280
S. T. Nichols et al.
2.2 Spike Rate Generation
The relative neural response in relation to different stimuli frequencies and intensities was mapped out using the data from [10], which showed that the spike rates
generated from S-cells matched the behavioral responses from the leeches in [8].
Specifically, the frequencies eliciting higher spike rates were the same or close
to the frequencies that lead to the highest find rates. A bi-modal distribution
was fit to the mechanical data from [10] with peak neural responses at around
3 Hz and 14 Hz (Fig. 2). Since the neural response to mechanical stimuli increases
with intensity, a linear scaling factor was included to model an increase in spike
rate due to intensity. A skewed distribution was used to fit the neural behavior
produced from visual stimuli with a peak around 1 Hz (Fig. 2).
2.3 Elliptical Model Construction
The spike rates are fed into sigmoid functions that output minimum and maximum spike rates for both the visual and mechanical stimuli. These minimum
and maximum spike rates are used to calculate the major and minor axes of
the elliptical model. Two sigmoid functions were used to take in relative neural
responses and output minimum and maximum spike rates for both the visual
and mechanical stimulus responses (Fig. 2 - panels 3i and 3ii). The maximum
spike rate was set at 70 and the minimum spike rate was set at 30; each of which
is an arbitrary value.
Per [11] and [13], and inspired by the anatomical structure of the leech,
the following equation was used to generate ellipses to represent populations
of spatially arranged neurons. This equation can be used for both visual and
mechanical stimuli.
S r (θ i ) =
A r B r
A 2
r cos 2 (θ i − φ) + B 2
r sin 2 (θ i − φ)
(2)
Subscript r refers to the mechanical response (mech), visual response (vis), or
integrated/effective response (int). θ i is the angular placement of the population
of the i
th population of neurons, and φ is the direction of the oncoming stimulus.
For each θ i , a population of neurons produces its own relative spike rates. A is
the maximum spike rate, B is the minimum spike rate. S r (θ i ) is a resultant
vector of spike rates. By letting x = cos (θ i − φ) and y = sin (θ i − φ), one can
verify that this equation has the form of an ellipse.
Once the ellipses for each sensory modality are computed, the integrated
response is calculated by taking the absolute value of the difference between
mechanical and visual responses [11].
S int = |S mech − S vis |
(3)
This approach models lateral inhibition between populations of neurons [11],
which has been observed in visual and tactile sensory processing, and results
in higher contrast between sensory responses. Neurons with the strong activation inhibit the activity of neighboring neurons. In a leech that uses two types
S. T. Nichols et al.
2.2 Spike Rate Generation
The relative neural response in relation to different stimuli frequencies and intensities was mapped out using the data from [10], which showed that the spike rates
generated from S-cells matched the behavioral responses from the leeches in [8].
Specifically, the frequencies eliciting higher spike rates were the same or close
to the frequencies that lead to the highest find rates. A bi-modal distribution
was fit to the mechanical data from [10] with peak neural responses at around
3 Hz and 14 Hz (Fig. 2). Since the neural response to mechanical stimuli increases
with intensity, a linear scaling factor was included to model an increase in spike
rate due to intensity. A skewed distribution was used to fit the neural behavior
produced from visual stimuli with a peak around 1 Hz (Fig. 2).
2.3 Elliptical Model Construction
The spike rates are fed into sigmoid functions that output minimum and maximum spike rates for both the visual and mechanical stimuli. These minimum
and maximum spike rates are used to calculate the major and minor axes of
the elliptical model. Two sigmoid functions were used to take in relative neural
responses and output minimum and maximum spike rates for both the visual
and mechanical stimulus responses (Fig. 2 - panels 3i and 3ii). The maximum
spike rate was set at 70 and the minimum spike rate was set at 30; each of which
is an arbitrary value.
Per [11] and [13], and inspired by the anatomical structure of the leech,
the following equation was used to generate ellipses to represent populations
of spatially arranged neurons. This equation can be used for both visual and
mechanical stimuli.
S r (θ i ) =
A r B r
A 2
r cos 2 (θ i − φ) + B 2
r sin 2 (θ i − φ)
(2)
Subscript r refers to the mechanical response (mech), visual response (vis), or
integrated/effective response (int). θ i is the angular placement of the population
of the i
th population of neurons, and φ is the direction of the oncoming stimulus.
For each θ i , a population of neurons produces its own relative spike rates. A is
the maximum spike rate, B is the minimum spike rate. S r (θ i ) is a resultant
vector of spike rates. By letting x = cos (θ i − φ) and y = sin (θ i − φ), one can
verify that this equation has the form of an ellipse.
Once the ellipses for each sensory modality are computed, the integrated
response is calculated by taking the absolute value of the difference between
mechanical and visual responses [11].
S int = |S mech − S vis |
(3)
This approach models lateral inhibition between populations of neurons [11],
which has been observed in visual and tactile sensory processing, and results
in higher contrast between sensory responses. Neurons with the strong activation inhibit the activity of neighboring neurons. In a leech that uses two types