The authors have declared that no competing interests exist.
Conceived and designed the experiments: MO. Performed the experiments: RTN CPJdK. Analyzed the data: RE MO. Contributed reagents/materials/analysis tools: RE. Wrote the paper: MO. Conceived and developed an earlier version of the registration tool: MH. Developed and implemented the present image processing and registration tools: RE.
Current address: Computational Neuroanatomy Group, Max Planck Institute for Biological Cybernetics, Tübingen, Germany
The three-dimensional (3D) structure of neural circuits is commonly studied by reconstructing individual or small groups of neurons in separate preparations. Investigation of structural organization principles or quantification of dendritic and axonal innervation thus requires integration of many reconstructed morphologies into a common reference frame. Here we present a standardized 3D model of the rat vibrissal cortex and introduce an automated registration tool that allows for precise placement of single neuron reconstructions. We (1) developed an automated image processing pipeline to reconstruct 3D anatomical landmarks, i.e., the barrels in Layer 4, the pia and white matter surfaces and the blood vessel pattern from high-resolution images, (2) quantified these landmarks in 12 different rats, (3) generated an average 3D model of the vibrissal cortex and (4) used rigid transformations and stepwise linear scaling to register 94 neuron morphologies, reconstructed from
For studying the neural basis of perception and behavior, it would be ideal to directly monitor sensory-evoked excitation streams within neural circuits, at sub-cellular and millisecond resolution. To do so, reverse engineering approaches of reconstructing circuit anatomy and synaptic wiring have been suggested. The resulting anatomically realistic models may then allow for computer simulations (
The morphology of neurons has been of interest for three main reasons. First, the morphology of the soma, dendrites, and axon is commonly used to identify types of neurons
For classification of neuronal cell types and analyzing biophysical properties, a single neuron may be a sufficient reference frame for morphological analysis. In contrast, the aim of inferring synaptic connectivity from structural overlap of neuronal morphologies requires the placement of neurons into a reference frame that is sufficiently precise and invariant to variability between experiments. Quantitative registration methods have been applied to neurons in the mammalian cortex from
For the analysis of cortical neuron ensembles in 3D, for example from experiments carried out
Due to its well-defined structural and functional layout, subdivided vertically into cortical barrel columns and horizontally into six cortical layers (L1–6), the rodent vibrissal cortex is a natural starting point for generating a precise 3D anatomical model of the mammalian cortex. A cortical column is thought to be the elementary functional unit of sensory cortices
Despite multiple studies that investigated the geometry of the rodent vibrissal cortex
The large anatomical variability within the vibrissal cortex of individual animals demands that neuron reconstructions need to be registered as close as possible to their original location. The automated registration tool presented here meets this demand. Rigid transformations and stepwise linear scaling along the vertical column axis are used to match the reference landmarks of a reconstructed neuron to their respective counterparts in the standardized cortex model. The 3D reconstructions of somata, dendrites and axons from
The vibrissal cortex in rats comprises 30 large barrels in L4, separated by septa between them (
(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.
Taking a coronal section through the barrel field reveals that the curvatures of the pia and white matter (WM) surfaces (
We defined five parameters for each barrel column to describe this location-specific 3D layout of the vibrissal cortex: (i) the
We determined these five parameters for 984 barrels from 104 different rats. To do so, brains were cut approximately tangential to the barrel field into 50 or 100 µm thick vibratome sections (
We manually traced 637 individual barrels on low-resolution images from 100 µm thick sections in 92 rats using Neurolucida software (MicroBrightfield, Williston, VT, USA). Only clearly stained barrels were traced, one contour per brain section. In addition, pia and WM contours were traced for all sections. The resultant average barrel area was 9.8±1.9×104 µm2 (mean ± SD). The average barrel height was 299±92 µm. The average pia-WM distance was 1949±100 µm.
The manual determination of the vertical extent of the barrel (i.e., BT and BB) proved to be difficult, because barrels were tilted with respect to the vertical cortex axis within a brain section. Consequently, we decided to determine the barrel dimensions by more objective criteria. Using an automated image processing pipeline (
(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.
(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).
Using this automated tracing method, we reconstructed 347 barrels from 50 µm thick sections in 12 different rats (6 male, 6 female). The average area of the automatically extracted barrels was 9.9±1.7×104 µm2. The average pia-WM distance was 1929±99 µm. Because the mean values as well as the standard deviations (SDs) of the two parameters were identical to their manually determined counterparts, we regard our automated algorithms as sufficiently accurate to reconstruct the five anatomical parameters describing the barrel field.
The automatically determined barrel height (348±34 µm) was slightly different from its manual counterpart (299±92 µm). Given the difficulties in manually determining the vertical borders of the barrels, we regard the automated result as more accurate. Further, we determined a systematic error of ∼10 µm for the automated detection of BT and BB, respectively. Thus, the automatically determined SD of 34 µm in barrel height likely reflects the ‘true’ biological variability between animals. In contrast, the 3-fold larger manually determined SD in barrel height of 92 µm may primarily reflect systematic limitations of the manual tracings and hence conceals the biological variability.
Consequently, the automated pipeline of imaging and image processing, presented here, is a fast and precise alternative to extract the 3D geometry of the vibrissal cortex, reaching at least the same accuracy as manual tracings, by using a smaller sample size. Therefore, only the 12 automatically reconstructed vibrissal cortices were subsequently used for quantification and standardization of the five geometrical parameters.
The cortical column and its cytoarchitectonic equivalent in the vibrissal cortex, the barrel column, has been regarded as an elementary building block of sensory cortices
However, the automated 3D reconstruction of 12 complete barrel fields, now allowed comparing the parameters of individual barrel column across the vibrissal field in a quantitative manner (
(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.
Barrel | Barrel height (µm) | Barrel top (µm) | Barrel bottom (µm) | Barrel area (×104 µm2) | Barrel volume (mm3) | Column height (µm) | Column diameter (µm) | Column volume (mm3) | Column orientation (°) |
A1 | 322±34 | 455±32 | 777±50 | 8.55±1.60 | 0.028±0.007 | 1651±126 | 330±31 | 0.14±0.03 | 8.3±4.1 |
A2 | 337±45 | 467±52 | 805±55 | 8.30±1.46 | 0.028±0.006 | 1759±113 | 325±29 | 0.15±0.02 | 12.9±4.8 |
A3 | 315±29 | 485±35 | 800±34 | 6.48±1.07 | 0.020±0.004 | 1825±98 | 287±24 | 0.12±0.02 | 15.5±4.4 |
A4 | 316±39 | 489±38 | 805±37 | 6.50±1.50 | 0.021±0.006 | 1916±94 | 288±33 | 0.12±0.03 | 16.9±4.5 |
Alpha | 308±39 | 479±53 | 788±48 | 8.79±2.50 | 0.028±0.010 | 1600±118 | 335±48 | 0.14±0.04 | 5.5±3.4 |
B1 | 346±34 | 481±48 | 827±56 | 8.74±1.59 | 0.030±0.006 | 1736±92 | 334±30 | 0.15±0.03 | 4.4±3.5 |
B2 | 344±27 | 490±45 | 834±47 | 9.01±1.48 | 0.031±0.005 | 1815±93 | 339±28 | 0.16±0.03 | 7.2±4.3 |
B3 | 354±29 | 490±53 | 844±57 | 7.66±1.07 | 0.027±0.004 | 1899±98 | 312±22 | 0.15±0.02 | 10.3±5.1 |
B4 | 352±21 | 501±52 | 853±52 | 7.89±1.15 | 0.028±0.005 | 1961±93 | 317±23 | 0.15±0.02 | 14.7±4.3 |
Beta | 338±43 | 472±45 | 810±47 | 10.18±1.66 | 0.035±0.008 | 1623±103 | 360±29 | 0.16±0.03 | 6.7±2.7 |
C1 | 358±24 | 478±58 | 836±65 | 10.08±1.73 | 0.036±0.007 | 1800±110 | 358±31 | 0.18±0.03 | 6.1±4.6 |
C2 | 360±24 | 496±43 | 856±37 | 10.30±1.37 | 0.037±0.005 | 1892±100 | 362±24 | 0.20±0.03 | 0 |
C3 | 354±31 | 534±61 | 889±56 | 10.44±2.05 | 0.037±0.007 | 1985±100 | 365±36 | 0.21±0.04 | 7.3±5.1 |
C4 | 363±47 | 557±80 | 920±70 | 9.03±2.25 | 0.033±0.011 | 2038±94 | 339±42 | 0.18±0.05 | 10.3±5.2 |
Gamma | 355±31 | 478±48 | 833±48 | 12.73±2.72 | 0.045±0.009 | 1713±132 | 403±43 | 0.22±0.04 | 11.1±5.6 |
D1 | 371±33 | 491±45 | 863±55 | 11.17±1.52 | 0.042±0.007 | 1865±104 | 377±26 | 0.21±0.03 | 7.8±4.4 |
D2 | 362±39 | 526±61 | 888±56 | 12.42±1.61 | 0.045±0.008 | 1957±101 | 398±26 | 0.24±0.04 | 5.1±4.5 |
D3 | 368±23 | 552±60 | 920±60 | 11.64±1.97 | 0.043±0.008 | 2046±87 | 385±33 | 0.24±0.04 | 3.2±2.4 |
D4 | 363±46 | 556±57 | 919±54 | 10.34±0.75 | 0.038±0.005 | 2081±98 | 363±13 | 0.22±0.02 | 5.9±3.2 |
Delta | 354±27 | 506±48 | 860±52 | 14.31±3.27 | 0.051±0.012 | 1845±95 | 427±49 | 0.26±0.06 | 12.4±4.5 |
E1 | 343±28 | 546±45 | 888±60 | 14.56±2.05 | 0.050±0.008 | 1977±77 | 431±30 | 0.29±0.04 | 9.4±5.1 |
E2 | 355±30 | 557±54 | 912±60 | 15.89±1.61 | 0.056±0.007 | 2096±58 | 450±23 | 0.33±0.04 | 7.6±5.1 |
E3 | 364±38 | 549±58 | 912±71 | 15.78±2.32 | 0.057±0.007 | 2117±84 | 448±33 | 0.33±0.05 | 6.5±3.6 |
E4 | 344±48 | 580±48 | 924±45 | 12.30±2.00 | 0.042±0.010 | 2111±91 | 396±32 | 0.26±0.04 | 5.9±2.9 |
Barrel volume, column diameter and column volume are derived quantities. Colum diameter derives from a circular approximation of the barrel area.
First, BT and BB ranged from 455 µm to 580 µm and 777 µm to 924 µm distances below the pia, respectively. Both parameters varied in a codependent manner (
Second, the barrel areas displayed substantial location-specific variations across the vibrissal field, ranging from 64,800 µm2 to 158,900 µm2. The ∼2.5-fold difference in barrel area again followed a well-defined gradient (
Third, the column heights (i.e., pia-WM distance) displayed a gradient similar to the ones obtained for BT and BB (
Fourth, the volumes of the barrel columns displayed a location-specific gradient, different from the ones observed for barrel areas or column heights (
Finally, the orientation (i.e., vertical axis) of the barrel columns with respect to each other was not parallel, but tilted, following the curvature of the pia. We defined the vertical axis of the C2-column as the Null direction and determined the tilt of the remaining columns with respect to this axis (
(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.
The curvature of the cortex and the resulting tilts of the BC axes yielded barrel columns that started to overlap in deep cortical layers (
The increasing overlap with cortical depth can alternatively be described by a depth-dependent change in volume that separates cortical barrel columns. The volume separating the barrels in L4 is commonly referred to as the septum. We adopted this terminology for the entire volume of the vibrissal cortex that was not covered by any cortical barrel column. We subdivided the entire volumes of the 12 reconstructed vibrissal cortices into voxels of size 10×10×10 µm3 and assigned each voxel either to a barrel column or the septum.
The resultant volume of the entire vibrissal cortex (α-δ, A1-E4) was 6.53±0.75 mm3, with 4.58±0.54 mm3 (∼70%) belonging to barrel columns and consequently 1.95±0.28 mm3 (∼30%) belonging to the septum. The total volume of the supragranular, granular and infragranular layers was 2.02±0.19, 1.29±0.15 and 3.06±0.46 mm3, respectively (
We investigated whether the anatomical variability of the respective five parameters describing the dimensions of each barrel column was sufficiently small across animals (
(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.
As a first qualitative assessment, we calculated the mean and SD of each parameter for each individual column
To obtain a more quantitative measure of the anatomical variability of the vibrissal cortex, we registered 12 reconstructed vibrissal cortices into a common coordinate system and created an average 3D cortex model by using only rigid transformations (i.e., translations and rotations) (
The average variability across BT locations in the tangential plane, as measured by the respective square root of the eigenvalues, was 67 µm along whisker rows and 49 µm along whisker arcs. The variability of the BB (row: 64 µm; arc: 48 µm) locations followed the variability of the BT (along rows: r = 0.96, along arcs: r = 0.92). In general, the variability of barrel locations in the tangential plane was much smaller than the average extent of the barrels (∼355 µm diameter) (
The variability in barrel location along the vertical column axis is exemplarily illustrated for the C2 barrel (
The variability between the 12 individually registered BT and BB locations from their counterparts in the standardized model, as measured by the respective square root of the eigenvalue, were similar to the respective average SDs determined across animals (e.g., BT: 51 µm vs. 35 µm). Hence, the precision of the BC axes in the standardized model was close to the variability in orientation across animals (i.e., 4.5° vs. 4.1°). Consequently, the rigid transformations and optimizations used to create the 3D standard model did not introduce any systematic biases. Taken together, the two quantitative measures indicate that the 3D geometry of the rat vibrissal cortex was preserved across animals and that the standardized model captures its average 3D layout.
So far, we considered the parameters from each barrel column individually, neglecting that positioning of the barrel columns with respect to each other may change between animals. We therefore introduced a set of three non-linear functions (2nd order polynomials) to parameterize the 3D layout of the entire vibrissal cortex separately for each reconstructed cortex and the standardized model. The 15 coefficients of the three functions may be interpreted as specific geometrical properties of the vibrissal cortex; for example measuring the deviation of the barrel field from a rectangular grid (see Materials and Methods).
The coefficients were determined by fitting the functions to the 24 BC locations of the standardized model of the vibrissal cortex (
(A) Fits of 2nd order polynomials in
The finding that not only the 3D dimensions of the respective barrel columns, but also the 3D layout of the entire vibrissal cortex, is preserved with approximately 5% accuracy across animals, is somewhat counter-intuitive when visually comparing individual cortices reconstructed in the present (
To assess how each individual cortex reconstruction matches the average model (i.e., standard layout of the vibrissal cortex) we performed a ‘leave-one-out’ cross validation analysis. Specifically, we determined the average coefficients from only 11 cortices and then computed the root mean squared error (RMSE) between the predicted and the actual 3D BC locations of the remaining cortex. The procedure was repeated 12 times, i.e., for each reconstructed vibrissal cortex. The average RMSE was 146 µm, but varied between animals and barrel columns (
Barrel | SE (µm) | SD (µm) | RMSE (µm) |
A1 | 27 | 95 | 179 |
A2 | 24 | 80 | 170 |
A3 | 27 | 89 | 166 |
A4 | 26 | 86 | 166 |
Alpha | 40 | 138 | 211 |
B1 | 19 | 65 | 106 |
B2 | 14 | 48 | 101 |
B3 | 15 | 51 | 108 |
B4 | 19 | 65 | 131 |
Beta | 36 | 124 | 158 |
C1 | 27 | 92 | 106 |
C2 | 20 | 69 | 104* |
C3 | 22 | 75 | 102 |
C4 | 30 | 102 | 167 |
Gamma | 42 | 139 | 176 |
D1 | 30 | 105 | 153 |
D2 | 28 | 98 | 121 |
D3 | 24 | 83 | 110 |
D4 | 27 | 95 | 150 |
Delta | 33 | 114 | 203 |
E1 | 20 | 71 | 148 |
E2 | 23 | 81 | 136 |
E3 | 26 | 91 | 160 |
E4 | 24 | 85 | 168 |
The average precision of the soma/dendrites/axon location within the principal column (i.e., containing the neuron's soma) is determined as the standard error of the barrel location (SE). The average precision of long-range projecting axons into columns surrounding the principal column is given by the standard deviation of the barrel location (SD). The minimal precision is derived from the leave-one-out analysis as the root mean squared error between the predicted and actual barrel location (RMSE). The RMSE of the C2 barrel (*) is computed as the average of C1 and C3, because the C2 BC is the origin of the coordinate system during parameterization.
The quantifications of the variability of the vibrissal cortex and the quality of its standardized model suggest that 3D reconstructions of neuron morphologies can be registered with high precision, if the respective reference landmarks are present in each tracing. Unfortunately, the high-contrast Cytochrome-oxidase staining needed to automatically extract the barrel landmarks prevents tracing biocytin-labeled
To do so, we manually traced all visible anatomical landmarks for 94 reconstructed neuron morphologies with somata located randomly within the vibrissal cortex and at varying cortical depth between L2 and L6 (recording depth: 222–1727 µm
(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.
The BC of the manually reconstructed principal column (i.e., containing the neuron's soma) was aligned with the respective BC of the standard cortex. Then, the remaining BC locations were registered by using only rigid transformations (
The orientation of the BC axis after the first registration step was on average more variable (SD: 7.6°) than the 4.5° deviation in column orientation determined for the standard vibrissal cortex. This likely reflected the observation that the manually determined contours defining BT and BB were less precise than their automated counterparts. We thus introduced a second rotation step. The apical dendrite of pyramidal neurons in the cortex usually projects along an axis perpendicular to the pia surface and thus, parallel to the large blood vessels in its immediate surrounding
After translations and rotations, the new BT, BB, pia and WM locations were systematically compared to their counterparts in the standardized cortex model. The average vertical locations of all landmarks deviated from the standard model (
Further, we measured the distance between the apical tuft endings and the reconstructed pia surface exemplarily for four neurons where the apical tufts reached the upper most part of L1 (i.e., true distance to the pia surface was zero). We found that the average distance of the apical tuft endings to the reconstructed pia surfaces was 39±5 µm. Thus, we shifted all manually traced contours by −39 µm with respect to the neuron tracing. In addition, the thickness of the first vibratome section may deviate from the assumed 100 µm thickness. We therefore compared the average distance to the pia for four neurons whose apical tufts ended within the first vibratome section and ten neurons with tufts already reaching the pia in deeper sections. We found that the reconstructed pia of the first section was on average 20 µm too high and corrected the vertical pia location accordingly.
In the final registration step, differences between the registered vertical locations of BT, BB, pia and WM of each individual neuron tracing were compared to the respective standardized landmarks (
In summary, by (i) coarse registration of BC locations, (ii) fine tuning of neuron orientation, (iii) shifting the vertical locations of BT, BB, pia and WM by their respective average differences between manually and automatically determined landmarks and (iv) stepwise linear scaling of the neuron along the BC axis, we found that the manually reconstructed vibrissal cortices could be matched to the standard cortex as precisely as the automatically reconstructed versions.
The precision of registering individual neurons to the standardized model may thus be expressed as the standard error (SE) of the average BC location as determined by the covariance matrix above, multiplied with the respective scaling values in supragranular, granular and infragranular layers, respectively. Specifically, the vertical precision of the supragranular layers can be determined as the SE of the BT locations, which was 15 µm, multiplied with the average scaling of 1.05, resulting in SEz,supra = 16 µm. The vertical precisions of the granular and infragranular layers can be determined accordingly by the SE in barrel and column heights (i.e., SEz,granular = 10 µm and SEz,infra = 28 µm), respectively. Combined with the precisions along the row and arc (SErow = 19 µm, SEarc = 14 µm, see above), we obtained a 3D registration accuracy for neurons located in supragranular layers of 28 µm, in the granular layer of 26 µm and in infragranular layers of 37 µm.
Consequently, the 3D location of the soma, as well as dendrites and axons close to the principal column, can on average be determined with ∼30 µm accuracy. However, the registration was optimized to match the BC location of the principal column. The registration accuracy of neuronal branches that project out of the principal column (i.e., long-range projections into septa and surrounding columns) was hence not determined by the SE of the surrounding BC locations, but by their average SDs. The average 3D registration accuracy of neuronal (long-range) projections within surrounding columns was thus ∼89 µm.
At this stage it should be emphasized that the present registration precisions are to be considered with respect to the average dimensions of the vibrissal cortex, i.e., SE and SD of the barrel location describe the precision of registered local and long-range projections, respectively. However, since the 3D layout of an individual cortex may deviate more from the standard cortex than the average of the 12 cortices, the ‘minimal’ precision of registration may be given as the average RMSE of the BC locations from the ‘leave-on-out’ analysis, i.e., 146 µm. For a summary of the column-specific registration precisions see
As a first application of the registration method, we compared the vertical locations of the somata after registration with their respective recording depths (i.e., penetration depth of the pipette,
The surprisingly small difference of on average 46 µm between the registered depth of the soma and the penetration depth of the recording pipette suggest that tissue shrinkage due to perfusion, fixation and histology (see Materials and Methods), which can be up to 20%
Various attempts to quantify the geometry of individual barrels in the rodent vibrissal cortex have been reported previously
Going beyond the scope of the previous 2D studies, we found that the five 3D column parameters varied substantially across the vibrissal cortex (e.g., the barrel area ranged from 65,000 to 160,000 µm2 or the cortical thickness ranged from 1,600 to 2,100 µm). Further, the differences in column dimensions were not random, but followed well-defined gradients. In contrast, the variability of the five parameters was remarkably small across different animals (i.e., the SD was usually ∼5% of the mean).
Moreover, we found that the precision of cutting the brain with exactly the same orientation into tangential sections was only around 14.0±7.6°. Hence, 2D reconstructions of the barrel geometry will likely be subject to systematic errors, because the vertical axes along which parameters, such as barrel area and height, are determined vary between preparations. Further, the curvatures of the pia and WM resulted in column orientations not parallel, but tilted with respect to each other. The tilt deviated along different axes and was most pronounced for neighboring columns along an axis perpendicular to the medial axis of the brain (i.e., 3-2-1 axis). Hence, even if the cutting angle would be identical across preparations, 2D measurements of barrel area and height will still be affected by systematic errors due to the curvatures of the cortex.
However, when evaluating the dimensions of only a single column, the tilt of the neighboring columns can be neglected and systematic errors in cutting angle may be compensated by large numbers of reconstructed barrel columns. Thus, the previously reported dimensions of the D2 column in rats, based on 2D tracings of axonal projections from the posterior medial division of the vibrissal thalamus (POm)
Several attempts to create 3D reference frames for precise registration of single neuron morphologies have been reported for various animal models previously.
For example, reconstructing stereotypical anatomical landmarks from multiple complete brains resulted in an average 3D reference frame of the entire bee brain
While the general idea of (i) determining the 3D dimensions of stereotypic anatomical landmarks, (ii) generating an average 3D model from these landmarks and (iii) registering neurons by matching anatomical landmarks to the average model are similar between the insect models and the model of vibrissal cortex presented in this study, there is one major difference: The registration to the insect brains uses non-rigid transformations (i.e., nonlinear deformations of 3D label fields), while our registration approach was based on rigid transformations (i.e., translations, rotations and stepwise linear scaling).
Typically, the 3D anatomical layout and even the number of neurons, as well as the 3D dendrite/axon projection patterns of individual neurons are stereotypic across insect brains
However, the mammalian cortex is different. Neither the numbers of neurons (e.g., per cortical column
The variability across animals of all parameters describing the 3D layout of the vibrissal cortex was sufficiently small to create an average cortex model. Further, the set of linear transformations, introduced here, was sufficient to create a standard model, which captured the average 3D layout of the vibrissal cortex. Specifically, we showed that all parameters describing the 3D layout of the standard model were very close to the respective parameters averaged across all reconstructed cortices (i.e., SD within 5% of the mean). Thus, the precision of the standard model was basically identical to the variability between animals. Therefore, the standard model can be regarded as an optimal reference frame for the vibrissal cortex. Finally, the precision of soma/dendrite/axon locations after rigid registration to the standard cortex was on average ∼30 µm within the principal column and ∼90 µm in surrounding columns, but at least ∼140 µm (see
In conclusion, lacking a sufficiently high density of reproducible anatomical landmarks, non-rigid deformations would artificially minimize the measured, true anatomical variability of the vibrissal cortex across animals, but would not improve the accuracy of the registration. Moreover, non-rigid transformations would deform the morphology of the cortical neurons, changing their path lengths, innervation domains and even electrotonic properties
Recently, a first attempt to register neuron morphologies to the mammalian brain has been reported, using a 3D model of the hippocampus in rats
Finally, magnetic resonance imaging (MRI) has been used to generate anatomical reference frames with voxel dimensions of ∼60 µm
Here we presented a novel, largely automated approach to (i) reconstruct the precise 3D geometry of the vibrissal cortex in rats, (ii) generate a standardized average cortex model and (iii) register dendrite and axon morphologies obtained from
First, the automated reconstruction of the barrel cortex geometry from high-resolution image stacks allowed extracting five parameters describing the geometry of each barrel column with higher precision than manual reconstructions. This allowed estimating the ‘true’ biological variability of column geometry within the vibrissal cortex and across animals. Second, the parameters of a respective column and the 3D layout of the entire vibrissal cortex were remarkably preserved across animals. This allowed generating a standard model that captured the average layout of the vibrissal cortex. Third, the accuracy of the standard model resembled the variability across animals, which rendered the maximal precision possible for registering single neuron morphologies. Fourth, the rigid registration approach allows placing soma/dendrites/axon at their true cortical position with ∼30 µm and ∼90 µm precision within the principal and surrounding columns, respectively.
Finally, the dimensions and orientations of individual barrel columns varied substantially across the vibrissal cortex, following well-defined gradients. This finding raises the question whether a cortical barrel column can be regarded as a stereotypical anatomical unit of the vibrissal cortex. In particular, two findings argue against this theory. First, the cortical column volume increases from the A- towards the E-row by ∼2.5-fold. Previous studies demonstrated that the average neuron density is rather constant across cortical columns
Thus, the column-specific (i) volume, (ii) number of neurons, (iii) overlap with surrounding columns and (iv) relative proportion of supragranular-to-granular-to-infragranular layers suggest that each barrel column is a unique anatomical and potentially functional unit, as was suggested previously by functional measurements in different barrel columns in freely behaving mice
All experiments were carried out in accordance with the animal welfare guidelines of the Max Planck Society and VU University Amsterdam, the Netherlands.
Neurons were filled with biocytin in urethane-anaesthetized or fentanyl-sedated Wistar rats either extracellularly by using juxtasomal recording and electroporation
Cytochrome-oxidase staining was performed on 50 or 100 µm thick sections using phosphate-buffered saline (0.05 M) containing 0.2 mg/ml Cytochrome C (Sigma), 0.2 mg/ml catalase (Sigma) and 0.5 µg/ml DAB. To perform manual tracings of barrel outlines in Cytochrome C positive sections, Cytochrome-oxidase staining was performed for 45–60 minutes at 37° C. For automated detection of barrels, Cytochrome-oxidase staining was performed overnight at 37°C.
Neuron tracings were performed on 50 or 100 µm thick vibratome sections, cut approximately tangential to the D2 barrel column. Ranging from the pia surface to the white matter, 40 or 24 sections were reconstructed per neuron. DAB-stained dendrites were detected manually using Neurolucida software (MicroBrightfield, Williston, VT, USA). Axons were detected and traced in each brain section using a previously described automated method
A standard transmitted light brightfield microscope (Olympus BX-52, Olympus, Japan) equipped with a motorized x-y-z stage (Märzhäuser, Wetzlar, Germany) was used for automated mosaic/optical-sectioning image acquisition, using Surveyor Software (Objective Imaging Ltd, Cambridge, UK). A 435±70 nm band-pass illumination filter, was attached to the diaphragm of the lighthouse to provide high contrast of the barrels. A 4× air objective (Olympus 4× UPLFLN; 0.3 NA) with a pixel size of 2.33 µm was used for reconstruction of pia, WM and blood vessels. A 40× oil immersion objective (Olympus 40× UPLFLN; 1.3 NA) with a pixel size of 0.23 µm and optical sectioning of 1 µm spacing was used for reconstructing the barrel field (
All processing was carried out on workstations with Intel Xeon processors (8 cores/12GB RAM) or compute-servers with Intel Xeon processors (24 cores/256GB RAM). Segmentation and reconstruction of blood vessel, pia, WM and barrel outlines was performed automatically using custom written C++ routines, in part based on ITK
Briefly, blood vessels are automatically extracted from low-resolution images and median projections of the high-resolution image stacks. Outlines of the pia and WM are automatically extracted from low-resolution images in each brain section using thresholding and region growing methods (
Barrel outlines are automatically detected in each optical section of the high resolution image stacks during three processing steps (
All automatically extracted contours (i.e., vessel, pia, WM, barrel) are converted into closed graphs. By manually or automatically matching the extracted blood vessel patterns
Using the pia surfaces, the orientation of the blood vessels is determined. Vessels that are not perpendicular to the pia (i.e., angle between the vessels and the normal vector of the pia triangle at the intersection point is larger than 10°) are deleted. The remaining vessels are used to constrain the vertical BC axes. For each BC, a set of candidate axes is determined for each triangle of the pia surface within a 2 mm radius. The quality of each axis is scored. The shorter the axis and the more perpendicular to the pia surface, the higher the score. Finally, from all candidate axes that are parallel to the average vessel orientation within the respective barrel, the one with the highest score is automatically chosen as the BC axis.
Finally, the reconstructed barrel contours are projected to the respective BC axis, defining the BT and BB points. Calculating the average barrel circumference and extrapolating it towards the pia and WM, completes the reconstruction pipeline and allows extracting the five parameters per column needed to quantitatively describe the 3D geometry of the rat vibrissal cortex (BT, BB, barrel area, BC axis and pia-WM distance).
The first step in generating a standard barrel cortex is registration of all reconstructions to a common coordinate system. Only translations and rotations are used for registration. Corresponding BT and BB points from all reconstructions are used to align different reconstructions. Further, the BC axis passes through these points. Aligning all corresponding BT and BB points therefore implicitly aligns the BC axes from different reconstructions. The transformations for each reconstruction are computed by minimizing the sum of squared differences
Briefly, one barrel reconstruction is arbitrarily selected as a reference. For all other barrel reconstructions, the optimal translation and rotation with respect to the reference reconstruction are computed separately. The centroids of all corresponding points are computed and used as reference during the next iteration. For every iteration step the optimal translation is given by aligning the overall centroid of the reference with the overall centroid of the reconstruction to be matched. The optimal rotation is then computed from the singular value decomposition of the product of the two point position matrices set up from the positions of all BT and BB points of the reference and the reconstruction to be matched. No scaling was allowed. Only one iteration step was necessary, because the change in BT and BB positions was less than 1 µm after the first iteration.
The position of the BT and BB points of each barrel in the standardized cortex model is set to the average centroid of the respective BT and BB after registration, resulting in average BC axes. In addition, a vector field representing the local orientation is created with a resolution of 50×50×50 µm3 voxels. The vector at each voxel is computed by linear interpolation of the orientation of the three nearest BC axes.
The standard barrel contour is created as a circle with cross-sectional area equal to the average cross-sectional area of the respective barrels (
When registering neuron morphologies to the standard cortex, the BC of the principal column (i.e., containing the neuron's soma) is aligned to the respective BC in the standard model of the vibrissal cortex. The remaining registration steps (i.e., minimizing the squared differences of all BC locations to obtain the optimal rotation angle) are as for generating the standard cortex. This method was chosen to guarantee the highest possible registration accuracy of soma/dendrites/axon within the principal column, at the cost of achieving less precision in surrounding columns (see Results).
The somatotopic layout of the barrel field in rows and arcs can be described as a map from the 2D discrete
Linear functions proved insufficient to describe the non-linear spacing between rows or the curvature of the barrel cortex. Higher-order polynomials showed no obvious improvement in the description of the 3D layout of the vibrissal cortex. The 15 coefficients of the three functions describe different features of the barrel field layout: The linear coefficients
For a numerical description of the 15 coefficients, the
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We thank Bert Sakmann for advice and assistance with pilot experiments; Randy Bruno for supply of biocytin-labeled dendrite and axon morphologies; Stefan Lang and Radoslav Enchev for assistance with pilot registration routines and Hanno-Sebastian Meyer for comments on the manuscript.