In all sensory modalities, the data acquired by the nervous system is shaped by the biomechanics, material properties, and the morphology of the peripheral sensory organs. The rat vibrissal (whisker) system is one of the premier models in neuroscience to study the relationship between physical embodiment of the sensor array and the neural circuits underlying perception. To date, however, the three-dimensional morphology of the vibrissal array has not been characterized. Quantifying array morphology is important because it directly constrains the mechanosensory inputs that will be generated during behavior. These inputs in turn shape all subsequent neural processing in the vibrissal-trigeminal system, from the trigeminal ganglion to primary somatosensory (“barrel”) cortex. Here we develop a set of equations for the morphology of the vibrissal array that accurately describes the location of every point on every whisker to within ±5% of the whisker length. Given only a whisker' s identity (row and column location within the array), the equations establish the whisker' s two-dimensional (2D) shape as well as three-dimensional (3D) position and orientation. The equations were developed via parameterization of 2D and 3D scans of six rat vibrissal arrays, and the parameters were specifically chosen to be consistent with those commonly measured in behavioral studies. The final morphological model was used to simulate the contact patterns that would be generated as a rat uses its whiskers to tactually explore objects with varying curvatures. The simulations demonstrate that altering the morphology of the array changes the relationship between the sensory signals acquired and the curvature of the object. The morphology of the vibrissal array thus directly constrains the nature of the neural computations that can be associated with extraction of a particular object feature. These results illustrate the key role that the physical embodiment of the sensor array plays in the sensing process.
Animals use movements to acquire and refine incoming sensory data as they explore and navigate the environment. This means that – except under rare conditions most often found in the laboratory – sensing is an active process, constrained and shaped by the biomechanics of the muscles and by the material properties and morphology of the sensing organs. It is impossible to meaningfully characterize sensory input to the nervous system during active behavior without considering the physical embodiment of the sensor array. The rat vibrissal (whisker) system is one of the oldest models in neuroscience for studying sensorimotor integration and active sensing [1], [2]. Approximately 30 macrovibrissae are arranged in a regular array on each side of the rat' s face [3]. Rats move their whiskers at frequencies between 5–25 Hz to acquire tactile information about objects in the environment, including size, shape, orientation, and texture [4], [5], [6], [7], [8]. The morphology of the vibrissal array directly constrains the spatiotemporal patterns of mechanosensory inputs that will be generated as the rat actively explores an object. These patterns of whisker-object contact in turn shape all subsequent patterns of neural activation along the vibrissal-trigeminal pathway, from the brainstem to primary somatosensory (“barrel”) cortex. To date, however, the shape and structure of the rat vibrissal array has not been quantified, and there is thus no rigorous way to predict the input patterns that will occur during a given exploratory sequence. The present study was undertaken to quantify the morphology of the rat vibrissal array and demonstrate its influence on the whisker-object contact patterns associated with tactile exploration of an object. A set of equations is developed that describes every point on every whisker in the entire vibrissal array. Given only a whisker' s identity (that is, its row and column within the array), the equations establish the whisker' s two dimensional (2D) shape as well as three-dimensional (3D) position and orientation. The final result is a model that accurately describes the 3D location of every point along a whisker to within 5% of the point' s distance from the whisker base. Simulations demonstrate that alterations in array morphology dramatically alter the mechanosensory signals that the rat would obtain as it whisks against an object. Specifically, for a particular head orientation, the average angle at which the whiskers contact a cylindrical object is uniquely related to the radius of the cylinder. The nervous system could potentially learn this relationship to allow the rat to determine object radius within the time span of a single whisk. If the morphology of the array is altered, however, the same head orientation no longer produces a unique relationship between average angle of contact and object radius. The morphology of the vibrissal array thus directly modulates the information available to the nervous system and constrains the nature of the computations that can be associated with extraction of a particular object feature. These results underscore the critical importance of physical embodiment in the sensing process.
The heads and vibrissal arrays of three rats were scanned in a 3D volumetric scanner (see Materials and Methods). In post-processing, the 3D point cloud of the rat' s head (Figure 1A) was placed in a standard position and orientation, defined using three criteria. First, the rat' s nose (the centroid of the two nostrils) was defined to lie at the origin (0,0, 0). Second, the “rostrocaudal midline” of the head was required to lie in the yz-plane, with the caudal-to-rostral vector pointing in the positive y-direction. The rostrocaudal midline was defined as the line between the mean coordinate of all macrovibrissal base-points and the origin. Finally, the “whisker row planes” were forced to lie parallel to the xy-plane (Figure 1B). For each row, the “whisker row plane” was defined as the best-fit plane to all whisker base-points within that row on both left and right sides of the face. The normal to each whisker row plane was averaged across all rows to obtain a single direction vector. Greek whiskers were omitted when computing best-fit planes. The maximum sum-squared-error across all planes was 1. 59 mm2 (maximum residual was 0. 86 mm). For each rat, the whisker row planes were all closely parallel (mean angle between normal vectors = 6. 86°, maximum difference = 17. 92°). Averaging the normal vectors of all best fit planes for a given rat yielded the head orientation that aligned the average row-plane normal vector with the positive z-axis. This ensured that all five planes were oriented as close as possible to parallel to the xy-plane. To evaluate the accuracy and precision of the model, an uncertainty analysis was performed. We used error propagation techniques to compute the variance of any point on the array given the variances of each of the model parameters [15]. To perform this propagation of error analysis, we determined the variability in each parameter across animals, and then examined how that variability would propagate through the final equation (eq. 11) used to generate the model. This analysis gives the variance of the model. Uncertainty in the model was determined by quantifying how variance in each of the parameters (θmp, φmp, ψmp, θbp φbp, s, and a) affected the location of every point along every whisker in the model. Note that orientation angles are not appropriate parameters to include in the error propagation analysis because these angles are actively controlled by the rat during whisking behavior and may be considered “inputs” to the model (see Discussion). Results of the error analysis for the locations of the whisker tip and base-points are shown in Figure 10. The tips of the whiskers are particularly useful locations to quantify error for two reasons: first, the tips were not explicitly modeled, and second, the tips are the most distal part of the array, and consequently will have the largest error of any point along the whisker. The whisker tip positions thus serve as the most conservative upper bound on the error in the model. Across all whiskers, the average standard error in tip position was 3. 2±1. 7 mm (standard deviation: 7. 8±4. 2 mm), and is depicted graphically in Figure 10A. The error in tip position was computed as the Euclidean distance between the location of the whisker tip and the tip point plus the standard deviation of the tip' s (x, y, z) coordinates. Across all whiskers, the average standard error at the whisker base was 1. 3±0. 26 mm (standard deviation 3. 7±0. 65 mm), and is depicted graphically in Figure 10B. The error in base position was computed as for tip positions. The 95% confidence interval for each point along the whisker arc length is shown graphically in Figure 10C, 10D, and 10E using colored surfaces. A conservative estimate of maximum error in our model is that tip positions are accurate to within a standard error of ±5 mm (3. 2+1. 7 mm). To generalize across whiskers, error was also quantified as a function of arc length. The standard error of any point along any whisker divided by the arc length between that point and the whisker base was typically 5%±1% of the arc length. This means, for example, that a point at an arc length of 10 mm will have a standard error of 0. 5 mm. Simulations using the model of the vibrissal array can provide insight into the patterns of mechanosensory input that might be generated as the rat actively explores an object. The morphology of the array directly affects how the whiskers contact the object, and thus the mechanical information available to the nervous system. This information in turn constrains the set of neural computations that can be used to extract particular object features. Here we consider – under a particular set of assumptions about head and whisker movement – how the morphology of the vibrissal array constrains the type of neural computations that could enable the rat to determine the curvature of an object.
Embodiment of the vibrissal array can be conceptualized as spanning at least four levels: the material properties of a single whisker (e. g. elasticity and damping), the morphology of a single whisker, the musculature and tissue surrounding each whisker, and the morphology of the entire whisker array. The present study examines this fourth level. Previous studies of vibrissal array morphology qualitatively characterized the locations of whisker base-points and identified systematic variations in whisker length [11], [12]. The grid-like arrangement of the vibrissae is one of the most easily observable features of mystical pad anatomy [1] [3]. Brecht et al. demonstrated that a set of governing geometric principles, conserved across species, could qualitatively explain this grid-like arrangement [11]. The present study now quantifies the three-dimensional vibrissal array architecture. Specifically, we provide a single equation that describes every point of every whisker. This work adds to the understanding of vibrissal array morphology in several important ways. First, the locations of the whisker base-points are quantified in three-dimensions, capturing the strong row- and column-based structure of the array, while also incorporating the underlying curve of the rat' s mystacial pad. Second, equations define the 2D shape of each whisker in terms of its intrinsic curvature as well as its length, and the angle ζ describes the orientation of each whisker' s intrinsic curvature. The orientation of a whisker during protraction will affect both the angle and time at which it will make contact with an object, and a recent study has shown that the rat can change ζ during a protraction [10]. Thus the intrinsic curvature as well as ζ are essential parameters for accurate models of whisker movement. Finally, quantifying vibrissal array features in analytical form allows for systematic, cross-species comparisons of structure-function relationships in the context of behavior and ethological niche, as described below. The present study uses basic techniques from geometric morphometrics to analyze the morphology of the rat vibrissal array. In general terms, morphometrics refers to the quantification of variations in the shapes of objects. When applied to biology, morphometrics can be used to quantify and compare the shapes of organisms within and across species [20]. In some “landmark-based” analyses, for example, deviations of individual specimens from an average morphology have revealed subtle morphological differences between taxa, sexes, ages, and geographic locations [21]. Importantly, morphometric analysis has also been used to distinguish morphological differences attributable to phylogeny from those arising from behaviors that a species or sub-species has adopted in response to the local environment. Once morphological features have been quantified, statistical techniques can provide estimates of which morphological variations are best explained by phylogenetic differences and which by environmental factors (for an example, see [22]). The model developed in the present study lays the groundwork to investigate the origin of cross-species differences in the morphology of the vibrissal array. For example, murid rodents closely related to the rat (e. g. , the mouse) may have a vibrissal morphology that simply scales with body size (a phylogenetic effect). More distant species may show changes in morphology that reflect adaptive traits enabling behaviors essential for species survival. The orientation angles of the whiskers (θ, φ, ψ, ζ) are the angles at which the whiskers emerge from the rat' s face. The facial muscles of the rat control the orientation angles, and these muscles have many degrees of freedom. They can move the whisker through a large range of orientation angles during natural whisking behavior. Because the 3D whisker scans were done post-mortem, rigor mortis of the facial muscles could have pulled the whiskers to orientation angles anywhere within their natural range of movement. Unsurprisingly, these angles were the parameters that exhibited the largest variability across animals, although smooth trends are clearly visible (Figure 8). The variability associated with the static, post-rigor measurement of orientation angle is not particularly meaningful, as the muscles could have pulled the whiskers into any number of orientation angles. Accordingly, this variability was deliberately excluded from the error analysis of the model. The orientation angles should not be thought of as fixed parameters of the model, but should instead be used as inputs to the model to simulate whisking behavior. Numerous studies have quantified changes in the horizontal angle θ during natural whisking [5], [7], [9], [10], [13], [14], [24], [25], [26], [27], [28], [29]. At least two studies have produced data from which it is possible to determine how the angles φ and ψ change over the course of a whisk [10], [25]. Finally, Knutsen et al. provided the first evidence that the whisker rolls about its own axis during active whisking. The roll can be described by the value of the angle ζ over the whisking cycle. Taken together, these studies determine the equations for changes in orientation angles throughout the whisking trajectory. In addition to the equations that describe whisker movements in terms of changes in orientation angles, a complete model of whisking kinematics will require an equation that relates the protraction angle θ to mystacial pad parameters. The mystacial pad translates [9] and also changes shape during the whisk cycle (unpublished observation), causing the whisker base-points to translate. In the model, positions of the whisker base-points translate with the underlying mystacial pad [9], and therefore can be determined based solely on ellipsoid shape. There are several potential uses of an accurate kinematic model of the vibrissal array; most importantly, it could be used to simulate the expected spatiotemporal patterns of whisker-object contact during exploratory behaviors. As shown in the present study, even without information about whisker velocity, the model can be used to simulate relationships between the sensory signals acquired and an object feature. However, these simulations only predicted the angles of whisker-object contact, while an accurate kinematic model could also predict the temporal sequence of contacts. Inter-whisker contact intervals are important in determining whether neural responses in barrel cortex will be suppressed or facilitated [23], [24], [25], [26]. A predictive model of kinematics could thus be used to probe expected neural responses given the head' s position and orientation relative to an object. A second possible use of the model is as a predictive tool to describe where whiskers should be. This could be especially helpful when tracking whiskers in behavioral datasets. In high speed videography, whiskers are often observed to cross, go out of focus, and blur. Predicting the 2D projection of a whisker could reduce the search space for a whisker-tracking algorithm, and provide an estimate of whisker identity at the same time. A growing theme in sensory neuroscience is the need to link movement and sensing behaviors [27]. The present study reflects the increasing need for simulations of dynamics in sensory neuroscience, as the model represents a first step towards the creation of an entirely “digital rat, ” that is, a simulation platform to test theories of whisker movement, mechanical modeling of whisker-object collisions, mechanotransduction, and neural coding. The morphology of the vibrissal array directly constrains the mechanosensory inputs that will be generated during behavior. The morphological model can be used in conjunction with models of whisker kinematics or dynamics to develop increasingly accurate predictions about exploratory patterns of freely behaving animals, and thus the neural computations that can be associated with extraction of particular object features. Responses of sensory neurons are likely to be conditioned on, or tuned to, the particular movements used to extract the data. An improved understanding of the dynamics of motor systems that acquire sensory data will improve our understanding of the complex interactions between sensorimotor structures, the nervous system, and the specific environments in which they function.
Animal protocols for this study were written in strict accordance with the recommendations in the Guide for the Care and Use of Laboratory Animals of the National Institutes of Health, and were approved in advance by the Animal Care and Use Committee of Northwestern University. A total of six adult, female Sprague-Dawley rats (>3 months old, approximately 300 grams) were used. The head and vibrissal arrays of three of the six rats were scanned in a three dimensional (3D) volumetric scanner. Rats were euthanized with a lethal dose of pentobarbital. Tiny incisions (∼1 mm) were made in the scalp to accommodate the implantation of four skull screws. Rigid positioning rods were attached to the screws with dental acrylic. The rat was decapitated and the positioning rods were used to mount the head stably within the 3D scanner. Three-dimensional scans occurred within two hours of euthanasia (after rigor mortis had set in). Immediately after the 3D scan, each macrovibrissa was grasped firmly at its base with tweezers and plucked in a single swift motion from the mystacial pad. Each isolated macrovibrissa was then scanned in two dimensions (2D) on a flatbed scanner within 4–12 hours after euthanasia. The remaining three rats were euthanized in unrelated experiments, and did not undergo 3D scanning. Their macrovibrissae were scanned in 2D, again within 4–12 hours after euthanasia. Neither the animals nor the whiskers were preserved prior to scanning in any way. Scans of whiskers in the A, B, C, D and E rows, along with the Greek column α, β, γ and δ, were obtained from both right and left whisker arrays. The first six whiskers of each row were analyzed because these whiskers are associated with sling muscles [3] and are therefore considered macrovibrissae. The arrangement of the microvibrissae was not quantified. In our specimens, the A row contained only four whiskers. The B row consistently contained four whiskers on the left side and five whiskers on the right side; this peculiarity is perhaps due to the specific strain of rats that used in the study (Sprague-Dawley). The C, D and E rows all contained six or more whiskers. This arrangement of whiskers is consistent with that described in previous reports [3], [11]. A Surveyor DS-3040 3D laser scanner (Laser Design Incorporated) was used for the 3D scans. The final scanner output was a finely digitized 3D point cloud (20 micron volumetric accuracy) as shown in Figure 1A of Results. The complete point cloud – including both head and whiskers – was imported into the software package RAPIDFORM XOR. Within this software package, data points corresponding to each macrovibrissae were extracted from the point cloud. An example of an extracted whisker is shown in Figure 13A. The extraction process involved manual rotation of the 3D scanned image to visually determine the set of points that clearly belonged to each whisker through all angles of rotation. The whisker base-point was then identified as the centroid of a small number of points (typically 8–20) on the mystacial pad that rotated the least relative to that identified macrovibrissa. Whisker identity was assigned using the well-known topographic arrangement of whiskers on the mystacial pad [3]. In the case that two or more whiskers emerged from the same follicle (as occurred for approximately 10% of follicles), only the largest whisker was used. After manual extraction, the 3D points belonging to each macrovibrissa were exported to Matlab and a moving average (21-sample window) was used to smooth the shape. The macrovibrissae from all six rats were plucked and scanned in 2D using a flatbed scanner. Isolated vibrissae were scanned at spatial resolutions ranging from ∼10. 6 microns/pixel to ∼3 microns/pixel using either an Epson Perfection 4180 or a UMAX Powerlook 2100 XL scanner. Two scanners were used to quickly and efficiently image the large number of whiskers. The 2D whisker shape was extracted using custom image processing algorithms. Each image was converted to black and white either in Adobe Photoshop v. 7 or in Matlab, and the whisker outline was extracted in Matlab (Figure 13B). When magnified, the upper and the lower edges of the whisker became apparent (heavy black lines in the inset of Figure 13B). The midpoint between the upper and lower whisker edges was determined at small increments along the extracted whisker length. The midpoints were connected to obtain the centerline of the whisker, which closely matched the overall whisker shape (grey line in the inset of Figure 13B). Throughout Results, 2D whisker shape was quantified using the centerline of the whisker. The vibrissal array was parameterized in terms of variables that are relatively easy to measure in behavioral studies. This parameterization relies on seven parameters specific to the mystacial pad and eight parameters specific to each whisker. These 15 parameters are listed in Table 1 of Results and described in more detail below: Resolution limits of the 3D scanner meant that the scan often did not capture the whisker' s most distal region. The fraction of each whisker that was captured in the 3D scan was calculated as the ratio of the 3D scan whisker length to the 2D scan whisker length. The 2D scan was sufficiently high resolution (between 3 and 10 pixels/micron) that it captured all of the whisker tips and can be considered “ground truth” for whisker length. In general, the 3D scan captured 50%±30% (STD) of the 2D whisker length. This is sufficient to estimate the whisker' s base-point location and angles of emergence, which require only the whisker' s most proximal portion. The parameter most greatly affected by the limited 3D scanner resolution is the ζ angle, which requires estimation of the whisker plane. For example, if only 10% of the whisker is scanned in 3D, the data will most likely be linear, and a plane would be poorly conditioned. The ζ angle was therefore only computed when a well-conditioned plane could be found (84 out of 158 whiskers scanned in 3D). To combine the mystacial pad parameters and the whisker specific parameters across all rats into a single model, we found the underlying relationship between each of the eight whisker specific parameters (θBP, φBP, s, a, θ, φ, ψ, ζ) and two independent variables: row and column identity. A two-way ANOVA was performed for each parameter with the row and column as possible factors to find identity-based relationships. To perform the analysis, each row was assigned an integer value between 1 and 5 (increasing from A to E) and each column an integer value between 1 and 6 (increasing from caudal to rostral). Greek columns were associated with an adjacent row (α: A, β: B, γ: C, δ: D) and assigned a column integer value of 0. For parameters that had only the row or the column as a significant predictor (p<0. 001), a least squares regression analysis was used to test four different underlying relationships between the parameter and the position variable of interest. The four types of models tested were: polynomial, rational, power, and exponential functions (see Supplementary Information Text S1 and Table S2 for a comprehensive list of equations). For parameters that had both the row and the column as significant factors (ANOVA, p<0. 001), only multivariate regression was performed to generate the underlying relationship. These parameters were tested with polynomial relationships. To avoid overfitting, a higher-order or non-polynomial fit was chosen as the appropriate fit only if it was significantly better than the linear fit (F-test of the correlation coefficients, p<0. 001). The final equation types used in our analysis included linear, exponential and 2D linear (equations shown in Table 4). The average mystical pad ellipsoid was calculated from the right and left ellipsoids of three rats. Parameters from left-side ellipsoids were mirror-imaged across the yz-plane so that they could be averaged with parameters from right-side ellipsoids. After averaging all seven parameters, the resulting average ellipsoid was mirrored back across the yz-plane to generate symmetric, average ellipsoids on both right and left sides. Finally, these averaged ellipsoids were rotated about the global x-axis to ensure that the mean of the final base-point row-planes was parallel to the xy-plane (by an angle of 8. 72°), therefore following the convention set in Results for the head orientation. The final values of ellipsoid parameters after this rotation are shown in Table 2.
Animals move in order to sense the world. Sensing is thus an active process, constrained by muscle biomechanics and by the material, shape, and structure of the sensing organs. The rat vibrissal system provides an ideal model to examine how the physical embodiment of a sensory array shapes the sensing process. Rats have approximately thirty macrovibrissae (whiskers) arranged in rows and columns on each side of their face. They brush their whiskers against objects to tactually extract object features. To date, however, the three-dimensional shape of the whisker array has not been characterized. We scanned six rats to develop equations for the complete structure of the whisker array. Given only a whisker' s row and column identity, the equations establish the whisker' s two-dimensional shape and three-dimensional position and orientation. We used this equation-based model to simulate the whisker-object contact patterns that would be generated as a rat uses its whiskers to tactually explore objects with varying curvatures. Altering the shape of the array dramatically altered the relationship between the simulated sensory input and object curvature. The structure of the whisker array thus directly constrains spatiotemporal input patterns and thereby, the nature of the neural processing associated with extraction of particular object features.
neuroscience/behavioral neuroscience
neuroscience/sensory systems
computational biology/computational neuroscience
evolutionary biology/animal behavior
computational biology/systems biology
The Morphology of the Rat Vibrissal Array: A Model for Quantifying Spatiotemporal Patterns of Whisker-Object Contact