balloon_RL

extensions.bold.PredefinedModels.balloon_RL(
    self,
    phi=1.0,
    kappa=1 / 1.54,
    gamma=1 / 2.46,
    E_0=0.34,
    tau=0.98,
    alpha=0.33,
    V_0=0.02,
    v_0=40.3,
    TE=40 / 1000.0,
    epsilon=1.43,
    r_0=25,
)

A balloon model with revised coefficients and linear BOLD equation derived from Stephan et al. (2007).

Equivalent code:

balloon_RL = BoldModel(
    parameters = '''
        second    = 1000.0
        phi       = 1.0
        kappa     = 1/1.54
        gamma     = 1/2.46
        E_0       = 0.34
        tau       = 0.98
        alpha     = 0.33
        V_0       = 0.02
        v_0       = 40.3
        TE        = 40/1000.
        epsilon   = 1.43
        r_0       = 25.
    ''',
    equations = '''
        # Single input
        I_CBF          = sum(I_CBF)                                                : init=0
        ds/dt          = (phi * I_CBF - kappa * s - gamma * (f_in - 1))/second     : init=0
        df_in/dt       = s / second                                                : init=1, min=0.01

        E              = 1 - (1 - E_0)**(1 / f_in)                                 : init=0.3424
        dq/dt          = (f_in * E / E_0 - (q / v) * f_out)/(tau*second)           : init=1, min=0.01
        dv/dt          = (f_in - f_out)/(tau*second)                               : init=1, min=0.01
        f_out          = v**(1 / alpha)                                            : init=1, min=0.01

        # Revised coefficients
        k_1            = 4.3 * v_0 * E_0 * TE
        k_2            = epsilon * r_0 * E_0 * TE
        k_3            = 1.0 - epsilon

        # Linear equation
        BOLD           = V_0 * ((k_1 + k_2) * (1 - q) + (k_3 - k_2) * (1 - v))         : init=0
    ''',
    inputs="I_CBF",
)

Parameters

Name	Type	Description	Default
phi		input coefficient	1.0
kappa		signal decay	1 / 1.54
gamma		feedback regulation	1 / 2.46
E_0		oxygen extraction fraction at rest	0.34
tau		time constant (in s!)	0.98
alpha		vessel stiffness	0.33
V_0		resting venous blood volume fraction	0.02
v_0		frequency offset at the outer surface of the magnetized vessel for fully deoxygenated blood at 1.5 T	40.3
TE		echo time	40 / 1000.0
epsilon		ratio of intra- and extravascular signal	1.43
r_0		slope of the relation between the intravascular relaxation rate and oxygen saturation	25