Whisker Contact Detection of Rodents Based on Slow and Fast Mechanical Inputs

Abstract

Rodents use their whiskers to locate nearby objects with an extreme precision. To perform such tasks, they need to detect whisker/object contacts with a high temporal accuracy. This contact detection is conveyed by classes of mechanoreceptors whose neural activity is sensitive to either slow or fast time varying mechanical stresses acting at the base of the whiskers. We developed a biomimetic approach to separate and characterize slow quasi-static and fast vibrational stress signals acting on a whisker base in realistic exploratory phases, using experiments on both real and artificial whiskers. Both slow and fast mechanical inputs are successfully captured using a mechanical model of the whisker. We present and discuss consequences of the whisking process in purely mechanical terms and hypothesize that free whisking in air sets a mechanical threshold for contact detection. The time resolution and robustness of the contact detection strategies based on either slow or fast stress signals are determined. Contact detection based on the vibrational signal is faster and more robust to exploratory conditions than the slow quasi-static component, although both slow/fast components allow localizing the object.

Keywords: rodents tactile perception; whisker contact detection; whiskers fast vibrations; whiskers slow deformations; whisking.

Figure 1

(A) Sketch of the experimental setup. Whiskers (orange color), either real or artificial, are attached at their base to the cylindrical shaft of a rheometer head which measures the component of the base torque normal to the (x, y) rotation plane. They can be maintained at a fixed base angle, and hit by a Plexiglas wedge mounted on a rotary motor, or alternatively rotated at a constant angular velocity while the wedge remains fixed (as shown on this sketch). The rotary motor is itself fixed to a linear rail, so that the contact point location can be moved along the whisker. In addition, a high speed camera records the whisker deflections in the rotation plane via a mirror. (B) Picture showing both artificial (top) and real (bottom) whiskers glued at their base to drilled studs. The white bar is 1 cm long. (C) Three types of experiments. From top to bottom: Fixed whisker experiment—the base angle is fixed while the wedge indents at constant velocity V the whisker whose initial position is shown with the dashed line cone; Rotating whisker experiment— the base angle of the whisker (initial position shown with the dashed line cone) is rotated at a constant angular velocity γ against a fixed wedge; Whisking experiment—the base angle oscillates sinusoidally between two extreme positions (red and green dashed line cones), while the wedge indents the whisker at constant V.

Figure 2

(A) Sketch of the whisker, modeled as a truncated cone of base radius b and conicity α. (B) Modeling the whiskers displacements in a shock experiment, for the case of a rotating whisker and a fixed indenter. The base angle φ is taken from the undeformed vertical position of the whisker (shown with the dashed lines).

Figure 3

(A) Base torque M(t) measured by the rheometer (blue squares) and base curvature C(t) obtained by image analysis (orange circles) in a fixed artificial whisker experiment (V = 2.743 ± 0.002 cm s⁻¹, ϵ = 0.49 ± 0.03, f_cam = 3000 fps). The proportionality factor between M(t) and C(t) is found to be K = (1.8 ± 0.1)10⁻⁴ Nm². (B) Typical measured base torque signal vs. the contact point displacement U(ϵ, t), in a fixed artificial whisker experiment (ϵ = 0.45 ± 0.03). Shown with the red crosses (resp. blue disks) is the measured signal for a large shock velocity V = 86.0 ± 0.1 cm s⁻¹ (resp. a small shock velocity V = 1.17 ± 0.01 cm s⁻¹). The difference between both signals yields the dynamic component (green plus signs). For both experiments, f_cam = 10, 000 fps.

Figure 4

Rate of change of the quasi-static base torque vs. d for (A) the fixed artificial whisker (blue circles), (B) the rotating artificial whisker (blue squares) and (C) the fixed real whisker (green crosses). In (A) [resp. (B)], the inset shows the base torque measured with the rheometer vs. time t (resp. φ), for increasing d—top to bottom curves. Similarly, in (C) the inset shows the base torque obtained by image analysis vs. t for increasing d. (D) Dimensionless curve $4/(3E\pi {(\alpha b)}^2)d{M}_{qs}/d(Vt)$ vs. d/L for the fixed artificial whisker (blue circles) and the fixed real whisker (green crosses). In (A–C), the red solid lines are fits with predicted rates of change (see Table 2). In (A), E = 1.19 GPa, V = 2.7 cm s⁻¹ and the fit yields [α = 7.8 ± 1.7 mrad, b = 700 ± 9 μm]. In (B), E = 1.19 GPa and the fit yields [α = 11.3 ± 0.3mrad, b = 712 ± 5μm]. In (C), α = 1.8 mrad, b = 88 μm, V = 2.7 cm.s⁻¹ and the fit yields E = 3.6 ± 0.4 GPa. In (D), the red solid line represents the function f(x) = 1/x²−1/x. Error bars represent the standard deviation.

Figure 5

Wave front propagation after a shock in fixed whisker experiments. (A) [resp. (B)] Total artificial (resp. real) whisker displacements vs. s at increasing times t—blue to red colors (V = 99 ± 3 cms⁻¹). For the artificial whisker in (A) ϵ = 0.21 ± 0.01, f_cam = 25, 000 fps; for the real whisker in (B) ϵ = 0.19 ± 0.01, f_cam = 6000 fps. Whiskers profiles are smoothed on a 41-pixel (~ 3 mm) wide window. (C,D) Close up of (A,B) to visualize the deflection wave. On both (C,D), the large solid arrow indicates the direction of propagation of the wave and the black disks localize the wave front position. (E) Wave front distance to base vs. t for the artificial whisker (blue solid squares) and the real one (green solid triangles). Fitting linearly the data points yields a wave propagation velocity V_w = 33 ± 2 m s⁻¹ and V_w = 13 ± 1 m s⁻¹ for the artificial and real whiskers, respectively. Error bars are smaller than the size of the symbols used.

Figure 6

(A) Torque at the base of the artificial whisker vs. time t, in a fixed whisker experiment, immediately after the shock (taken at t = 0) for five repeated shocks in the same experimental conditions (colored symbols), namely ϵ = 0.44 ± 0.02 and V = 68.9 ± 0.2 cm s⁻¹. The solid black line is the mean torque averaged over all five experiments. (B) Time derivative of the base torque shown in (A) vs. t. The shock triggers at the base a large oscillation with a maximal variation ΔṀ that is reached after a time delay τ. (C) Amplitude ΔṀ vs. shock velocity V. The red solid line is a linear fit of the data of the form pV with p = 3.94 ± 0.07 N. (D) Delay τ vs. V. The red solid line corresponds to the mean value of τ averaged over all τ(V), equal to (4.5 ± 0.4)10⁻⁴ s. In both (C,D), ϵ = 0.44 ± 0.02 and f_cam = 25, 000 fps. Error bars represent the standard deviation.

Figure 7

(A) Dependence of ΔṀ = Ṁ₊−Ṁ₋ (blue disks) with the contact point location ϵ in a fixed artificial whisker experiment, along with that of Ṁ₊ (green upward triangles) and Ṁ₋ (red downward triangles). (B) τ vs. ϵ (blue disks). On both (A,B), V = 99 ± 3 cm s⁻¹, f_cam = 25, 000 fps, and the dashed lines correspond to the predictions of the model. Error bars represent the standard deviation.

Figure 8

(A) Sketch of the whisking experiment. Horizontal distances H_i separating the whisker base and trajectory of the object are fixed and assume three values H₁ = 2.07 ± 0.01 cm (orange color), H₂ = 2.60 ± 0.01 cm (red color), and H₃ = 3.17 ± 0.01 cm (magenta color). The angular amplitude of the whisking is φ₀, and the position of the object is defined by both the angle φ_c at contact and the distance H. (B) Base torque M as a function of time t for the three H values as sketched in (A). Inset: whisker base angle as a function of t. For sake of clarity, curves have been arbitrarily shifted vertically. Disk symbols mark the instants of contact with the object and corresponding φ = φ_c values. (C) Power Spectral Density (PSD) plot of the base torque signals averaged on all contacts, and performed over a duration of 14.7 ms from the time of contact. The blue solid line represents the base torque PSD averaged over the free whisking phases. The two vertical black dashed lines are drawn at the low and high cutoff frequencies, respectively 80 and 1000 Hz. The arrows indicate the vibration frequencies f₀. (D) Spectrogram (in logarithmic scale) of M for the experiment performed at H₂. Vertical black solid lines mark the instants of contact.

Figure 9

Acuity and delay of contact detection. (A) Normalized base torque M/σ_M for the whisking experiment (red solid line) with 4 successive contacts labeled ①, ②, ③ and ④. The normalized filtered base torque $\tilde{M}/{\sigma }_{\tilde{M}}$ (blue curve) is obtained by applying a first order bandpass filter to the total base torque signal. The vertical lines mark the onset of contact. The horizontal dashed line represents M = 3σ_M. (B) Close up at contact ① in (A) (shaded area). (C) Same with contact ②. The time delay between the onset of contact and the time at which M > 3σ_M, (resp. $\tilde{M}>3{\sigma }_{\tilde{M}}$) is denoted τ_M (resp. ${\tau }_{\tilde{M}}$).

Figure 10

Colormaps of (A) τ_M(ϵ, φ_c/φ₀) and (B) ${\tau }_{\tilde{M}}(ϵ,{\phi }_c/{\phi }_0)$ obtained with numerics. The white zones correspond to undetected contacts. Detected contacts are shown with the color bar whose units are given in milliseconds. On both (A,B), data points of all three experiments performed at H₁, H₂, and H₃ have also been plotted for comparison, with disk symbols when the contact is detected and plus sign symbols when it is not. The colors of the edge of the disks and of the plus signs have been chosen to match those of Figures 8A–C and correspond to different H_i [H₁ (orange color), H₂ (red color), H₃ (magenta color)]. The inner color of the disks gives the value of the detection time, using the same color code as the one used to represent the numerical results.