Determining the biomechanical response of a filiform hair array : a low Reynolds number fluid-structure model
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A model system that has been the subject of many anatomical, developmental, functional, and theoretical studies over the last 30 years is the cercal sensory system of the cricket. This system is composed of two antenna-like appendages covered with hundreds of filiform mechanosensory hairs, and encodes information about the direction and dynamics of low-velocity air currents. The encoding is determined by the biomechanical properties of the mechanosensory hairs. These properties are poorly understood, primarily because accurate experimental measurements of the air-current-driven movements of the hairs are difficult to obtain, and adequate mathematical tools for modeling arbitrarily complex hair-to-hair interactions within the canopy have been absent. The study presented here solves fundamental problems in both of these areas. Previous studies have characterized the biomechanics of the filiform hairs, but only one study considered the fluid-mediated interaction of closely-packed hairs. A major goal of our work was to model the motion of a dense patch of thin filaments driven by bulk fluid flow, in a context that is immediately relevant to the cercal system. To understand the function of the sensory epithelium as a whole, we developed a numerical model based on a novel mathematical tool: the method of regularized unsteady Stokeslets. This method is generally applicable to low Reynolds number fluid flow in domains that are subject to periodic forcing along the boundary. The numerical scheme associated with our mathematical model is fast, scalable, accounts for the interaction between arbitrary arrangements of hairs. We measured the biomechanical stimulus-response properties of 19 filiform hairs, and used that data to fit parameters to our mathematical model. We demonstrate for the first time that one of the mechanical parameters controlling filiform hair motion depends on the frequency of the air stimulus. Our numerical simulations demonstrate that damped and synergistic hair interactions can occur between closely-packed hairs. Low frequency signals (< 50 Hz) are damped, and higher frequency signals (50-200 Hz) are amplified. We hypothesize that the characteristic dense patch of hairs at the proximal end of the cercus acts as a noise cancellation filter that removes low frequency components of ambient environmental stimuli.