QUICK SEARCH:   [advanced] Author: Keyword(s):
Home     Help     Feedback     Subscriptions     Archive     Search     Table of Contents

First published online August 30, 2006
Journal of Experimental Biology 209, 3636-3651 (2006)
Published by The Company of Biologists 2006
doi: 10.1242/jeb.02403

This Article Summary Full Text Full Text (PDF) Alert me when this article is cited Alert me if a correction is posted Services Email this article to a friend Similar articles in this journal Similar articles in PubMed Alert me to new issues of the journal Download to citation manager Citing Articles Citing Articles via HighWire Citing Articles via Google Scholar Google Scholar Articles by Babineau, D. Articles by Lewis, J. E. Search for Related Content PubMed PubMed Citation Articles by Babineau, D. Articles by Lewis, J. E.

Modeling the electric field of weakly electric fish

David Babineau¹, André Longtin¹ and John E. Lewis^2,*

¹ Department of Physics
² Department of Biology, University of Ottawa, Ottawa, Ontario K1N 6N5, Canada

View larger version (15K): [in a new window]   Fig. 1. Electric field models. (A) Complete view of the model geometry, composed of an aquarium, grounding and reference electrodes and the model fish. (B) Close-up of morphologically accurate `fish' model consisting of a thin skin layer, an electric organ (EO) and an interior body component (between the EO and skin). The EO is 15.47 cm long and 0.08 cm thick, the skin is 0.01 cm thick and the fish is 21cm long and 1.4 cm wide. (C,D) Geometrically simple models used for studying (C) different fish tapers (see text for explanation) and (D) various body and skin properties. To achieve different tapers in C, the left side of the model (here shown for a width of 1.82 cm) is varied. The EO length and skin thickness for C and D are the same as in B. Model C is referred to as the `taper' model and model D is referred to as the `box' model. x and y axes, as well as grounding and reference electrodes, are not to scale.

View larger version (17K): [in a new window]   Fig. 2. Optimal model parameters. (A) The optimal EO current density profile (red), called `skewed', is the sum of two Gaussian curves: a narrow (dotted green) sink in the tail region and a wide (dotted blue) source in the mid-body. Rostral curve is centered 15 cm from the tip of the head and has a standard deviation of 4.46 cm; caudal curve is centered 18.04 cm from the tip of the head with a standard deviation of 0.5 cm. The ratio of the peak amplitudes of the two curves is 1:8.38. (B) Optimal conductivity values for the EO (blue), skin (green) and body (red). Optimal parameter values are normalized to one and the errors associated with each optimal parameter value are set to zero. Abscissa values are given as ratios of the optimal parameter value (for each respective curve) and ordinate values are given as field RMS% errors above minimal error (28.6%; see text for details on error measure). Optimal conductivity values are: EO, 0.927 S m-1; body, 0.356 S m-1; skin, 0.0017 S m-1. Although all parameters here were varied homogeneously, it should be noted that the optimal skin conductivity is not uniform along the length of the fish (see Fig. 8A).

View larger version (38K): [in a new window]   Fig. 3. Model calibration. (A) 2D field potential surrounding the fish. Top: experimental data obtained from Assad (Assad, 1997). Bottom: simulated values obtained with optimal parameters (including non-uniform skin conductivity). Color maps represent potential with respect to an electrode placed laterally to the fish, near its zero-potential line (as in Fig. 1A). All values below approx. -7.6 mV have been mapped to dark blue in order to show a better contrast between the positive and negative regions of the dipolar field (measured potential in tail region reaches approx. -30 mV). The zero-potential line is shown in yellow. (B) Un-weighted % error and (C) absolute potential differences between data and simulated values found in A. Broken lines show cross-sections at which the potentials are plotted in (D) and (E). Potential differences in C greater than 5 mV are all mapped to dark red. (D) Potential along dotted line near head (5 cm caudal from the tip of the head) in B for model (red) and data (blue). (E) Potential along dotted line near tail (20 cm caudal from the tip of the head) in B for model (red) and data (blue).

View larger version (26K): [in a new window]   Fig. 4. Electric field characterization: study of the fish's filtering properties and comparison with an ideal voltage divider. (A) Potential values at the electric organ (blue) and at the interior (green) and exterior (red) skin boundaries along the EO segment (zero corresponds to the rostral end, one to the caudal end), for a 5-cycle sinusoidal current density (fish model). (B) Right axis, green trace shows the normalized energy of the exterior skin potential curve as a function of rostro-caudal position along the fish body (fish model; solid line was obtained using the `shape-preserving interpolant' fitting function in MATLAB). This energy quantifies the level of `smoothness' of a given trace (see text for details). Left axis, blue trace shows the filtering along the EO segment for a 50-cycle sinusoidal current density (fish model). Filtering quantifies how much the energy has decreased from the EO to the skin (see text for details). The red line represents the start of the EO in the fish model (x=4.42 cm; see Fig. 1B). (C) Filtering along the EO segment for the fish model (green) and for the taper model with low (black) and high (blue) taper values. Red broken line represents the location of taper change in the fish model. (D) Comparison between the fish and an ideal voltage divider (taper model, taper=0.05). Theoretical (green) and simulated (blue) transdermal potentials along the EO segment for a 5-cycle sinusoidal current density. Red trace shows the difference between simulation and theory (see text for details).

View larger version (19K): [in a new window]   Fig. 5. Effect of object location on electric images (fish model). (A) Electric images for an object located 2 cm (red), 2.5 cm (blue), 3.5 cm (green), 5 cm (black) and 10 cm (pink) lateral of the fish's midline (5 cm caudal from the tip of the head). The electric image is calculated as the change in transdermal potential caused by the object. (B) Electric images for an object located 5 cm (red), 7.5 cm (black), 10 cm (green), 12.5 cm (blue), 15 cm (pink), 17.5 cm (orange) caudal from the start of the head at a lateral distance of 3 cm (from the fish's midline). The simulated object for A and B is a metal disc (brass; conductivity=2.13x107 S m-1; 1 cm radius).

View larger version (21K): [in a new window]   Fig. 6. Effect of EO current density profile on electric images (fish model). (A) Normalized current densities versus normalized EO position. The green trace shows the 1-cycle sinusoidal current density; the blue trace shows the optimal skewed current density (sum of two Gaussian curves); the red trace shows the `impulse' current density (single Gaussian function offset in order to have a mean of zero). All current densities are zero-mean. (B) Normalized electric images produced by a metal disc located in the middle of the fish (black vertical line), 3 cm lateral from the midline (see inset), for skewed (blue), impulse (red) and sinusoidal (green) current density profiles. The green markers `xR', `x0' and `xC' illustrate the `x' or rostro-caudal positions of the three points that characterize bimodal electric images: the rostral peak, the zero-crossing (located between rostral and caudal peaks) and the caudal peak, respectively.

View larger version (25K): [in a new window]   Fig. 7. Positions and amplitudes of the bimodal electric image's characteristic points (`xR', `x0' and `xC') for different rostro-caudal object locations (box model; optimal uniform skin conductivity; object centered 3 cm away from the fish's midline). (A,C) Normalized peak positions for sinusoidal (A) and skewed (C) current densities. Peak positions and object locations are normalized with respect to EO coordinates, with the rostral side corresponding to zero. Blue and green traces are the positions of the rostral and caudal peaks, respectively, while red traces show the positions of the zero-crossings. The solid black curve shows the identity line, where the location of the electric image's dominant peak at the skin corresponds exactly to the rostro-caudal location of the object. Black broken lines delimit zones in which certain characteristic curves are closest to the solid black trace: e.g. in C, the blue trace (xR) is closest to the identity line in the rostral zone, i.e. the bimodal image's rostral peak is closest to the object's actual location in this zone. (B,D) Absolute potentials of the bimodal electric image's rostral and caudal peaks for sinusoidal (B) and skewed (D) current densities. Blue traces show absolute potential values for the rostral peak while caudal peak values are shown in green.

View larger version (28K): [in a new window]   Fig. 8. Effect of skin conductivity on electric image shape (box model; skewed current density). (A) Optimal non-uniform skin conductivity profile, which has a low 0.00025 S m-1 conductivity at the head, a high 0.0025 S m-1 conductivity in the tail region and a linear conductivity increase between the two constant conductivity regions (delimited by pink dotted lines). Black broken lines delimit the EO. (B) The electric images produced by a 1 cm-radius metal object located at 0.39 along the normalized length of the EO, 3 cm lateral to the fish's midline (black dotted line; see inset) for different values and shapes of skin conductivity are shown. Green trace shows the electric image obtained with the non-uniform skin conductivity. Red and blue traces show the electric images obtained with uniform skin conductivities of 0.00025 S m-1 (head) and 0.0025 S m-1 (tail), respectively.

View larger version (20K): [in a new window]   Fig. 9. Effect of object size and lateral distance on bimodal electric images (box model; skewed current density; optimal uniform skin conductivity). Lateral distance is measured with respect to object centers. (A) Un-normalized (actual amplitudes) and (C) normalized (with respect to the caudal peak's amplitude) electric images produced by three different-sized metal objects located half way along the fish's body, 4 cm away from the midline: 0.5 cm (blue), 1.1 cm (green) and 2 cm (red) radius (see inset). Both images are plotted versus the normalized box model length, in which the rostral side corresponds to zero. (B) Peak-to-peak potentials of the electric images found in A as a function of lateral distance away from the fish's midline for the three different objects (object sizes same as in A; see inset). (D) Delta, defined as the difference between the rostral and caudal peak locations, found in either A or C, as a function of lateral distance from the fish's midline for the three different objects; delta for the 1.1 cm object is shown in A and C. Black broken lines in B and D show the distance (4 cm away from the fish's midline) at which the objects were located for the images shown in A and C.

View larger version (23K): [in a new window]   Fig. 10. Effect of object size and lateral distance on bimodal electric images. All panels are the same as in Fig. 9 except that lateral distance is measured here with respect to the object's edge. (A) Un-normalized and (C) normalized electric images produced by three different-sized metal objects located half way along the fish's body, with the object edges 2 cm away from the midline: 0.5 cm (blue), 1.1 cm (green) and 2 cm (red) radius (see inset). Red traces are the same as in Fig. 9A,C since a lateral edge distance of 2 cm for the 2 cm-radius object corresponds to a lateral object center distance of 4 cm. (B) Peak-to-peak potentials of the electric images found in A as a function of lateral distance away from the fish's midline for the three different objects (object sizes same as in A; see inset). (D) Delta found in either A or C, as a function of lateral distance from the fish's midline for the three different objects; delta for the 1.1 cm object is shown in A and C. Black broken lines in B and D show the distance (2 cm away from the fish's midline) at which the objects were located for the images shown in A and C.