TheVirtualBrain:
TheDocumentationwebsite.
A collection of neuronal dynamics models.
Specific models inherit from the abstract class Model.
Bases: enum.Enum
An enumeration.
This module defines the common imports and abstract base class for model definitions.
Bases: tvb.basic.neotraits._core.HasTraits
Defines the abstract base class for neuronal models.
gid : tvb.basic.neotraits._core.HasTraits.gid = Attr(field_type=<class ‘uuid.UUID’>, default=None, required=True)
Defines the dynamic equations. That is, the derivative of the state-variables given their current state state_variables, the past state from other regions of the brain currently arriving coupling, and the current state of the “local” neighbourhood local_coupling.
Generates uniformly distributed initial conditions, bounded by the state variable limits defined by the model.
Generate initial conditions with integrator and shape.
Computes the state space trajectory of a single mass model system where coupling is static, with a deterministic Euler method.
Models expect coupling of shape (n_cvar, n_node), so if this method is called with coupling (:, n_cvar, n_ode), it will compute a stationary trajectory for each coupling[i, ...]
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.
Bases: tvb.simulator.models.base.Model
Base model for Numba-implemented dfuns.
gid : tvb.basic.neotraits._core.HasTraits.gid = Attr(field_type=<class ‘uuid.UUID’>, default=None, required=True)
Hindmarsh-Rose-Jirsa Epileptor model.
Bases: tvb.simulator.models.base.ModelNumbaDfun
The Epileptor is a composite neural mass model of six dimensions which has been crafted to model the phenomenology of epileptic seizures. (see [Jirsaetal_2014])
Equations and default parameters are taken from [Jirsaetal_2014].
Table 1 Parameter Value I_rest1 3.1 I_rest2 0.45 r 0.00035 x_0 -1.6 slope 0.0 Integration parameter dt 0.1 simulation_length 4000 Noise nsig [0., 0., 0., 1e-3, 1e-3, 0.] Jirsa et al. 2014
[Jirsaetal_2014] (1, 2) Jirsa, V. K.; Stacey, W. C.; Quilichini, P. P.; Ivanov, A. I.; Bernard, C. On the nature of seizure dynamics. Brain, 2014. Variables of interest to be used by monitors: -y[0] + y[3]
\[\begin{split}\dot{x_{1}} &=& y_{1} - f_{1}(x_{1}, x_{2}) - z + I_{ext1} \\ \dot{y_{1}} &=& c - d x_{1}^{2} - y{1} \\ \dot{z} &=& \begin{cases} r(4 (x_{1} - x_{0}) - z-0.1 z^{7}) & \text{if } x<0 \\ r(4 (x_{1} - x_{0}) - z) & \text{if } x \geq 0 \end{cases} \\ \dot{x_{2}} &=& -y_{2} + x_{2} - x_{2}^{3} + I_{ext2} + 0.002 g - 0.3 (z-3.5) \\ \dot{y_{2}} &=& 1 / \tau (-y_{2} + f_{2}(x_{2}))\\ \dot{g} &=& -0.01 (g - 0.1 x_{1})\end{split}\]
- where:
and:
\[\begin{split}f_{2}(x_{2}) = \begin{cases} 0 & \text{if } x_{2} <-0.25\\ a_{2}(x_{2} + 0.25) & \text{if } x_{2} \geq -0.25 \end{cases}\end{split}\]Note Feb. 2017: the slow permittivity variable can be modify to account for the time difference between interictal and ictal states (see [Proixetal_2014]).
[Proixetal_2014] Proix, T.; Bartolomei, F; Chauvel, P; Bernard, C; Jirsa, V.K. * Permittivity coupling across brain regions determines seizure recruitment in partial epilepsy.* J Neurosci 2014, 34:15009-21.
gid : tvb.basic.neotraits._core.HasTraits.gid = Attr(field_type=<class ‘uuid.UUID’>, default=None, required=True)
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.
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.
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.
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.
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.
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.
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.
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.
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.
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.
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.
Computes the derivatives of the state variables of the Epileptor with respect to time.
Implementation note: we expect this version of the Epileptor to be used in a vectorized manner. Concretely, y has a shape of (6, n) where n is the number of nodes in the network. An consequence is that the original use of if/else is translated by calculated both the true and false forms and mixing them using a boolean mask.
Variables of interest to be used by monitors: -y[0] + y[3]
\[\begin{split}\dot{x_{1}} &=& y_{1} - f_{1}(x_{1}, x_{2}) - z + I_{ext1} \\ \dot{y_{1}} &=& c - d x_{1}^{2} - y{1} \\ \dot{z} &=& \begin{cases} r(4 (x_{1} - x_{0}) - z-0.1 z^{7}) & \text{if } x<0 \\ r(4 (x_{1} - x_{0}) - z) & \text{if } x \geq 0 \end{cases} \\ \dot{x_{2}} &=& -y_{2} + x_{2} - x_{2}^{3} + I_{ext2} + 0.002 g - 0.3 (z-3.5) \\ \dot{y_{2}} &=& 1 / \tau (-y_{2} + f_{2}(x_{2}))\\ \dot{g} &=& -0.01 (g - 0.1 x_{1})\end{split}\]
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.
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.
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.
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.
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
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.
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.
The attribute is a list of values. Choices and type are reinterpreted as applying not to the list but to the elements of it
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.
Bases: tvb.simulator.models.base.ModelNumbaDfun
Two-dimensional reduction of the Epileptor.
Taking advantage of time scale separation and focusing on the slower time scale, the five-dimensional Epileptor reduces to a two-dimensional system (see [Proixetal_2014, Proixetal_2017]).
Note: the slow permittivity variable can be modify to account for the time difference between interictal and ictal states (see [Proixetal_2014]).
Equations and default parameters are taken from [Proixetal_2014]:
\[\begin{split}\dot{x_{1,i}} &=& - x_{1,i}^{3} - 2x_{1,i}^{2} + 1 - z_{i} + I_{ext1,i} \\ \dot{z_{i}} &=& r(h - z_{i})\end{split}\]
- with
- h = begin{cases} x_{0} + 3 / (exp((x_{1} + 0.5)/0.1)) & text{if } modification\ 4 (x_{1,i} - x_{0}) & text{else } end{cases}
- References:
[Proixetal_2014] Proix, T.; Bartolomei, F; Chauvel, P; Bernard, C; Jirsa, V.K. * Permittivity coupling across brain regions determines seizure recruitment in partial epilepsy.* J Neurosci 2014, 34:15009-21.
[Proixetal_2017] Proix, T.; Bartolomei, F; Guye, M.; Jirsa, V.K. Individual brain structure and modelling predict seizure propagation. Brain 2017, 140; 641–654.
gid : tvb.basic.neotraits._core.HasTraits.gid = Attr(field_type=<class ‘uuid.UUID’>, default=None, required=True)
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.
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.
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.
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.
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.
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.
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.
Computes the derivatives of the state-variables of the Epileptor 2D with respect to time.
Equations and default parameters are taken from [Proixetal_2014]:
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.
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.
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.
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
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.
The attribute is a list of values. Choices and type are reinterpreted as applying not to the list but to the elements of it
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.
Hopfield model with modifications following Golos & Daucé.
Bases: tvb.simulator.models.base.Model
The Hopfield neural network is a discrete time dynamical system composed of multiple binary nodes, with a connectivity matrix built from a predetermined set of patterns. The update, inspired from the spin-glass model (used to describe magnetic properties of dilute alloys), is based on a random scanning of every node. The existence of a fixed point dynamics is guaranteed by a Lyapunov function. The Hopfield network is expected to have those multiple patterns as attractors (multistable dynamical system). When the initial conditions are close to one of the ‘learned’ patterns, the dynamical system is expected to relax on the corresponding attractor. A possible output of the system is the final attractive state (interpreted as an associative memory).
Various extensions of the initial model have been proposed, among which a noiseless and continuous version [Hopfield 1984] having a slightly different Lyapunov function, but essentially the same dynamical properties, with more straightforward physiological interpretation. A continuous Hopfield neural network (with a sigmoid transfer function) can indeed be interpreted as a network of neural masses with every node corresponding to the mean field activity of a local brain region, with many bridges with the Wilson Cowan model [WC_1972].
References:
[Hopfield1982] Hopfield, J. J., Neural networks and physical systems with emergent collective computational abilities, Proc. Nat. Acad. Sci. (USA) 79, 2554-2558, 1982.
[Hopfield1984] Hopfield, J. J., Neurons with graded response have collective computational properties like those of two-sate neurons, Proc. Nat. Acad. Sci. (USA) 81, 3088-3092, 1984. See also, http://www.scholarpedia.org/article/Hopfield_network
Dynamic equations:
- dfun equation
- dfun dynamic equation
The phase-plane for the Hopfield model.
gid : tvb.basic.neotraits._core.HasTraits.gid = Attr(field_type=<class ‘uuid.UUID’>, default=None, required=True)
Set the threshold as a state variable for a dynamical threshold.
The fast, \(x\), and slow, \(\theta\), state variables are typically considered to represent a membrane potentials of nodes and the global inhibition term, respectively:
\[\begin{split}\dot{x_{i}} &= 1 / \tau_{x} (-x_{i} + c_0)\end{split}\]
The fast, \(x\), and slow, \(\theta\), state variables are typically considered to represent a membrane potentials of nodes and the inhibition term(s), respectively:
\[\begin{split}\dot{x_{i}} &= 1 / \tau_{x} (-x_{i} + c_0(i)) \\ \dot{\theta_{i}} &= 1 / \tau_{\theta_{i}} (-\theta + c_1(i))\end{split}\]
where c_0 is the coupling term and c_1 should be the direct output.
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.
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
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.
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.
The attribute is a list of values. Choices and type are reinterpreted as applying not to the list but to the elements of it
Jansen-Rit and derivative models.
Bases: tvb.simulator.models.base.ModelNumbaDfun
The Jansen and Rit is a biologically inspired mathematical framework originally conceived to simulate the spontaneous electrical activity of neuronal assemblies, with a particular focus on alpha activity, for instance, as measured by EEG. Later on, it was discovered that in addition to alpha activity, this model was also able to simulate evoked potentials.
[JR_1995] (1, 2) Jansen, B., H. and Rit V., G., Electroencephalogram and visual evoked potential generation in a mathematical model of coupled cortical columns, Biological Cybernetics (73) 357:366, 1995.
[J_1993] Jansen, B., Zouridakis, G. and Brandt, M., A neurophysiologically-based mathematical model of flash visual evoked potentials The (\(y_4\), \(y_5\)) phase-plane for the Jansen and Rit model.
The dynamic equations were taken from [JR_1995]
\[\begin{split}\dot{y_0} &= y_3 \\ \dot{y_3} &= A a\,S[y_1 - y_2] - 2a\,y_3 - a^2\, y_0 \\ \dot{y_1} &= y_4\\ \dot{y_4} &= A a \,[p(t) + \alpha_2 J + S[\alpha_1 J\,y_0]+ c_0] -2a\,y - a^2\,y_1 \\ \dot{y_2} &= y_5 \\ \dot{y_5} &= B b (\alpha_4 J\, S[\alpha_3 J \,y_0]) - 2 b\, y_5 - b^2\,y_2 \\ S[v] &= \frac{2\, \nu_{max}}{1 + \exp^{r(v_0 - v)}}\end{split}\]
Firing threshold (PSP) for which a 50% firing rate is achieved. In other words, it is the value of the average membrane potential corresponding to the inflection point of the sigmoid [mV].
The usual value for this parameter is 6.0.
gid : tvb.basic.neotraits._core.HasTraits.gid = Attr(field_type=<class ‘uuid.UUID’>, default=None, required=True)
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.
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.
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.
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.
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.
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.
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.
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.
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.
The dynamic equations were taken from [JR_1995]
\(p(t)\) can be any arbitrary function, including white noise or random numbers taken from a uniform distribution, representing a pulse density with an amplitude varying between 120 and 320
For Evoked Potentials, a transient component of the input, representing the impulse density attribuable to a brief visual input is applied. Time should be in seconds.
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.
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.
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.
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.
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.
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
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.
The attribute is a list of values. Choices and type are reinterpreted as applying not to the list but to the elements of it
Bases: tvb.simulator.models.base.Model
Zetterberg et al derived a model inspired by the Wilson-Cowan equations. It served as a basis for the later, better known Jansen-Rit model.
[ZL_1978] Zetterberg LH, Kristiansson L and Mossberg K. Performance of a Model for a Local Neuron Population. Biological Cybernetics 31, 15-26, 1978.
[JB_1995] Jansen, B., H. and Rit V., G., Electroencephalogram and visual evoked potential generation in a mathematical model of coupled cortical columns, Biological Cybernetics (73) 357:366, 1995.
[JB_1993] Jansen, B., Zouridakis, G. and Brandt, M., A neurophysiologically-based mathematical model of flash visual evoked potentials
[M_2007] Moran
[S_2010] Spiegler
[A_2012] Auburn
gid : tvb.basic.neotraits._core.HasTraits.gid = Attr(field_type=<class ‘uuid.UUID’>, default=None, required=True)
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.
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.
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.
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.
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.
Zetterberg et al derived a model inspired by the Wilson-Cowan equations. It served as a basis for the later, better known Jansen-Rit model.
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.
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.
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.
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.
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.
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.
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.
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.
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.
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.
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.
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.
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.
Neuronal activation function. This sigmoidal function increases from 0 to Q_max as “sv” increases. sv represents a membrane potential state variable (V).
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
The attribute is a list of values. Choices and type are reinterpreted as applying not to the list but to the elements of it
Larter-Breakspear model based on the Morris-Lecar equations.
Bases: tvb.simulator.models.base.Model
A modified Morris-Lecar model that includes a third equation which simulates the effect of a population of inhibitory interneurons synapsing on the pyramidal cells.
[Larteretal_1999] Larter et.al. A coupled ordinary differential equation lattice model for the simulation of epileptic seizures. Chaos. 9(3): 795, 1999.
[Breaksetal_2003_a] (1, 2) Breakspear, M.; Terry, J. R. & Friston, K. J. Modulation of excitatory synaptic coupling facilitates synchronization and complex dynamics in an onlinear model of neuronal dynamics. Neurocomputing 52–54 (2003).151–158
[Breaksetal_2003_b] (1, 2, 3) M. J. Breakspear et.al. Modulation of excitatory synaptic coupling facilitates synchronization and complex dynamics in a biophysical model of neuronal dynamics. Network: Computation in Neural Systems 14: 703-732, 2003.
[Honeyetal_2007] Honey, C.; Kötter, R.; Breakspear, M. & Sporns, O. * Network structure of cerebral cortex shapes functional connectivity on multiple time scales*. (2007) PNAS, 104, 10240
[Honeyetal_2009] Honey, C. J.; Sporns, O.; Cammoun, L.; Gigandet, X.; Thiran, J. P.; Meuli, R. & Hagmann, P. Predicting human resting-state functional connectivity from structural connectivity. (2009), PNAS, 106, 2035-2040
[Alstottetal_2009] Alstott, J.; Breakspear, M.; Hagmann, P.; Cammoun, L. & Sporns, O. Modeling the impact of lesions in the human brain. (2009)), PLoS Comput Biol, 5, e1000408 Equations and default parameters are taken from [Breaksetal_2003_b]. All equations and parameters are non-dimensional and normalized. For values of d_v < 0.55, the dynamics of a single column settles onto a solitary fixed point attractor.
Parameters used for simulations in [Breaksetal_2003_a] Table 1. Page 153. Two nodes were coupled. C=0.1
Table 1 Parameter Value I 0.3 a_ee 0.4 a_ei 0.1 a_ie 1.0 a_ne 1.0 a_ni 0.4 r_NMDA 0.2 delta 0.001 Breakspear et al. 2003
Table 2 Parameter Value gK 2.0 gL 0.5 gNa 6.7 gCa 1.0 a_ne 1.0 a_ni 0.4 a_ee 0.36 a_ei 2.0 a_ie 2.0 VK -0.7 VL -0.5 VNa 0.53 VCa 1.0 phi 0.7 b 0.1 I 0.3 r_NMDA 0.25 C 0.1 TCa -0.01 d_Ca 0.15 TK 0.0 d_K 0.3 VT 0.0 ZT 0.0 TNa 0.3 d_Na 0.15 d_V 0.65 d_Z d_V QV_max 1.0 QZ_max 1.0 Alstott et al. 2009 NOTES about parameters
\(\delta_V\) : for \(\delta_V\) < 0.55, in an uncoupled network, the system exhibits fixed point dynamics; for 0.55 < \(\delta_V\) < 0.59, limit cycle attractors; and for \(\delta_V\) > 0.59 chaotic attractors (eg, d_V=0.6,aee=0.5,aie=0.5, gNa=0, Iext=0.165)
\(\delta_Z\) this parameter might be spatialized: ones(N,1).*0.65 + modn*(rand(N,1)-0.5);
\(C\) The long-range coupling \(\delta_C\) is ‘weak’ in the sense that the model is well behaved for parameter values for which C < a_ee and C << a_ie.
The (\(V\), \(W\)) phase-plane for the Larter-Breakspear model.
Dynamic equations:
\[\begin{split}\dot{V}_k & = - (g_{Ca} + (1 - C) \, r_{NMDA} \, a_{ee} \, Q_V + C \, r_{NMDA} \, a_{ee} \, \langle Q_V\rangle^{k}) \, m_{Ca} \, (V - VCa) \\ & \,\,- g_K \, W \, (V - VK) - g_L \, (V - VL) \\ & \,\,- (g_{Na} \, m_{Na} + (1 - C) \, a_{ee} \, Q_V + C \, a_{ee} \, \langle Q_V\rangle^{k}) \,(V - VNa) \\ & \,\,- a_{ie} \, Z \, Q_Z + a_{ne} \, I \\ & \\ \dot{W}_k & = \phi \, \dfrac{m_K - W}{\tau_{K}} \\ & \nonumber\\ \dot{Z}_k &= b (a_{ni}\, I + a_{ei}\,V\,Q_V) \\ Q_{V} &= Q_{V_{max}} \, (1 + \tanh\left(\dfrac{V_{k} - VT}{\delta_{V}}\right)) \\ Q_{Z} &= Q_{Z_{max}} \, (1 + \tanh\left(\dfrac{Z_{k} - ZT}{\delta_{Z}}\right))\end{split}\]See Equations (7), (3), (6) and (2) respectively in [Breaksetal_2003_a]. Pag: 705-706
gid : tvb.basic.neotraits._core.HasTraits.gid = Attr(field_type=<class ‘uuid.UUID’>, default=None, required=True)
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.
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.
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.
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.
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.
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.
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.
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.
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.
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.
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.
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.
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.
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.
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.
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.
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.
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.
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.
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.
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.
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.
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.
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.
Dynamic equations:
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.
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.
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.
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.
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.
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.
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
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.
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.
The attribute is a list of values. Choices and type are reinterpreted as applying not to the list but to the elements of it
Generic linear model.
Bases: tvb.simulator.models.base.Model
variables_of_interest : tvb.simulator.models.linear.Linear.variables_of_interest = List(of=<class ‘str’>, default=(‘x’,), required=True)
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)
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
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.
The attribute is a list of values. Choices and type are reinterpreted as applying not to the list but to the elements of it
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
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
The attribute is a list of values. Choices and type are reinterpreted as applying not to the list but to the elements of it
Oscillator models.
Bases: tvb.simulator.models.base.ModelNumbaDfun
The Generic2dOscillator model is a generic dynamic system with two state variables. The dynamic equations of this model are composed of two ordinary differential equations comprising two nullclines. The first nullcline is a cubic function as it is found in most neuron and population models; the second nullcline is arbitrarily configurable as a polynomial function up to second order. The manipulation of the latter nullcline’s parameters allows to generate a wide range of different behaviours.
Equations:
\[\begin{split}\dot{V} &= d \, \tau (-f V^3 + e V^2 + g V + \alpha W + \gamma I) \\ \dot{W} &= \dfrac{d}{\tau}\,\,(c V^2 + b V - \beta W + a)\end{split}\]See:
[FH_1961] FitzHugh, R., Impulses and physiological states in theoretical models of nerve membrane, Biophysical Journal 1: 445, 1961.
[Nagumo_1962] Nagumo et.al, An Active Pulse Transmission Line Simulating Nerve Axon, Proceedings of the IRE 50: 2061, 1962.
[SJ_2011] Stefanescu, R., Jirsa, V.K. Reduced representations of heterogeneous mixed neural networks with synaptic coupling. Physical Review E, 83, 2011.
[SJ_2010] Jirsa VK, Stefanescu R. Neural population modes capture biologically realistic large-scale network dynamics. Bulletin of Mathematical Biology, 2010.
[SJ_2008_a] Stefanescu, R., Jirsa, V.K. A low dimensional description of globally coupled heterogeneous neural networks of excitatory and inhibitory neurons. PLoS Computational Biology, 4(11), 2008). The model’s (\(V\), \(W\)) time series and phase-plane its nullclines can be seen in the figure below.
The model with its default parameters exhibits FitzHugh-Nagumo like dynamics.
Table 1 EXCITABLE CONFIGURATION Parameter Value a -2.0 b -10.0 c 0.0 d 0.02 I 0.0 limit cycle if a is 2.0
Table 2 BISTABLE CONFIGURATION Parameter Value a 1.0 b 0.0 c -5.0 d 0.02 I 0.0 monostable regime: fixed point if Iext=-2.0 limit cycle if Iext=-1.0
Table 3 EXCITABLE CONFIGURATION (similar to Morris-Lecar) Parameter Value a 0.5 b 0.6 c -4.0 d 0.02 I 0.0 excitable regime if b=0.6 oscillatory if b=0.4
Table 4 GhoshetAl, 2008 KnocketAl, 2009 Parameter Value a 1.05 b -1.00 c 0.0 d 0.1 I 0.0 alpha 1.0 beta 0.2 gamma -1.0 e 0.0 g 1.0 f 1/3 tau 1.25 frequency peak at 10Hz
Table 5 SanzLeonetAl 2013 Parameter Value a
- 0.5
b -10.0 c 0.0 d 0.02 I 0.0 intrinsic frequency is approx 10 Hz NOTE: This regime, if I = 2.1, is called subthreshold regime. Unstable oscillations appear through a subcritical Hopf bifurcation.
The (\(V\), \(W\)) phase-plane for the generic 2D population model for default parameters. The dynamical system has an equilibrium point.
- dfun(vw, c, local_coupling=0.0)[source]¶
The two state variables \(V\) and \(W\) are typically considered to represent a function of the neuron’s membrane potential, such as the firing rate or dendritic currents, and a recovery variable, respectively. If there is a time scale hierarchy, then typically \(V\) is faster than \(W\) corresponding to a value of \(\tau\) greater than 1.
The equations of the generic 2D population model read
\[\begin{split}\dot{V} &= d \, \tau (-f V^3 + e V^2 + g V + \alpha W + \gamma I) \\ \dot{W} &= \dfrac{d}{\tau}\,\,(c V^2 + b V - \beta W + a)\end{split}\]where external currents \(I\) provide the entry point for local, long-range connectivity and stimulation.
gid : tvb.basic.neotraits._core.HasTraits.gid = Attr(field_type=<class ‘uuid.UUID’>, default=None, required=True)
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.
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.
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.
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.
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.
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.
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.
The two state variables \(V\) and \(W\) are typically considered to represent a function of the neuron’s membrane potential, such as the firing rate or dendritic currents, and a recovery variable, respectively. If there is a time scale hierarchy, then typically \(V\) is faster than \(W\) corresponding to a value of \(\tau\) greater than 1.
The equations of the generic 2D population model read
where external currents \(I\) provide the entry point for local, long-range connectivity and stimulation.
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.
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.
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.
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.
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
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.
The attribute is a list of values. Choices and type are reinterpreted as applying not to the list but to the elements of it
Bases: tvb.simulator.models.base.Model
The Kuramoto model is a model of synchronization phenomena derived by Yoshiki Kuramoto in 1975 which has since been applied to diverse domains including the study of neuronal oscillations and synchronization.
See:
[YK_1975] Y. Kuramoto, in: H. Arakai (Ed.), International Symposium on Mathematical Problems in Theoretical Physics, Lecture Notes in Physics, page 420, vol. 39, 1975.
[SS_2000] S. H. Strogatz. From Kuramoto to Crawford: exploring the onset of synchronization in populations of coupled oscillators. Physica D, 143, 2000.
[JC_2011] J. Cabral, E. Hugues, O. Sporns, G. Deco. Role of local network oscillations in resting-state functional connectivity. NeuroImage, 57, 1, 2011. The \(\theta\) variable is the phase angle of the oscillation.
- Dynamic equations:
gid : tvb.basic.neotraits._core.HasTraits.gid = Attr(field_type=<class ‘uuid.UUID’>, default=None, required=True)
The \(\theta\) variable is the phase angle of the oscillation.
where \(I\) is the input via local and long range connectivity, passing first through the Kuramoto coupling function,
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.
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
The attribute is a list of values. Choices and type are reinterpreted as applying not to the list but to the elements of it
Bases: tvb.simulator.models.base.ModelNumbaDfun
The supHopf model describes the normal form of a supercritical Hopf bifurcation in Cartesian coordinates. This normal form has a supercritical bifurcation at a=0 with a the bifurcation parameter in the model. So for a < 0, the local dynamics has a stable fixed point and the system corresponds to a damped oscillatory state, whereas for a > 0, the local dynamics enters in a stable limit cycle and the system switches to an oscillatory state.
See for examples:
[Kuznetsov_2013] Kuznetsov, Y.A. Elements of applied bifurcation theory. Springer Sci & Business Media, 2013, vol. 112.
[Deco_2017a] Deco, G., Kringelbach, M.L., Jirsa, V.K., Ritter, P. The dynamics of resting fluctuations in the brain: metastability and its dynamical cortical core Sci Reports, 2017, 7: 3095. The equations of the supHopf equations read as follows:
\[\begin{split}\dot{x}_{i} &= (a_{i} - x_{i}^{2} - y_{i}^{2})x_{i} - {\omega}{i}y_{i} \\ \dot{y}_{i} &= (a_{i} - x_{i}^{2} - y_{i}^{2})y_{i} + {\omega}{i}x_{i}\end{split}\]where a is the local bifurcation parameter and omega the angular frequency.
gid : tvb.basic.neotraits._core.HasTraits.gid = Attr(field_type=<class ‘uuid.UUID’>, default=None, required=True)
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.
Computes the derivatives of the state-variables of supHopf with respect to time.
The equations of the supHopf equations read as follows:
where a is the local bifurcation parameter and omega the angular frequency.
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.
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
The attribute is a list of values. Choices and type are reinterpreted as applying not to the list but to the elements of it
Models developed by Stefanescu-Jirsa, based on reduced-set analyses of infinite populations.
Bases: tvb.simulator.models.base.Model
gid : tvb.basic.neotraits._core.HasTraits.gid = Attr(field_type=<class ‘uuid.UUID’>, default=None, required=True)
Bases: tvb.simulator.models.stefanescu_jirsa.ReducedSetBase
A reduced representation of a set of Fitz-Hugh Nagumo oscillators, [SJ_2008].
The models (\(\xi\), \(\eta\)) phase-plane, including a representation of the vector field as well as its nullclines, using default parameters, can be seen below:
The (\(\xi\), \(\eta\)) phase-plane for the first mode of a reduced set of Fitz-Hugh Nagumo oscillators.
The (\(\xi\), \(\eta\)) phase-plane for the second mode of a reduced set of Fitz-Hugh Nagumo oscillators.
The (\(\xi\), \(\eta\)) phase-plane for the third mode of a reduced set of Fitz-Hugh Nagumo oscillators.
The system’s equations for the i-th mode at node q are:
\[\begin{split}\dot{\xi}_{i} &= c\left(\xi_i-e_i\frac{\xi_{i}^3}{3} -\eta_{i}\right) + K_{11}\left[\sum_{k=1}^{o} A_{ik}\xi_k-\xi_i\right] - K_{12}\left[\sum_{k =1}^{o} B_{i k}\alpha_k-\xi_i\right] + cIE_i \\ &\, + \left[\sum_{k=1}^{o} \mathbf{\Gamma}(\xi_{kq}, \xi_{kr}, u_{qr})\right] + \left[\sum_{k=1}^{o} W_{\zeta}\cdot\xi_{kr} \right] \\ \dot{\eta}_i &= \frac{1}{c}\left(\xi_i-b\eta_i+m_i\right) \\ & \\ \dot{\alpha}_i &= c\left(\alpha_i-f_i\frac{\alpha_i^3}{3}-\beta_i\right) + K_{21}\left[\sum_{k=1}^{o} C_{ik}\xi_i-\alpha_i\right] + cII_i \\ & \, + \left[\sum_{k=1}^{o} \mathbf{\Gamma}(\xi_{kq}, \xi_{kr}, u_{qr})\right] + \left[\sum_{k=1}^{o} W_{\zeta}\cdot\xi_{kr}\right] \\ & \\ \dot{\beta}_i &= \frac{1}{c}\left(\alpha_i-b\beta_i+n_i\right)\end{split}\]
- update_derived_parameters()[source]¶
Calculate coefficients for the Reduced FitzHugh-Nagumo oscillator based neural field model. Specifically, this method implements equations for calculating coefficients found in the supplemental material of [SJ_2008].
Include equations here...
#NOTE: In the Article this modelis called StefanescuJirsa2D
gid : tvb.basic.neotraits._core.HasTraits.gid = Attr(field_type=<class ‘uuid.UUID’>, default=None, required=True)
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.
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.
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.
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.
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.
The system’s equations for the i-th mode at node q are:
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.
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.
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
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.
Calculate coefficients for the Reduced FitzHugh-Nagumo oscillator based neural field model. Specifically, this method implements equations for calculating coefficients found in the supplemental material of [SJ_2008].
Include equations here...
The attribute is a list of values. Choices and type are reinterpreted as applying not to the list but to the elements of it
Bases: tvb.simulator.models.stefanescu_jirsa.ReducedSetBase
[SJ_2008] (1, 2, 3, 4, 5, 6) Stefanescu and Jirsa, PLoS Computational Biology, A Low Dimensional Description of Globally Coupled Heterogeneous Neural Networks of Excitatory and Inhibitory 4, 11, 26–36, 2008. The models (\(\xi\), \(\eta\)) phase-plane, including a representation of the vector field as well as its nullclines, using default parameters, can be seen below:
The (\(\xi\), \(\eta\)) phase-plane for the first mode of a reduced set of Hindmarsh-Rose oscillators.
The (\(\xi\), \(\eta\)) phase-plane for the second mode of a reduced set of Hindmarsh-Rose oscillators.
The (\(\xi\), \(\eta\)) phase-plane for the third mode of a reduced set of Hindmarsh-Rose oscillators.
The dynamic equations were orginally taken from [SJ_2008].
The equations of the population model for i-th mode at node q are:
\[\begin{split}\dot{\xi}_i &= \eta_i-a_i\xi_i^3 + b_i\xi_i^2- \tau_i + K_{11} \left[\sum_{k=1}^{o} A_{ik} \xi_k - \xi_i \right] - K_{12} \left[\sum_{k=1}^{o} B_{ik} \alpha_k - \xi_i\right] + IE_i \\ &\, + \left[\sum_{k=1}^{o} \mathbf{\Gamma}(\xi_{kq}, \xi_{kr}, u_{qr})\right] + \left[\sum_{k=1}^{o} W_{\zeta}\cdot\xi_{kr} \right] \\ & \\ \dot{\eta}_i &= c_i-d_i\xi_i^2 -\tau_i \\ & \\ \dot{\tau}_i &= rs\xi_i - r\tau_i -m_i \\ & \\ \dot{\alpha}_i &= \beta_i - e_i \alpha_i^3 + f_i \alpha_i^2 - \gamma_i + K_{21} \left[\sum_{k=1}^{o} C_{ik} \xi_k - \alpha_i \right] + II_i \\ &\, +\left[\sum_{k=1}^{o}\mathbf{\Gamma}(\xi_{kq}, \xi_{kr}, u_{qr})\right] + \left[\sum_{k=1}^{o}W_{\zeta}\cdot\xi_{kr}\right] \\ & \\ \dot{\beta}_i &= h_i - p_i \alpha_i^2 - \beta_i \\ \dot{\gamma}_i &= rs \alpha_i - r \gamma_i - n_i\end{split}\]
- update_derived_parameters(corrected_d_p=True)[source]¶
Calculate coefficients for the neural field model based on a Reduced set of Hindmarsh-Rose oscillators. Specifically, this method implements equations for calculating coefficients found in the supplemental material of [SJ_2008].
Include equations here...
#NOTE: In the Article this modelis called StefanescuJirsa3D
gid : tvb.basic.neotraits._core.HasTraits.gid = Attr(field_type=<class ‘uuid.UUID’>, default=None, required=True)
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.
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.
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.
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.
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.
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.
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.
The equations of the population model for i-th mode at node q are:
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.
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.
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.
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.
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
Calculate coefficients for the neural field model based on a Reduced set of Hindmarsh-Rose oscillators. Specifically, this method implements equations for calculating coefficients found in the supplemental material of [SJ_2008].
Include equations here...
The attribute is a list of values. Choices and type are reinterpreted as applying not to the list but to the elements of it
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 equations based model definition.
Bases: tvb.simulator.models.base.Model
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 models (\(E\), \(I\)) phase-plane, including a representation of the vector field as well as its nullclines, using default parameters, can be seen below:
The (\(E\), \(I\)) phase-plane for the Wilson-Cowan model.
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:
\[\begin{split}\dot{E}_k &= \dfrac{1}{\tau_e} (-E_k + (k_e - r_e E_k) \mathcal{S}_e (\alpha_e \left( c_{ee} E_k - c_{ei} I_k + P_k - \theta_e + \mathbf{\Gamma}(E_k, E_j, u_{kj}) + W_{\zeta}\cdot E_j + W_{\zeta}\cdot I_j\right) ))\\ \dot{I}_k &= \dfrac{1}{\tau_i} (-I_k + (k_i - r_i I_k) \mathcal{S}_i (\alpha_i \left( c_{ie} E_k - c_{ee} I_k + Q_k - \theta_i + \mathbf{\Gamma}(E_k, E_j, u_{kj}) + W_{\zeta}\cdot E_j + W_{\zeta}\cdot I_j\right) ))\end{split}\]
gid : tvb.basic.neotraits._core.HasTraits.gid = Attr(field_type=<class ‘uuid.UUID’>, default=None, required=True)
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.
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.
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.
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.
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.
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.
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.
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.
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.
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.
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.
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.
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.
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.
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.
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.
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.
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.
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
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.
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.
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.
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.
The attribute is a list of values. Choices and type are reinterpreted as applying not to the list but to the elements of it
Models based on Wong-Wang’s work.
Bases: tvb.simulator.models.base.ModelNumbaDfun
[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] (1, 2) 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 32(27), 11239-11252, 2013. Equations taken from [DPA_2013] , page 11242
\[\begin{split}x_k &= w\,J_N \, S_k + I_o + J_N \mathbf\Gamma(S_k, S_j, u_{kj})\\ H(x_k) &= \dfrac{ax_k - b}{1 - \exp(-d(ax_k -b))}\\ \dot{S}_k &= -\dfrac{S_k}{\tau_s} + (1 - S_k) \, H(x_k) \, \gamma\end{split}\]
gid : tvb.basic.neotraits._core.HasTraits.gid = Attr(field_type=<class ‘uuid.UUID’>, default=None, required=True)
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.
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.
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.
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.
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.
Equations taken from [DPA_2013] , page 11242
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.
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.
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
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
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.
The attribute is a list of values. Choices and type are reinterpreted as applying not to the list but to the elements of it
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.
