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Example of MRI response functions#
Within this example we are going to plot the hemodynamic response function (HRF) model in SPM together with the HRF shape proposed by G.Glover, as well as their time and dispersion derivatives. We also illustrate how users can input a custom response function, which can for instance be useful when dealing with non human primate data acquired using a contrast agent. In our case, we input a custom response function for MION, a common agent used to enhance contrast on MRI images of monkeys.
The HRF is the filter which couples neural responses to the metabolic-related changes in the MRI signal. HRF models are simply phenomenological.
In current analysis frameworks, the choice of HRF model is essentially left to the user. Fortunately, using the SPM or Glover model does not make a huge difference. Adding derivatives should be considered whenever timing information has some degree of uncertainty, and is actually useful to detect timing issues.
This example requires matplotlib and scipy.
Define stimulus parameters and response models#
To get an impulse response, we simulate a single event occurring at time t=0, with duration 1s.
import numpy as np time_length = 30.0 frame_times = np.linspace(0, time_length, 61) onset, amplitude, duration = 0.0, 1.0, 1.0 exp_condition = np.array((onset, duration, amplitude)).reshape(3, 1)
Make a time array of this condition for display:
stim = np.zeros_like(frame_times) stim[(frame_times > onset) * (frame_times <= onset + duration)] = amplitude
Define custom response functions for MION. Custom response functions should at least take tr and oversampling as arguments:
from scipy.stats import gamma def mion_response_function(tr, oversampling=16, onset=0.0): """Implement the MION response function model. Parameters ---------- tr: float scan repeat time, in seconds oversampling: int, optional temporal oversampling factor onset: float, optional hrf onset time, in seconds Returns ------- response_function: array of shape(length / tr * oversampling, dtype=float) response_function sampling on the oversampled time grid """ dt = tr / oversampling time_stamps = np.linspace( 0, time_length, np.rint(time_length / dt).astype(int) ) time_stamps -= onset # parameters of the gamma function delay = 1.55 dispersion = 5.5 response_function = gamma.pdf(time_stamps, delay, loc=0, scale=dispersion) response_function /= response_function.sum() response_function *= -1 return response_function def mion_time_derivative(tr, oversampling=16.0): """Implement the MION time derivative response function model. Parameters ---------- tr: float scan repeat time, in seconds oversampling: int, optional temporal oversampling factor, optional Returns ------- drf: array of shape(time_length / tr * oversampling, dtype=float) derived_response_function sampling on the provided grid """ do = 0.1 drf = ( mion_response_function(tr, oversampling) - mion_response_function(tr, oversampling, do) ) / do return drf
Define response function models to be displayed:
rf_models = [ ("spm + derivative + dispersion", "SPM HRF", None), ("glover + derivative + dispersion", "Glover HRF", None), ( [mion_response_function, mion_time_derivative], "Mion RF + derivative", ["main", "main_derivative"], ), ]
Sample and plot response functions#
import matplotlib.pyplot as plt from nilearn.glm.first_level import compute_regressor oversampling = 16 fig = plt.figure(figsize=(9, 4)) for i, (rf_model, model_title, labels) in enumerate(rf_models): # compute signal of interest by convolution signal, _labels = compute_regressor( exp_condition, rf_model, frame_times, con_id="main", oversampling=oversampling, ) # plot signal plt.subplot(1, len(rf_models), i + 1) plt.fill(frame_times, stim, "k", alpha=0.5, label="stimulus") for j in range(signal.shape): plt.plot( frame_times, signal.T[j], label=( labels[j] if labels is not None else (_labels[j] if _labels is not None else None) ), ) plt.xlabel("time (s)") plt.legend(loc=1) plt.title(model_title) # adjust plot plt.subplots_adjust(bottom=0.12) plt.show()
Total running time of the script: ( 0 minutes 1.678 seconds)
Estimated memory usage: 8 MB