Abstract
The paper deals with the mechanical vibrational motion of vibrissae during natural exploratory behaviour of mammals. The theoretical analysis is based on a mechanical model of a cylindrical beam with circular natural configuration under an applied periodic force at the tip, which corresponds to the surface roughness of an investigated object. The equation of motion of the beam is studied using the Euler-Bernoulli beam theory and asymptotic methods of mechanics. It is shown that from the mechanical point of view the phenomenon of parametric resonance of the vibrissa is possible. It means that the amplitude of forced vibrations of a vibrissa increases exponentially with time, if it is stimulated within a specific resonance frequency range, which depends on biomechanical parameters of the vibrissa. The most intense parametric resonance occurs, when the excitation frequency is close to the doubled natural frequency of free vibrations. Thus, it may be used to distinguish and amplify specific periodic components of a complex roughness profile during texture discrimination.
Article PDF
Similar content being viewed by others
Explore related subjects
Discover the latest articles, news and stories from top researchers in related subjects.Avoid common mistakes on your manuscript.
References
Tropea C, Bleckmann H (eds.). Nature inspired fluid mechanics. Notes on Numerical Fluid Mechanics and Multidisciplinary Design, Springer-Verlag, Berlin Heidelberg, Germany, 2012.
Zimmermann K, Zeidis I, Behn C. Mechanics of Terrestrial Locomotion: With a Focus on Non-pedal Motion Systems. Springer-Verlag, Berlin Heidelberg, Germany, 2009.
Lepora N, Verschure P, Prescott T. The state of the art in biomimetics. Bioinspiration & Biomimetics, 2013, 8, 1–11.
Wu J, Yang H, Yan S. Energy saving strategies of honeybees in dipping nectar. Scientific Reports, 2015, 5, 15002.
Zhao J, Wu J, Yan S. Erection mechanism of glossal hairs during honeybee feeding. Journal of Theoretical Biology, 2015, 386, 62–68.
Behn C. Mathematical Modeling and Control of Biologically Inspired Uncertain Motion Systems with Aadaptive Features. Habilitation thesis, Technische Universität Ilmenau, Germany, 2013.
Schmidt M, Witte H, Zimmermann K, Niederschuh S, Helbig T, Voges D, Husung I, Volkova T, Will C, Behn C, Steigenberger J, Klauer G. Technical, non-visual characterization of substrate contact using carpal vibrissae as a biological model: An overview. Proceedings of the 58th International Scientific Colloquium, Ilmenau, Germany, 2014.
Vincent S. The function of vibrissae in the behavior of the white rat. Behavior Monographs, 1912, 1, 1–81.
Ahl A. The role of vibrissae in behavior: A status review. Veterinary Research Communications, 1986, 10, 245–268.
Ebara S, Kumamoto K, Matsuura T, Mazurkiewicz J, Rice F. Similarities and differences in the innervation of mystacial vibrissal follicle-sinus complexes in the rat and cat: A confocal microscopic study. Journal of Comparative Neurology, 2002, 449, 103–119.
Dörfl J. The musculature of the mystacial vibrissae of the white mouse. Journal of Anatomy, 1982, 135, 147–154.
Haidarliu S, Simony E, Golomb D, Ahissar E. Muscle architecture in the mystacial pad of the rat. The Anatomical Record, 2010, 293, 1192–1206.
Carvell G, Simons D. Biometric analyses of vibrissal tactile discrimination in the rat. The Journal of Neuroscience, 1990, 10, 2638–2648.
Niederschuh S, Witte H, Schmidt M. The role of vibrissal sensing in forelimb position control during travelling locomotion in the rat (Rattus norvegicus, Rodentia). Zoology, 2014, 118, 51–62.
Prescott T, Ahissar E, Izhikevich E (eds.). Scholarpedia of Touch, Atlantis Press, Paris, France, 2016.
Neimark M, Andermann M, Hopfield J, Moore C. Vibrissa resonance as a transduction mechanism for tactile encoding. The Journal of Neuroscience, 2003, 23, 6499–6509.
Andermann M, Moore C. Mechanical resonance enhances the sensitivity of the vibrissa sensory system to near-threshold stimuli. Brain Research, 2008, 1235, 74–81.
Jadhav S, Feldman D. Texture coding in the whisker system. Current Opinion in Neurobiology, 2010, 20, 313–318.
Hartmann M, Johnson N, Towal R, Assad C. Mechanical characteristics of rat vibrrissae: Resonant frequencies and damping in isolated whiskers and in the awake behaving animal. The Journal of Neuroscience, 2003, 23, 6510–6519.
Yan W, Kan Q, Kergrene K, Kang G, Feng X, Rajan R. A truncated conical beam model for analysis of the vibration of rat whiskers. Journal of Biomechanics, 2013, 46, 1987–1995.
Quist B, Seghete V, Huet L, Murphey T, Hartmann M. Modeling forces and moments at the base of a rat vibrissa during noncontact whisking and whisking against an object. The Journal of Neuroscience, 2014, 34, 9828–9844.
Landau L, Lifshitz E. Mechanics. Course of Theoretical Physics, 2nd ed., Pergamon Press, Oxford, United Kingdom, 1969.
Geisler C. From Sound to Synapse, Oxford University Press, New York, USA, 1998.
Warren R. Auditory Perception: An Analysis and Synthesis, 3rd ed., Cambridge University Press, Cambridge, United Kingdom, 2008.
Berg R, Kleinfeld D. Rhythmic whisking by rat: Retraction as well as protraction of the vibrissae is under active muscular control. Journal of Neurophysiology, 2003, 89, 104–117.
Mitchinson B, Gurney K, Redgrave P, Melhuish C, Pipe A, Pearson M, Gilhespy I, Prescott T. Empirically inspired simulated electro-mechanical model of the rat mystacial follicle-sinus complex. Proceedings of the Royal Society of London B: Biological Sciences, 2004, 271, 2509–2516.
Hill D, Bermejo R, Zeigler H, Kleinfeld D. Biomechanics of the vibrissa motor plant in rat: Rhythmic whisking consists of triphasic neuromuscular activity. The Journal of Neuroscience, 2008, 28, 3438–3455.
Behn C, Schmitz T, Witte H, Zimmermann K. Animal vibrissae: modelling and adaptive control of bio-inspired sensors. Proceedings of the 12th International Work-Conference on Artificial Neural Networks, Tenerife, Spain, 2013, 159–170.
Scholz G, Rahn C. Profile sensing with an actuated whisker. IEEE Transactions on Robotics and Automation, 2004, 20, 124–127.
Schäfer M, Schmitz T, Will C, Behn C. Transversal vibrations of beams with boundary damping in the context of animal vibrissae. Proceedings of the 56th International Scientific Colloquium, Ilmenau, Germany, 2011.
Will C, Steigenberger J, Behn C. Object contour reconstruction using bio-inspired sensors. Proceedings of the 11th International Conference on Informatics in Control, Automation and Robotics, Vienna, Austria, 2014, 459–467.
Quist B, Hartmann M. Mechanical signals at the base of a rat vibrissa: the effect of intrinsic vibrissa curvature and implications for the tactile exploration. Journal of Neurophysiology, 2012, 107, 2298–2312.
Carl K. Technische Biologie des Tasthaar-Sinnessystems als Gestaltungsgrundlage für taktile stiftführende Mechanosensoren. Ph.D. thesis, Technische Universität Ilmenau, Germany, 2009. (in German)
Zimmer U. Self-localization in dynamic environments. IEEE/SOFT International Workshop BIES′95, Tokio, Japan, 1995.
Kaneko M, Kanayama N, Tsuji T. Vision based active antenna. IEEE International Conference on Robotics and Automation, Minneapolis, USA, 1996, 3, 2555–2560.
Pearson M, Mitchinson B, Sullivan J, Pipe A, Prescott T. Biomimetic vibrissal sensing for robots. Proceedings of the Royal Society of London B: Biological Sciences, 2011, 366, 3085–3096.
Fend M, Bovet S, Hafner V. The artificial mouse-A robot with whiskers and vision. 35th International Symposium on Robotics, Paris, France, 2004.
Knutsen P, Biess A, Ahissar E. Vibrissal kinematics in 3D: Tight coupling of azimuth, elevation, and torsion across different whisking modes. Neuron, 2008, 59, 35–42.
Voges D, Carl K, Klauer G, Uhlig R, Schilling C, Behn C, Witte H. Structural characterization of the whisker system of the rat. IEEE Sensors Journal, 2012, 12, 332–339.
Zuo Y, Perkon I, Diamond M. Whisking and whisker kinematics during a texture classification task. Philosophical Transactions of the Royal Society B, 2011, 366, 3058–3069.
Gopal V, Hartmann M. Using hardware models to quantify sensory data acquisition across the rat vibrissal array. Bioinspiration & Biomimetics, 2007, 2, S135–S145.
Stüttgen M, Kullmann S, Schwarz C. Responses of rat trigeminal ganglion neurons to longitudinal whisker stimulation. Journal of Neurophysiology, 2008, 100, 1879–1884.
Svetlitsky V. Dynamics of Rods, Springer-Verlag, Berlin Heidelberg, Germany, 2005.
Quist B, Faruqi R, Hartmann M. Variation in young’s modulus along the length of a rat vibrissa. Journal of Biomechanics, 2011, 44, 2775–2781.
Kantorovich L, Krylov V. Approximate Methods of Higher Analysis, Groningen, Netherlands, 1958.
Bogolyubov N, Mitropoliskii Y. Asymptotic Methods in the Theory of Nonlinear Oscillations. Gordon and Breach Science Publishers, New York, USA, 1961.
Malkin I. Theory of Stability of Motion, United States Atomic Energy Commission, Washington, D.C., USA, 1959.
Brecht M, Preilowski B, Merzenich M. Functional architecture of the mystacial vibrissae. Behavioural Brain Research, 1997, 84, 81–97.
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Volkova, T., Zeidis, I., Witte, H. et al. Analysis of the vibrissa parametric resonance causing a signal amplification during whisking behaviour. J Bionic Eng 13, 312–323 (2016). https://doi.org/10.1016/S1672-6529(16)60304-9
Published:
Issue Date:
DOI: https://doi.org/10.1016/S1672-6529(16)60304-9