Mechanical signals at the base of a rat vibrissa: the effect of intrinsic vibrissa curvature and implications for tactile exploration

Abstract

Rats actively tap and sweep their large mystacial vibrissae (whiskers) against objects to tactually explore their surroundings. When a vibrissa makes contact with an object, it bends, and this bending generates forces and bending moments at the vibrissa base. Researchers have only recently begun to quantify these mechanical variables. The present study quantifies the forces and bending moments at the vibrissa base with a quasi-static model of vibrissa deflection. The model was validated with experiments on real vibrissae. Initial simulations demonstrated that almost all vibrissa-object collisions during natural behavior will occur with the concave side of the vibrissa facing the object, and we therefore paid particular attention to the role of the vibrissa's intrinsic curvature in shaping the forces at the base. Both simulations and experiments showed that vibrissae with larger intrinsic curvatures will generate larger axial forces. Simulations also demonstrated that the range of forces and moments at the vibrissal base vary over approximately three orders of magnitude, depending on the location along the vibrissa at which object contact is made. Both simulations and experiments demonstrated that collisions in which the concave side of the vibrissa faces the object generate longer-duration contacts and larger net forces than collisions with the convex side. These results suggest that the orientation of the vibrissa's intrinsic curvature on the mystacial pad may increase forces during object contact and provide increased sensitivity to detailed surface features.

Fig. 1.

Key variables used to describe vibrissa shape and orientation. A: the intrinsic curvature of the vibrissa (A) is approximately quadratic. B: the orientation of the intrinsic curvature of the vibrissa on the rat's mystacial pad is defined by the angle ζ.

Fig. 2.

Key variables used to describe 3-dimensional (3D) vibrissa collisions. A: in a 3D collision, there are 3 relevant planes: the plane of the intrinsic curvature of the vibrissa, the plane of rotation, and the plane of the object surface. The plane of the vibrissa is defined by the angle ζ. The plane of rotation is defined as the plane normal to the axis about which the vibrissa rotates. This plane is independent of the angle ζ. Finally, the plane of the object surface is defined as the plane tangent to the object surface at the point of vibrissa contact. The relative angles between the 3 planes dictate how the vibrissa will interact with the object. For the purposes of this study, the plane of the object surface is always perpendicular to the plane of rotation. B: there exists a continuum of vibrissa collision types, categorized broadly as occurring against either the concave forward (CF) or the concave backward (CB) face of the vibrissa. A perfectly CF/CB collision occurs when the intrinsic curvature of the vibrissa remains in the plane of rotation. This study focuses specifically on the 2 extremes of the collision spectrum: perfectly CF and perfectly CB collisions. Note that in this particular figure the plane of rotation happens to be the horizontal plane, but in principle it can be any plane.

Fig. 3.

Key variables used to describe vibrissa mechanics. A: schematic of a vibrissa rotating against a point object. The arc length at which the vibrissa makes contact with the object, s, is represented as a fraction of the total arc length of the vibrissa. Rotations of the vibrissa against the object in the plane of rotation (in this example, the x-y plane) are indicated with theta push (θ_p). θ_p equals 0° at the angle at which the vibrissa first makes contact with the object. B: in the most general case, there will be 3 reaction forces and 3 reaction moments at the base of the vibrissa resulting from an applied force. If we assume that the intrinsic curvature of the vibrissa always lies in the plane of rotation, then this reduces to 2 reaction forces (axial force F_x and transverse force F_y) and 1 reaction moment (M_z) at the base. All variables are negative in the directions shown.

Fig. 4.

Experimental setup and images of vibrissa deflections. A: schematic of experimental setup. A vibrissa is mounted to a motor and rotated against a custom-built force sensor, positioned with a micromanipulator. CW, clockwise; CCW, counterclockwise. B: the vibrissa was rotated so that either its CF or its CB face collided with the object. 2D, 2-dimensional. C: the full shape of the vibrissa was tracked as it was rotated against a peg. Color changes from white to black as the vibrissa is rotated through an increasing angle against the peg. Images are separated by 5° of rotation.

Fig. 5.

A force applied to a vibrissa will generate different reaction forces F_x and F_y depending on the intrinsic curvature of the vibrissa. A: a vibrissa with a large intrinsic curvature (large value of A). B: a vibrissa with a small intrinsic curvature (small value of A).

Fig. 6.

Intrinsic curvature of the vibrissae varies across the array. A: the coefficient A, a measure of intrinsic curvature, decreases with vibrissal arc length. On average, shorter vibrissae have larger intrinsic curvature. B: fraction of vibrissae (of 354 total) with given intrinsic curvatures. Line at 5% of vibrissae corresponds to an A coefficient of 0.0065/mm. Data are from Towal et al. (2011).

Fig. 7.

Orientations of the vibrissae on the rat's face define the directions that each vibrissa would have to rotate to experience a perfectly CF collision. The base points of each vibrissae are represented by the large circles. The arrows in each of the circles are unit-normals that lie in the plane of intrinsic vibrissa curvature and are perpendicular to the vibrissa at its base as it emerges from the mystacial pad. Arrows indicate the CF direction of the vibrissa's intrinsic curvature. Orientations are shown for the vibrissal array at rest (gray) and after a simulated protraction of 40° (black). For each vibrissa, a short bar near bottom indicates the orientation of a surface normal to the plane of vibrissa curvature. The radial distance from the vibrissa to the short bar is arbitrary and selected to be approximately equidistant from the center of the array. Surface orientations are again shown for the vibrissal array at rest (gray) and after a simulated protraction of 40° (black). Inset: approximate orientation of the vibrissal array on the rat's mystacial pad.

Fig. 8.

Simulations of CF (black) and CB (gray) rotations of the vibrissa against a point object. Each of the small subplots illustrates the shape of the vibrissa at specific values of θ_p (5° increments). The shape of the deflected vibrissa is in the vibrissa coordinate frame; therefore, force components at the vibrissa base are aligned with the coordinate axes of the plot. Dotted lines indicate the shape and orientation that the vibrissa would have had, had it rotated through θ_p but not collided with an object. In each of the small subplots, the value of θ_p is assigned a color. Corresponding colored circles in the central plot indicate the force components at that value of θ_p.

Fig. 9.

Bending moment and forces as a vibrissa is simulated to rotate against a point object placed at different radial distances from the vibrissa base. Angle of rotation into the object is the pushing angle θ_p. Radial object distance s is indicated as % of vibrissa arc length at top. In all subplots, black traces represent results for a vibrissa with intrinsic curvature undergoing a CF collision, dark gray dashed traces represent results for a straight vibrissa (ST), and light gray traces represent results for a vibrissa with intrinsic curvature undergoing a CB collision. Force and moment traces in all plots stop at the angle at which the simulation became numerically unstable. Top: bending moment (M_z) at the vibrissa base. For all radial distances and all vibrissa curvatures, the magnitude of M_z increases monotonically with rotation angle until contact with the object is lost. Middle: transverse force F_y at the vibrissa base. Bottom: axial force F_x at the vibrissa base.

Fig. 10.

Range of forces and moments that will be present at the base of the vibrissa during object contact: change in the magnitudes of moment and forces at the vibrissa as a function of radial distance and θ_p. For all plots, the thin black line corresponds to a θ_p of 1°; the thick black line corresponds to a θ_p of 10°. The magnitude of moment M_z (A), transverse force F_y (B), and axial force F_x (C) all vary over ∼3 orders of magnitude along the vibrissa arc length.

Fig. 11.

Combined effect of curvature and θ_p on moments and forces at the vibrissa base. For all subplots, the pushing angle (θ_p) is indicated with color and ranges from 1° (light gray) to 10° (black) in 1° increments. Positive curvatures correspond to CF collisions; negative curvatures correspond to CB collisions. Radial object distance s is indicated as % of vibrissa arc length at top. The curves from Fig. 9 can be thought of as “slices” through these traces at for values of A = 0 and A = ±0.0233. Top: M_z. Middle: F_y. Bottom: F_x.

Fig. 12.

Bending moment and forces measured at the base of a C3 vibrissa as it was rotated against a 2D force sensor placed at different radial distances from the vibrissa base. Angle of rotation against the sensor is the push angle, θ_p. Radial object distance s is indicated as % of vibrissa arc length at top. In all subplots, black traces represent results for a CF collision and light gray traces represent results for a CB collision. Force and moment in all plots stop when the vibrissa slipped off the sensor. Each trace represents the averaged and then filtered result of 25 individual trials. Standard deviation for all trials was ∼10 μN for forces and 0.3 mN-mm for moment. Top: bending moment M_z at the vibrissa base. Middle: F_y at the vibrissa base. Bottom: F_x at the vibrissa base. Arrowhead in the bottom row for s = 75% indicates a typical stick-slip event.

Fig. 13.

Match between experiment and model. The vibrissa was rotated against a point object located either 25% or 90% out along the vibrissa length. The shape of the vibrissa and the forces generated at its base were measured experimentally, and the shape and forces were predicted from a simulation of the same rotation against the object. Top: the simulated shape of the vibrissa during the rotation (black) is plotted on top of the vibrissa shape measured experimentally (gray). The gray trace with no model overlay represents the undeflected shape of the vibrissa. Each trace is separated by a 5° rotation of the vibrissa. Arrows indicate the direction of the deflection. Scale bars, 5 mm. Bottom: differences between predicted forces and measured forces. Black, axial force; gray: transverse force.

Fig. 14.

The maximum angle through which the vibrissa can rotate against an object without flicking past depends on the curvature orientation. CF collisions permit the vibrissa to maintain contact with the object through a larger protraction angle than CB collisions. Marker color denotes radial distance and ranges from s = 25% (black) to s = 95% (light gray).

Fig. 15.

Influence of curvature orientation on the trajectory of forces that will be generated at the vibrissa base. CF collisions generate larger net force vectors. For all subplots, colored circles indicate the angle through which the vibrissa has rotated against the sensor (inset, A). CB collision force trajectory plotted in gray; CF collision force trajectory plotted in black. A: force trajectory for the sensor positioned at 25% of the vibrissal arc length. B: force trajectory for the sensor positioned at 50% arc length. C: force trajectory for the sensor positioned at 75% arc length.

Fig. 16.

Flowchart for applying the results of this study to behavioral data. ^[1]Results will apply up to θ_p of 40°, depending on the degree to which the plane of intrinsic vibrissa curvature aligns with the plane of rotation.

Fig. 17.

Implications of the orientation of intrinsic vibrissa curvature for the behaving rat. All schematics illustrate the same vibrissa at different points in time during protraction against an object. Arrow indicates direction of protraction. A: CB collision of a vibrissa with a point object. As the vibrissa protracts, the vibrissa becomes more convex to slip past the object. B: CF collision of a vibrissa with a point object. As the vibrissa protracts, it first straightens. Next, the vibrissa tip bends backwards to permit the vibrissa to slip past the object. C: CF collision with a wall. As the vibrissa protracts, the tip is first to strike the surface. This may provide an initial “spike” in axial force before general deformation of the vibrissa.