Figure 1.
(A) Representative point cloud obtained from the 3D scanner. (B) Standard position and orientation for the head. The rat's snout is placed at the origin, and the rostrocaudal midline is collinear with the y-axis. Base points of whiskers in each row are aligned in planes (colored by row) that lie parallel to the xy-plane on average.
Table 1.
Vibrissal array parameters.
Figure 2.
Ellipsoidal fits to the mystacial pad.
(A) An example from one rat of the best-fit ellipsoid to whisker base-points on the right side of the mystacial pad. Whisker base-points are shown in blue and the best-fit ellipsoid in cyan. The rat head is placed in the standard position and orientation, and the view for this figure was chosen so as to best illustrate the mystacial pad. (B–D) Aerial view of the mystacial pad ellipsoid fits for each of the three rats scanned in 3D. Note the close fits to the contours of the rat's cheek (gray curve). (E) Model ellipsoid obtained from ellipsoids averaged across all rats. All base-points from all rats scanned in 3D are shown. For all plots B–E, left array base-points and best-fit ellipsoids are in blue; right array base-points and best-fit ellipsoids are in red; and grid lines represent 5 mm increments on all axes.
Table 2.
Mystacial pad ellipsoid parameter values.
Figure 3.
Base-point locations of whiskers vary with row and column.
(A) Schematic illustrating the conversion of the (x,y,z) base-point location to mystacial pad ellipsoid coordinates (rBP, φBP, and θBP). Each base-point was constrained to lie on the ellipsoid surface (blue circle). The axis-aligned ellipsoid radii (ra, rb, rc) are shown in red. (B) The base-point θBP was strongly correlated with whisker column. (C) The base-point φBP was strongly correlated with whisker row. For both B and C, different marker colors (black, gray, and light gray) indicate rat of origin and indicate that no significant differences were found across rats.
Figure 4.
(A) Comparison between the 3D scan (blue) and the 2D scan (black) for one whisker. The xy-plane is shaded and transparent to show 3D points above and below the plane. (B) Planar residuals for 84 whiskers. Individual whiskers are plotted in transparent gray, so that overlapping whisker points appear darker. Red lines indicate the planar threshold criteria of ±150 microns. Note that the whisker lengths are normalized by the 2D whisker lengths. Thus not all 3D whiskers extend to one (100%) because the 3D laser scanner did not always capture the entire length of the whisker (see Materials and Methods). Inset: Zoomed-in region from 0% to 50% of the normalized whisker length. (C) Histogram of the number of whiskers at each planar percentage. Bin size is 5%.
Figure 5.
Whisker length dependence on position in the array.
(A) Each panel shows whisker length as a function of column position within a single whisker row. Error bars are standard deviations of the mean in all panels (G = Greek). The solid gray line in the bottom right panel shows the best linear fit to the averaged data (correlation coefficient r = −0.74). (B) Thick black lines show the whisker length trend within a row (across columns) and the thin black lines show the trends within a column. Grey panels are visual aids only.
Figure 6.
Quadratic approximation to the whisker 2D shape.
(A) Examples of quadratic fits to the right C row whiskers from one rat. The scanned whisker data is shown in black. Each whisker has been offset vertically to reflect the whisker's column. The best parabolic fit to each whisker is shown as a dotted gray line. (B) Quadratic coefficient a versus whisker column in the array for all 2D whisker data. Marker color indicates rat of origin and indicates that no significant differences were found across rats.
Figure 7.
Whisker angle convention on the rat head.
(A) Schematic of projection angles that describe whisker orientation in 3D. Whisker is indicated by the thick black line. Whisker projections into the three planes of the head coordinate frame are shown in gray, along with the corresponding projection angle. (B) Definition and range of the angle θ. θ increases from 0° to 180° on both right and left sides as the whisker protracts (identical definition for θ as [13], [14]). (C) Definition and range of the angle ψ. (D) Definition and range of the angle φ. (E, F) Definition and range of the angle ζ (identical definition for ζ as [10]). Whiskers on the right side of the face follow the same convention as the left for ζ; therefore, a ζ of +90° has the whisker tip pointing forward for both the left and right side of the face.
Figure 8.
Dependence of θ, φ, ψ and ζ on whisker identity (row and column location in the array).
(A–D) The angles θ, φ, ψ and ζ for each whisker, averaged across both right and left sides of all three rats. Color scales are different for each subplot. (E–H) The angles θ, φ, ψ and ζ obtained from all rats, plotted against the dominant factor(s) (either row or column or both). Different marker colors (black, gray, and light gray) indicate rat of origin, and indicate that no significant differences were found across rats.
Table 3.
Equations relating each whisker parameter to whisker identity.
Figure 9.
Comparison between photographs of the vibrissal array, 3D scans of the vibrissal array, and the model of the vibrissal array.
Care was taken to ensure similar head orientations for all images within a row. (Left column) Photographs of an anesthetized rat. (Middle column) Scanned 3D images of another rat. (Right column) Model of the vibrissal array generated from the parameter values in Table 2, equations in Table 3, and equation 10.
Figure 10.
(A) Standard error (mm) at each whisker tip. (B) Standard error (mm) at each whisker base. (C–E) Horizontal, sagittal, and coronal views of the final model with error surfaces surrounding each whisker. The error cylinder radius at each arc length is equal to the 95% confidence interval based on the propagated standard deviation and assuming a normal distribution of errors. Colors in C–E are visual aids only; they do not represent error.
Figure 11.
Array morphology constrains the information available to the nervous system about object curvature.
(A) Schematic showing the different cylinder radii tested. Negative radii and curvature were defined such that the convex face of the object faced the rat. Note that the cylinder approaches a plane as the radius goes to infinity and curvature goes to zero. (B) Schematic illustrating the calculation of the angle of initial contact. Red dashed line indicates the angle at the base of the whisker at which the whisker makes its first contact with the object. This figure also illustrates a situation in which a more rostral whisker will contact at a more protracted angle than a more caudal whisker. (C) Angles of initial contact are shown for each whisker of the C row. Each trace represents results for a cylinder with a different radius, color coded as shown in the legend. Gr indicates the gamma whisker. (D) Average angle of initial contact versus cylinder curvature (1/radius). The most curved cylinders are represented at the graph extremes. (E) Difference across columns in the average angles of initial contact versus cylinder curvature. In both D and E, error bars indicate the standard error of the mean (averaged across all whiskers in the model).
Figure 12.
Effect of array morphology on information available to the nervous system.
Average angles of initial contact with cylinders of varying curvatures were calculated for each array morphology. If all whiskers are oriented concave forward (ζ = +90, green), the relationship between the average angle of contact and the object curvature is mostly a shifted version of the relationship obtained for the actual morphology (blue). If all whiskers are oriented concave backwards (ζ = −90, red), the functional relationship changes dramatically. No significant relationship exists between the angle of initial contact and object curvature. Gray lines show the value of the mean angle of contact for the largest negative curvature for each morphology, and are intended to guide the eye.
Figure 13.
Experimental dataset and standard orientations.
(A) An example whisker (right B1), extracted in 3D from the scanned rat head shown in Figure 1A of Results. (B) Shape of the whisker extracted from the 2D scan. The inset shows a magnified portion of the whisker with both x and y axes in units of mm. The light gray line is the centerline.
Table 4.
Functions for the idealized whisker array.
Figure 14.
Simulation of whisker-object collisions.
Circles are centered on the whisker base-point and constrain the movement of points on each whisker within a given rotation plane. Four locations along the whisker are indicated as black dots. The object (a cylinder) is indicated as a heavy black line. Only one whisker is shown and its length has been exaggerated for visual clarity.