growth_curve_gaussian


Name:
growth_curve_gaussian - Gaussian version of a growth curve
Description:
 
This class represents a Gaussian growth rule for the number of synaptic
elements inside a neuron. The creation and deletion of synaptic elements
when structural plasticity is enabled, allows the dynamic rewiring of the
network during the simulation.
This type of growth curve uses a forward Euler integration method to update
the number of synaptic elements:
dz/dt = nu (2 * e^(- ((Ca(t) - xi)/z)^2 ) - 1)
where xi = (eta + eps)/2,
zeta = (eps - eta)/2 * sqrt(ln(2))),
eta is the minimum calcium concentration required for any synaptic element
to be created, eps is the target mean calcium concentration in the neuron
and nu is the growth rate in elements/ms. The growth rate nu is defined in
the SynapticElement class.

Parameters:
 
eta double - Minimum amount of calcium concentration that the
neuron needs to start creating synaptic elements.
eta can have a negative value, making the growth
curve move its maximum to the left. For example, if
eta=-0.5 and eps=0.5 [Ca2+], the maximum growth rate
(elements/ms) will be achieved at 0.0 [Ca2+]. If
eta=0.0 [Ca2+] and eps=0.5 [Ca2+] the maximum growth
rate will be achieved at 0.25 [Ca2+] while at 0.0
[Ca+2] no new elements will be created.

eps double - The target calcium concentration that
the neuron should look to achieve by creating or
deleting synaptic elements. It should always be a
positive value. It is important to note that the
calcium concentration is linearly proportional to the
firing rate. This is because dCa/dt = - Ca(t)/tau_Ca
+ beta_Ca if the neuron fires and dCa/dt = -
Ca(t)/tau_Ca otherwise, where tau_Ca is the calcium
concentration decay constant and beta_Ca is the
calcium intake constant (see SynapticElement class).
This means that eps can also be seen as the desired
firing rate that the neuron should achieve. For
example, an eps = 0.05 [Ca2+] with tau_Ca = 10000.0
and beta_Ca = 0.001 for a synaptic element means a
desired firing rate of 5Hz.

nu double - Growth rate in elements/ms. The growth rate nu is
defined in the SynapticElement class. Can be negative.

References:
 
[1] Butz, Markus, Florentin Wörgötter, and Arjen van Ooyen.
"Activity-dependent structural plasticity." Brain research reviews 60.2
(2009): 287-305.

[2] Butz, Markus, and Arjen van Ooyen. "A simple rule for dendritic spine
and axonal bouton formation can account for cortical reorganization after
focal retinal lesions." PLoS Comput Biol 9.10 (2013): e1003259.

Author:
Mikael Naveau  
FirstVersion:
July 2013  
SeeAlso: Source:
/home/nest/work/nest-2.14.0/nestkernel/growth_curve.h