Hydrodynamic object formation: Perception, neuronal representation, and multimodal integration

Abstract

Lateral-line encoding is diffuse, needing at least a large part of the fish body and several detectors to measure the information contained in the velocity or pressure field surrounding a fish or an aquatic frog such as Xenopus. This paper presents a careful analysis of the mathematical mechanisms and algorithms underlying neuronal information processing as it is performed by the lateral-line system both in the perception ensuing from neuromasts and in the resulting neuronal representations, the maps. The goal is to explicitly show how the lateral line can simultaneously perceive several objects, e.g., identical ones, which role fish geometry plays in lateral-line detection, and why its direct range is short, about one fish length. A lateral-line ‘object’ in the outside world has both position and shape and the lateral line can handle both, at the price of having a restricted range. Detection of vortex wakes as hydrodynamic entities exhibiting the consequence of conservation of angular momentum is also analyzed and contrasted with the instantaneous momentum transfer studied as the usual lateral-line stimulus. Finally, it is shown how lateral-line ‘objects’ may arise neuronally both separately and in the context of a multimodal integration of the lateral-line system and vision, and a concrete theory of map formation in the torus on the basis of neuroanatomy and spike-timing-dependent plasticity (STDP) in conjunction with local excitation and global inhibition is presented. An appendix gives a full and simple mathematical account of surface-wave hydrodynamics, including surface tension.