A truncated conical beam model for analysis of the vibration of rat whiskers (original) (raw)
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The mathematical whisker: A review of numerical models of the rat׳s vibrissa biomechanics
The vibrissal system of the rat refers to specialized hairs the animal uses for tactile sensory perception. Rats actively move their whiskers in a characteristic way called “whisking”. Interaction with the environment produces elastic deformation of the whiskers, generating mechanical signals in the whisker–follicle complex. Advances in our understanding of the vibrissal complex biomechanics is of interest not only for the biological research field, but also for biomimetic approaches. The recent development of whisker numerical models has contributed to comprehending its sophisticated movements and its interactions with the follicle. The great diversity of behavioral patterns and complexities of the whisker–follicle ensemble encouraged the creation of many different biomechanical models. This review analyzes most of the whisker biomechanical models that have been developed so far. This review was written so as to render it accessible to readers coming from different research areas.
The Journal of neuroscience : the official journal of the Society for Neuroscience, 2003
We investigated the natural resonance properties and damping characteristics of rat macrovibrissae (whiskers). Isolated whiskers rigidly fixed at the base showed first-mode resonance peaks between 27 and 260 Hz, principally depending on whisker length. These experimentally measured resonant frequencies were matched using a theoretical model of the whisker as a conical cantilever beam, with Young's modulus as the only free parameter. The best estimate for Young's modulus was approximately 3-4 GPa. Results of both vibration and impulse experiments showed that the whiskers are strongly damped, with damping ratios between 0.11 and 0.17. In the behaving animal, whiskers that deflected past an object were observed to resonate but were damped significantly more than isolated whiskers. The time course of damping varied depending on the individual whisker and the phase of the whisking cycle, which suggests that the rat may modulate biomechanical parameters that affect damping. No res...
Topography of whisking II: Interaction of whisker and pad
Somatosensory & Motor Research, 2005
The peripheral effector system mediating rodent whisking produces protraction/retraction movements of the whiskers and translation movements of the collagenous mystacial pad. To examine the interaction of these movements during whisking in air we used high-resolution, optoelectronic methods for two-dimensional monitoring of whisker and pad movements in head-fixed rats. Under these testing conditions (1) whisker movements on the same side of the face are synchronous and of similar amplitude; (2) pad movements exhibit the characteristic 'exploratory' rhythm (6-12 Hz) of whisking but their movements often have a low frequency (1-2 Hz) component; (3) Pad movements occur in both antero-posterior and dorso-ventral planes but there are considerable variations in the amplitude and topography of movement parameters in the two planes. We conclude that (a) both whisker and pad receive input from a common central rhythm generator; (b) differences in whisker and pad amplitude and topography probably reflect differences in the biomechanical properties of the structures receiving that input; (c) pad movements make a significant contribution to the kinematics of whisking behavior and (d) the two-dimensional nature of pad translation movements significantly increases the rat's flexible control of its mobile sensor.
Journal of Bionic Engineering, 2016
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.
The Matrix: A new tool for probing the whisker-to-barrel system with natural stimuli
Journal of Neuroscience Methods, 2010
The whisker to barrel system in rodents has become one of the major models for the study of sensory processing. Several tens of whiskers (or vibrissae) are distributed in a regular manner on both sides of the snout. Many tactile discrimination tasks using this system need multiple contacts with more than one whisker to be solved. With the aim of mimicking those multi-whisker stimuli during electrophysiological recordings, we developed a novel mechanical stimulator composed of 24 independent multi-directional piezoelectric benders adapted to the five rows and the five caudal arcs of the rat whisker pad. The most widely used technology for producing mechanical deflections of the whiskers is based on piezoelectric benders that display a non-linear behavior when driven with high frequency input commands and, if not compensated, show high unwanted ringing at particular resonance frequencies. If not corrected, this nonlinear behavior precludes the application of high frequency deflections and the study of cortical responses to behaviorally relevant stimuli. To cope with the ringing problem, a mechanical and a software based solutions have been developed. With these corrections, the upper bound of the linear range of the bender is increased to 1 kHz. This new device allows the controlled delivery of large scale natural patterns of whisker deflections characterized by rapid high frequency vibrations of multiple whiskers.
The Mechanical Variables Underlying Object Localization along the Axis of the Whisker
Rodents move their whiskers to locate objects in space. Here we used psychophysical methods to show that head-fixed mice can localize objects along the axis of a single whisker, the radial dimension, with one-millimeter precision. High-speed videography allowed us to estimate the forces and bending moments at the base of the whisker, which underlie radial distance measurement. Mice judged radial object location based on multiple touches. Both the number of touches (1-17) and the forces exerted by the pole on the whisker (up to 573 N; typical peak amplitude, 100 N) varied greatly across trials. We manipulated the bending moment and lateral force pressing the whisker against the sides of the follicle and the axial force pushing the whisker into the follicle by varying the compliance of the object during behavior. The behavioral responses suggest that mice use multiple variables (bending moment, axial force, lateral force) to extract radial object localization. Characterization of whisker mechanics revealed that whisker bending stiffness decreases gradually with distance from the face over five orders of magnitude. As a result, the relative amplitudes of different stress variables change dramatically with radial object distance. Our data suggest that mice use distance-dependent whisker mechanics to estimate radial object location using an algorithm that does not rely on precise control of whisking, is robust to variability in whisker forces, and is independent of object compliance and object movement. More generally, our data imply that mice can measure the amplitudes of forces in the sensory follicles for tactile sensation.
Muscular Basis of Whisker Torsion in Mice and Rats
Anatomical Record-advances in Integrative Anatomy and Evolutionary Biology, 2017
Whisking mammals move their whiskers in the rostrocaudal and dorsoventral directions with simultaneous rolling about their long axes (torsion). Whereas muscular control of the first two types of whisker movement was already established, the anatomic muscular substrate of the whisker torsion remains unclear. Specifically, it was not clear whether torsion is induced by asymmetrical operation of known muscles or by other largely unknown muscles. Here, we report that mystacial pads of newborn and adult rats and mice contain oblique intrinsic muscles (OMs) that connect diagonally adjacent vibrissa follicles. Each of the OMs is supplied by a cluster of motor end plates. In rows A and B, OMs connect the ventral part of the rostral follicle with the dorsal part of the caudal follicle. In rows C-E, in contrast, OMs connect the dorsal part of the rostral follicle to the ventral part of the caudal follicle. This inverse architecture is consistent with previous behavioral observations [Knutsen et al.: Neuron 59 (2008) 35-42]. In newborn mice, torsion occurred in irregular single twitches. In adult anesthetized rats, microelectrode mediated electrical stimulation of an individual OM that is coupled with two adjacent whiskers was sufficient to induce a unidirectional torsion of both whiskers. Torsional movement was associated with protracting movement, indicating that in the vibrissal system, like in the ocular system, torsional movement is mechanically coupled to horizontal and vertical movements. This study shows that torsional whisker rotation is mediated by specific OMs whose morphology and attachment sites determine rotation direction and mechanical coupling, and motor innervation determines rotation dynamics.
A Mathematical Model for a Vibrating Human Head
International Journal of Artificial Life Research, 2010
In this paper, a mathematical model has been formulated to study the vibration of the human head. In the mathematical analysis of the model, the skull is considered as an anisotropic spherical shell and brain matter is represented as an inviscid compressible fluid. Also, in the model, the translational acceleration is considered as a general function of time. The authors use the method of Laplace transformation to achieve the analytical solution of the problem, while the analytical expressions have been used to compute the stress distribution in the system by resorting to numerical techniques.