"""
Example of MRI response functions
=================================
Within this example we are going to plot the hemodynamic response function
(:term:`HRF`) model in :term:`SPM` together with the :term:`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 :term:`HRF` is the filter which couples neural responses to the
metabolic-related changes in the MRI signal. :term:`HRF` models
are simply phenomenological.
In current analysis frameworks, the choice of :term:`HRF` model is essentially
left to the user. Fortunately, using the :term:`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.
"""
try:
import matplotlib.pyplot as plt
except ImportError:
raise RuntimeError("This script needs the matplotlib library")
# %%
# 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 :term:`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
# ----------------------------------
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[1]):
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()