This model has been tested by stimulating *Brienomyrus brachyistius*
KOs with head-tail or transverse electric field geometries designed to
stimulate receptors sequentially, and uniform geometry designed to
stimulate them synchronously while recording *in vivo* evoked
potentials from the posterior exterolateral nucleus (ELp), the sole
recipient of ELa small cell output. Given that electric field strength
was sufficient to drive “all” KOs, we predicted no evoked potentials in
ELp under uniform geometry compared to a large evoked potential under
head-tail and transverse geometry.

To interpret this experiment, a simulation of certain elements of the neural network was performed. The next sections outline the simulation and some results.

Xu-Friedman MA, Hopkins CD (1999)

**Simulation Assumptions**

- A simplified geometric model of a fish body was constructed with four isopotential quadrants, each with a specified number of electrorecptors. Electric fields are assumed to be applied left/right or front/back with either polarity, or uniformly across the entire body.
- About 100 receptor cells are used, modeling the actual number on a
fish. Each electroreceptor consists of a linear convolution filter and
a rectifier, followed by a spike generation scheme:
- The filter and rectifier transduce a voltage into a current that will directly control the probability of firing a neuron.
- Each electroreceptor has independently settable parameters for
filtering, time constant, threshold and threshold noise. The filter
center frequencies are log-normal distributed. For the front half of the
fish the mean frequency was 1500 Hz, with a range of 200 to 4000 Hz.
The distribution used was
`exp(log(1500)+randn*0.55)`

. For the back half of the fish the mean frequency was 2000 Hz, with a range of 1500 to 2500 Hz. The distribution was`exp(log(2000)+randn*0.18)`

. The function`randn`

returns a normally distributed number with mean zero and standard deviation one. - The distribution of center frequencies as used to construct butterworth bandpass filters with a lower cutoff of
`(cf-cf*0.8)`

and a higher cutoff of`(cf+300)`

where`cf`

are the center frequencies from the step above. These particular values were chosen to approximate the shapes of the response curves from actual fish. - The output of each receptor was a spike train. The probability of firing is a free parameter and was set to 0.05 per time step per unit input current. There was a refractory period during which a spike could not occur. This was set to 1.2 mSec based on Bell and Grant (1989).

- The output of the receptor cells go through a simplified pathway,
modeled by delays, to small cells in the ELa. About 1000 small cells
were modeled. Each small cell was modeled as an integrate-and-fire with
delayed inputs from the receptors:
- Each small cell had two inputs, picked at random from all receptors. One excitatory, one inhibitory.
- Delay assumptions:
- First Pass:
- The inhibitory input had a delay chosen from a normal distribution with mean of 56 microSec, standard deviation of 11 microSec, and with a minimum of 10 microseconds. (Friedman and Hopkins 1998, measured by Laurieanne)
- The excitatory input had a delay chosen from a normal distribution with mean of 386 microSec, standard deviation of 52 microSec, and with a minimum of 10 microseconds. (Friedman and Hopkins 1998, measured by Laurieanne)

- Second pass. There is a long tail on the excitatory delay distribution toward low delay.
this tail was explicitly inculded in the model.
- The inhibitory input had a delay chosen from a normal distribution with mean of 56 microSec, standard deviation of 11 microSec, and with a minimum of 10 microseconds. (Friedman and Hopkins 1998, measured by Laurieanne)
- The excitatory input had a delay chosen from the actual measured distribution. (Friedman and Hopkins 1998, measured by Laurieanne)

- First Pass:
- The strength of the inhibitory input is much greater the the strength of the excitatory input. The strength...