BoldModel

extensions.bold.BoldModel.BoldModel(
    self,
    parameters,
    equations,
    inputs,
    output=['BOLD'],
    name='Custom BOLD model',
    description='',
)

Base class to define a BOLD model to be used in a BOLD monitor.

A BOLD model is quite similar to a regular rate-coded neuron. It gets a weighted sum of inputs with a specific target (e.g. I_CBF) and compute a single output variable (called BOLD in the predefined models, but it could be anything).

The main difference is that a BOLD model should also declare which targets are used for the input signal:

bold_model = BoldModel(
    parameters = '''
        tau = 1000.
    ''',
    equations = '''
        I_CBF = sum(I_CBF)
        # ...
        tau * dBOLD/dt = I_CBF - BOLD
    ''',
    inputs = "I_CBF"
)

The provided BOLD models follow the Balloon model (Buxton et al., 1998) with the different variations studied in (Stephan et al., 2007). Those models all compute the vascular response to neural activity through a dampened oscillator:

\frac{ds}{dt} = \phi \, I_\text{CBF} - \kappa \, s - \gamma \, (f_{in} - 1)

\frac{df_{in}}{dt} = s

This allows to compute the oxygen extraction fraction:

E = 1 - (1 - E_{0})^{ \frac{1}{f_{in}} }

The (normalized) venous blood volume is computed as:

\tau_0 \, \frac{dv}{dt} = (f_{in} - f_{out})

f_{out} = v^{\frac{1}{\alpha}}

The level of deoxyhemoglobin into the venous compartment is computed by:

\tau_0 \, \frac{dq}{dt} = f_{in} \, \frac{E}{E_0} - \frac{q}{v} \, f_{out}

Using the two signals v and q, there are two ways to compute the corresponding BOLD signal:

  • N: Non-linear BOLD equation:

BOLD = v_0 \, ( k_1 \, (1-q) + k_2 \, (1- \dfrac{q}{v}) + k_3 \, (1 - v) )

  • L: Linear BOLD equation:

BOLD = v_0 \, ((k_1 + k_2) \, (1 - q) + (k_3 - k_2) \, (1 - v))

Additionally, the three coefficients k_1, k_2, k_3 can be computed in two different ways:

  • C: classical coefficients from (Buxton et al., 1998):

k_1 = (1 - v_0) \, 4.3 \, v_0 \, E_0 \, \text{TE}

k_2 = 2 \, E_0

k_3 = 1 - \epsilon

  • R: revised coefficients from (Obata et al., 2004):

k_1 = 4.3 \, v_0 \, E_0 \, \text{TE}

k_2 = \epsilon \, r_0 \, E_0 \, \text{TE}

k_3 = 1 - \epsilon

This makes a total of four different BOLD model (balloon_RN, balloon_RL, balloon_CN, balloon_CL) which are provided by the extension. The different parameters can be modified in the constructor. Additionally, we also provide the model that was used in (Maith et al., 2021) and the two-inputs model of (Maith et al, 2022).

Buxton, R. B., Wong, E. C., and Frank, L. R. (1998). Dynamics of blood flow and oxygenation changes during brain activation: the balloon model. Magnetic resonance in medicine 39, 855-864. doi:10.1002/mrm.1910390602

Friston et al. (2000). Nonlinear responses in fMRI: the balloon model, volterra kernels, and other hemodynamics. NeuroImage 12, 466-477

Buxton et al. (2004). Modeling the hemodynamic response to brain activation. Neuroimage 23, 220-233. doi:10.1016/j.neuroimage.2004.07.013

Stephan et al. (2007). Comparing hemodynamic models with DCM. Neuroimage 38, 387-401. doi:10.1016/j.neuroimage.2007.07.040

Maith et al. (2021) A computational model-based analysis of basal ganglia pathway changes in Parkinson’s disease inferred from resting-state fMRI. European Journal of Neuroscience. 2021; 53: 2278-2295. doi:10.1111/ejn.14868

Maith et al. (2022) BOLD monitoring in the neural simulator ANNarchy. Frontiers in Neuroinformatics 16. doi:10.3389/fninf.2022.790966.

Parameters

Name Type Description Default
parameters parameters of the model and their initial value. required
equations equations defining the temporal evolution of variables. required
inputs single variable or list of input signals (e.g. ‘I_CBF’ or [‘I_CBF’, ‘I_CMRO2’]). required
output output variable of the model (default is ‘BOLD’). ['BOLD']
name optional model name. 'Custom BOLD model'
description optional model description. ''