MixtureOfGammasHRFKernel

MixtureOfGammasHRFKernel#

class brainmass.MixtureOfGammasHRFKernel(a_1=6.0, a_2=13.0, l=1.0, c=0.4, duration=Quantity(20., 's'))#

Mixture-of-gammas HRF kernel (Glover 1999).

A difference of two gamma densities – the canonical SPM-style HRF [1]:

\[h(t) = \frac{(\lambda t)^{a_1 - 1} e^{-\lambda t}}{\Gamma(a_1)} - c\,\frac{(\lambda t)^{a_2 - 1} e^{-\lambda t}}{\Gamma(a_2)},\]

with \(t\) in seconds. The first gamma models the positive BOLD peak; the second, scaled by \(c\), the post-stimulus undershoot.

Parameters:

  • a_1 (float) – Shape parameter of the first (peak) gamma (default 6.0).

  • a_2 (float) – Shape parameter of the second (undershoot) gamma (default 13.0).

  • l (float) – Rate / inverse-scale parameter \(\lambda\) (default 1.0).

  • c (float) – Relative amplitude of the undershoot gamma (default 0.4).

  • duration (brainunit.Quantity) – Kernel support (default 20 * u.second).

References

Examples

>>> import brainmass
>>> import brainunit as u
>>> import jax.numpy as jnp
>>> k = brainmass.MixtureOfGammasHRFKernel()
>>> h = k(jnp.linspace(0., 20000., 256) * u.ms)
>>> h.shape
(256,)
__init__(a_1=6.0, a_2=13.0, l=1.0, c=0.4, duration=Quantity(20., 's'))[source]#