{ "metadata": { "name": "", "signature": "sha256:af48a011b61c0135723423c8add07044fe151f8b889b6f5ef70264370ba07c08" }, "nbformat": 3, "nbformat_minor": 0, "worksheets": [ { "cells": [ { "cell_type": "code", "collapsed": false, "input": [ "# - compatibility with Python 3\n", "from __future__ import print_function # print('me') instead of print 'me'\n", "from __future__ import division # 1/2 == 0.5, not 0" ], "language": "python", "metadata": {}, "outputs": [], "prompt_number": 1 }, { "cell_type": "code", "collapsed": false, "input": [ "# - show figures inside the notebook\n", "%matplotlib inline" ], "language": "python", "metadata": {}, "outputs": [], "prompt_number": 2 }, { "cell_type": "code", "collapsed": false, "input": [ "# - import common modules\n", "import numpy as np # the Python array package\n", "import matplotlib.pyplot as plt # the Python plotting package" ], "language": "python", "metadata": {}, "outputs": [], "prompt_number": 3 }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Making our own hemodynamic response function" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The file `mt_hrf_estimates.txt` contains the estimated FMRI signal from voxels in the MT motion area at 0, 2, 4, ..., 28 seconds after a brief moving visual stimulus (see: http://nipy.org/nitime/examples/event_related_fmri.html).\n", "\n", "Here are the first four rows. The numbers are in exponential floating point format:\n", "\n", "```\n", "1.394086932967517900e-01\n", "3.938585701431884800e-01\n", "5.012927230566770476e-01\n", "5.676763716149294536e-01\n", "```\n", "\n", "Read the values from the file into an array `mt_hrf_estimates`. Make a new array `mt_hrf_times` with the times of acquisition (0, 2, ...). Plot them together to see the HRF estimate at these times:" ] }, { "cell_type": "code", "collapsed": false, "input": [ "# Load the estimated values from the text file into an array\n", "# Make an array of corresponding times\n", "# Plot signal by time\n", "mt_hrf_estimates = np.loadtxt('mt_hrf_estimates.txt')\n", "mt_hrf_times = np.arange(0, 30, 2)\n", "plt.plot(mt_hrf_times, mt_hrf_estimates)" ], "language": "python", "metadata": {}, "outputs": [ { "metadata": {}, "output_type": "pyout", "prompt_number": 4, "text": [ "[]" ] }, { "metadata": {}, "output_type": "display_data", "png": 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"text": [ "" ] } ], "prompt_number": 4 }, { "cell_type": "markdown", "metadata": {}, "source": [ "We want to make a hemodynamic response function that matches this shape.\n", "\n", "Our function will accept an array that gives the times we want to calculate the HRF for, and returns the values of the HRF for those times. We will assume that the true HRF starts at zero, and gets to zero sometime before 35 seconds.\n", "\n", "Like SPM, I'm going to try using the sum of two [gamma distribution](https://en.wikipedia.org/wiki/Gamma_distribution) probability density functions." ] }, { "cell_type": "code", "collapsed": false, "input": [ "# - import the gamma density function\n", "from scipy.stats import gamma" ], "language": "python", "metadata": {}, "outputs": [], "prompt_number": 5 }, { "cell_type": "markdown", "metadata": {}, "source": [ "Here's my first shot:" ] }, { "cell_type": "code", "collapsed": false, "input": [ "# - my attempt - you can do better than this\n", "def not_great_hrf(times):\n", " \"\"\" Return values for HRF at given times \"\"\"\n", " # Gamma pdf for the peak\n", " peak_values = gamma.pdf(times, 6)\n", " # Gamma pdf for the undershoot\n", " undershoot_values = gamma.pdf(times, 12)\n", " # Combine them\n", " values = peak_values - 0.35 * undershoot_values\n", " # Scale max to 0.6\n", " return values / np.max(values) * 0.6" ], "language": "python", "metadata": {}, "outputs": [], "prompt_number": 6 }, { "cell_type": "code", "collapsed": false, "input": [ "# - plot the data against our estimate\n", "plt.plot(mt_hrf_times, not_great_hrf(mt_hrf_times), label='not_great_hrf')\n", "plt.plot(mt_hrf_times, mt_hrf_estimates, label='mt_hrf_estimates')\n", "plt.legend()" ], "language": "python", "metadata": {}, "outputs": [ { "metadata": {}, "output_type": "pyout", "prompt_number": 7, "text": [ "" ] }, { "metadata": {}, "output_type": "display_data", "png": 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SkpozDspKi5eXUfgXLLAu5vD6w1m4byEXb120LqgQIkc4XNGfs3MOTUs3pWqx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\nmL7BK188bee1pVVAK/6v5f+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"text": [ "" ] } ], "prompt_number": 7 }, { "cell_type": "markdown", "metadata": {}, "source": [ "Now see if you can make a better function by playing with the Gamma distribution pdf parameter, and the mix of the two gamma distribution functions. Call your function `mt_hrf`" ] }, { "cell_type": "code", "collapsed": false, "input": [ "# Your \"mt_hrf\" function here\n", "def mt_hrf(times):\n", " \"\"\" Return values for HRF at given times \"\"\"\n", " # Gamma pdf for the peak\n", " peak_values = gamma.pdf(times, 7)\n", " # Gamma pdf for the undershoot\n", " undershoot_values = gamma.pdf(times, 20)\n", " # Combine them\n", " values = peak_values - undershoot_values\n", " # Scale max to 0.6\n", " return values / np.max(values) * 0.6" ], "language": "python", "metadata": {}, "outputs": [], "prompt_number": 8 }, { "cell_type": "code", "collapsed": false, "input": [ "# Plot your function against the mt_hrf_estimates data to test\n", "plt.plot(mt_hrf_times, mt_hrf(mt_hrf_times), label='mt_hrf')\n", "plt.plot(mt_hrf_times, mt_hrf_estimates, label='mt_hrf_estimates')\n", "plt.legend()" ], "language": "python", "metadata": {}, "outputs": [ { "metadata": {}, "output_type": "pyout", "prompt_number": 9, "text": [ "" ] }, { "metadata": {}, "output_type": "display_data", "png": 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4FaintT4VT1vRZRiuh1yn8ITCHOpyiDwZn/aHg22UL282/65Tx+6ncmkhj0PJ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\nWWaRsmzfbubc+/qa3r21c+7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"text": [ "" ] } ], "prompt_number": 9 }, { "cell_type": "markdown", "metadata": {}, "source": [ "For extra points - other than looking at these plots, how would you convince me your function is better than mine?" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Getting a predicted neural time course" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "We are going to be analyzing the data for the 4D image `ds114_sub009_t2r1.nii` again.\n", "\n", "Load the image into an image object with nibabel, and get the image data array. Print the shape." ] }, { "cell_type": "code", "collapsed": false, "input": [ "# Load the image with nibabel, get the image data array, print the data shape\n", "import nibabel as nib\n", "img = nib.load('ds114_sub009_t2r1.nii')\n", "data = img.get_data()\n", "data.shape" ], "language": "python", "metadata": {}, "outputs": [ { "metadata": {}, "output_type": "pyout", "prompt_number": 10, "text": [ "(64, 64, 30, 173)" ] } ], "prompt_number": 10 }, { "cell_type": "markdown", "metadata": {}, "source": [ "Last week we read in the stimulus file for this run to make an on - off timeseries.\n", "\n", "The stimulus file is `ds114_sub009_t2r1_cond.txt`.\n", "\n", "Here's a version of the same thing we did last week, as a function:" ] }, { "cell_type": "code", "collapsed": false, "input": [ "# - read in stimulus file, return neural prediction\n", "def events2neural(task_fname, tr, n_trs):\n", " \"\"\" Return predicted neural time course from event file\n", " \n", " Parameters\n", " ----------\n", " task_fname : str\n", " Filename of event file\n", " tr : float\n", " TR in seconds\n", " n_trs : int\n", " Number of TRs in functional run\n", " \n", " Returns\n", " -------\n", " time_course : array shape (n_trs,)\n", " Predicted neural time course, one value per TR\n", " \"\"\"\n", " task = np.loadtxt(task_fname)\n", " if task.ndim != 2 or task.shape[1] != 3:\n", " raise ValueError(\"Is {0} really a task file?\", task_fname)\n", " task[:, :2] = task[:, :2] / tr\n", " time_course = np.zeros(n_trs)\n", " for onset, duration, amplitude in task:\n", " time_course[onset:onset + duration] = amplitude\n", " return time_course" ], "language": "python", "metadata": {}, "outputs": [], "prompt_number": 11 }, { "cell_type": "markdown", "metadata": {}, "source": [ "Use this function to read `ds114_sub009_t2r1_cond.txt` and return a predicted neural time course.\n", "\n", "The TR for this run is 2.5. You know the number of TRs from the image data shape above." ] }, { "cell_type": "code", "collapsed": false, "input": [ "# Read the stimulus data file and return a predicted neural time course.\n", "# Plot the predicted neural time course.\n", "tr = 2.5\n", "neural_prediction = events2neural('ds114_sub009_t2r1_cond.txt', tr, data.shape[-1])\n", "plt.plot(neural_prediction)\n", "plt.ylim(0, 1.2)" ], "language": "python", "metadata": {}, "outputs": [ { "metadata": {}, "output_type": "pyout", "prompt_number": 12, "text": [ "(0, 1.2)" ] }, { "metadata": {}, "output_type": "display_data", "png": 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"text": [ "" ] } ], "prompt_number": 12 }, { "cell_type": "markdown", "metadata": {}, "source": [ "We discovered last week that the first volume in this run was bad. Use your slicing skills to make a new array called `data_no_0` that is the data array without the first volume:" ] }, { "cell_type": "code", "collapsed": false, "input": [ "# Make new array excluding the first volume\n", "# data_no_0 = ?\n", "data_no_0 = data[..., 1:]" ], "language": "python", "metadata": {}, "outputs": [], "prompt_number": 13 }, { "cell_type": "markdown", "metadata": {}, "source": [ "Our neural prediction time series currently has one value per volume, including the first volume. To match the data,\n", "make a new neural prediction variable that does not include the first value of the time series. Call this new variable `neural_prediction_no_0`." ] }, { "cell_type": "code", "collapsed": false, "input": [ "# Knock the first element off the neural prediction time series\n", "# neural_prediction_no_0 = ?\n", "neural_prediction_no_0 = neural_prediction[1:]" ], "language": "python", "metadata": {}, "outputs": [], "prompt_number": 14 }, { "cell_type": "markdown", "metadata": {}, "source": [ "For now, we're going to play with data for a single voxel.\n", "\n", "Last week, we subtracted the rest from the task scans, something like this:" ] }, { "cell_type": "code", "collapsed": false, "input": [ "# - subtracting rest from task scans\n", "task_scans = data_no_0[..., neural_prediction_no_0 == 1]\n", "rest_scans = data_no_0[..., neural_prediction_no_0 == 0]\n", "difference = np.mean(task_scans, axis=-1) - np.mean(rest_scans, axis=-1)" ], "language": "python", "metadata": {}, "outputs": [], "prompt_number": 15 }, { "cell_type": "code", "collapsed": false, "input": [ "# - showing slice 14 from the difference image\n", "plt.imshow(difference[:, :, 14], cmap='gray')" ], "language": "python", "metadata": {}, "outputs": [ { "metadata": {}, "output_type": "pyout", "prompt_number": 16, "text": [ "" ] }, { "metadata": {}, "output_type": "display_data", "png": 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I2vQsZwEyN4785K7YfD5vFShnRrJ3GjjfZO10lFoTZn6S5/qsvNNmlXRvu+xq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\nGf1mtN6DgyrfaSVB4rgwZYiMbZNfLSG7vLyMs7O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1Fa0KrYDyu9CT+Rw2+6DQ7yWDaXA9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"text": [ "" ] } ], "prompt_number": 16 }, { "cell_type": "markdown", "metadata": {}, "source": [ "It looks like there's a voxel that is greater for activation than rest at about (i, j, k) == (45, 43, 14).\n", "\n", "Get and plot the values for this voxel position, for every volume in the 4D data (not including the first volume). You can do it with a loop, but slicing is much nicer." ] }, { "cell_type": "code", "collapsed": false, "input": [ "# Get the values for (i, j, k) = (45, 43, 14) and every volume\n", "# Plot the values (voxel time course)\n", "voxel_values = data_no_0[45, 43, 14, :]\n", "plt.plot(voxel_values)" ], "language": "python", "metadata": {}, "outputs": [ { "metadata": {}, "output_type": "pyout", "prompt_number": 17, "text": [ "[]" ] }, { "metadata": {}, "output_type": "display_data", "png": 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3cyYCRvGoSBHw8wf98Y86gKetLXMqCNI7gdpaza0++6yKQLT4lpwOylcEfDoo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\nZ49eoQ8YoI10dNGWqBNIfr98bt+LQLS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"text": [ "" ] } ], "prompt_number": 17 }, { "cell_type": "markdown", "metadata": {}, "source": [ "Correlate the predicted neural time series with the voxel time course:" ] }, { "cell_type": "code", "collapsed": false, "input": [ "# Correlation of predicted neural time course with voxel signal time course\n", "np.corrcoef(neural_prediction_no_0, voxel_values)" ], "language": "python", "metadata": {}, "outputs": [ { "metadata": {}, "output_type": "pyout", "prompt_number": 18, "text": [ "array([[ 1. , 0.31166306],\n", " [ 0.31166306, 1. ]])" ] } ], "prompt_number": 18 }, { "cell_type": "markdown", "metadata": {}, "source": [ "Now we will do a predicted hemodynamic time course using convolution.\n", "\n", "Next we need to get the HRF vector to convolve with.\n", "\n", "Remember we have defined the HRF as a function of time, not TRs.\n", "\n", "For our convolution, we need to *sample* the HRF at times corresponding the start of the TRs.\n", "\n", "So, we need to sample at times (0, 2.5, ...)\n", "\n", "Make a vector of times at which to sample the HRF. We want to sample every TR up until (but not including) somewhere near 35 seconds (where the HRF should have got close to zero again)." ] }, { "cell_type": "code", "collapsed": false, "input": [ "# Make a vector of times at which to sample the HRF\n", "hrf_times = np.arange(0, 35, tr)\n", "hrf_times" ], "language": "python", "metadata": {}, "outputs": [ { "metadata": {}, "output_type": "pyout", "prompt_number": 19, "text": [ "array([ 0. , 2.5, 5. , 7.5, 10. , 12.5, 15. , 17.5, 20. ,\n", " 22.5, 25. , 27.5, 30. , 32.5])" ] } ], "prompt_number": 19 }, { "cell_type": "markdown", "metadata": {}, "source": [ "Sample your HRF function at these times and plot:" ] }, { "cell_type": "code", "collapsed": false, "input": [ "# Sample HRF at given times\n", "# Plot HRF samples against times\n", "hrf_signal = mt_hrf(hrf_times)\n", "plt.plot(hrf_times, hrf_signal)" ], "language": "python", "metadata": {}, "outputs": [ { "metadata": {}, "output_type": "pyout", "prompt_number": 20, "text": [ "[]" ] }, { "metadata": {}, "output_type": "display_data", "png": 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"text": [ "" ] } ], "prompt_number": 20 }, { "cell_type": "markdown", "metadata": {}, "source": [ "Convolve the predicted neural time course with the HRF samples:" ] }, { "cell_type": "code", "collapsed": false, "input": [ "# Convolve predicted neural time course with HRF samples\n", "hemodynamic_prediction = np.convolve(neural_prediction_no_0, hrf_signal)" ], "language": "python", "metadata": {}, "outputs": [], "prompt_number": 21 }, { "cell_type": "markdown", "metadata": {}, "source": [ "The default output of convolve is longer than the input neural prediction vector, by the length of the convolving vector (the HRF samples) minus 1. Knock these last values off the result of the convolution to get a vector the same length as the neural prediction:" ] }, { "cell_type": "code", "collapsed": false, "input": [ "# Remove extra tail of values put there by the convolution\n", "hemodynamic_prediction = hemodynamic_prediction[:len(neural_prediction_no_0)]" ], "language": "python", "metadata": {}, "outputs": [], "prompt_number": 22 }, { "cell_type": "markdown", "metadata": {}, "source": [ "Plot the convolved neural prediction, and then, on the same plot, plot the unconvolved neural prediction." ] }, { "cell_type": "code", "collapsed": false, "input": [ "# Plot convolved neural prediction and unconvolved neural prediction\n", "plt.plot(neural_prediction, label='unconvolved')\n", "plt.plot(hemodynamic_prediction, label='convolved')\n", "plt.legend()" ], "language": "python", "metadata": {}, "outputs": [ { "metadata": {}, "output_type": "pyout", "prompt_number": 23, "text": [ "" ] }, { "metadata": {}, "output_type": "display_data", "png": 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wgHFL6EY52FeRW8GB7gMhzydj2d9YG7oKmmNxWqU5pbT0tjDiDr0SWSJ7AIFd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\nrIJesJ9mbRfWox2ADX9Qu2mORa+Ukqa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"text": [ "" ] } ], "prompt_number": 23 }, { "cell_type": "markdown", "metadata": {}, "source": [ "Does the new convolved time course correlate better with the voxel time course?" ] }, { "cell_type": "code", "collapsed": false, "input": [ "# Correlation of the convolved time course with voxel time course\n", "np.corrcoef(hemodynamic_prediction, voxel_values)" ], "language": "python", "metadata": {}, "outputs": [ { "metadata": {}, "output_type": "pyout", "prompt_number": 24, "text": [ "array([[ 1. , 0.33029022],\n", " [ 0.33029022, 1. ]])" ] } ], "prompt_number": 24 }, { "cell_type": "markdown", "metadata": {}, "source": [ "Plot the hemodynamic prediction against the actual signal (voxel values). Remember to use a marker such as '+' to give you a scatter plot. How does it look?" ] }, { "cell_type": "code", "collapsed": false, "input": [ "plt.plot(hemodynamic_prediction, voxel_values, '+')\n", "plt.xlabel('hemodynamic prediction')\n", "plt.ylabel('voxel values')" ], "language": "python", "metadata": {}, "outputs": [ { "metadata": {}, "output_type": "pyout", "prompt_number": 25, "text": [ "" ] }, { "metadata": {}, "output_type": "display_data", "png": 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