Command: testsuite::test_iaf_psp_peak

Synopsis

(test_iaf_psp_peak) run -> compare expression with numerics

[1] Weisstein Lambert W-function

Several NEST neuron models have an alpha-shaped post-synaptic current (PSC).

In these models the PSC is normalized to unit amplitude. Thus a synaptic weight

w leads to a PSC with amplitude w in units of pA.

In order to adjust the amplitude of the post-synaptic potential (PSP) of a

neuron model with an alpha-shaped post-synaptic current (PSC) to a particular

amplitude we need to first find the location of the maximum tmax of the PSP.

Here this is done in two different ways:

1. We numerically search for the root of the derivative of the PSP

2. We used a closed form expression to compute the position of the maximum

The test verifies that the methods lead to the same result. The test file

test_iaf_psp_normalized shows how this value is used to specify w such that a

PSP with a desired amplitude u in units of mV results.

The closed form expression can be found by first transforming the expression

d psp(t) / dt = 0

into the normal form

exp(s) = 1 + a * s

where s is the scaled time s=bt and a and b depend on the time constants

a = tau_m/tau_alpha b = 1/tau_alpha - 1/tau_m .

The solution for s can then be expressed with the help of the Lambert W-function W

which is the inverse of x=W*exp(W) and reads

s = 1/a * ( -a W(-exp(-1/a)/a) - 1 )

References

[1] Weisstein Lambert W-function

Description

Several NEST neuron models have an alpha-shaped post-synaptic current (PSC).

In these models the PSC is normalized to unit amplitude. Thus a synaptic weight

w leads to a PSC with amplitude w in units of pA.

In order to adjust the amplitude of the post-synaptic potential (PSP) of a

neuron model with an alpha-shaped post-synaptic current (PSC) to a particular

amplitude we need to first find the location of the maximum tmax of the PSP.

Here this is done in two different ways:

1. We numerically search for the root of the derivative of the PSP

2. We used a closed form expression to compute the position of the maximum

The test verifies that the methods lead to the same result. The test file

test_iaf_psp_normalized shows how this value is used to specify w such that a

PSP with a desired amplitude u in units of mV results.

The closed form expression can be found by first transforming the expression

d psp(t) / dt = 0

into the normal form

exp(s) = 1 + a * s

where s is the scaled time s=bt and a and b depend on the time constants

a = tau_m/tau_alpha b = 1/tau_alpha - 1/tau_m .

The solution for s can then be expressed with the help of the Lambert W-function W

which is the inverse of x=W*exp(W) and reads

s = 1/a * ( -a W(-exp(-1/a)/a) - 1 )

File

testsuite/unittests/test_iaf_psp_peak.sli

Author

July 2009
Diesmann