Variations in vibrissal geometry across the rat mystacial pad: base diameter, medulla, and taper

Abstract

Many rodents tactually sense the world through active motions of their vibrissae (whiskers), which are regularly arranged in rows and columns (arcs) on the face. The present study quantifies several geometric parameters of rat whiskers that determine the tactile information acquired. Findings include the following. 1) A meta-analysis of seven studies shows that whisker base diameter varies with arc length with a surprisingly strong dependence on the whisker's row position within the array. 2) The length of the whisker medulla varies linearly with whisker length, and the medulla's base diameter varies linearly with whisker base diameter. 3) Two parameters are required to characterize whisker "taper": radius ratio (base radius divided by tip radius) and radius slope (the difference between base and tip radius, divided by arc length). A meta-analysis of five studies shows that radius ratio exhibits large variability due to variations in tip radius, while radius slope varies systematically across the array. 4) Within the resolution of the present study, radius slope does not differ between the proximal and distal segments of the whisker, where "proximal" is defined by the presence of the medulla. 5) Radius slope of the medulla is offset by a constant value from radius slope of the proximal portion of the whisker. We conclude with equations for all geometric parameters as functions of row and column position.NEW & NOTEWORTHY Rats tactually explore their world by brushing and tapping their whiskers against objects. Each whisker's geometry will have a large influence on its mechanics and thus on the tactile signals the rat obtains. We performed a meta-analysis of seven studies to generate equations that describe systematic variations in whisker geometry across the rat's face. We also quantified the geometry of the whisker medulla. A database provides access to geometric parameters of over 500 rat whiskers.

Keywords: active sensing; behavior; touch; trigeminal; whisker.

Fig. 1.

Geometric parameters of the whisker. A: each whisker is identified by its row and column position. In this photo, black and red dots have been drawn on the basepoint locations of the whiskers for visual clarity. From dorsal to ventral, the five rows are identified by the letters A–E, while the arcs (columns) are given the numbers 1–7 from caudal to rostral. The four whiskers of the caudal-most arc (colored red) are called the “Greek arc” or “Greek column” and are denoted from dorsal to ventral by the letters α, β, γ, and δ. B: schematic (not to scale) of the structural elements of the whisker. The whisker is modeled as a straight, tapered, conical frustum with base diameter (D_Base) and tip diameter (D_Tip). The medulla is represented as a hollow cone that occupies the proximal region of the whisker. The diameter of the medulla at its base is denoted by D_Med, and the diameter of the whisker at the point of medulla termination is labeled as D_MedT. The total whisker arc length (S_Total) is divided into a proximal portion occupied by the medulla (S_Prox) and a distal portion that does not include the medulla (S_Dist). The geometry of the cuticle was not quantified separately from the cortex in the present work. C: scanned image of the E2 whisker is shown along with three representative images to illustrate typical whisker geometry near the base, middle, and tip. The three images were not obtained from the E2 whisker; they were chosen to best illustrate the features described. The image near the base is from a C1 whisker (×10 magnification; left). The image at the location of medulla termination is from an E5 whisker (×20 magnification; middle). The image near the tip is from an E3 whisker (×20 magnification; right).

Fig. 2.

Diameter of the whisker base (D_Base) as a function of arc length (S_Total) for seven studies (519 whiskers total). The relationship between D_Base and S_Total obtained in the present study (418 whiskers) is not significantly different from the relationship for 101 whiskers obtained from six previous studies. Notice the large scatter about the trend line and the presence of four to five distinct diagonal “bands” within the data, sloping upwards from left to right.

Fig. 3.

Relationship between base diameter (D_Base) and whisker arc length (S_Total) as a function of column and row position. A: when color coded by column position within the array, clear diagonal bands characterize the relationship between D_Base and S_Total. Best linear fits for each of the columns are indicated in Table 2. Column 0 indicates the Greek arc. B–F: clear groupings also emerge when the relationship between D_Base and S_Total is color coded by row position within the array. Although the slope is similar for all rows, the intercept varies considerably, as can be seen in the upwards vertical translation of the line of best fit from Row A to Row E, respectively (see Table 2). G: Eq. 2 predicts D_Base with a high degree of accuracy as a function of S_Total and row and column position.

Fig. 4.

Length of the medulla (S_Prox) and base diameter of the medulla (D_Med) as a function of whisker arc length (S_Total) and base diameter (D_Base), respectively. A–D: data from the 70 whiskers of dataset 2. A: the medulla arc length is linearly related to the total arc length. The linear fit excludes 3 whiskers with length less than 10 mm. B: the fraction of the total arc length occupied by the medulla increases for longer whiskers. C: the diameter of the medulla at the whisker base is linearly related to the base diameter. Dashed line is where the medulla diameter equals the base diameter. D: the medulla diameter occupies 11–46% of the base diameter. E: schematics provide visual intuition for the size and shape of the medulla compared with the shape of the whole whisker. Relative to shorter whiskers, longer vibrissae have a larger fraction of their length occupied by the medulla, but the ratio of medulla base diameter to whisker base diameter increases only slightly for larger whiskers.

Fig. 5.

Quantification of radius ratio (Ratio_R) and radius slope (Slope_R) as functions of whisker arc length. B–G use data from all 122 whiskers across the 5 studies of the meta-analysis, with error bars computed via propagation of error. A: two parameters are required to define the geometry of a whisker. The top schematic illustrates that two whiskers with the same Slope_R can have very different Ratio_R. The bottom schematic illustrates that two whiskers with different Slope_R can have the same Ratio_R. B: the Ratio_R (R_Base/R_Tip) is extremely variable and does not exhibit a strong relationship with arc length (S_Total). Ratio_R is extremely sensitive to changes in the radius of the whisker tip, which can vary considerably due to wear, damage, and barbering. Error bounds vary greatly. C: Slope_R [(R_Base − R_Tip)/S_Total] is larger for shorter whiskers than for longer whiskers. Error bounds are much smaller than those calculated for Ratio_R. D: Slope_R increases with column position from caudal to rostral. E: within each column, Slope_R tends to increase slightly from dorsal (row A) to ventral (row E). F: schematic of Slope_R as a function of both row and column position across the array shows a strong trend by column and weak trend by row. G: the best prediction for Slope_R (Eq. 7) is linear with row and quadratic with column. The diagonal line represents the relationship where actual Slope_R = predicted Slope_R.

Fig. 6.

Both subplots use reduced dataset 2, which consisted of 52 whiskers. A: within the resolution of the present study, radius slope is not significantly different between proximal and distal whisker segments. Out of 52 whiskers, 36.5% had a proximal radius slope greater than that in the distal region; the remaining 63.5% had a distal radius slope greater than the proximal slope. B: the medulla radius slope is smaller by a constant offset than the proximal radius slope of the whisker. The offset is 0.0012.