| value | |
|---|---|
| Equation type | FirstOrderVolterra | \n",
"
| equation | 1/3. * exp(-0.5*(var / tau_s)) * (sin(sqrt(1./tau_f - 1./(4.*tau_s**2)) * var)) / (sqrt(1./tau_f - 1./(4.*tau_s**2))) | \n",
"
| parameters | {'tau_s': 0.8, 'tau_f': 0.4, 'k_1': 5.6, 'V_0': 0.02} | \n",
"
\n",
" \n",
" 
\n",
"
\n",
" "
],
"text/plain": [
"Canvas(toolbar=Toolbar(toolitems=[('Home', 'Reset original view', 'home', 'home'), ('Back', 'Back to previous …"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"# plot the kernel\n",
"plt.plot(bold._stock_time, bold.hemodynamic_response_function.T[::-1]); \n",
"plt.ylabel('hrf');\n",
"plt.xlabel('time [sec]')\n",
"\n",
"# plot the maximum\n",
"plt.plot(bold._stock_time[bold.hemodynamic_response_function.T[::-1].argmax()], bold.hemodynamic_response_function.T[::-1].max(), 'ko')"
]
},
{
"cell_type": "code",
"execution_count": 7,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"Rising peak is around 0.80 seconds\n"
]
}
],
"source": [
"print ('Rising peak is around %1.2f seconds' % bold._stock_time[bold.hemodynamic_response_function.T[::-1].argmax()])"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Exploring other HRF kernels\n",
"---------------------------\n",
"\n",
" \n",
"First, we will create new instances of the Bold monitor.\n",
"\n",
"Second, the equation defining the hrf kernel has to be changed. To achieve this we will make use of the predefined functions as Equations datatypes \n",
"\n",
"- In [2] they used a simple gamma function; in [3] a difference of damped oscillators was fitted to functional data from the visual cortex; the mixture of gammas is the function used in softwares like SPM. "
]
},
{
"cell_type": "code",
"execution_count": 8,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"\n",
" \n",
" \n",
" 
\n",
"
\n",
" "
],
"text/plain": [
"Canvas(toolbar=Toolbar(toolitems=[('Home', 'Reset original view', 'home', 'home'), ('Back', 'Back to previous …"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"hrf_kernels = [equations.FirstOrderVolterra(),\n",
" equations.DoubleExponential(),\n",
" equations.MixtureOfGammas(),\n",
" equations.Gamma()]\n",
"\n",
"plt.figure()\n",
"for hrf in hrf_kernels: \n",
" bold_monitor = monitors.Bold(hrf_kernel=hrf)\n",
" bold_monitor.dt = 2**-4\n",
" bold_monitor.compute_hrf()\n",
" plt.plot(bold_monitor._stock_time,\n",
" bold_monitor.hemodynamic_response_function.T[::-1], \n",
" label=hrf.__class__.__name__);\n",
"\n",
"plt.ylabel('hrf');\n",
"plt.xlabel('time [sec]') \n",
"plt.legend()"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"* [1] Friston, K., Mechelli, A., Turner, R., and Price, C., *Nonlinear Responses in fMRI: The Balloon Model, Volterra Kernels, and Other Hemodynamics*, NeuroImage, 12, 466 - 477, 2000. \n",
"\n",
"* [2] Geoffrey M. Boynton, Stephen A. Engel, Gary H. Glover and David J. Heeger (1996). *Linear Systems Analysis of Functional Magnetic Resonance Imaging in Human V1*. J Neurosci 16: 4207-4221\n",
"\n",
"* [3] Alex Polonsky, Randolph Blake, Jochen Braun and David J. Heeger (2000). *Neuronal activity in human primary visual cortex correlates with perception during binocular rivalry*. Nature Neuroscience 3: 1153-1159\n",
"\n",
"* [4] Glover, G. *Deconvolution of Impulse Response in Event-Related BOLD fMRI*. NeuroImage 9, 416-429, 1999.\n",
"\n",
"* [5] Have a look at this tutorial: https://nbviewer.thevirtualbrain.org/github/practical-neuroimaging/pna-notebooks/blob/master/convolution.ipynb\n",
"\n",
"* [6] Drysdale, P. M.; Huber, J. P.; Robinson, P. A. & Aquino, K. M. *Spatiotemporal BOLD dynamics from a poroelastic hemodynamic model*. J Theor Biol, 2010, 265, 524–534\n",
"\n",
"* [7] http://en.wikibooks.org/wiki/SPM/Haemodynamic_Response_Function\n"
]
}
],
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\n",
"