DoubleExponentialHRFKernel

DoubleExponentialHRFKernel#

class brainmass.DoubleExponentialHRFKernel(tau_1=7.22, tau_2=7.4, f_1=0.03, f_2=0.12, amp_1=0.1, amp_2=0.1, a=0.1, duration=Quantity(40., 's'))#

Double-exponential (damped-oscillation difference) HRF kernel.

A difference of two damped sinusoids (Polonsky et al. 2000) [1]:

\[h(t) \propto a_1 e^{-t/\tau_1}\sin(2\pi f_1 t) - a_2 e^{-t/\tau_2}\sin(2\pi f_2 t),\]

peak-normalised and rescaled to amplitude \(a\) (matching TVB’s DoubleExponential equation). \(t\) is in seconds.

Parameters:

  • tau_1 (float) – Time constants of the two exponentials in seconds (defaults 7.22, 7.4).

  • tau_2 (float) – Time constants of the two exponentials in seconds (defaults 7.22, 7.4).

  • f_1 (float) – Frequencies of the two sinusoids in Hz (defaults 0.03, 0.12).

  • f_2 (float) – Frequencies of the two sinusoids in Hz (defaults 0.03, 0.12).

  • amp_1 (float) – Amplitudes of the two terms (defaults 0.1, 0.1).

  • amp_2 (float) – Amplitudes of the two terms (defaults 0.1, 0.1).

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

  • duration (brainunit.Quantity) – Kernel support (default 40 * u.second).

References

Examples

>>> import brainmass
>>> import brainunit as u
>>> import jax.numpy as jnp
>>> k = brainmass.DoubleExponentialHRFKernel()
>>> h = k(jnp.linspace(0., 40000., 512) * u.ms)
>>> bool(jnp.isclose(h.max(), 0.1, rtol=1e-5))
True
__init__(tau_1=7.22, tau_2=7.4, f_1=0.03, f_2=0.12, amp_1=0.1, amp_2=0.1, a=0.1, duration=Quantity(40., 's'))[source]#