MODELING OF
BIOLOGICAL NEURONS
WITH
ARTIFICIAL NEURAL NETWORKS
by:
Pinchas Tandeitnik and Hugo Guterman
Department of Electrical and Computer Engineering
Ben-Gurion University of the Negev
P.O. Box 653, Beer-Sheva, Israel 84105
Email: [email protected], [email protected]
IEEE
(1) Jerusalem 1996
The aim of this work:
•
•
Building a model of biological neuron.
Building an interactive simulator to examine
biological networks topology.
IEEE
(2) Jerusalem 1996
Out lines:
•
Introduction
•
System Identification
•
The Equivalent Current Model
•
Biological Simulator
•
Conclusions
IEEE
(3) Jerusalem 1996
A
B
C
20mV
50msec
0.8nA
50msec
Neuronal activity levels
Neuron activity pattern:
•
•
•
IEEE
Sub threshold depolarization activity area.
Over threshold depolarization activity area.
Hyper polarization activity area.
(4) Jerusalem 1996
Dynamic Systems
y(n)=Non_linear_mapping{y(n-1),...y(n-k),u(n),...u(n-l)}
=NN_model{y(n-1),... y(n-k),u(n),... u(n-l)}
Modelin Dynamic Systems:
2
E = ∑ p y p ( k ) − y p ( k ) = ∑ p y p ( k ) − NN_ model( k )
y p ( k ) − actual values
y p ( k ) − estimated values
E − Energy function
IEEE
(5) Jerusalem 1996
2
The advantage of System Identification
with Artificial Neural Networks:
•
•
•
•
•
No need of a priori information about the system
dynamics.
Capability
to
extract
mapping
(generalization) from the training set.
rules
Any given mapping function (linear/non-linear)
can be approximated by ANN (with high number
of neurons at the hidden layer).
A close loop feed forward ANN has dynamic
properties.
The PCA criteria algorithm that makes an
educated guess based on the statistical analysis of
the input/output data based.
ANN approach drawback:
•
•
•
IEEE
Computational
parameters).
expensive
(large
number
of
What is the adequate training set?
The solution is sensative to the initial condition of
the parameters.
(6) Jerusalem 1996
Types of neurons:
A. The Regular Spiking (RS) cells
exhibit adaptation of spike frequency
during prolongs depolarizing current
pulses. During the square current pulse
that exceeds action-potential threshold,
spikes frequency steadily declined at all
current intensities.
B.
Fast-Spiking (FS) cells do not exhibit
any frequency adaptation for prolonged
square current pulses.
IEEE
(7) Jerusalem 1996
The equivalent average current model
A combination of three ANN was used to
mimic the neuronal activity pattern.
The model phases are:
•
NN_1 - This phase exhibits the sub
threshold depolarization activity.
•
NN_2 - This phase exhibits the over
threshold depolarization activity.
•
NN_3 - This phase exhibits the hyper
polarization activity.
A
B
C
20mV
50msec
0.8nA
50msec
IEEE
(8) Jerusalem 1996
The equivalent current model block diagram
sub-threshold
depolarization
MUX
NN_1
1
spike
shape
2
v(t)
3
NN_2
hyperpolarization
NN_3
t_spike
Controller
I(t)
IEEE
v(t-1)
(9) Jerusalem 1996
z-1
v(t)
z-1
v(t-1)
z-1
v(t-2)
z-1
v(t-3)
v(t+1)
z-1
v(t-4)
Wo
z-1
v(t-6)
WH
I(t)
Bias
Neuron
Bias
Neuron
Inner structure of the NN_1 phase
IEEE
(10) Jerusalem 1996
Controler software
case (I)
I>0:
I=0:
I<0:
•
•
•
•
case(V)
V≥ Vrp:
if (V<Vth) then
The rising part of sub threshold phase
(NN_1) is activated.
else
Over threshold depolarization phase
(NN_2) is activated. (Spike generation
rules are activated*)
V<Vrp:
Rising part of hyper polarization phase
(NN_3) is activated
case (V)
V>Vrp:
The falling part of sub threshold
depolarization phase is activated (NN_1)
V=Vrp:
No change
V<Vrp:
The rising part of hyper polarization phase
(NN_3) is activated
case (V)
V>Vrp:
The falling part of depolarization phase
(NN_1) is activated
V≤ Vrp:
The falling part of hyper polarization phase
(NN_3) is activated
Notes:
I - Input current
V - neuron voltage
Vth - above this voltage the neuron generates voltage oscillation
Vrp - neuron resting potential
* The spike generation rule is different for various activity patterns
IEEE
(11) Jerusalem 1996
Regular Spiking cells model
20mV
20msec
RS activity pattern
IEEE
(12) Jerusalem 1996
Inter Spike Interval(ISI) curve
20mV
20msec
T3
T2
T1
t1
ISI( k ) = NN_ model I( k ), ISI( k − 1)
k
IEEE
p
(13) Jerusalem 1996
Fast Spiking cells model
20mV
20msec
FS cells response to input current of 0.8nA
FS cells F-I curve
IEEE
(14) Jerusalem 1996
Conclusions
•
•
•
•
The equivalent current model is an alternative
approach for neurons modeling.
The model simple fragments decrease the
parameter adaptation time.
On the basis of a simple set of laboratory
experiments it is possible to build the
equivalent current model for the biological
neuron.
The single neuron model can be used to
examine networks topology.
IEEE
(15) Jerusalem 1996