{"title": "Simulation and Measurement of the Electric Fields Generated by Weakly Electric Fish", "book": "Advances in Neural Information Processing Systems", "page_first": 436, "page_last": 443, "abstract": null, "full_text": "436 \n\nSIMULATION AND MEASUREMENT OF \nTHE ELECTRIC FIELDS GENERATED \n\nBY WEAKLY ELECTRIC FISH \n\nBrian Rasnow1, Christopher Assad2, Mark E. Nelson3 and James M. Bow~ \n\nDivisions of Physics1 ,Elecbical Engineerini, and Biolo~ \n\nCaltech, Pasadena, 91125 \n\nABSTRACT \n\nThe weakly electric fish, Gnathonemus peters;;, explores its environment by gener(cid:173)\nating pulsed elecbic fields and detecting small pertwbations in the fields resulting from \nnearby objects. Accordingly, the fISh detects and discriminates objects on the basis of a \nsequence of elecbic \"images\" whose temporal and spatial properties depend on the tim(cid:173)\ning of the fish's electric organ discharge and its body position relative to objects in its en(cid:173)\nvironmenl We are interested in investigating how these fish utilize timing and body-po(cid:173)\nsition during exploration to aid in object discrimination. We have developed a fmite-ele(cid:173)\nment simulation of the fish's self-generated electric fields so as to reconstruct the elec(cid:173)\ntrosensory consequences of body position and electric organ discharge timing in the fish. \nThis paper describes this finite-element simulation system and presents preliminary elec(cid:173)\ntric field measurements which are being used to tune the simulation. \n\nINTRODUCTION \n\nThe active positioning of sensory structures (i.e. eyes, ears, whiskers, nostrils, etc.) \nis characteristic of the information seeking behavior of all exploratory animals. Yet, in \nmost existing computational models and in many standard experimental paradigms, the \nactive aspects of sensory processing are either eliminated or controlled (e.g. by stimulat(cid:173)\ning fIXed groups of receptors or by stabilizing images). However, it is clear that the ac(cid:173)\ntive positioning of receptor surfaces directly affects the content and quality of the sensory \ninfonnation received by the nervous system. Thus. controlling the position of sensors \nduring sensory exploration constitutes an important feature of an animals strategy for \nmaking sensory discriminations. Quantitative study of this process could very well shed \nlight on the algorithms and internal representations used by the nervous system in dis(cid:173)\ncriminating peripheral objects. \n\nStudies of the active use of sensory surfaces generally can be expected to pose a \nnumber of experimental challenges. This is because, in many animals, the sensory surfac(cid:173)\nes involved are themselves structurally complicated, making it difficult to reconstruct p0-\nsition sequences or the consequences of any repositioning. For example, while the sen-\n\n\fSimulation and Measurement of the Weakly Electric Fish \n\n437 \n\nsory systems of rats have been the subjects of a great deal of behavioral (Welker, 1964) \nand neurophysiological study (Gibson & Welker, 1983), it is extremely difficult to even \nmonitor the movements of the perioral surfaces (lips, snout, whiskers) used by these ani(cid:173)\nmals in their exploration of the world let alone reconstruct the sensory consequences. For \nthese reasons we have sought an experimental animal with a sensory system in which \nthese sensory-motor interactions can be more readily quantified. \n\nThe experimental animal which we have selected for studying the control of sensory \nsurface position during exploration is a member of a family of African freshwater fish \n(Monniridae) that use self-generated electric fields to detect and discriminate objects in \ntheir environment (Bullock & Heiligenberg, 1986). The electrosensory system in these \nfish relies on an \"electric organ\" in their tails which produces a weak pulsed electric field \nin the surrounding environment (significant within 1-2 body lengths) that is then detected \nwith an array of electrosensors that are extremely sensitive to voltage drops across the \nskin. These \"electroreceptors\" allow the fISh to respond to the perturbations in the elec(cid:173)\ntric field resulting from objects in the environment which differ in conductivity from the \nsurrounding water (Fig. 1). \n\nobject \n\n.. conducting \n\u2022 \nIIID electric organ \n\n\u00a7 electroreceptors \n\nelectric \nfield lines \n\nFigure 1. The peripheral electrosensory system of Gnathonemus petersii \nconsists of an \"electric organ\" current source at the base of the tail and sev(cid:173)\neral thousand \"electroreceptor\" cells distributed non uniformly over the \nfish's body. A conducting object near the fish causes a local increase in the \ncurrent through the skin. \n\nThese fISh are nocturnal, and rely more on their electric sense than on any other sensory \nsystem in perfonning a wide range of behaviors (eg. detecting and localizing objects such \nas food). It is also known that these fish execute exploratory movements, changing their \nbody position actively as they attempt an electrosensory discrimination (Toerring & \nBelbenoit, 1979). Our objective is to understand how these movements change the distri(cid:173)\nbution of the electric field on the animals skin, and to determine what, if any, relationship \nthis has to the discrimination process. \n\nThere are several clear advantages of this system for our studies. First, the electrore-\n\n\f438 \n\nRasnow, Assad, Nelson and Bower \n\nceptors are in a fixed position with respect to each other on the surface of the animal. \nTherefore, by knowing the overall body position of the animal it is possible to know the \nexact spatial relationship of electroreceptors with respect to objects in the environment. \nSecond, the physical equations governing the self-generated electric fIeld in the fish's en(cid:173)\nvironment are well understood. As a consequence, it is relatively straightforward to re(cid:173)\nconstruct perturbations in the electric field resulting from objects of different shape and \nconductance. Third, the electric potential can be readily measured, providing a direct \nmeasure of the electric field at a distance from the fish which can be used to reconstruct \nthe potential difference across the animals skin. And finally, in the particular species of \nfish we have chosen to work with, Gnathonemus petersii, individual animals execute a \nbrief (100 J.1Sec) electric organ discharge (BOD) at intervals of 30 msec to a few seconds. \nModification of the firing pattern is 1cnown to be correlated with changes in the electrical \nenvironment (Lissmann, 1958). Thus, when the electric organ discharges, it is probable \nthat the animal is interested in \"taking a look\" at its surroundings. In few other sensory \nsystems is there as direct an indication of the attentional state of the subject. \n\nHaving stated the advantages of this system for the study we have undertaken, it is \nalso the case that considerable effort will still be necessary to answer the questions we \nhave posed. For example, as described in this paper, in order to use electric field mea(cid:173)\nsurements made at a distance to infer the voltages across the surface of the animal's skin, \nit is necessary to develop a computer model of the fish and its environment. This will \nallow us to predict the field on the animal's skin surface given different body poSitions \nrelative to objects in the environment. This paper describes our first steps in constructing \nthis simulation system. \n\nExperimental Approach and Methods \n\nSimulations of Fish Electric Fields \n\nThe electric potential, cll(x), generated by the EOD of a weakly electric fish in a fish \n\ntank is a solution ofPoisson's equation: \n\nVe(pVell) = f \n\nwhere p(x)and f(x) are the impedance magnitude and source density at each point x in(cid:173)\nside and surrounding the fish. Our goal is to solve this equation for ell given the current \nsource density, f, generated by the electric organ and the impedances, p, corresponding to \nthe properties of the fish and external objects (rocks, worms, etc.). Given p and f. this \nequation can be solved for the potential ell using a variety of iterative approximation \nschemes. Iterative methods, in general, first discretize the spatial domain of the problem \ninto a set of \"node\" points, and convert Poisson's equation into a set of algebraic equa(cid:173)\ntions with the nodal potentials as the unknown parameters. The node values, in this case, \neach represent an independent degree of freedom of the system and, as a consequence, \nthere are as many equations as there are nodes. This very large system of equations can \n\n\fSimulation and Measurement of the Weakly Electric Fish \n\n439 \n\nthen be solved using a variety of standard techniques, including relaxation methods, con(cid:173)\njugate gradient minimization, domain decomposition and multi-grid methods. \n\nTo simulate the electric fields generated by a fish, we currently use a 2-dimensional \nfmite element domain discretization (Hughes, 1987) and conjugate gradient solver. We \nchose the finite element method because it allows us to simulate the electric fields at \nmuch higher resolution in the area of interest close to the animal's body where the elec(cid:173)\ntric field is largest and where errors due to the discretization would be most severe. The \nfmite element method is based on minimizing a global function that corresponds to the \npotential energy of the electric field. To compute this energy, the domain is decomposed \ninto a large number of elements, each with uniform impedance (see Fig. 2). The global \nenergy is expressed as a sum of the contributions from each element, where the potential \nwithin each element is assumed to be a linear interpolation of the potentials at the nodes \nor vertices of each element The conjugate gradient solver determines the values of the \nnode potentials which minimize the global energy function. \n\n1\\ IVrv'V \n\n1\\ 1\\ rv:V J J 1\\/1\\ \n\n.J 1\\/ 1\\11\\/1\\/1\\11\\/1\\/1\\ 1\\11\\/[\\ 1\\1 IV \n\nV \n\nv \n\nv \n\nr--.. \n\n7' \n\n[7 \n\nIf\\ If\\ '\\ '\\ V\\ V If\\ J\\ 1'\\ 'w l/\\ V 11'\\ '\\ 1/ :1'\\ \n\n'\\ '\\ '\\ V '\\ 1'\\\" '\\ 11\\ 1/\\ \\ '\\ V \n\nFigure 2. The inner region of a fmite element grid constructed for simulat(cid:173)\ning in 2-dimensions the electric field generated by an electric fish. \n\nMeasurement of Fish Electric Fields \n\nAnother aspect of our experimental approach involves the direct measurement of \nthe potential generated by a fish's EOD in a fish tank using arrays of small electrodes and \ndifferential amplifiers. The electrodes and electronics have a high impedance which min(cid:173)\nimizes their influence on the electric fields they are designed to measure. The electrodes \nare made by pulling a 1mm glass capillary tube across a heated tungsten filament, result(cid:173)\ning in a fine tapered tip through which a 1~ silver wire is run. The end of this wire is \nmelted in a flame leaving a 200J,un ball below the glass insulation. Several electrodes are \nthen mounted as an array on a microdrive attached to a modified X-Yplotter under com(cid:173)\nputer control and giving better than 1mm positioning accuracy. Generated potentials are \namplified by a factor of 10 - 100, and digitized at a rate of 100kHz per channel with a 12 \nbit AID converter using a Masscomp 5700 computer. An array processor searches this \n\n\f440 \n\nRasnow, Assad, Nelson and Bower \n\ncontinuous stream of data for EOD wavefonns. which are extracted and saved along with \nthe position of the electrode array. \n\nCalibration of the Simulator \n\nResults \n\nIn order to have confidence in the overall system, it was fD'St necessary to calibrate \nboth the recording and the simulation procedures. To do this we set up relatively simple \ngeometrical arrangements of sources and conductors in a fish tank for which the potential \ncould be found analytically. The calibration source was an electronic \"fake fish\" circuit \nthat generated signals resembling the discharge of Gnathonemus. \n\nPoint current source \n\nA point source in a 2-dimensional box is perhaps the simplest configuration with \nwhich to initially test our electric field reconstruction system. The analytic solution for \nthe potential from a point current source centered in a grounded. conducting 2-dimen(cid:173)\nsional box is: \n\n00 sm(\"2 sm L \n4>(x. y) = L \nn =1 \n\n. (.n7t). (n7tx). h (.n7ty ) \nsm \\L \nri1t \n\nn L cosh(T) \n\nOur fmite element simulation. based on a regular 80 x 80 node grid differs from the \nabove expression by less than 1 %. except in the elements adjacent to the source. where \nthe potential change across these elements is large and is not as accurately reconstructed \nby a linear interpolation (Fig. 3). Smaller elements surrounding the source would im(cid:173)\nprove the accuracy. however. one should note the analytic solution is infmite at the loca(cid:173)\ntion of the \"point\" source whereas the measured and simulated sources (and real fish) \nhave finite current densities. \n\nTo measure the real equivalent of a point source in a 2-dimensional box. we used a \nlinear current source (a wire) which ran the full depth of a real 3-dimensional tank. \nMeasurements made in the midplane of the tank agree with the simulation and analytic \nsolution to better than 5% (Fig. 3.). Uncertainty in the positions of the ClUTent source and \nrecording sites relative to the position of the conducting walls probably accounts for \nmuch of this difference. \n\n\fSimulation and Measurement of the Weakly Electric Fish \n\n441 \n\n1----~~--~--~----~-------\n\no - measured \nx - simulated \n\n00 \n\n2 \n\n4 \n\n6 \n\n8 \n\n10 12 14 16 \n\nFigure 3. Electric potential of a point current source centered in a grounded \n2-dimensional box. \n\ndislaDce from source \n\nMeasurements of Fish Fields and 2-Dimensional Simulations \n\nCalibration of our fmite element model of an electric fish requires direct measure(cid:173)\nments of the electric potential close to a discharging fish. Fig. 4 shows a recording of a \nsingle EOD sampled with 5 colinear electrodes near a restrained fish. The wavefonn is \nbipolar, with the fIrst phase positive if recorded near the animals head and negative if re(cid:173)\ncorded near the tail (relative to a remote reference). We used the peak amplitude of the \nlarger second phase of the wavefonn to quantify the electric potential recorded at each \nlocation. Note that the potential reverses sign at a point approximately midway along the \ntail. This location corresponds to the location of the null potential shown in Fig. 5. \n\n1500 \n\n1000 \n\n$' \n\n5500 I 0 -1r-\n\n-soo \n\n-1000 \n\no \n\n200 ~sec \n\nFigure 4. EOD waveform sampled simultaneously from 5 electrodes. \n\n\f442 \n\nRasnow, Assad, Nelson and Bower \n\nMeasurements of EODs from a restrained fish exhibited an extraordinarily small vari(cid:173)\nance in amplitude and waveform over long periods of time. In fact, the peak-peak ampli(cid:173)\ntude of the EOD varied by less than 0.4% in a sample of 40 EOD's randomly chosen dur(cid:173)\ning a 30 minute period. Thus we are able to directly compare waveforms sampled se(cid:173)\nquentially without renonnalizing for fluctuations in EOD amplitude. \n\nFigure 5 shows equipotential lines reconstructed from a set of 360 measurements \nmade in the midplane of a restrained Gnathonemus. Although the observed potential re(cid:173)\nsembles that from a purely dipolar source (Fig. 6), careful inspection reveals an asymme(cid:173)\ntry between the head and tail of the fISh. This asymmetry can be reproduced in our simu(cid:173)\nlations by adjusting the electrical properties of the fish. Qualitatively, the measured \nfields can be reproduced by assigning a low impedance to the internal body cavity and a \nhigh impedance to the skin. However, in order to match the location of the null potential, \nthe skin impedance must vary over the length of the body. We are currently quantifying \nthese parameters, as described in the next section. \n\n!!!!m 1'!I!fl!IPf!~m II \n\u2022\u2022 1 .. . ...... 1 \u2022\u2022\u2022 !~ ....... . \n\nFigure 5. Measured potentials (at peak of second phase of EOD) recorded \nfrom a restrained Gnathonemus petersii in the midplane of the fish. \nEquipotential lines are 20 m V apart. Inset shows relative location of fish \nand sampling points in the fISh tank. \n\nFigure 6. Equipotential lines from a 2-dimensional finite element simula(cid:173)\ntion of a dipole using the grid of Fig. 2. The resistivity of the fish was set \nequal to that of the sWToundings in this simulation. \n\n\fSimulation and Measurement of the Weakly Electric Fish \n\n443 \n\nFuture Directions \n\nThere is still a substantial amount of work that remains to be done before we \nachieve our goal of being able to fully reconstruct the pattern of electroreceptor activa(cid:173)\ntion for any arbitrary body position in any particular environment. First. it is clear that \nwe require more information about the electrical structure of the fISh itself. We need an \naccurate representation of the internal impedance distribution p(x) of the body and skin \nas well as of the source density f(x) of the electric organ. To some extent this can be ad(cid:173)\ndressed as an inverse problem, namely given the measured potential cl>(x), what choice of \np(x) and f(x) best reproduces the data. Unfortunately, in the absence of further con(cid:173)\nstraints, there are many equally valid solution, thus we will need to directly measure the \nskin and body impedance of the fish. Second, we need to extend our finite-element sim(cid:173)\nulations of the fish to 3-dimensions which, although conceptually straight forward, re(cid:173)\nquires substantial technical developments to be able to (a) specify and visualize the \nspace-filling set of 3-dimensional finite-elements (eg. tetrahedrons) for arbitrary configu(cid:173)\nrations, (b) compute the solution to the much larger set of equations (typically a factor of \n100-1(00) in a reasonable time, and (c) visualize and analyze the resulting solutions for \nthe 3-dimensional electrical fields. As a possible solution to (b), we are developing and \ntesting a parallel processor implementation of the simulator. \n\nReferences \n\nBullock, T. H. & Heiligenberg, W. (Eds.) (1986). \"Electroreception\", Wiley & Sons, \n\nNew York. \n\nGibson, J. M. & Welker. W. I. (1983). Quantitative Studies of Stimulus Coding in First(cid:173)\n\nOrder Vibrissa Afferents of Rats. 1. Receptive Field Properties and Threshold \nDistributions. Somatosensory Res. 1:51-67. \n\nHughes, T. J. (1987). The Finite Element Method: Linear Static and Dynamic Finite \n\nElement Analysis. Prentice-Hall, New Jersey. \n\nLissmann. H.W. (1958). On the function and evolution of electric organs in fish. J. Exp. \n\nBioi. 35:156-191. \n\nToening, M. J. and Belbenoit. P. (1979). Motor Programmes and Electroreception in \n\nMonnyrid Fish. Behav. Ecol. Sociobiol. 4:369-379. \n\nWelker, W. I. (1964). Analysis of Sniffing of the Albino Rat Behaviour 22:223-244. \n\n\f", "award": [], "sourceid": 152, "authors": [{"given_name": "Brian", "family_name": "Rasnow", "institution": null}, {"given_name": "Christopher", "family_name": "Assad", "institution": null}, {"given_name": "Mark", "family_name": "Nelson", "institution": null}, {"given_name": "James", "family_name": "Bower", "institution": null}]}