Neuronal activity gives rise to the blood-oxygen-level-dependent signal detected in fMRI through a hemodynamic process that is well-described by the Balloon-Windkessel model [19] (link), comprised of four dynamical variables: vasodilatory signal s(t), blood inflow f(t), blood volume v(t) and deoxyhemoglobin content q(t). The system of differential equations is:
where z(t) is the neuronal activity, given by the sum of the neuronal firing rates calculated through Eq. ( 5), and κ, γ, τ B , α and ρ are parameters describing the rate of signal decay, rate of flow-dependent elimination, hemodynamic transit time, Grubb's exponent of blood outflow and resting oxygen extraction fraction, respectively. The BOLD signal, B(t), is then a volume-weighted sum of intra-and extravascular contributions to blood volume and deoxyhemoglobin content:
with 𝑉 0 the resting blood volume fraction.
where z(t) is the neuronal activity, given by the sum of the neuronal firing rates calculated through Eq. ( 5), and κ, γ, τ B , α and ρ are parameters describing the rate of signal decay, rate of flow-dependent elimination, hemodynamic transit time, Grubb's exponent of blood outflow and resting oxygen extraction fraction, respectively. The BOLD signal, B(t), is then a volume-weighted sum of intra-and extravascular contributions to blood volume and deoxyhemoglobin content:
with 𝑉 0 the resting blood volume fraction.
