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datatypes Package

plot Package

# models Package¶

## linear_with_stimulus¶

Generic linear model. .. moduleauthor:: Dionysios Perdikis <dionysios.perdikis@charite.de>

class tvb.contrib.scripts.models.linear_with_stimulus.Linear(**kwargs)[source]
I_o : tvb.contrib.scripts.models.linear_with_stimulus.Linear.I_o = NArray(label=’$$I_o$$‘, dtype=float64, default=array([0.]), dim_names=(), ndim=None, required=True)
External stimulus
G : tvb.contrib.scripts.models.linear_with_stimulus.Linear.G = NArray(label=’$$G$$‘, dtype=float64, default=array([0.]), dim_names=(), ndim=None, required=True)
Global coupling scaling
tau : tvb.contrib.scripts.models.linear_with_stimulus.Linear.tau = NArray(label=’$$\\tau$$‘, dtype=float64, default=array([1.]), dim_names=(), ndim=None, required=True)
Time constant
tau_rin : tvb.contrib.scripts.models.linear_with_stimulus.Linear.tau_rin = NArray(label=’$$\\tau_rin_e$$‘, dtype=float64, default=array([10.]), dim_names=(), ndim=None, required=True)
[ms]. Excitatory population instant spiking rate time constant.
state_variable_boundaries : tvb.contrib.scripts.models.linear_with_stimulus.Linear.state_variable_boundaries = Final(field_type=<class ‘dict’>, default={‘R’: array([0.0, None], dtype=object), ‘Rin’: array([0.0, None], dtype=object)}, required=True)
The values for each state-variable should be set to encompass the boundaries of the dynamic range of that state-variable. Set None for one-sided boundaries
state_variable_range : tvb.contrib.scripts.models.linear_with_stimulus.Linear.state_variable_range = Final(field_type=<class ‘dict’>, default={‘R’: array([ 0, 100]), ‘Rin’: array([ 0, 100])}, required=True)
Range used for state variable initialization and visualization.

variables_of_interest : tvb.contrib.scripts.models.linear_with_stimulus.Linear.variables_of_interest = List(of=<class ‘str’>, default=(‘R’, ‘Rin’), required=True)

gamma : tvb.simulator.models.linear.Linear.gamma = NArray(label=’$$\\gamma$$‘, dtype=float64, default=array([-10.]), dim_names=(), ndim=None, required=True)
The damping coefficient specifies how quickly the node’s activity relaxes, must be larger than the node’s in-degree in order to remain stable.

coupling_terms : tvb.simulator.models.linear.Linear.coupling_terms = Final(field_type=<class ‘list’>, default=[‘c’], required=True)

state_variable_dfuns : tvb.simulator.models.linear.Linear.state_variable_dfuns = Final(field_type=<class ‘dict’>, default={‘x’: ‘gamma * x + c’}, required=True)

parameter_names : tvb.simulator.models.linear.Linear.parameter_names = List(of=<class ‘str’>, default=(‘gamma’,), required=True)

gid : tvb.basic.neotraits._core.HasTraits.gid = Attr(field_type=<class ‘uuid.UUID’>, default=None, required=True)

G

Declares a numpy array. dtype enforces the dtype. The default dtype is float32. An optional symbolic shape can be given, as a tuple of Dim attributes from the owning class. The shape will be enforced, but no broadcasting will be done. domain declares what values are allowed in this array. It can be any object that can be checked for membership Defaults are checked if they are in the declared domain. For performance reasons this does not happen on every attribute set.

I_o

Declares a numpy array. dtype enforces the dtype. The default dtype is float32. An optional symbolic shape can be given, as a tuple of Dim attributes from the owning class. The shape will be enforced, but no broadcasting will be done. domain declares what values are allowed in this array. It can be any object that can be checked for membership Defaults are checked if they are in the declared domain. For performance reasons this does not happen on every attribute set.

cvar = array([0], dtype=int32)
dfun(state, coupling, local_coupling=0.0)[source]
$dR/dt = (-R + G * coupling) / { au} + I_o$
integration_variables = ('R',)
state_variable_boundaries

An attribute that can only be set once. If a default is provided it counts as a set, so it cannot be written to. Note that if the default is a mutable type, the value is shared with all instances of the owning class. We cannot enforce true constancy in python

state_variable_range

An attribute that can only be set once. If a default is provided it counts as a set, so it cannot be written to. Note that if the default is a mutable type, the value is shared with all instances of the owning class. We cannot enforce true constancy in python

state_variables = ('R', 'Rin')
tau

Declares a numpy array. dtype enforces the dtype. The default dtype is float32. An optional symbolic shape can be given, as a tuple of Dim attributes from the owning class. The shape will be enforced, but no broadcasting will be done. domain declares what values are allowed in this array. It can be any object that can be checked for membership Defaults are checked if they are in the declared domain. For performance reasons this does not happen on every attribute set.

tau_rin

Declares a numpy array. dtype enforces the dtype. The default dtype is float32. An optional symbolic shape can be given, as a tuple of Dim attributes from the owning class. The shape will be enforced, but no broadcasting will be done. domain declares what values are allowed in this array. It can be any object that can be checked for membership Defaults are checked if they are in the declared domain. For performance reasons this does not happen on every attribute set.

update_derived_parameters()[source]

When needed, this should be a method for calculating parameters that are calculated based on paramaters directly set by the caller. For example, see, ReducedSetFitzHughNagumo. When not needed, this pass simplifies code that updates an arbitrary models parameters – ie, this can be safely called on any model, whether it’s used or not.

update_non_state_variables_after_integration(state_variables)[source]
variables_of_interest

The attribute is a list of values. Choices and type are reinterpreted as applying not to the list but to the elements of it

## reduced_wong_wang_exc_io¶

Models based on Wong-Wang’s work. .. moduleauthor:: Dionysios Perdikis <dionysios.perdikis@charite.de>

class tvb.contrib.scripts.models.reduced_wong_wang_exc_io.ReducedWongWangExcIO(**kwargs)[source]
 [WW_2006] Kong-Fatt Wong and Xiao-Jing Wang, A Recurrent Network Mechanism of Time Integration in Perceptual Decisions. Journal of Neuroscience 26(4), 1314-1328, 2006.
 [DPA_2013] Deco Gustavo, Ponce Alvarez Adrian, Dante Mantini, Gian Luca Romani, Patric Hagmann, and Maurizio Corbetta. Resting-State Functional Connectivity Emerges from Structurally and Dynamically Shaped Slow Linear Fluctuations. The Journal of Neuroscience 33(27), 11239 –11252, 2013.
__init__(**kwargs)

The default init accepts kwargs for all declarative attrs and sets them to the given values

Equations taken from [DPA_2013] , page 11242

$\begin{split}x_{ek} &= w_p\,J_N \, S_{ek} - J_iS_{ik} + W_eI_o + GJ_N \mathbf\Gamma(S_{ek}, S_{ej}, u_{kj}),\\ H(x_{ek}) &= \dfrac{a_ex_{ek}- b_e}{1 - \exp(-d_e(a_ex_{ek} -b_e))},\\ \dot{S}_{ek} &= -\dfrac{S_{ek}}{\tau_e} + (1 - S_{ek}) \, \gammaH(x_{ek}) \,\end{split}$
a : tvb.contrib.scripts.models.reduced_wong_wang_exc_io.ReducedWongWangExcIO.a = NArray(label=’$$a$$‘, dtype=float64, default=array([270.]), dim_names=(), ndim=None, required=True)
[n/C]. Input gain parameter, chosen to fit numerical solutions.
b : tvb.contrib.scripts.models.reduced_wong_wang_exc_io.ReducedWongWangExcIO.b = NArray(label=’$$b$$‘, dtype=float64, default=array([108.]), dim_names=(), ndim=None, required=True)
[Hz]. Input shift parameter chosen to fit numerical solutions.
d : tvb.contrib.scripts.models.reduced_wong_wang_exc_io.ReducedWongWangExcIO.d = NArray(label=’$$d$$‘, dtype=float64, default=array([0.154]), dim_names=(), ndim=None, required=True)
[s]. Parameter chosen to fit numerical solutions.
gamma : tvb.contrib.scripts.models.reduced_wong_wang_exc_io.ReducedWongWangExcIO.gamma = NArray(label=’$$\\gamma$$‘, dtype=float64, default=array([0.000641]), dim_names=(), ndim=None, required=True)
Kinetic parameter
tau_s : tvb.contrib.scripts.models.reduced_wong_wang_exc_io.ReducedWongWangExcIO.tau_s = NArray(label=’$$\\tau_S$$‘, dtype=float64, default=array([100.]), dim_names=(), ndim=None, required=True)
[ms]. NMDA decay time constant.
w : tvb.contrib.scripts.models.reduced_wong_wang_exc_io.ReducedWongWangExcIO.w = NArray(label=’$$w$$‘, dtype=float64, default=array([0.9]), dim_names=(), ndim=None, required=True)
Excitatory recurrence
J_N : tvb.contrib.scripts.models.reduced_wong_wang_exc_io.ReducedWongWangExcIO.J_N = NArray(label=’$$J_{N}$$‘, dtype=float64, default=array([0.2609]), dim_names=(), ndim=None, required=True)
Excitatory recurrence
I_o : tvb.contrib.scripts.models.reduced_wong_wang_exc_io.ReducedWongWangExcIO.I_o = NArray(label=’$$I_{o}$$‘, dtype=float64, default=array([0.3]), dim_names=(), ndim=None, required=True)
[nA] Effective external input
G : tvb.contrib.scripts.models.reduced_wong_wang_exc_io.ReducedWongWangExcIO.G = NArray(label=’$$G$$‘, dtype=float64, default=array([2.]), dim_names=(), ndim=None, required=True)
Global coupling scaling
sigma_noise : tvb.contrib.scripts.models.reduced_wong_wang_exc_io.ReducedWongWangExcIO.sigma_noise = NArray(label=’$$\\sigma_{noise}$$‘, dtype=float64, default=array([1.e-09]), dim_names=(), ndim=None, required=True)
[nA] Noise amplitude. Take this value into account for stochatic integration schemes.
tau_rin : tvb.contrib.scripts.models.reduced_wong_wang_exc_io.ReducedWongWangExcIO.tau_rin = NArray(label=’$$\\tau_rin_e$$‘, dtype=float64, default=array([100.]), dim_names=(), ndim=None, required=True)
[ms]. Excitatory population instant spiking rate time constant.
state_variable_boundaries : tvb.contrib.scripts.models.reduced_wong_wang_exc_io.ReducedWongWangExcIO.state_variable_boundaries = Final(field_type=<class ‘dict’>, default={‘S’: array([0., 1.]), ‘Rint’: array([0.0, None], dtype=object), ‘R’: array([0.0, None], dtype=object), ‘Rin’: array([0.0, None], dtype=object), ‘I’: array([None, None], dtype=object)}, required=True)
The values for each state-variable should be set to encompass the boundaries of the dynamic range of that state-variable. Set None for one-sided boundaries
state_variable_range : tvb.contrib.scripts.models.reduced_wong_wang_exc_io.ReducedWongWangExcIO.state_variable_range = Final(field_type=<class ‘dict’>, default={‘S’: array([0., 1.]), ‘Rint’: array([ 0., 1000.]), ‘R’: array([ 0., 1000.]), ‘Rin’: array([ 0., 1000.]), ‘I’: array([0., 2.])}, required=True)
Population firing rate
variables_of_interest : tvb.contrib.scripts.models.reduced_wong_wang_exc_io.ReducedWongWangExcIO.variables_of_interest = List(of=<class ‘str’>, default=(‘S’, ‘Rint’, ‘R’, ‘Rin’, ‘I’), required=True)
default state variables to be monitored

gid : tvb.basic.neotraits._core.HasTraits.gid = Attr(field_type=<class ‘uuid.UUID’>, default=None, required=True)

G

Declares a numpy array. dtype enforces the dtype. The default dtype is float32. An optional symbolic shape can be given, as a tuple of Dim attributes from the owning class. The shape will be enforced, but no broadcasting will be done. domain declares what values are allowed in this array. It can be any object that can be checked for membership Defaults are checked if they are in the declared domain. For performance reasons this does not happen on every attribute set.

I_o

Declares a numpy array. dtype enforces the dtype. The default dtype is float32. An optional symbolic shape can be given, as a tuple of Dim attributes from the owning class. The shape will be enforced, but no broadcasting will be done. domain declares what values are allowed in this array. It can be any object that can be checked for membership Defaults are checked if they are in the declared domain. For performance reasons this does not happen on every attribute set.

J_N

Declares a numpy array. dtype enforces the dtype. The default dtype is float32. An optional symbolic shape can be given, as a tuple of Dim attributes from the owning class. The shape will be enforced, but no broadcasting will be done. domain declares what values are allowed in this array. It can be any object that can be checked for membership Defaults are checked if they are in the declared domain. For performance reasons this does not happen on every attribute set.

a

Declares a numpy array. dtype enforces the dtype. The default dtype is float32. An optional symbolic shape can be given, as a tuple of Dim attributes from the owning class. The shape will be enforced, but no broadcasting will be done. domain declares what values are allowed in this array. It can be any object that can be checked for membership Defaults are checked if they are in the declared domain. For performance reasons this does not happen on every attribute set.

b

Declares a numpy array. dtype enforces the dtype. The default dtype is float32. An optional symbolic shape can be given, as a tuple of Dim attributes from the owning class. The shape will be enforced, but no broadcasting will be done. domain declares what values are allowed in this array. It can be any object that can be checked for membership Defaults are checked if they are in the declared domain. For performance reasons this does not happen on every attribute set.

cvar = array([0], dtype=int32)
d

Declares a numpy array. dtype enforces the dtype. The default dtype is float32. An optional symbolic shape can be given, as a tuple of Dim attributes from the owning class. The shape will be enforced, but no broadcasting will be done. domain declares what values are allowed in this array. It can be any object that can be checked for membership Defaults are checked if they are in the declared domain. For performance reasons this does not happen on every attribute set.

dfun(x, c, local_coupling=0.0)[source]
gamma

Declares a numpy array. dtype enforces the dtype. The default dtype is float32. An optional symbolic shape can be given, as a tuple of Dim attributes from the owning class. The shape will be enforced, but no broadcasting will be done. domain declares what values are allowed in this array. It can be any object that can be checked for membership Defaults are checked if they are in the declared domain. For performance reasons this does not happen on every attribute set.

non_integrated_variables = ['R', 'Rin', 'I']
sigma_noise

Declares a numpy array. dtype enforces the dtype. The default dtype is float32. An optional symbolic shape can be given, as a tuple of Dim attributes from the owning class. The shape will be enforced, but no broadcasting will be done. domain declares what values are allowed in this array. It can be any object that can be checked for membership Defaults are checked if they are in the declared domain. For performance reasons this does not happen on every attribute set.

state_variable_boundaries

An attribute that can only be set once. If a default is provided it counts as a set, so it cannot be written to. Note that if the default is a mutable type, the value is shared with all instances of the owning class. We cannot enforce true constancy in python

state_variable_range

An attribute that can only be set once. If a default is provided it counts as a set, so it cannot be written to. Note that if the default is a mutable type, the value is shared with all instances of the owning class. We cannot enforce true constancy in python

state_variables = ['S', 'Rint', 'R', 'Rin', 'I']
tau_rin

Declares a numpy array. dtype enforces the dtype. The default dtype is float32. An optional symbolic shape can be given, as a tuple of Dim attributes from the owning class. The shape will be enforced, but no broadcasting will be done. domain declares what values are allowed in this array. It can be any object that can be checked for membership Defaults are checked if they are in the declared domain. For performance reasons this does not happen on every attribute set.

tau_s

Declares a numpy array. dtype enforces the dtype. The default dtype is float32. An optional symbolic shape can be given, as a tuple of Dim attributes from the owning class. The shape will be enforced, but no broadcasting will be done. domain declares what values are allowed in this array. It can be any object that can be checked for membership Defaults are checked if they are in the declared domain. For performance reasons this does not happen on every attribute set.

update_derived_parameters()[source]

When needed, this should be a method for calculating parameters that are calculated based on paramaters directly set by the caller. For example, see, ReducedSetFitzHughNagumo. When not needed, this pass simplifies code that updates an arbitrary models parameters – ie, this can be safely called on any model, whether it’s used or not.

update_state_variables_before_integration(state_variables, coupling, local_coupling=0.0, stimulus=0.0)[source]
use_numba = True
variables_of_interest

The attribute is a list of values. Choices and type are reinterpreted as applying not to the list but to the elements of it

w

Declares a numpy array. dtype enforces the dtype. The default dtype is float32. An optional symbolic shape can be given, as a tuple of Dim attributes from the owning class. The shape will be enforced, but no broadcasting will be done. domain declares what values are allowed in this array. It can be any object that can be checked for membership Defaults are checked if they are in the declared domain. For performance reasons this does not happen on every attribute set.

## reduced_wong_wang_exc_io_inh_i¶

Models based on Wong-Wang’s work. .. moduleauthor:: Dionysios Perdikis <dionysios.perdikis@charite.de>

class tvb.contrib.scripts.models.reduced_wong_wang_exc_io_inh_i.ReducedWongWangExcIOInhI(**kwargs)[source]

Bases: tvb.simulator.models.wong_wang_exc_inh.ReducedWongWangExcInh

 [WW_2006] Kong-Fatt Wong and Xiao-Jing Wang, A Recurrent Network Mechanism of Time Integration in Perceptual Decisions. Journal of Neuroscience 26(4), 1314-1328, 2006.
 [DPA_2014] Deco Gustavo, Ponce Alvarez Adrian, Patric Hagmann, Gian Luca Romani, Dante Mantini, and Maurizio Corbetta. How Local Excitation–Inhibition Ratio Impacts the Whole Brain Dynamics. The Journal of Neuroscience 34(23), 7886 –7898, 2014.
__init__(**kwargs)

The default init accepts kwargs for all declarative attrs and sets them to the given values

Equations taken from [DPA_2014]

$\begin{split}x_{ek} &= w_p\,J_N \, S_{ek} - J_iS_{ik} + W_eI_o + GJ_N \mathbf\Gamma(S_{ek}, S_{ej}, u_{kj}),\\ H(x_{ek}) &= \dfrac{a_ex_{ek}- b_e}{1 - \exp(-d_e(a_ex_{ek} -b_e))},\\ \dot{S}_{ek} &= -\dfrac{S_{ek}}{\tau_e} + (1 - S_{ek}) \, \gammaH(x_{ek}) \,\end{split}$$\begin{split}x_{ik} &= J_N \, S_{ek} - S_{ik} + W_iI_o + \lambdaGJ_N \mathbf\Gamma(S_{ik}, S_{ej}, u_{kj}),\\ H(x_{ik}) &= \dfrac{a_ix_{ik} - b_i}{1 - \exp(-d_i(a_ix_{ik} -b_i))},\\ \dot{S}_{ik} &= -\dfrac{S_{ik}}{\tau_i} + \gamma_iH(x_{ik}) \,\end{split}$
tau_rin_e : tvb.contrib.scripts.models.reduced_wong_wang_exc_io_inh_i.ReducedWongWangExcIOInhI.tau_rin_e = NArray(label=’$$\\tau_rin_e$$‘, dtype=float64, default=array([1.]), dim_names=(), ndim=None, required=True)
[ms]. Excitatory population instant spiking rate time constant.
tau_rin_i : tvb.contrib.scripts.models.reduced_wong_wang_exc_io_inh_i.ReducedWongWangExcIOInhI.tau_rin_i = NArray(label=’$$\\tau_rin_i$$‘, dtype=float64, default=array([1.]), dim_names=(), ndim=None, required=True)
[ms]. Inhibitory population instant spiking rate time constant.
state_variable_boundaries : tvb.contrib.scripts.models.reduced_wong_wang_exc_io_inh_i.ReducedWongWangExcIOInhI.state_variable_boundaries = Final(field_type=<class ‘dict’>, default={‘S_e’: array([0., 1.]), ‘S_i’: array([0., 1.]), ‘R_e’: array([0.0, None], dtype=object), ‘R_i’: array([0.0, None], dtype=object), ‘Rin_e’: array([0.0, None], dtype=object), ‘Rin_i’: array([0.0, None], dtype=object), ‘I_e’: array([None, None], dtype=object), ‘I_i’: array([None, None], dtype=object)}, required=True)
The values for each state-variable should be set to encompass the boundaries of the dynamic range of that state-variable. Set None for one-sided boundaries
state_variable_range : tvb.contrib.scripts.models.reduced_wong_wang_exc_io_inh_i.ReducedWongWangExcIOInhI.state_variable_range = Final(field_type=<class ‘dict’>, default={‘S_e’: array([0., 1.]), ‘S_i’: array([0., 1.]), ‘R_e’: array([ 0., 1000.]), ‘R_i’: array([ 0., 1000.]), ‘Rin_e’: array([ 0., 1000.]), ‘Rin_i’: array([ 0., 1000.]), ‘I_e’: array([0., 2.]), ‘I_i’: array([0., 1.])}, required=True)
Population firing rate
variables_of_interest : tvb.contrib.scripts.models.reduced_wong_wang_exc_io_inh_i.ReducedWongWangExcIOInhI.variables_of_interest = List(of=<class ‘str’>, default=(‘S_e’, ‘S_i’, ‘R_e’, ‘R_i’, ‘Rin_e’, ‘Rin_i’, ‘I_e’, ‘I_i’), required=True)
default state variables to be monitored
a_e : tvb.simulator.models.wong_wang_exc_inh.ReducedWongWangExcInh.a_e = NArray(label=’$$a_e$$‘, dtype=float64, default=array([310.]), dim_names=(), ndim=None, required=True)
[n/C]. Excitatory population input gain parameter, chosen to fit numerical solutions.
b_e : tvb.simulator.models.wong_wang_exc_inh.ReducedWongWangExcInh.b_e = NArray(label=’$$b_e$$‘, dtype=float64, default=array([125.]), dim_names=(), ndim=None, required=True)
[Hz]. Excitatory population input shift parameter chosen to fit numerical solutions.
d_e : tvb.simulator.models.wong_wang_exc_inh.ReducedWongWangExcInh.d_e = NArray(label=’$$d_e$$‘, dtype=float64, default=array([0.16]), dim_names=(), ndim=None, required=True)
[s]. Excitatory population input scaling parameter chosen to fit numerical solutions.
gamma_e : tvb.simulator.models.wong_wang_exc_inh.ReducedWongWangExcInh.gamma_e = NArray(label=’$$\\gamma_e$$‘, dtype=float64, default=array([0.000641]), dim_names=(), ndim=None, required=True)
Excitatory population kinetic parameter
tau_e : tvb.simulator.models.wong_wang_exc_inh.ReducedWongWangExcInh.tau_e = NArray(label=’$$\\tau_e$$‘, dtype=float64, default=array([100.]), dim_names=(), ndim=None, required=True)
[ms]. Excitatory population NMDA decay time constant.
w_p : tvb.simulator.models.wong_wang_exc_inh.ReducedWongWangExcInh.w_p = NArray(label=’$$w_p$$‘, dtype=float64, default=array([1.4]), dim_names=(), ndim=None, required=True)
Excitatory population recurrence weight
J_N : tvb.simulator.models.wong_wang_exc_inh.ReducedWongWangExcInh.J_N = NArray(label=’$$J_N$$‘, dtype=float64, default=array([0.15]), dim_names=(), ndim=None, required=True)
[nA] NMDA current
W_e : tvb.simulator.models.wong_wang_exc_inh.ReducedWongWangExcInh.W_e = NArray(label=’$$W_e$$‘, dtype=float64, default=array([1.]), dim_names=(), ndim=None, required=True)
Excitatory population external input scaling weight
a_i : tvb.simulator.models.wong_wang_exc_inh.ReducedWongWangExcInh.a_i = NArray(label=’$$a_i$$‘, dtype=float64, default=array([615.]), dim_names=(), ndim=None, required=True)
[n/C]. Inhibitory population input gain parameter, chosen to fit numerical solutions.
b_i : tvb.simulator.models.wong_wang_exc_inh.ReducedWongWangExcInh.b_i = NArray(label=’$$b_i$$‘, dtype=float64, default=array([177.]), dim_names=(), ndim=None, required=True)
[Hz]. Inhibitory population input shift parameter chosen to fit numerical solutions.
d_i : tvb.simulator.models.wong_wang_exc_inh.ReducedWongWangExcInh.d_i = NArray(label=’$$d_i$$‘, dtype=float64, default=array([0.087]), dim_names=(), ndim=None, required=True)
[s]. Inhibitory population input scaling parameter chosen to fit numerical solutions.
gamma_i : tvb.simulator.models.wong_wang_exc_inh.ReducedWongWangExcInh.gamma_i = NArray(label=’$$\\gamma_i$$‘, dtype=float64, default=array([0.001]), dim_names=(), ndim=None, required=True)
Inhibitory population kinetic parameter
tau_i : tvb.simulator.models.wong_wang_exc_inh.ReducedWongWangExcInh.tau_i = NArray(label=’$$\\tau_i$$‘, dtype=float64, default=array([10.]), dim_names=(), ndim=None, required=True)
[ms]. Inhibitory population NMDA decay time constant.
J_i : tvb.simulator.models.wong_wang_exc_inh.ReducedWongWangExcInh.J_i = NArray(label=’$$J_{i}$$‘, dtype=float64, default=array([1.]), dim_names=(), ndim=None, required=True)
[nA] Local inhibitory current
W_i : tvb.simulator.models.wong_wang_exc_inh.ReducedWongWangExcInh.W_i = NArray(label=’$$W_i$$‘, dtype=float64, default=array([0.7]), dim_names=(), ndim=None, required=True)
Inhibitory population external input scaling weight
I_o : tvb.simulator.models.wong_wang_exc_inh.ReducedWongWangExcInh.I_o = NArray(label=’$$I_{o}$$‘, dtype=float64, default=array([0.382]), dim_names=(), ndim=None, required=True)
[nA]. Effective external input
I_ext : tvb.simulator.models.wong_wang_exc_inh.ReducedWongWangExcInh.I_ext = NArray(label=’$$I_{ext}$$‘, dtype=float64, default=array([0.]), dim_names=(), ndim=None, required=True)
[nA]. Effective external stimulus input
G : tvb.simulator.models.wong_wang_exc_inh.ReducedWongWangExcInh.G = NArray(label=’$$G$$‘, dtype=float64, default=array([2.]), dim_names=(), ndim=None, required=True)
Global coupling scaling
lamda : tvb.simulator.models.wong_wang_exc_inh.ReducedWongWangExcInh.lamda = NArray(label=’$$\\lambda$$‘, dtype=float64, default=array([0.]), dim_names=(), ndim=None, required=True)
Inhibitory global coupling scaling

gid : tvb.basic.neotraits._core.HasTraits.gid = Attr(field_type=<class ‘uuid.UUID’>, default=None, required=True)

cvar = array([0], dtype=int32)
dfun(x, c, local_coupling=0.0)[source]
non_integrated_variables = ['Rin_e', 'Rin_i', 'I_e', 'I_i']
state_variable_boundaries

An attribute that can only be set once. If a default is provided it counts as a set, so it cannot be written to. Note that if the default is a mutable type, the value is shared with all instances of the owning class. We cannot enforce true constancy in python

state_variable_range

An attribute that can only be set once. If a default is provided it counts as a set, so it cannot be written to. Note that if the default is a mutable type, the value is shared with all instances of the owning class. We cannot enforce true constancy in python

state_variables = ['S_e', 'S_i', 'R_e', 'R_i', 'Rin_e', 'Rin_i', 'I_e', 'I_i']
tau_rin_e

Declares a numpy array. dtype enforces the dtype. The default dtype is float32. An optional symbolic shape can be given, as a tuple of Dim attributes from the owning class. The shape will be enforced, but no broadcasting will be done. domain declares what values are allowed in this array. It can be any object that can be checked for membership Defaults are checked if they are in the declared domain. For performance reasons this does not happen on every attribute set.

tau_rin_i

Declares a numpy array. dtype enforces the dtype. The default dtype is float32. An optional symbolic shape can be given, as a tuple of Dim attributes from the owning class. The shape will be enforced, but no broadcasting will be done. domain declares what values are allowed in this array. It can be any object that can be checked for membership Defaults are checked if they are in the declared domain. For performance reasons this does not happen on every attribute set.

update_derived_parameters()[source]

When needed, this should be a method for calculating parameters that are calculated based on paramaters directly set by the caller. For example, see, ReducedSetFitzHughNagumo. When not needed, this pass simplifies code that updates an arbitrary models parameters – ie, this can be safely called on any model, whether it’s used or not.

update_state_variables_before_integration(state_variables, coupling, local_coupling=0.0, stimulus=0.0)[source]
use_numba = True
variables_of_interest

The attribute is a list of values. Choices and type are reinterpreted as applying not to the list but to the elements of it

## spiking_wong_wang_exc_io_inh_i¶

Models based on Wong-Wang’s work. .. moduleauthor:: Dionysios Perdikis <dionysios.perdikis@charite.de>

class tvb.contrib.scripts.models.spiking_wong_wang_exc_io_inh_i.SpikingWongWangExcIOInhI(**kwargs)[source]
V_L : tvb.contrib.scripts.models.spiking_wong_wang_exc_io_inh_i.SpikingWongWangExcIOInhI.V_L = NArray(label=’$$V_L$$‘, dtype=float64, default=array([-70.]), dim_names=(), ndim=None, required=True)
[mV]. Resting membrane potential.
V_thr : tvb.contrib.scripts.models.spiking_wong_wang_exc_io_inh_i.SpikingWongWangExcIOInhI.V_thr = NArray(label=’$$V_thr$$‘, dtype=float64, default=array([-50.]), dim_names=(), ndim=None, required=True)
[mV]. Threshold membrane potential.
V_reset : tvb.contrib.scripts.models.spiking_wong_wang_exc_io_inh_i.SpikingWongWangExcIOInhI.V_reset = NArray(label=’$$V_reset$$‘, dtype=float64, default=array([-55.]), dim_names=(), ndim=None, required=True)
[mV]. Refractory membrane potential.
tau_AMPA : tvb.contrib.scripts.models.spiking_wong_wang_exc_io_inh_i.SpikingWongWangExcIOInhI.tau_AMPA = NArray(label=’$$tau_AMPA$$‘, dtype=float64, default=array([2.]), dim_names=(), ndim=None, required=True)
[ms]. AMPA synapse time constant.
tau_NMDA_rise : tvb.contrib.scripts.models.spiking_wong_wang_exc_io_inh_i.SpikingWongWangExcIOInhI.tau_NMDA_rise = NArray(label=’$$tau_NMDA_rise$$‘, dtype=float64, default=array([2.]), dim_names=(), ndim=None, required=True)
[ms]. NMDA synapse rise time constant.
tau_NMDA_decay : tvb.contrib.scripts.models.spiking_wong_wang_exc_io_inh_i.SpikingWongWangExcIOInhI.tau_NMDA_decay = NArray(label=’$$tau_NMDA_decay$$‘, dtype=float64, default=array([100.]), dim_names=(), ndim=None, required=True)
[ms]. NMDA synapse decay time constant.
tau_GABA : tvb.contrib.scripts.models.spiking_wong_wang_exc_io_inh_i.SpikingWongWangExcIOInhI.tau_GABA = NArray(label=’$$tau_GABA$$‘, dtype=float64, default=array([10.]), dim_names=(), ndim=None, required=True)
[ms]. GABA synapse time constant.
alpha : tvb.contrib.scripts.models.spiking_wong_wang_exc_io_inh_i.SpikingWongWangExcIOInhI.alpha = NArray(label=’$$alpha$$‘, dtype=float64, default=array([0.5]), dim_names=(), ndim=None, required=True)
[kHz]. NMDA synapse rate constant.
beta : tvb.contrib.scripts.models.spiking_wong_wang_exc_io_inh_i.SpikingWongWangExcIOInhI.beta = NArray(label=’$$beta$$‘, dtype=float64, default=array([0.062]), dim_names=(), ndim=None, required=True)
[]. NMDA synapse exponential constant.
lamda_NMDA : tvb.contrib.scripts.models.spiking_wong_wang_exc_io_inh_i.SpikingWongWangExcIOInhI.lamda_NMDA = NArray(label=’$$lamda_NMDA$$‘, dtype=float64, default=array([0.28]), dim_names=(), ndim=None, required=True)
[]. NMDA synapse constant.
lamda : tvb.contrib.scripts.models.spiking_wong_wang_exc_io_inh_i.SpikingWongWangExcIOInhI.lamda = NArray(label=’$$lamda$$‘, dtype=float64, default=array([0.]), dim_names=(), ndim=None, required=True)
[kHz]. Feedforward inhibition parameter.
I_ext : tvb.contrib.scripts.models.spiking_wong_wang_exc_io_inh_i.SpikingWongWangExcIOInhI.I_ext = NArray(label=’$$I_ext$$‘, dtype=float64, default=array([0.]), dim_names=(), ndim=None, required=True)
[pA]. External current stimulation.
spikes_ext : tvb.contrib.scripts.models.spiking_wong_wang_exc_io_inh_i.SpikingWongWangExcIOInhI.spikes_ext = NArray(label=’$$spikes_ext$$‘, dtype=float64, default=array([0.]), dim_names=(), ndim=None, required=True)
[spike weight]. External spikes’ stimulation.
G : tvb.contrib.scripts.models.spiking_wong_wang_exc_io_inh_i.SpikingWongWangExcIOInhI.G = NArray(label=’$$G$$‘, dtype=float64, default=array([2.]), dim_names=(), ndim=None, required=True)
Global coupling scaling
N_E : tvb.contrib.scripts.models.spiking_wong_wang_exc_io_inh_i.SpikingWongWangExcIOInhI.N_E = NArray(label=’$$N_E$$‘, dtype=float64, default=array([100]), dim_names=(), ndim=None, required=True)
Number of excitatory population neurons.
V_E : tvb.contrib.scripts.models.spiking_wong_wang_exc_io_inh_i.SpikingWongWangExcIOInhI.V_E = NArray(label=’$$V_E$$‘, dtype=float64, default=array([0.]), dim_names=(), ndim=None, required=True)
[mV]. Excitatory reversal potential.
w_EE : tvb.contrib.scripts.models.spiking_wong_wang_exc_io_inh_i.SpikingWongWangExcIOInhI.w_EE = NArray(label=’$$w_EE$$‘, dtype=float64, default=array([1.55]), dim_names=(), ndim=None, required=True)
Excitatory within population synapse weight.
w_EI : tvb.contrib.scripts.models.spiking_wong_wang_exc_io_inh_i.SpikingWongWangExcIOInhI.w_EI = NArray(label=’$$w_EI$$‘, dtype=float64, default=array([1.]), dim_names=(), ndim=None, required=True)
Excitatory to inhibitory population synapse weight.
C_m_E : tvb.contrib.scripts.models.spiking_wong_wang_exc_io_inh_i.SpikingWongWangExcIOInhI.C_m_E = NArray(label=’$$C_m_E$$‘, dtype=float64, default=array([500.]), dim_names=(), ndim=None, required=True)
[pF]. Excitatory population membrane capacitance.
g_m_E : tvb.contrib.scripts.models.spiking_wong_wang_exc_io_inh_i.SpikingWongWangExcIOInhI.g_m_E = NArray(label=’$$g_m_E$$‘, dtype=float64, default=array([25.]), dim_names=(), ndim=None, required=True)
[nS]. Excitatory population membrane conductance.
g_AMPA_ext_E : tvb.contrib.scripts.models.spiking_wong_wang_exc_io_inh_i.SpikingWongWangExcIOInhI.g_AMPA_ext_E = NArray(label=’$$g_AMPA_ext_E$$‘, dtype=float64, default=array([2.496]), dim_names=(), ndim=None, required=True)
[nS]. Excitatory population external AMPA conductance.
g_AMPA_E : tvb.contrib.scripts.models.spiking_wong_wang_exc_io_inh_i.SpikingWongWangExcIOInhI.g_AMPA_E = NArray(label=’$$g_AMPA_E$$‘, dtype=float64, default=array([0.104]), dim_names=(), ndim=None, required=True)
[nS]. Excitatory population AMPA conductance.
g_NMDA_E : tvb.contrib.scripts.models.spiking_wong_wang_exc_io_inh_i.SpikingWongWangExcIOInhI.g_NMDA_E = NArray(label=’$$g_NMDA_E$$‘, dtype=float64, default=array([0.327]), dim_names=(), ndim=None, required=True)
[nS]. Excitatory population NMDA conductance.
g_GABA_E : tvb.contrib.scripts.models.spiking_wong_wang_exc_io_inh_i.SpikingWongWangExcIOInhI.g_GABA_E = NArray(label=’$$g_GABA_E$$‘, dtype=float64, default=array([4.375]), dim_names=(), ndim=None, required=True)
[nS]. Excitatory population GABA conductance.
tau_ref_E : tvb.contrib.scripts.models.spiking_wong_wang_exc_io_inh_i.SpikingWongWangExcIOInhI.tau_ref_E = NArray(label=’$$tau_ref_E$$‘, dtype=float64, default=array([2.]), dim_names=(), ndim=None, required=True)
[ms]. Excitatory population refractory time.
N_I : tvb.contrib.scripts.models.spiking_wong_wang_exc_io_inh_i.SpikingWongWangExcIOInhI.N_I = NArray(label=’$$N_I$$‘, dtype=float64, default=array([100]), dim_names=(), ndim=None, required=True)
Number of inhibitory population neurons.
V_I : tvb.contrib.scripts.models.spiking_wong_wang_exc_io_inh_i.SpikingWongWangExcIOInhI.V_I = NArray(label=’$$V_I$$‘, dtype=float64, default=array([-70.]), dim_names=(), ndim=None, required=True)
[mV]. Inhibitory reversal potential.
w_II : tvb.contrib.scripts.models.spiking_wong_wang_exc_io_inh_i.SpikingWongWangExcIOInhI.w_II = NArray(label=’$$w_II$$‘, dtype=float64, default=array([1.]), dim_names=(), ndim=None, required=True)
Inhibitory within population synapse weight.
w_IE : tvb.contrib.scripts.models.spiking_wong_wang_exc_io_inh_i.SpikingWongWangExcIOInhI.w_IE = NArray(label=’$$w_IE$$‘, dtype=float64, default=array([1.]), dim_names=(), ndim=None, required=True)
Feedback inhibition: Inhibitory to excitatory population synapse weight.
C_m_I : tvb.contrib.scripts.models.spiking_wong_wang_exc_io_inh_i.SpikingWongWangExcIOInhI.C_m_I = NArray(label=’$$C_m_I$$‘, dtype=float64, default=array([200.]), dim_names=(), ndim=None, required=True)
[pF]. Inhibitory population membrane capacitance.
g_m_I : tvb.contrib.scripts.models.spiking_wong_wang_exc_io_inh_i.SpikingWongWangExcIOInhI.g_m_I = NArray(label=’$$g_m_I$$‘, dtype=float64, default=array([20.]), dim_names=(), ndim=None, required=True)
[nS]. Inhibitory population membrane conductance.
g_AMPA_ext_I : tvb.contrib.scripts.models.spiking_wong_wang_exc_io_inh_i.SpikingWongWangExcIOInhI.g_AMPA_ext_I = NArray(label=’$$g_AMPA_ext_I$$‘, dtype=float64, default=array([1.944]), dim_names=(), ndim=None, required=True)
[nS]. Inhibitory population external AMPA conductance.
g_AMPA_I : tvb.contrib.scripts.models.spiking_wong_wang_exc_io_inh_i.SpikingWongWangExcIOInhI.g_AMPA_I = NArray(label=’$$g_AMPA_I$$‘, dtype=float64, default=array([0.081]), dim_names=(), ndim=None, required=True)
[nS]. Inhibitory population AMPA conductance.
g_NMDA_I : tvb.contrib.scripts.models.spiking_wong_wang_exc_io_inh_i.SpikingWongWangExcIOInhI.g_NMDA_I = NArray(label=’$$g_NMDA_I$$‘, dtype=float64, default=array([0.258]), dim_names=(), ndim=None, required=True)
[nS]. Inhibitory population NMDA conductance.
g_GABA_I : tvb.contrib.scripts.models.spiking_wong_wang_exc_io_inh_i.SpikingWongWangExcIOInhI.g_GABA_I = NArray(label=’$$g_GABA_I$$‘, dtype=float64, default=array([3.4055]), dim_names=(), ndim=None, required=True)
[nS]. Inhibitory population GABA conductance.
tau_ref_I : tvb.contrib.scripts.models.spiking_wong_wang_exc_io_inh_i.SpikingWongWangExcIOInhI.tau_ref_I = NArray(label=’$$tau_ref_I$$‘, dtype=float64, default=array([1]), dim_names=(), ndim=None, required=True)
[ms]. Inhibitory population refractory time.
state_variable_boundaries : tvb.contrib.scripts.models.spiking_wong_wang_exc_io_inh_i.SpikingWongWangExcIOInhI.state_variable_boundaries = Final(field_type=<class ‘dict’>, default={‘s_AMPA’: array([0., 1.]), ‘x_NMDA’: array([0.0, None], dtype=object), ‘s_NMDA’: array([0., 1.]), ‘s_GABA’: array([0., 1.]), ‘s_AMPA_ext’: array([ 0., 800.]), ‘V_m’: array([None, None], dtype=object), ‘t_ref’: array([0.0, None], dtype=object), ‘spikes_ext’: array([0.0, None], dtype=object), ‘spikes’: array([0., 1.]), ‘I_L’: array([None, None], dtype=object), ‘I_AMPA’: array([None, None], dtype=object), ‘I_GABA’: array([None, None], dtype=object), ‘I_NMDA’: array([None, None], dtype=object), ‘I_AMPA_ext’: array([None, None], dtype=object)}, required=True)
The values for each state-variable should be set to encompass the boundaries of the dynamic range of that state-variable. Set None for one-sided boundaries
state_variable_range : tvb.contrib.scripts.models.spiking_wong_wang_exc_io_inh_i.SpikingWongWangExcIOInhI.state_variable_range = Final(field_type=<class ‘dict’>, default={‘s_AMPA’: array([0., 1.]), ‘x_NMDA’: array([ 0., 200.]), ‘s_NMDA’: array([0., 1.]), ‘s_GABA’: array([0., 1.]), ‘s_AMPA_ext’: array([0., 1.]), ‘V_m’: array([-70., -50.]), ‘t_ref’: array([0., 1.]), ‘spikes_ext’: array([0. , 0.5]), ‘spikes’: array([0. , 0.5]), ‘I_L’: array([ 0., 1000.]), ‘I_AMPA’: array([-1000., 0.]), ‘I_NMDA’: array([-1000., 0.]), ‘I_GABA’: array([ 0., 1000.]), ‘I_AMPA_ext’: array([-10., 0.])}, required=True)
Population firing rate
variables_of_interest : tvb.contrib.scripts.models.spiking_wong_wang_exc_io_inh_i.SpikingWongWangExcIOInhI.variables_of_interest = List(of=<class ‘str’>, default=(‘s_AMPA’, ‘x_NMDA’, ‘s_NMDA’, ‘s_GABA’, ‘s_AMPA_ext’, ‘V_m’, ‘t_ref’, ‘spikes_ext’, ‘spikes’, ‘I_L’, ‘I_AMPA’, ‘I_NMDA’, ‘I_GABA’, ‘I_AMPA_ext’), required=True)
default state variables to be monitored

gid : tvb.basic.neotraits._core.HasTraits.gid = Attr(field_type=<class ‘uuid.UUID’>, default=None, required=True)

C_m_E

Declares a numpy array. dtype enforces the dtype. The default dtype is float32. An optional symbolic shape can be given, as a tuple of Dim attributes from the owning class. The shape will be enforced, but no broadcasting will be done. domain declares what values are allowed in this array. It can be any object that can be checked for membership Defaults are checked if they are in the declared domain. For performance reasons this does not happen on every attribute set.

C_m_I

Declares a numpy array. dtype enforces the dtype. The default dtype is float32. An optional symbolic shape can be given, as a tuple of Dim attributes from the owning class. The shape will be enforced, but no broadcasting will be done. domain declares what values are allowed in this array. It can be any object that can be checked for membership Defaults are checked if they are in the declared domain. For performance reasons this does not happen on every attribute set.

G

Declares a numpy array. dtype enforces the dtype. The default dtype is float32. An optional symbolic shape can be given, as a tuple of Dim attributes from the owning class. The shape will be enforced, but no broadcasting will be done. domain declares what values are allowed in this array. It can be any object that can be checked for membership Defaults are checked if they are in the declared domain. For performance reasons this does not happen on every attribute set.

I_ext

Declares a numpy array. dtype enforces the dtype. The default dtype is float32. An optional symbolic shape can be given, as a tuple of Dim attributes from the owning class. The shape will be enforced, but no broadcasting will be done. domain declares what values are allowed in this array. It can be any object that can be checked for membership Defaults are checked if they are in the declared domain. For performance reasons this does not happen on every attribute set.

N_E

Declares a numpy array. dtype enforces the dtype. The default dtype is float32. An optional symbolic shape can be given, as a tuple of Dim attributes from the owning class. The shape will be enforced, but no broadcasting will be done. domain declares what values are allowed in this array. It can be any object that can be checked for membership Defaults are checked if they are in the declared domain. For performance reasons this does not happen on every attribute set.

N_I

Declares a numpy array. dtype enforces the dtype. The default dtype is float32. An optional symbolic shape can be given, as a tuple of Dim attributes from the owning class. The shape will be enforced, but no broadcasting will be done. domain declares what values are allowed in this array. It can be any object that can be checked for membership Defaults are checked if they are in the declared domain. For performance reasons this does not happen on every attribute set.

V_E

Declares a numpy array. dtype enforces the dtype. The default dtype is float32. An optional symbolic shape can be given, as a tuple of Dim attributes from the owning class. The shape will be enforced, but no broadcasting will be done. domain declares what values are allowed in this array. It can be any object that can be checked for membership Defaults are checked if they are in the declared domain. For performance reasons this does not happen on every attribute set.

V_I

Declares a numpy array. dtype enforces the dtype. The default dtype is float32. An optional symbolic shape can be given, as a tuple of Dim attributes from the owning class. The shape will be enforced, but no broadcasting will be done. domain declares what values are allowed in this array. It can be any object that can be checked for membership Defaults are checked if they are in the declared domain. For performance reasons this does not happen on every attribute set.

V_L

Declares a numpy array. dtype enforces the dtype. The default dtype is float32. An optional symbolic shape can be given, as a tuple of Dim attributes from the owning class. The shape will be enforced, but no broadcasting will be done. domain declares what values are allowed in this array. It can be any object that can be checked for membership Defaults are checked if they are in the declared domain. For performance reasons this does not happen on every attribute set.

V_reset

Declares a numpy array. dtype enforces the dtype. The default dtype is float32. An optional symbolic shape can be given, as a tuple of Dim attributes from the owning class. The shape will be enforced, but no broadcasting will be done. domain declares what values are allowed in this array. It can be any object that can be checked for membership Defaults are checked if they are in the declared domain. For performance reasons this does not happen on every attribute set.

V_thr

Declares a numpy array. dtype enforces the dtype. The default dtype is float32. An optional symbolic shape can be given, as a tuple of Dim attributes from the owning class. The shape will be enforced, but no broadcasting will be done. domain declares what values are allowed in this array. It can be any object that can be checked for membership Defaults are checked if they are in the declared domain. For performance reasons this does not happen on every attribute set.

alpha

Declares a numpy array. dtype enforces the dtype. The default dtype is float32. An optional symbolic shape can be given, as a tuple of Dim attributes from the owning class. The shape will be enforced, but no broadcasting will be done. domain declares what values are allowed in this array. It can be any object that can be checked for membership Defaults are checked if they are in the declared domain. For performance reasons this does not happen on every attribute set.

beta

Declares a numpy array. dtype enforces the dtype. The default dtype is float32. An optional symbolic shape can be given, as a tuple of Dim attributes from the owning class. The shape will be enforced, but no broadcasting will be done. domain declares what values are allowed in this array. It can be any object that can be checked for membership Defaults are checked if they are in the declared domain. For performance reasons this does not happen on every attribute set.

cvar = array([0], dtype=int32)
dfun(x, c, local_coupling=0.0)[source]
g_AMPA_E

Declares a numpy array. dtype enforces the dtype. The default dtype is float32. An optional symbolic shape can be given, as a tuple of Dim attributes from the owning class. The shape will be enforced, but no broadcasting will be done. domain declares what values are allowed in this array. It can be any object that can be checked for membership Defaults are checked if they are in the declared domain. For performance reasons this does not happen on every attribute set.

g_AMPA_I

Declares a numpy array. dtype enforces the dtype. The default dtype is float32. An optional symbolic shape can be given, as a tuple of Dim attributes from the owning class. The shape will be enforced, but no broadcasting will be done. domain declares what values are allowed in this array. It can be any object that can be checked for membership Defaults are checked if they are in the declared domain. For performance reasons this does not happen on every attribute set.

g_AMPA_ext_E

Declares a numpy array. dtype enforces the dtype. The default dtype is float32. An optional symbolic shape can be given, as a tuple of Dim attributes from the owning class. The shape will be enforced, but no broadcasting will be done. domain declares what values are allowed in this array. It can be any object that can be checked for membership Defaults are checked if they are in the declared domain. For performance reasons this does not happen on every attribute set.

g_AMPA_ext_I

Declares a numpy array. dtype enforces the dtype. The default dtype is float32. An optional symbolic shape can be given, as a tuple of Dim attributes from the owning class. The shape will be enforced, but no broadcasting will be done. domain declares what values are allowed in this array. It can be any object that can be checked for membership Defaults are checked if they are in the declared domain. For performance reasons this does not happen on every attribute set.

g_GABA_E

Declares a numpy array. dtype enforces the dtype. The default dtype is float32. An optional symbolic shape can be given, as a tuple of Dim attributes from the owning class. The shape will be enforced, but no broadcasting will be done. domain declares what values are allowed in this array. It can be any object that can be checked for membership Defaults are checked if they are in the declared domain. For performance reasons this does not happen on every attribute set.

g_GABA_I

Declares a numpy array. dtype enforces the dtype. The default dtype is float32. An optional symbolic shape can be given, as a tuple of Dim attributes from the owning class. The shape will be enforced, but no broadcasting will be done. domain declares what values are allowed in this array. It can be any object that can be checked for membership Defaults are checked if they are in the declared domain. For performance reasons this does not happen on every attribute set.

g_NMDA_E

Declares a numpy array. dtype enforces the dtype. The default dtype is float32. An optional symbolic shape can be given, as a tuple of Dim attributes from the owning class. The shape will be enforced, but no broadcasting will be done. domain declares what values are allowed in this array. It can be any object that can be checked for membership Defaults are checked if they are in the declared domain. For performance reasons this does not happen on every attribute set.

g_NMDA_I

Declares a numpy array. dtype enforces the dtype. The default dtype is float32. An optional symbolic shape can be given, as a tuple of Dim attributes from the owning class. The shape will be enforced, but no broadcasting will be done. domain declares what values are allowed in this array. It can be any object that can be checked for membership Defaults are checked if they are in the declared domain. For performance reasons this does not happen on every attribute set.

g_m_E

Declares a numpy array. dtype enforces the dtype. The default dtype is float32. An optional symbolic shape can be given, as a tuple of Dim attributes from the owning class. The shape will be enforced, but no broadcasting will be done. domain declares what values are allowed in this array. It can be any object that can be checked for membership Defaults are checked if they are in the declared domain. For performance reasons this does not happen on every attribute set.

g_m_I

Declares a numpy array. dtype enforces the dtype. The default dtype is float32. An optional symbolic shape can be given, as a tuple of Dim attributes from the owning class. The shape will be enforced, but no broadcasting will be done. domain declares what values are allowed in this array. It can be any object that can be checked for membership Defaults are checked if they are in the declared domain. For performance reasons this does not happen on every attribute set.

lamda

Declares a numpy array. dtype enforces the dtype. The default dtype is float32. An optional symbolic shape can be given, as a tuple of Dim attributes from the owning class. The shape will be enforced, but no broadcasting will be done. domain declares what values are allowed in this array. It can be any object that can be checked for membership Defaults are checked if they are in the declared domain. For performance reasons this does not happen on every attribute set.

lamda_NMDA

Declares a numpy array. dtype enforces the dtype. The default dtype is float32. An optional symbolic shape can be given, as a tuple of Dim attributes from the owning class. The shape will be enforced, but no broadcasting will be done. domain declares what values are allowed in this array. It can be any object that can be checked for membership Defaults are checked if they are in the declared domain. For performance reasons this does not happen on every attribute set.

non_integrated_variables = ['spikes_ext', 'spikes', 'I_L', 'I_AMPA', 'I_NMDA', 'I_GABA', 'I_AMPA_ext']
number_of_modes = 200
spikes_ext

Declares a numpy array. dtype enforces the dtype. The default dtype is float32. An optional symbolic shape can be given, as a tuple of Dim attributes from the owning class. The shape will be enforced, but no broadcasting will be done. domain declares what values are allowed in this array. It can be any object that can be checked for membership Defaults are checked if they are in the declared domain. For performance reasons this does not happen on every attribute set.

state_variable_boundaries

An attribute that can only be set once. If a default is provided it counts as a set, so it cannot be written to. Note that if the default is a mutable type, the value is shared with all instances of the owning class. We cannot enforce true constancy in python

state_variable_range

An attribute that can only be set once. If a default is provided it counts as a set, so it cannot be written to. Note that if the default is a mutable type, the value is shared with all instances of the owning class. We cannot enforce true constancy in python

state_variables = ['s_AMPA', 'x_NMDA', 's_NMDA', 's_GABA', 's_AMPA_ext', 'V_m', 't_ref', 'spikes_ext', 'spikes', 'I_L', 'I_AMPA', 'I_NMDA', 'I_GABA', 'I_AMPA_ext']
tau_AMPA

Declares a numpy array. dtype enforces the dtype. The default dtype is float32. An optional symbolic shape can be given, as a tuple of Dim attributes from the owning class. The shape will be enforced, but no broadcasting will be done. domain declares what values are allowed in this array. It can be any object that can be checked for membership Defaults are checked if they are in the declared domain. For performance reasons this does not happen on every attribute set.

tau_GABA

Declares a numpy array. dtype enforces the dtype. The default dtype is float32. An optional symbolic shape can be given, as a tuple of Dim attributes from the owning class. The shape will be enforced, but no broadcasting will be done. domain declares what values are allowed in this array. It can be any object that can be checked for membership Defaults are checked if they are in the declared domain. For performance reasons this does not happen on every attribute set.

tau_NMDA_decay

Declares a numpy array. dtype enforces the dtype. The default dtype is float32. An optional symbolic shape can be given, as a tuple of Dim attributes from the owning class. The shape will be enforced, but no broadcasting will be done. domain declares what values are allowed in this array. It can be any object that can be checked for membership Defaults are checked if they are in the declared domain. For performance reasons this does not happen on every attribute set.

tau_NMDA_rise

Declares a numpy array. dtype enforces the dtype. The default dtype is float32. An optional symbolic shape can be given, as a tuple of Dim attributes from the owning class. The shape will be enforced, but no broadcasting will be done. domain declares what values are allowed in this array. It can be any object that can be checked for membership Defaults are checked if they are in the declared domain. For performance reasons this does not happen on every attribute set.

tau_ref_E

Declares a numpy array. dtype enforces the dtype. The default dtype is float32. An optional symbolic shape can be given, as a tuple of Dim attributes from the owning class. The shape will be enforced, but no broadcasting will be done. domain declares what values are allowed in this array. It can be any object that can be checked for membership Defaults are checked if they are in the declared domain. For performance reasons this does not happen on every attribute set.

tau_ref_I

Declares a numpy array. dtype enforces the dtype. The default dtype is float32. An optional symbolic shape can be given, as a tuple of Dim attributes from the owning class. The shape will be enforced, but no broadcasting will be done. domain declares what values are allowed in this array. It can be any object that can be checked for membership Defaults are checked if they are in the declared domain. For performance reasons this does not happen on every attribute set.

update_derived_parameters()[source]

When needed, this should be a method for calculating parameters that are calculated based on paramaters directly set by the caller. For example, see, ReducedSetFitzHughNagumo. When not needed, this pass simplifies code that updates an arbitrary models parameters – ie, this can be safely called on any model, whether it’s used or not.

update_state_variables_before_integration(state_variables, coupling, local_coupling=0.0, stimulus=0.0)[source]
variables_of_interest

The attribute is a list of values. Choices and type are reinterpreted as applying not to the list but to the elements of it

w_EE

Declares a numpy array. dtype enforces the dtype. The default dtype is float32. An optional symbolic shape can be given, as a tuple of Dim attributes from the owning class. The shape will be enforced, but no broadcasting will be done. domain declares what values are allowed in this array. It can be any object that can be checked for membership Defaults are checked if they are in the declared domain. For performance reasons this does not happen on every attribute set.

w_EI

Declares a numpy array. dtype enforces the dtype. The default dtype is float32. An optional symbolic shape can be given, as a tuple of Dim attributes from the owning class. The shape will be enforced, but no broadcasting will be done. domain declares what values are allowed in this array. It can be any object that can be checked for membership Defaults are checked if they are in the declared domain. For performance reasons this does not happen on every attribute set.

w_IE

Declares a numpy array. dtype enforces the dtype. The default dtype is float32. An optional symbolic shape can be given, as a tuple of Dim attributes from the owning class. The shape will be enforced, but no broadcasting will be done. domain declares what values are allowed in this array. It can be any object that can be checked for membership Defaults are checked if they are in the declared domain. For performance reasons this does not happen on every attribute set.

w_II

Declares a numpy array. dtype enforces the dtype. The default dtype is float32. An optional symbolic shape can be given, as a tuple of Dim attributes from the owning class. The shape will be enforced, but no broadcasting will be done. domain declares what values are allowed in this array. It can be any object that can be checked for membership Defaults are checked if they are in the declared domain. For performance reasons this does not happen on every attribute set.

## wilson_cowan_constraint¶

Wilson-Cowan equations based model definition. .. moduleauthor:: Dionysios Perdikis <dionysios.perdikis@charite.de>

class tvb.contrib.scripts.models.wilson_cowan_constraint.WilsonCowan(**kwargs)[source]

References:

 [WC_1972] (1, 2) Wilson, H.R. and Cowan, J.D. Excitatory and inhibitory interactions in localized populations of model neurons, Biophysical journal, 12: 1-24, 1972.
 [WC_1973] Wilson, H.R. and Cowan, J.D A Mathematical Theory of the Functional Dynamics of Cortical and Thalamic Nervous Tissue
 [D_2011] Daffertshofer, A. and van Wijk, B. On the influence of amplitude on the connectivity between phases Frontiers in Neuroinformatics, July, 2011

Used Eqns 11 and 12 from [WC_1972] in dfun. P and Q represent external inputs, which when exploring the phase portrait of the local model are set to constant values. However in the case of a full network, P and Q are the entry point to our long range and local couplings, that is, the activity from all other nodes is the external input to the local population.

The default parameters are taken from figure 4 of [WC_1972], pag. 10

In [WC_1973] they present a model of neural tissue on the pial surface is. See Fig. 1 in page 58. The following local couplings (lateral interactions) occur given a region i and a region j:

E_i-> E_j E_i-> I_j I_i-> I_j I_i-> E_j
Table 1
SanzLeonetAl, 2014
Parameter Value
k_e, k_i 1.00
r_e, r_i 0.00
tau_e, tau_i 10.0
c_1 10.0
c_2 6.0
c_3 1.0
c_4 1.0
a_e, a_i 1.0
b_e, b_i 0.0
theta_e 2.0
theta_i 3.5
alpha_e 1.2
alpha_i 2.0
P 0.5
Q 0
c_e, c_i 1.0
alpha_e 1.2
alpha_i 2.0
frequency peak at 20 Hz

The parameters in Table 1 reproduce Figure A1 in [D_2011] but set the limit cycle frequency to a sensible value (eg, 20Hz).

Model bifurcation parameters:
• $$c_1$$
• $$P$$

The builders ($$E$$, $$I$$) phase-plane, including a representation of the vector field as well as its nullclines, using default parameters, can be seen below:

The general formulation for the textit{textbf{Wilson-Cowan}} model as a dynamical unit at a node $k$ in a BNM with $l$ nodes reads:

$\begin{split}\dot{E}_k &= \dfrac{1}{\tau_e} (-E_k + (k_e - r_e E_k) \mathcal{S}_e (\alpha_e \left( c_{ee} E_k - c_{ei} I_k + P_k - \theta_e + \mathbf{\Gamma}(E_k, E_j, u_{kj}) + W_{\zeta}\cdot E_j + W_{\zeta}\cdot I_j\right) ))\\ \dot{I}_k &= \dfrac{1}{\tau_i} (-I_k + (k_i - r_i I_k) \mathcal{S}_i (\alpha_i \left( c_{ie} E_k - c_{ee} I_k + Q_k - \theta_i + \mathbf{\Gamma}(E_k, E_j, u_{kj}) + W_{\zeta}\cdot E_j + W_{\zeta}\cdot I_j\right) )),\end{split}$
tau_Ein : tvb.contrib.scripts.models.wilson_cowan_constraint.WilsonCowan.tau_Ein = NArray(label=’$$\\tau_Ein$$‘, dtype=float64, default=array([50.]), dim_names=(), ndim=None, required=True)
[ms]. Excitatory population instant spiking rate time constant.
tau_Iin : tvb.contrib.scripts.models.wilson_cowan_constraint.WilsonCowan.tau_Iin = NArray(label=’$$\\tau_Iin$$‘, dtype=float64, default=array([50.]), dim_names=(), ndim=None, required=True)
[ms]. Inhibitory population instant spiking rate time constant.
state_variable_boundaries : tvb.contrib.scripts.models.wilson_cowan_constraint.WilsonCowan.state_variable_boundaries = Final(field_type=<class ‘dict’>, default={‘E’: array([0., 1.]), ‘I’: array([0., 1.]), ‘Ein’: array([0., 1.]), ‘Iin’: array([0., 1.])}, required=True)
The values for each state-variable should be set to encompass the boundaries of the dynamic range of that state-variable. Set None for one-sided boundaries.
state_variable_range : tvb.contrib.scripts.models.wilson_cowan_constraint.WilsonCowan.state_variable_range = Final(field_type=<class ‘dict’>, default={‘E’: array([0. , 0.5]), ‘I’: array([0. , 0.5]), ‘Ein’: array([0. , 0.5]), ‘Iin’: array([0. , 0.5])}, required=True)
The values for each state-variable should be set to encompass the expected dynamic range of that state-variable for the current parameters, it is used as a mechanism for bounding random inital conditions when the simulation isn’t started from an explicit history, it is also provides the default range of phase-plane plots.
variables_of_interest : tvb.contrib.scripts.models.wilson_cowan_constraint.WilsonCowan.variables_of_interest = List(of=<class ‘str’>, default=(‘E’, ‘I’, ‘Ein’, ‘Iin’), required=True)
default state variables to be monitored
c_ee : tvb.simulator.models.wilson_cowan.WilsonCowan.c_ee = NArray(label=’$$c_{ee}$$‘, dtype=float64, default=array([12.]), dim_names=(), ndim=None, required=True)
Excitatory to excitatory coupling coefficient
c_ei : tvb.simulator.models.wilson_cowan.WilsonCowan.c_ei = NArray(label=’$$c_{ei}$$‘, dtype=float64, default=array([4.]), dim_names=(), ndim=None, required=True)
Inhibitory to excitatory coupling coefficient
c_ie : tvb.simulator.models.wilson_cowan.WilsonCowan.c_ie = NArray(label=’$$c_{ie}$$‘, dtype=float64, default=array([13.]), dim_names=(), ndim=None, required=True)
Excitatory to inhibitory coupling coefficient.
c_ii : tvb.simulator.models.wilson_cowan.WilsonCowan.c_ii = NArray(label=’$$c_{ii}$$‘, dtype=float64, default=array([11.]), dim_names=(), ndim=None, required=True)
Inhibitory to inhibitory coupling coefficient.
tau_e : tvb.simulator.models.wilson_cowan.WilsonCowan.tau_e = NArray(label=’$$\\tau_e$$‘, dtype=float64, default=array([10.]), dim_names=(), ndim=None, required=True)
Excitatory population, membrane time-constant [ms]
tau_i : tvb.simulator.models.wilson_cowan.WilsonCowan.tau_i = NArray(label=’$$\\tau_i$$‘, dtype=float64, default=array([10.]), dim_names=(), ndim=None, required=True)
Inhibitory population, membrane time-constant [ms]
a_e : tvb.simulator.models.wilson_cowan.WilsonCowan.a_e = NArray(label=’$$a_e$$‘, dtype=float64, default=array([1.2]), dim_names=(), ndim=None, required=True)
The slope parameter for the excitatory response function
b_e : tvb.simulator.models.wilson_cowan.WilsonCowan.b_e = NArray(label=’$$b_e$$‘, dtype=float64, default=array([2.8]), dim_names=(), ndim=None, required=True)
Position of the maximum slope of the excitatory sigmoid function
c_e : tvb.simulator.models.wilson_cowan.WilsonCowan.c_e = NArray(label=’$$c_e$$‘, dtype=float64, default=array([1.]), dim_names=(), ndim=None, required=True)
The amplitude parameter for the excitatory response function
theta_e : tvb.simulator.models.wilson_cowan.WilsonCowan.theta_e = NArray(label=’$$\\theta_e$$‘, dtype=float64, default=array([0.]), dim_names=(), ndim=None, required=True)
Excitatory threshold
a_i : tvb.simulator.models.wilson_cowan.WilsonCowan.a_i = NArray(label=’$$a_i$$‘, dtype=float64, default=array([1.]), dim_names=(), ndim=None, required=True)
The slope parameter for the inhibitory response function
b_i : tvb.simulator.models.wilson_cowan.WilsonCowan.b_i = NArray(label=’$$b_i$$‘, dtype=float64, default=array([4.]), dim_names=(), ndim=None, required=True)
Position of the maximum slope of a sigmoid function [in threshold units]
theta_i : tvb.simulator.models.wilson_cowan.WilsonCowan.theta_i = NArray(label=’$$\\theta_i$$‘, dtype=float64, default=array([0.]), dim_names=(), ndim=None, required=True)
Inhibitory threshold
c_i : tvb.simulator.models.wilson_cowan.WilsonCowan.c_i = NArray(label=’$$c_i$$‘, dtype=float64, default=array([1.]), dim_names=(), ndim=None, required=True)
The amplitude parameter for the inhibitory response function
r_e : tvb.simulator.models.wilson_cowan.WilsonCowan.r_e = NArray(label=’$$r_e$$‘, dtype=float64, default=array([1.]), dim_names=(), ndim=None, required=True)
Excitatory refractory period
r_i : tvb.simulator.models.wilson_cowan.WilsonCowan.r_i = NArray(label=’$$r_i$$‘, dtype=float64, default=array([1.]), dim_names=(), ndim=None, required=True)
Inhibitory refractory period
k_e : tvb.simulator.models.wilson_cowan.WilsonCowan.k_e = NArray(label=’$$k_e$$‘, dtype=float64, default=array([1.]), dim_names=(), ndim=None, required=True)
Maximum value of the excitatory response function
k_i : tvb.simulator.models.wilson_cowan.WilsonCowan.k_i = NArray(label=’$$k_i$$‘, dtype=float64, default=array([1.]), dim_names=(), ndim=None, required=True)
Maximum value of the inhibitory response function
P : tvb.simulator.models.wilson_cowan.WilsonCowan.P = NArray(label=’$$P$$‘, dtype=float64, default=array([0.]), dim_names=(), ndim=None, required=True)
External stimulus to the excitatory population. Constant intensity.Entry point for coupling.
Q : tvb.simulator.models.wilson_cowan.WilsonCowan.Q = NArray(label=’$$Q$$‘, dtype=float64, default=array([0.]), dim_names=(), ndim=None, required=True)
External stimulus to the inhibitory population. Constant intensity.Entry point for coupling.
alpha_e : tvb.simulator.models.wilson_cowan.WilsonCowan.alpha_e = NArray(label=’$$\\alpha_e$$‘, dtype=float64, default=array([1.]), dim_names=(), ndim=None, required=True)
External stimulus to the excitatory population. Constant intensity.Entry point for coupling.
alpha_i : tvb.simulator.models.wilson_cowan.WilsonCowan.alpha_i = NArray(label=’$$\\alpha_i$$‘, dtype=float64, default=array([1.]), dim_names=(), ndim=None, required=True)
External stimulus to the inhibitory population. Constant intensity.Entry point for coupling.

gid : tvb.basic.neotraits._core.HasTraits.gid = Attr(field_type=<class ‘uuid.UUID’>, default=None, required=True)

dfun(state_variables, coupling, local_coupling=0.0)[source]
$\begin{split}\tau \dot{x}(t) &= -z(t) + \phi(z(t)) \\ \phi(x) &= \frac{c}{1-exp(-a (x-b))}\end{split}$
state_variable_boundaries

An attribute that can only be set once. If a default is provided it counts as a set, so it cannot be written to. Note that if the default is a mutable type, the value is shared with all instances of the owning class. We cannot enforce true constancy in python

state_variable_range

An attribute that can only be set once. If a default is provided it counts as a set, so it cannot be written to. Note that if the default is a mutable type, the value is shared with all instances of the owning class. We cannot enforce true constancy in python

state_variables = ['E', 'I', 'Ein', 'Iin']
tau_Ein

Declares a numpy array. dtype enforces the dtype. The default dtype is float32. An optional symbolic shape can be given, as a tuple of Dim attributes from the owning class. The shape will be enforced, but no broadcasting will be done. domain declares what values are allowed in this array. It can be any object that can be checked for membership Defaults are checked if they are in the declared domain. For performance reasons this does not happen on every attribute set.

tau_Iin

Declares a numpy array. dtype enforces the dtype. The default dtype is float32. An optional symbolic shape can be given, as a tuple of Dim attributes from the owning class. The shape will be enforced, but no broadcasting will be done. domain declares what values are allowed in this array. It can be any object that can be checked for membership Defaults are checked if they are in the declared domain. For performance reasons this does not happen on every attribute set.

update_derived_parameters()[source]

When needed, this should be a method for calculating parameters that are calculated based on paramaters directly set by the caller. For example, see, ReducedSetFitzHughNagumo. When not needed, this pass simplifies code that updates an arbitrary models parameters – ie, this can be safely called on any model, whether it’s used or not.

variables_of_interest

The attribute is a list of values. Choices and type are reinterpreted as applying not to the list but to the elements of it