Figure 1.
3D parameterization of barrels and barrel columns in rat vibrissal cortex.
(A) Tangential view of the left hemisphere of a rat brain. The barrel field is located in the primary somatosensory cortex (S1), adjacent to the secondary somatosensory cortex (S2). (B) The barrels are arranged in a somatotopic layout of rows (A–E) and arcs (1–6). The four barrels in front of the first arc are given greek labels (α-δ). The barrel center (BC) is the centroid of a barrel and is used to describe the 3D location of individual barrels. The coordinate system used to describe the 3D layout of the barrel field based on the position of the BCs is centered on the C2 barrel (red), which is centrally located within the barrel field. The z axis points vertically along the C2 barrel column axis, the x axis is chosen to point towards the C3 barrel center (approximately along the row) and the y axis is perpendicular to the x and z axes and points approximately along the arc. (C) View of a coronal section of the left hemisphere (see dashed line in a). Barrels can be visualized by preparing cortical sections tangential to the barrel cortex. (D) The barrel cortex is organized into vertical barrel columns. These are obtained by cylindrical extrapolation of the barrel outlines along their respective BC axis to the pia and subcortical White matter (WM), respectively. The location of a barrel along the BC axis is described by the barrel top (BT) and barrel bottom (BB) points. (E) Tangential sections through rat cortex, indicating the relative depth below the pia, with automatically detected anatomical landmarks: red – pia, blue – WM, orange – blood vessels. The inset in section S13 shows an example of a high-resolution optical section of the barrel field.
Figure 2.
Reconstruction of barrel outlines from high-resolution optical section.
(A) Optical section of the barrel field. Manual landmarks (yellow) are placed in barrels that are going to be segmented. White contours show the final segmentation result of this section. (B) Result of gray-value based image segmentation. Gray lines overlaid indicate the Voronoi regions (VR) of the manual landmarks used for region growing (G). (C) Final result of VR-based barrel segmentation. (D) Raw image data of barrel with red contour in A. Line shows pixels included in the line profile in E. (E) Line profiles of the intensity values along the lines before (gray; see D) and after filtering (black; see F). Dashed lines indicate threshold values used to separate different barrels from septum. (F) Result of image filtering. Line shows pixels included in the line profile in E. (G) VR-based region growing. White lines indicate border of the VR of the manual landmark. (H) VR-based barrel detection turns the binary- segmented image into an object image by assigning every segmented pixel to a barrel. (I) Closing merges all fragments belonging to one barrel.
Figure 3.
Reconstruction of 3D barrel dimensions.
(A) Barrel contour in a single optical section overlaid on the filtered image (gray values linearly enhanced for visualization). White lines indicate border of the VR of this barrel. Dashed circles with diameters of 90 and 170 pixels (approx. 165 and 315 µm) indicate the regions used to estimate the barrel extent. (B) Histogram of background pixels inside the barrel contour in A (black) and histogram of background pixels in septum (gray), i.e. outside of the barrel contour and inside of the VR. Dashed white lines mark mean gray value. (C) Ratio of means inside/outside of the contour as a function of the contour radius. Black: circular regions in A; red: segmented contour. (D) Side view of all segmented contours. Subsequent tangential sections are aligned using blood vessels. (E) Top row: Individual optical sections from different tangential sections (marked bold in D). Red – regular segmented contours. Green – optimized minimal contours. Bottom row: Radial dependence of the ratio of means for all contours in the corresponding optical sections. The slope of the black line gives an estimate of the relative size of the true barrel extent compared to the segmented contour. At the top and bottom of the barrel it may be necessary to segment an optimized minimal contour (see Supplemental Materials).
Figure 4.
3D reconstruction of barrels and barrel columns.
(A) Segmented barrel contours are smoothed in the z-direction to remove segmentation artifacts. (B) Anatomical structures are reconstructed in 3D. Blood vessels (orange) are reconstructed as 3D lines. Pia and WM are reconstructed as surfaces. The BC axis (dashed line) is found based on directions of blood vessels located around the BC and the orientation with respect to the pia. The column orientation is computed with respect to the C2 column. (C–E) Average dimensions of barrels and barrel columns are arranged on a grid in the layout of the barrel field. The arrows indicate the direction of the average gradient of the parameters.
Table 1.
Average values and variability between animals of all anatomical parameters for individual barrels and barrel columns (mean ± SD, n = 12).
Figure 5.
Cortical curvature leads to anisotropic overlap of barrel columns.
(A) The granular layer is subdivided into barrels and the septum between barrels. The vectors describe the direction along the row (e.g., D1-D2-D3), arc (e.g., C2-D2-E2) and the 3-2-1 direction (e.g., C3-D2-E1). (B) Top: overlap of neighboring barrel columns in one reconstructed barrel cortex in different directions, based on a cylindrical extrapolation of the column. The magnitude of the overlap is influenced by the distance between neighboring columns and the magnitude of the curvature in different directions. Bottom: average values across all columns and all reconstructions. Error bars are 1 standard deviation. (C) Measurement of the average volume inside barrel columns and septa in all reconstructed barrel cortices. Error bars are ±1 standard deviation.
Figure 6.
Creation of an average 3D model of the barrel cortex.
(A) All barrel fields reconstructed automatically in this study. In three animals it was not possible to reconstruct all barrels, because individual barrels were not completely distinguishable from background (female 1: A2,A3; female 2: A4; female 3: γ). (B) Standardized barrels, pia and WM shown from a tangential view. (C) Three standardized barrels and barrel columns (B3, C2, D1), pia and WM shown from a (semi-coronal) side view. (D) Variability of the registered BT points measured along rows/arcs. Barrels in shaded region are shown in the side view in (E). (E) Vertical axis of the error ellipses shows the variability of the registered BT, BB, pia and WM along the barrel column axis. Dashed region indicates horizontal variability induced by variability of the column axis. Because the angular variability has a fixed value for each barrel, the induced horizontal variability increases with distance from the barrel center. This is illustrated by the horizontal axis of the error ellipses. This error is smaller than the variability along rows and arcs between animals (D), and thus negligible at the BT and BB.
Figure 7.
Quantitative description of the 3D anatomical layout of the barrel field.
(A) Fits of 2nd order polynomials in (Row, Arc) coordinates to the x/y/z coordinates of the BC points of the standardized barrel field. (B) Mean coefficients (black) of the fits to all reconstructed barrel fields and coefficients of the fit to the standardized barrel field (red). Error bars are ±1 standard deviation. (C) Difference between the mean coefficients and the coefficients of the standardized barrel field in units of standard deviation.
Table 2.
Precision of registration for each barrel column.
Figure 8.
Registration of 3D neuron morphologies to the standardized barrel cortex.
(A) Example of a L5 thick-tufted neuron reconstructed from 100 µm thick sections. Outlines of pia, WM and barrels are added to the reconstruction in the coordinate system given by the slicing direction. (B) Side view of (A). The slicing direction does not match the orientation of the column containing the neuron soma. (C) Reconstruction of landmarks in 3D and registration of the barrels to the standardized barrel field. It may be necessary to correct the orientation of the neuron to match the direction of the local column axis (gray – before rotation, red – after rotation). The histograms show the rotation angle used to align the barrel field outlines with the standardized barrel field (global orientation) and the angle of the subsequent rotation aligning the neuron orientation with the local column orientation. (D) The barrel outlines in the reconstruction are of lower resolution along the slicing direction and thus show a systematic offset compared to the standardized barrel landmarks. This is corrected for by translation along the local column axis. (E) The variability between different reconstructions is minimized by scaling the supragranular, granular and infragranular structures such that the landmarks of the reconstructed neuron coincide with the standardized landmarks. The average scaling factors for the individual layers are very close to 1. (F) Registration of the neuron to the standardized barrel cortex allows objective determination of anatomical parameters such as the soma location in 3D. Comparison of the registered depth of 56 neurons with the penetration depth of the pipette recorded during the experiment shows that this recording depth is on average 46 µm lower than the registered depth, but varies in a range of up to 200 µm around the registered depth.