Mammalian Whiskers and the Euler Spiral

Dougill, Gary ORCID: https://orcid.org/0000-0002-8885-6166, Starostin, Eugene, van der Heijden, Gert, Goss, Geoff and Grant, Robyn (2019) Mammalian Whiskers and the Euler Spiral. In: International Congress of Vertebrate Morphology, 21 July 2019 - 25 July 2019, Prague.

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Abstract

Mammal whiskers are often used as a model for understanding the sensory circuits in the brain. Signals from the whiskers, especially their forces, are processed throughout the brain, particularly in the somatosensory “barrel” cortex. Before attempting to interpret the neuronal signals, it is imperative to understand the signals received by the whisker follicles themselves and therefore accurately modelling whisker mechanics is important. Previously, whiskers have been modelled as a parabola based on Cartesian coordinates of the whisker centerline, but we propose that an Euler spiral model is a simple way to capture many aspects of whisker shape. In this study, we model 516 rat (Rattus norvegicus) whiskers as plane model curves with a linear relationship between arc length, s, and curvature, k, such that k(s) = A(s) + B and show that any original rat whisker can be mapped onto a normalized Euler spiral. The Euler spiral provides a convenient and highly accurate model for analytical studies, particularly intrinsically curved rods such as whiskers. The simplistic description in terms of coefficients A and B allows average whiskers to be created from data sets. In addition, vibrissae of many different species, such as pygmy shrew or grey seal, can be readily compared based on their shape alone.