Modeling the electric image produced by objects with complex impedance in weakly electric fish

Weakly electric fish generate an electric field around their body by electric organ discharge (EOD). By measuring the modulation of the electric field produced by an object in the field these fish are able to accurately locate an object. Theoretical and experimental studies have focused on the amplitude modulations of EODs produced by resistive objects. However, little is known about the phase modulations produced by objects with complex impedance. The fish must be able to detect changes in object impedance to discriminate between food and nonfood objects. To investigate the features of electric images produced by objects with complex impedance, we developed a model that can be used to map the electric field around the fish body. The present model allows us to calculate the spatial distribution of the amplitude and phase shift in an electric image. This is the first study to investigate the changes in amplitude and phase shift of electric images induced by objects with complex impedance in wave-type fish. Using the model, we show that the amplitude of the electric image exhibits a sigmoidal change as the capacitance and resistance of an object are increased. Similarly, the phase shift exhibits a significant change within the object capacitance range of 0.1-100 nF. We also show that the spatial distribution of the amplitude and phase shifts of the electric image resembles a "Mexican hat" in shape for varying object distances and sizes. The spatial distribution of the phase shift and the amplitude was dependent on the object distance and size. Changes in the skin capacitance were associated with a tradeoff relationship between the magnitude of the amplitude and phase shift of the electric image. The specific range of skin capacitance (1-100 nF) allows the receptor afferents to extract object features that are relevant to electrolocation. These results provide a useful basis for the study of the neural mechanisms by which weakly electric fish recognize object features such as distance, size, and impedance.