# fmri.hrf¶

## Functions¶

nitime.fmri.hrf.gamma_hrf(duration, A=1.0, tau=1.08, n=3, delta=2.05, Fs=1.0)

A gamma function hrf model, with two parameters, based on [Boynton1996]

Parameters: duration: float : the length of the HRF (in the inverse units of the sampling rate) A: float : a scaling factor, sets the max of the function, defaults to 1 tau: float : The time constant of the gamma function, defaults to 1.08 n: int : The phase delay of the gamma function, defaults to 3 delta: float : A pure delay, allowing for an additional delay from the onset of the time-series to the beginning of the gamma hrf, defaults to 2.05 Fs: float : The sampling rate, defaults to 1.0 h: the gamma function hrf, as a function of time :

Notes

This is based on equation 3 in Boynton (1996):

$h(t) = \frac{(\frac{t-\delta}{\tau})^{(n-1)} e^{-(\frac{t-\delta}{\tau})}}{\tau(n-1)!}$

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

nitime.fmri.hrf.polonsky_hrf(A, B, tau1, f1, tau2, f2, t_max, Fs=1.0)

HRF based on Polonsky (2000):

$H(t) = exp(\frac{-t}{\tau_1}) sin(2\cdot\pi f_1 \cdot t) -a\cdot exp(-\frac{t}{\tau_2})*sin(2\pi f_2 t)$

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