Figure 1.
Image Generation in a Fish with Realistic Internal Conductivity and Homogeneous Highly Conductive Skin
(A) The coloured background represents the difference in voltage between each point surrounding the fish and an infinitely distant point, using a non-linear arctangent colour scale (used to highlight values close to zero) shown in the colour bar below for the basal field (in the absence of objects). The black line shows the zero equipotential surface, which is perpendicular to the axis of the EO equivalent dipole distribution.
(B) A similar coloured representation shows the perturbing field (i.e., the field in the presence of the object minus the basal field) produced by a metal cube (1 cm3) close to the skin (0.5 mm). The black line shows the zero equipotential surface, which is perpendicular to the axis of the object equivalent dipole distribution.
(C) Electric image of the metal object depicted in a colour map on the modelled realistic fish from a scorci view.
(D) Electric image along the intersection of the skin with the sagittal plane, illustrating its “Mexican hat” profile.
Figure 2.
Image Generation in a Fish with Internal Conductivity like That of Water and with a Homogeneous Highly Conductive Skin
The black bars show the zero equipotential surfaces as in Figure 1.
(A) Basal field (in the absence of objects). (B) Perturbing field produced by the same scene as in Figure 1B.
(C) Electric image of the metal object depicted in a colour map on the modelled transparent fish from a scorci view.
(D) Electric image along the intersection of the skin with the sagittal plane.
Figure 3.
The Effect of Internal Conductivity on the Image Generation of a Dipole
(A) Electric image of a dipole placed at 0.5 mm from a “transparent” fish seen from a scorci view; the modelled dipole axis is perpendicular to the longitudinal axis of the fish.
(B) Same scene as (A) for fish with realistic internal conductivity.
(C) Electric image (transcutaneous current density) along the intersection of the skin with the sagittal plane (left), and the coronal plane (right), for the same dipole as in (A) and (B). Red traces show the images on a transparent fish, while blue traces correspond to a fish with realistic internal conductivity. Note that the ordinate for the realistic fish (left) is twice that for the transparent fish (right).
Figure 4.
The Effect of Internal Conductivity on Electric Image Generation
(A) Normalized electric images of the same metal cube (identical position) on fish with different internal conductivities. Red: 16.5 μScm−1 (the same as water conductivity), cyan: 165 μScm−1, blue: 1,650 μScm−1, black: 16,500 μScm−1 (normal conductivity), magenta: 165,000 μScm−1. The skin is modelled for all cases, with a homogeneous conductivity of 500,000 μScm−1. The dashed line shows the case of a fish with realistic internal conductivity and skin conductivity distribution. rl, realistic internal conductivity; rlh, realistic internal conductivity, heterogeneous skin distribution.
(B) Peak amplitude of the electric image of a metal cube (1 cm3) placed at 0.5 mm from the fish, as a function of body internal conductivity. The difference in the peak amplitude of the electric image corresponding to the realistic internal conductivity fish shown in this figure and that shown in Figure 1 is due to the use of two compartment bodies (see Materials and Methods).
Figure 5.
The Effect of Skin Conductivity on Electric Image Generation
(A) Transcutaneous current density (electric image) of a metal cube (1cm3) placed at 0.5 mm from the skin, modelled on skin with different conductivities. Red: 10 μScm−2, cyan: 100 μScm−2 (similar to mormyromast epithelium), blue: 1,000 μScm−2, black: 10,000 μScm−2, magenta: 100,000 μScm−2. All these fish have an internal conductivity of 3,300 μScm−1. Dashed line shows the case of a fish with realistic internal conductivity and skin conductivity distribution.
(B) Transcutaneous voltage calculated from the transcutaneous current densities shown in (A), using the same colour code.
(C) Current peak (right axis, red trace) and voltage peak (left axis, blue trace) as a function of skin conductivity for fish with homogeneous skin.
(D) Normalized plot for (B), using same colour code. mel, mormyromast epithelium-like conductivity; rlh, realistic internal conductivity, heterogeneous skin distribution.
Figure 6.
Schematic Representation of Electric Image Generation
First row, generation of stimulation in the presence of the object; second row, basal stimulation in the absence of objects; third row, sensory image.
(A) Fish with water-like internal conductivity. Imprimence generation (yellow boxes) precedes image generation (purple boxes). A field perturbation (green arrows) is induced as a consequence of the object interaction with the basal field (dark-blue arrows). The electric image is the difference between the perturbing (light-blue arrow) and the basal fields at the skin.
(B) Fish with realistic internal conductivity. The interaction of the body with the field perturbed by the object (red arrows) introduces another component (orange arrow) to the electrosensory stimulus (magenta arrow). The electric image (yellow arrow) is the electrosensory stimulus minus the basal field (blue arrow, representing the sum of the effects of the fish body and the object in the presence of each other). (See Discussion for explanation.)