simply wrapper functions for *nibabel*.\n", + "See docstrings for details." + ], + "metadata": { + "collapsed": false, + "pycharm": { + "name": "#%% md\n" + } + } + } + ], + "metadata": { + "kernelspec": { + "display_name": "Python 3", + "language": "python", + "name": "python3" + }, + "language_info": { + "codemirror_mode": { + "name": "ipython", + "version": 2 + }, + "file_extension": ".py", + "mimetype": "text/x-python", + "name": "python", + "nbconvert_exporter": "python", + "pygments_lexer": "ipython2", + "version": "2.7.6" + } + }, + "nbformat": 4, + "nbformat_minor": 0 +} \ No newline at end of file diff --git a/src/t2star_fit.py b/src/t2star_fit.py new file mode 100644 index 0000000..617cf12 --- /dev/null +++ b/src/t2star_fit.py @@ -0,0 +1,167 @@ +"""Functions to fit MRI SPGR signal to obtain T2* or T2. + +Created 17 October 2023 +@authors: Michael Thrippleton +@email: m.j.thrippleton@ed.ac.uk +@institution: University of Edinburgh, UK + +Classes: + MultiEchoT2sLinear + MultiEchoT2sNonLinear + +Functions: + multiecho_signal: get signal +""" + +import numpy as np +from scipy.optimize import least_squares +from fitting import Fitter + + +class MultiEchoT2sLinear(Fitter): + """Linear multi-echo T2* estimation. + + Subclass of Fitter. + """ + + def __init__(self, te, min_signal=0.): + """ + + Args: + te (ndarray): 1D array containing the echo times (s) + min_signal (float): exclude echoes where signal is below this + value. Defaults to zero. + + """ + self.te = te + self.min_signal = min_signal + + def output_info(self): + """Get output info. Overrides superclass method. + """ + return ('s0', False), ('t2s', False) + + def proc(self, s): + """Estimate T2*. Overrides superclass method. + + Args: + s (ndarray): 1D array containing the signals + + Returns: + tuple: (s0, t1) + s0 (float): signal without T2* decay + t2s (float): T2* (s) + + """ + if any(np.isnan(s)): + raise ArithmeticError( + f'Unable to calculate T2s: nan signal received.') + + te_mask = s > self.min_signal + if np.sum(te_mask) < 2: + raise ArithmeticError( + f'Unable to calculate T2s: fewer than 2 included TE values.') + + y = np.log(s[te_mask]) + x = self.te[te_mask] + A = np.stack([x, np.ones(x.shape)], axis=1) + slope, intercept = np.linalg.lstsq(A, y, rcond=None)[0] + + if (intercept < 0) or (0. < slope): + raise ArithmeticError('T2s estimation failed.') + + t2s, s0 = -1. / slope, np.exp(intercept) + + return s0, t2s + + +class MultiEchoT2sNonLinear(Fitter): + """Non-linear multi-echo T2* estimation. + + Subclass of Fitter. + """ + + def __init__(self, te, min_signal=0.): + """ + + Args: + te (ndarray): 1D array containing the echo times (s) + min_signal (float): exclude echoes where signal is below this + value. Defaults to zero. + + """ + self.te = te + self.min_signal = min_signal + self.linear_fitter = MultiEchoT2sLinear(te, min_signal) + + def output_info(self): + """Get output info. Overrides superclass method. + """ + return ('s0', False), ('t2s', False) + + def proc(self, s): + """Estimate T2*. Overrides superclass method. + + Args: + s (ndarray): 1D array containing the signals + + Returns: + tuple: (s0, t1) + s0 (float): signal without T2* decay + t2s (float): T2* (s) + + """ + if any(np.isnan(s)): + raise ArithmeticError( + f'Unable to calculate T2s: nan signal received.') + + te_mask = s > self.min_signal + if np.sum(te_mask) < 2: + raise ArithmeticError( + f'Unable to calculate T2s: fewer than 2 included TE values.') + + # use linear fit to obtain initial guess, otherwise set arbitrary values + try: + x0 = np.array(self.linear_fitter.proc(s)) + except ArithmeticError: + x0 = np.array([s[0], 10e-3]) + + s = s[te_mask] + te = self.te[te_mask] + + result = least_squares(self.__residuals, x0, args=(s, te), bounds=( + (1e-8, 1e-8), (np.inf, np.inf)), method='trf', x_scale=x0) + if result.success is False: + raise ArithmeticError(f'Unable to fit multiecho data:' + f' {result.message}') + + s0, t2s = result.x + return s0, t2s + + @staticmethod + def __residuals(x, s, te): + s0, t2s = x + s_est = multiecho_signal(s0, t2s, te) + return s - s_est + + +def multiecho_signal(s0, t2s, te): + """Return signal for multiple echoes / echo times. + + Parameters + ---------- + s0 : float + Signal without T2/T2* decay. + t2s : float + T2*/T2 value (s). + te : float + TE value (s). + + Returns + ------- + s : float + Signal. + """ + s = s0 * np.exp(-te/t2s) + + return s