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CbNeuron

The Model

The membrane voltage V_m is governed by

$$C_m \frac{V_m}{dt} = -\frac{V_m-E_m}{R_m} - \sum_{c=1}^{N_c} ... ...s(t) + \sum_{s=1}^{G_s} g_s(t)(V_m-E_{rev}^{(s)}) + I_{inject}$$

with the following meanings of symbols

• C_m membrane capacity (Farad)
• E_m reversal potential of the leak current (Volts)
• R_m membrane resistance (Ohm)
• N_c total number of channels (active + synaptic)
• g_c(t) current conductance of channel c (Siemens)
• E_rev^c reversal potential of channel c (Volts)
• N_s total number of current supplying synapses
• I_s(t) current supplied by synapse s (Ampere)
• G_s total number of coductance based synapses
• g_s(t) coductance supplied by synapse s (Siemens)
• E_rev^(s) reversal potential of synapse s (Volts)
• I_inject injected current (Ampere)

At time t=0 V_m ist set to V_init .

The value of E_m is calculated to compensate for ionic currents such that V_m actually has a resting value of $V_\mathit{resting}$ .

Spiking and reseting the membrane voltage

If the membrane voltage V_m exceeds the threshold V_tresh the CbNeuron sends a spike to all its outgoing synapses.

The membrane voltage is reseted and clamped during the absolute refractory period of length T_refract to V_reset if the flag doReset=1. This is similar to a LIF neuron (see LifNeuron).

If the flag doReset=0 the membrane voltage is not reseted and the above equation is also applied during the absolute refractory period but the event of threshold crossing is transmitted as a spike to outgoing synapses. This is usfull if one includes channels which produce a real action potential (see HH_K_Channel and HH_Na_Channel) but one still just wants to communicate the spikes as events in time.

Implementation

The exponential Euler method is used for numerical integration.

Read/writable Fields

Vthresh (V) :

If V_m exceeds V_thresh a spike is emmited.

Vreset (V) :

The voltage to reset V_m to after a spike.

doReset (flag) :

Flag which determines wheter V_m should be reseted after a spike

Trefract (sec) :

Length of the absolute refractory period.

nummethod (flag) :

Numerical method for the solution of the differential equation: Exp. Euler = 0, Crank-Nicolson = 1

type :

Type (e.g. inhibitory or excitatory) of the neuron

Cm (F) :

The membrane capacity C_m

Rm (Ohm) :

The membrane resistance R_m

Vresting (V) :

The resting membrane voltage.

Vinit (V) :

Initial condition forV_m at time t=0.

VmScale (V) :

Defines the difference between Vresting and the Vthresh for the calculation of the iongate tables and the ionbuffer Erev.

Inoise (W²) :

Variance of the noise to be added each integration time constant.

Iinject (A) :

Constant current to be injected into the CB neuron.

Readonly Fields

Em (V) :

The reversal potential of the leakage channel

Vm (V) :

The membrane voltage

Isyn :

synaptic input current

Gsyn :

synaptic input conductance

nIncoming :

Number of incoming synapses

nOutgoing :

Number of outgoing synapses

nBuffers :

Number of ion buffers

nChannels :

Number of channels

(C) 2003, Thomas Natschläger

last modified 07/10/2006