BOLDSignal#
- class brainmass.BOLDSignal(in_size, gamma=0.41, k=0.65, alpha=0.32, tau=0.98, rho=0.34, V0=0.02, init=Constant(value=1.0))#
Balloon-Windkessel hemodynamic model of Friston et al. (2003) [1].
The Balloon-Windkessel model describes the coupling of perfusion to BOLD signal, with a dynamical model of the transduction of neuronal activity into perfusion changes. The model assumes that the BOLD signal is a static nonlinear function of the normalized total deoxyhemoglobin voxel content, normalized venous volume, resting net oxygen extraction fraction by the capillary bed, and resting blood volume fraction. The BOLD-signal estimation for each brain area is computed by the level of synaptic activity in that particular cortical area, noted \(z_i\) for a given cortical are \(i\).
For the i-th region, synaptic activity \(z_i\) causes an increase in a vasodilatory signal \(x_i\) that is subject to autoregulatory feedback. Inflow \(f_i\) responds in proportion to this signal with concomitant changes in blood volume \(v_i\) and deoxyhemoglobin content \(q_i\). The equations relating these biophysical processes are as follows:
\[\begin{split} \begin{gathered} \dot{x}_i=z_i-k_i x_i-\gamma_i\left(f_i-1\right) \\ \dot{f}_i=x_i \\ \tau_i \dot{v}_i=f_i-v_i^{1 / \alpha} \\ \tau_i \dot{q}_i=\frac{f_i}{\rho}\left[1-(1-\rho)^{1 / f_i}\right]-q_i v_i^{1 / \alpha-1}, \end{gathered} \end{split}\]where \(\rho\) is the resting oxygen extraction fraction. The BOLD signal is given by the following:
\[ \mathrm{BOLD}_i=V_0\left[k_1\left(1-q_i\right)+k_2\left(1-q_i / v_i\right)+k_3\left(1-v_i\right)\right], \]where \(V_0 = 0.02, k1 = 7\rho, k2 = 2\), and \(k3 = 2\rho − 0.2\). All biophysical parameters were taken as in Friston et al. (2003) [1]. The BOLD model converts the local synaptic activity of a given cortical area into an observable BOLD signal and does not actively couple the signals from other cortical areas.
- Parameters:
in_size (int) – Size of the input vector (number of brain regions).
gamma (
Callable|Array|ndarray|bool|number|bool|int|float|complex|Quantity|Param) – Rate of signal decay (default is 0.41).k (
Callable|Array|ndarray|bool|number|bool|int|float|complex|Quantity|Param) – Rate of flow-dependent elimination (default is 0.65).alpha (
Callable|Array|ndarray|bool|number|bool|int|float|complex|Quantity|Param) – Grubb’s exponent (default is 0.32).tau (
Callable|Array|ndarray|bool|number|bool|int|float|complex|Quantity|Param) – Hemodynamic transit time (default is 0.98).rho (
Callable|Array|ndarray|bool|number|bool|int|float|complex|Quantity|Param) – Resting oxygen extraction fraction (default is 0.34).V0 (
float) – Resting blood volume fraction (default is 0.02).
- Return type:
Any
References