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Simulation of traveling activity in
spatially distributed neural networks
 
Select synaptic weight =   then click to see the movie

An array of 250 by 250 neurons is simulated. Each neuron receives excitatory input from two of the nearest eight neighboring neurons.  A pseudo-random generator is used to chose connections for each neuron. There is no inhibition in the network  Repetitive firing activity in the network is triggered by one cell in the center of the array at the beginning of the simulation (i.e. the selected cell received an input current 15.0 mA/cm2 strong enough to evoke a burst of action potentials). Integration step: 0.01 msec. Simulation time: 1.0 sec.

Synaptic parameters
 synaptic weight w = 25 - 70  Esyn_e=-10.0 mV   to = 0.5 msec 
 Synaptic delay = 1.6 msec  Aep=0.0112    td = 3.0 msec
 
Model parameters
VL = -50.0 mV GL = 0.3 mS/cm2  
VNa = 55.0 mV GNa = 120.0 mS/cm2  
VK = -72.0 mV  GK = 15.0 mS/cm2  
VCa = 124.0 mV GCa = 1.0 mS/cm2 tx= 25.0; Kc = 2.0; Kp = 0.0002; R=0.006
  GA = 12.5 mS/cm2 tb = 10.0
  GK(Ca) = 3.5 mS/cm2 Kd = 0.5
 
 
a(m) = 0.065  a(A) = 0.02 a(X) = 2.0  a(W) = 0.055 a(B) = -0.095 
V1/2(m) = -31.0 mV  V1/2(A) = -20.0 mV V1/2(X) = -45.0 mV  V1/2(W) = -35.0 mV  V1/2(B) = -70.0 mV 

γ = 0.08

Neuron model

Cm dV/dt = Iext -INa -ICa -IK -IA -IK(Ca) -IL -Isyn                         
dW/dt =[Winf (V)-W]/tw(V)                                                         
dX/dt = [Xinf (V) -X]/tx                                                                 
dB/dt = [Binf (V) -B]/tb                                                               
dC/dt = Kp(-ICa) - RC                                                                 

where:
INa=gNaminf3(V)(1-W)(V-VNA)                                                    
ICa = gCa X2[Kc/(Kc+C)](V-VCa)                                             
IK = gKW4(V-VK)                                                                        
IA = gAAinf (V)B(V-VK)                                                                
IK(Ca) = gK(Ca)[C/(Kd+C)](V-VK)                                           
IL = gL(V-VL)                                                                              

and:
Pinf (V) = (1+ exp[-2a(P)(V-V(P)1/2)])-1                                   
   for P = [W,m,X,A,B]
tw(V) = (γ exp[a(W)(V-V(W)1/2)] + γ exp[-a(W)(V-V(W)1/2)])-1    
 
Synaptic model

Isyn = Σ wjg j(t) (V-Esyn)                                                             
g(t) = AepΣ exp((ti-t)/td) - exp((ti-t)/to)                                    

where i denotes summation over time and  j over the number of input synapses.

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