GammaHRFKernel

class brainmass.GammaHRFKernel(tau=1.08, n=3.0, a=0.1, duration=Quantity(20., 's'))

Gamma HRF kernel (Boynton et al. 1996).

A peak-normalised gamma probability density [1]:

\[h(t) \propto \frac{(t/\tau)^{n-1} e^{-t/\tau}}{\tau\,(n-1)!},\]

rescaled so its peak equals the amplitude factor \(a\) (matching TVB’s Gamma equation). \(t\) is in seconds.

Parameters:

• tau (float) – Exponential time constant in seconds (default 1.08).

• n (float) – Phase-delay / shape parameter (default 3.0).

• a (float) – Amplitude after peak-normalisation (default 0.1).

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

References

[1]

Boynton GM, Engel SA, Glover GH, Heeger DJ (1996). Linear systems analysis of functional magnetic resonance imaging in human V1. J Neurosci 16(13): 4207-4221.

Examples

>>> import brainmass
>>> import brainunit as u
>>> import jax.numpy as jnp
>>> k = brainmass.GammaHRFKernel()
>>> h = k(jnp.linspace(0., 20000., 256) * u.ms)
>>> bool(jnp.isclose(h.max(), 0.1, rtol=1e-5))
True

__init__(tau=1.08, n=3.0, a=0.1, duration=Quantity(20., 's'))