{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "## Preparation" ] }, { "cell_type": "code", "execution_count": 2, "metadata": {}, "outputs": [], "source": [ "%matplotlib inline\n", "import nibabel as nib\n", "import numpy as np\n", "import pandas as pd\n", "import statsmodels.formula.api as smf\n", "import matplotlib.pyplot as plt\n", "plt.style.use('ggplot')" ] }, { "cell_type": "code", "execution_count": 3, "metadata": {}, "outputs": [], "source": [ "%%bash\n", "# download all the necessary files\n", "\n", "# noise_idx\n", "wget -q -O sub-controlGE140_ses-pre_task-flanker_bold_AROMAnoiseICs.csv https://osf.io/ye3dm/download/\n", "# melodic_mix\n", "wget -q -O sub-controlGE140_ses-pre_task-flanker_bold_MELODICmix.tsv https://osf.io/dq6jz/download/\n", "# brainmask\n", "wget -q -O sub-controlGE140_ses-pre_task-flanker_bold_space-MNI152NLin2009cAsym_brainmask.nii.gz https://osf.io/vp8xz/download/\n", "# raw_img (fmriprep output)\n", "wget -q -O sub-controlGE140_ses-pre_task-flanker_bold_space-MNI152NLin2009cAsym_preproc.nii.gz https://osf.io/wtzde/download/\n", "# denoised_smooth_img (fmriprep output with --use-aroma)\n", "wget -q -O sub-controlGE140_ses-pre_task-flanker_bold_space-MNI152NLin2009cAsym_variant-smoothAROMAnonaggr_preproc.nii.gz https://osf.io/kb468/download/\n", "# denoised_img (calculated via fsl_regfilt with melodic_mix and noise_ics)\n", "wget -q -O sub-controlGE140_ses-pre_task-flanker_bold_space-MNI152NLin2009cAsym_variant-AROMAnonaggr_preproc.nii.gz https://osf.io/jyfxs/download/" ] }, { "cell_type": "code", "execution_count": 4, "metadata": {}, "outputs": [], "source": [ "# load all the files into python\n", "noise_idx = np.loadtxt('./sub-controlGE140_ses-pre_task-flanker_bold_AROMAnoiseICs.csv', delimiter=\",\", dtype='int') - 1\n", "melodic_mix = np.loadtxt('./sub-controlGE140_ses-pre_task-flanker_bold_MELODICmix.tsv')\n", "\n", "# brainmask\n", "brainmask_img = nib.load('./sub-controlGE140_ses-pre_task-flanker_bold_space-MNI152NLin2009cAsym_brainmask.nii.gz')\n", "brainmask_data = brainmask_img.get_data().astype(bool)\n", "\n", "# fmriprep output\n", "raw_img = nib.load('./sub-controlGE140_ses-pre_task-flanker_bold_space-MNI152NLin2009cAsym_preproc.nii.gz')\n", "raw_data = raw_img.get_data()\n", "raw_data_masked = raw_data[brainmask_data]\n", "\n", "# fmriprep output (denoised with ica-aroma)\n", "denoised_smooth_img = nib.load('./sub-controlGE140_ses-pre_task-flanker_bold_space-MNI152NLin2009cAsym_variant-smoothAROMAnonaggr_preproc.nii.gz')\n", "denoised_smooth_data = denoised_smooth_img.get_data()\n", "denoised_smooth_data_masked = denoised_smooth_data[brainmask_data]\n", "\n", "# calculated with fsl_regfilt\n", "denoised_img = nib.load('./sub-controlGE140_ses-pre_task-flanker_bold_space-MNI152NLin2009cAsym_variant-AROMAnonaggr_preproc.nii.gz')\n", "denoised_data = denoised_img.get_data()\n", "denoised_data_masked = denoised_data[brainmask_data]\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## reproduce Chris's python version of non-aggressive denoising" ] }, { "cell_type": "code", "execution_count": 5, "metadata": {}, "outputs": [], "source": [ "# split melodic_mix into noise and signal components\n", "noise_components = melodic_mix[:,noise_idx]\n", "signal_components = np.delete(melodic_mix, noise_idx, axis=1)\n", "\n", "# reorganize the components into design\n", "design = np.ones((315, 74))\n", "design[:, 1:11] = signal_components\n", "design[:, 12:74] = noise_components\n", "unmixMatrix = np.linalg.pinv(design)\n", "\n", "maps = np.dot(raw_data_masked, unmixMatrix.T)\n", "noisemap = maps[:,np.r_[12:74]]\n", "nonagg_res = np.dot(noise_components, noisemap.T)\n", "newData_nonagg = raw_data_masked - nonagg_res.T" ] }, { "cell_type": "code", "execution_count": 6, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "6.10352090006927e-05" ] }, "execution_count": 6, "metadata": {}, "output_type": "execute_result" } ], "source": [ "# compare newData_nonagg with denoised_data_masked\n", "np.max(newData_nonagg - denoised_data_masked)\n", "# they are almost identical, just rounding error differences.\n", "# yay! confirms Chris's code" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Testing\n", "If I perform global signal regression, I can pull the average signal either from the raw_data (as is currently done in fmriprep) or I can pull it from the denoised_data. Then I can regress the global signal (either derived from the raw_data_masked or from the denoised_data_masked) from a test voxel in the denoised_data_mask dataset. Theoretically, the residual from such an analysis should be the same whether the global signal was calculated with raw_data_masked or denoised_data_masked. The regression would result in the same outcome because the only additional variance represented in the gs_raw that isn't represented in gs_denoised is the variance associated with the noise components, which denoised_data_masked is already orthagonal to meaning that additional variance shouldn't have an impact on the data.\n", "\n", "**H0:** `y ~ gs_raw == y ~ gs_denoised`\n", "\n", "**H1:** `y ~ gs_raw != y ~ gs_denoised`" ] }, { "cell_type": "code", "execution_count": 7, "metadata": {}, "outputs": [], "source": [ "# global signal\n", "gs_raw = np.mean(raw_data_masked, axis=0)\n", "gs_denoised = np.mean(denoised_data_masked, axis=0)\n", "\n", "# example voxel from the denoised data\n", "ex_denoised_coord = denoised_data_masked[500,:]" ] }, { "cell_type": "code", "execution_count": 8, "metadata": { "scrolled": true }, "outputs": [], "source": [ "ts_dict = {'gs_raw': gs_raw, 'gs_denoised': gs_denoised, 'denoised_bold': ex_denoised_coord}\n", "regression_df = pd.DataFrame(data=ts_dict)\n", "\n", "# regression of the global signal (derived from raw_data_masked) from the example voxel\n", "mod_raw = smf.ols(formula='denoised_bold ~ gs_raw', data=regression_df)\n", "res_raw = mod_raw.fit()\n", "resid_raw = res_raw.resid\n", "\n", "# regression of the global signal (derived from denoised_data_masked) from the example voxel\n", "mod_denoised = smf.ols(formula='denoised_bold ~ gs_denoised', data=regression_df)\n", "res_denoised = mod_denoised.fit()\n", "resid_denoised = res_denoised.resid" ] }, { "cell_type": "code", "execution_count": 9, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "5.947608615006175" ] }, "execution_count": 9, "metadata": {}, "output_type": "execute_result" } ], "source": [ "# there appears to be substantial difference between the two, supports H1\n", "np.max(resid_raw - resid_denoised)" ] }, { "cell_type": "code", "execution_count": 10, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "" ] }, "execution_count": 10, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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CTNSj3N02qSS3cJEe2yj8Nj/0sgZytLJnPZjkos+j8PALFEjAUxlsK0b4pdAVwj/++OMz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lhR1yEMQ/zFX/wFDhw4gNe+9rVYvXo1isUiGGMA4uO0OYoxhmKxiPHxcWNfLSVWPOGn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\nDBmOE/z/jnGIyaCDTEgAAAAASUVORK5CYII=\n", "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "plt.plot(resid_raw, label='raw')\n", "plt.plot(resid_denoised, label='denoised')\n", "plt.legend()\n", "# supports H1" ] }, { "cell_type": "code", "execution_count": 11, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "" ] }, "execution_count": 11, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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A5eXlPPvss+i6zsUXX8xVV10FQENDA48//jgul4vRo0dz++23Y7FYCAaDPPHEE1RVVZGX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\n71X+nStOzWF2YD+/Lv8Tg8eeRm3ecGp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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "# plot out power spectrum for each residual time series\n", "ps_raw = np.abs(np.fft.fft(resid_raw))**2\n", "ps_denoised = np.abs(np.fft.fft(resid_denoised))**2\n", "time_step = 1 / .5\n", "freqs = np.fft.fftfreq(resid_raw.size, time_step)\n", "idx = np.argsort(freqs)\n", "plt.plot(freqs[idx], ps_raw[idx], label='raw')\n", "plt.plot(freqs[idx], ps_denoised[idx], label='denoised')\n", "plt.legend()\n", "# supports H1" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Conclusion\n", "\n", "There appears to be a difference between the two methods, but please check my work, I'm not confident in the models I set up." ] }, { "cell_type": "code", "execution_count": null, "metadata": { "collapsed": true }, "outputs": [], "source": [] } ], "metadata": { "kernelspec": { "display_name": "Python 3", "language": "python", "name": "python3" }, "language_info": { "codemirror_mode": { "name": "ipython", "version": 3 }, "file_extension": ".py", "mimetype": "text/x-python", "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython3", "version": "3.6.1" } }, "nbformat": 4, "nbformat_minor": 2 }