## Abstract

Whether vascular distribution is spatially specific among cortical columns is a fundamental yet controversial question. Here, we have obtained 1-μm resolution 3D datasets that cover the whole mouse barrel cortex by combining Nissl staining with micro-optical sectioning tomography to simultaneously visualize individual cells and blood vessels, including capillaries. Pinpointing layer IV of the posteromedial barrel subfield, direct 3D reconstruction and quantitative analysis showed that (1) penetrating vessels preferentially locate in the interbarrel septa/barrel wall (75.1%) rather than the barrel hollows, (2) the branches of 70% penetrating vessels only reach the neighboring but not always all the neighboring barrels and the other 30% extend beyond the neighboring barrels and may provide cross-barrel blood supply or drainage, (3) the branches of 59.6% penetrating vessels reach all the neighboring barrels, while the rest only reach part of them, and (4) the length density of microvessels in the interbarrel septa/barrel wall is lower than that in the barrel hollows with a ratio of 0.92. These results reveal that the penetrating vessels and microvessels exhibit a barrel-specific organization, whereas the branches of penetrating vessels do not, which suggests a much more complex vascular distribution pattern among cortical columns than previously thought.

## Introduction

The neurons and glial cells of the brain receive continuous blood flow that is mediated via neurovascular coupling (Iadecola and Nedergaard 2007; Attwell et al. 2010), which is the fundamental contrast source in widely used functional brain imaging techniques (Logothetis and Pfeuffer 2004; Logothetis 2008; Chugh et al. 2009). The ability of functional brain imaging to distinguish the cortical columns relies heavily on whether the blood in these columns is supplied or drained by a specific vascular module, and a detailed investigation is needed to characterize the vascular distribution among cortical columns, preferably using direct 3D reconstruction and quantitative analysis (Gardner 2010; Hirsch et al. 2012).

Because a one-to-one correlation exists between the whiskers and the distinct barrels in the cerebral cortex (Welker 1971; Simons 1978), the barrel field is an ideal model in which to study the vascular distribution among cortical columns (Woolsey and Van der 1970; Lu et al. 2004). A model of the vascular supply to these barrels in layer IV was previously proposed by Woolsey et al. (1996), which indicated that both the arteries and the veins penetrate the cerebral cortex inside the barrel septa, and that the branches of these vessels stretch into the neighboring barrel hollows. It was hypothesized that blood supply and drainage in these barrels are mediated by a specific vascular module (Cox et al. 1993; Woolsey et al. 1996). Recently, Blinder et al. (2013) built a local cortical angiome and analyzed the vascular architecture in the barrel field. The analysis suggested that the vascular network is closely interconnected with the noncolumnar pattern of blood flow, which is contrary to the observations of Woolsey et al. (1996) and makes the barrel-specific vascular model controversial. This issue was considered to be one of the most important questions in the field of vascular architecture analysis (Gardner 2010; Hirsch et al. 2012). Moreover, Meyer et al. (2010) raised another open question about whether the cellular and vascular architectures are similar across barrels. Both issues require further detailed investigation of the vascular and cellular architecture in the barrel field.

To tackle these problems, there is an urgent need to visualize the barrels and vascular architecture simultaneously. It was demonstrated that Nissl staining could be used to identify the barrels according to the cell density variation (Woolsey and Van der 1970), and a modified Nissl staining was proved to distinguish the cells and blood vessels simultaneously (Ramos et al. 2008; Wu et al. 2014). Moreover, our home-made micro-optical sectioning tomography (MOST) system (Li et al. 2010) enabled whole mouse brain visualization with a 1-μm voxel resolution, which is sufficient to resolve both cells and capillaries. Thus, we combined the modified Nissl staining with MOST to investigate the structural organization of blood vessels among barrels in the mouse barrel cortex. Based on this approach, we recently developed a 3D brainwide cellular and vascular analysis protocol, 3D BrainCV (Wu et al. 2014), which provides a solid technical base for our study.

## Experimental Procedures

### Sample Preparation

Five 8-week-old male mice (4 C57BL/6J, 1 Chinese Kunming) were used in this study. The modified Nissl staining method was detailed in Wu et al. (2014). Briefly, the mice were anesthetized with 1% sodium pentobarbital and then perfused intracardially with 4% paraformaldehyde. The whole mouse brains were removed from the skull and postfixed in 4% paraformaldehyde for 24 h. The brains were then washed in running water for 24 h and immersed with a 0.2% thionine solution for 10 days. The stained brains were washed in running water for 24 h and dehydrated in a graded series of ethanol and acetone, and the brains were subsequently embedded in Spurr resin, which made the brains hard enough for robust thin sectioning. All animal experiments followed the procedures approved by the Institutional Animal Ethics Committee of the Huazhong University of Science and Technology.

During sample preparation, the brains shrunk and we used the linear shrinkage to represent the shrinkage percentage, which was estimated by measuring the volume alteration and could be used to correct the quantitative analysis results (Wu et al. 2014). As a result, the average linear shrinkage was estimated to be 25.9 ± 1.0% in the 5 brains.

### Data Acquisition

The mouse brains were sectioned and imaged automatically using our home-made MOST (Li et al. 2010), with a section thickness of 1 μm and a voxel size of 0.35 × 0.4 × 1 μm. MOST is made up of a microtome, a light microscope, and a time delay and integration charge-coupled device. It simultaneously performs thin sectioning (thickness: 1 μm) and imaging (40×, numerical aperture 0.8). The coordinates of all the image tiles were recorded during sectioning. Benefiting from the high-precision positioning system (programmable precision: 100 nm and feedback accuracy: 20 nm), all the image tiles can be aligned automatically to reconstruct intact 3D brains according to the recorded coordinates.

### Image Processing

#### Preprocessing

The acquired original images were preprocessed using the customized MATLAB (MathWorks, Inc., Natick, MA, USA) software (Ding et al. 2013). Briefly, owing to the nonuniform illumination, the center of the original image tiles is brighter than the marginal region with some periodic noise (Fig. 1a). Along the X and Y axis in each single tile, the pixel intensity was revised by $I′=(h×I)/p,$ where the I and I′ indicate the intensity before and after correction, respectively; p denotes the mean projection along the Y and X axis, and h denotes the corresponding point of a smooth fitting curve of p. After the correction, the background intensity became uniform and the periodic noise was reduced (Fig. 1b).

Figure 1.

Image preprocessing pipeline. (a and b) The images before and after the nonuniform illumination correction show that the pixel intensity becomes uniform and the periodic noises are reduced. The morphology of both the cells and blood vessels that span the strip boundary was well maintained. The scale bar is 20 μm. (c and d) The coronal sections before and after the uneven staining calibration show that the coronal background intensity becomes uniform. The scale bar is 1 mm. (e and f) The background intensity among the coronal sections was adjusted to a constant after block-face correction. The scale bar is 50 μm. The intensity becomes uniform in 3D. (a, b, e, and f) are enlarged views of the region indicated by a white arrow in (d).

Figure 1.

Image preprocessing pipeline. (a and b) The images before and after the nonuniform illumination correction show that the pixel intensity becomes uniform and the periodic noises are reduced. The morphology of both the cells and blood vessels that span the strip boundary was well maintained. The scale bar is 20 μm. (c and d) The coronal sections before and after the uneven staining calibration show that the coronal background intensity becomes uniform. The scale bar is 1 mm. (e and f) The background intensity among the coronal sections was adjusted to a constant after block-face correction. The scale bar is 50 μm. The intensity becomes uniform in 3D. (a, b, e, and f) are enlarged views of the region indicated by a white arrow in (d).

Owing to the uneven staining, the background intensity value in the brain center is higher than that in the surface (Fig. 1c). The background of the coronal sections was estimated by a low-pass filter and subtracted. After calibration, the uniformity of the background intensity was effectively enhanced (Fig. 1d).

There is a slight difference in the background intensity between the neighboring sections in the axial direction (Fig. 1e). The tissue region was roughly binarized by Otsu thresholding, and the background intensity was estimated to be the average intensity, s. Then, the revised intensity of the coronal section pixels was $I′=(128×I)/s,$ where I denotes the intensity before correction. After correction, the background intensity of the coronal sections became consistent (Fig. 1f).

#### Cell Localization

All the cells were vectorized and represented by central points using 3D BrainCV (Wu et al. 2014). Briefly, the images were binarized and then the binary holes were filled by morphological operations and small regions were eliminated by connectivity analysis. Subsequently, a multiscale 3D Laplacian of Gaussian filter was applied to detect candidate seeds. Finally, the seeds in the background and with small volume were eliminated, and the nearing seeds were merged.

The cells could be reconstructed for qualitative assessment (Supplementary Video 1). To perform the quantitative assessment, we compared the detected cells to the manually labeled cells (Supplementary Video 1). Several evenly spaced image stacks with a size of 105 μm × 105 μm × 105 μm were extracted from the pial surface to the white matter, and the inner cells were manually labeled using Amira (Visage Imaging). The manually labeled cells were used as a reference to evaluate the algorithm performance. The autodetected and manually labeled cell centroids with a distance of <10 μm were considered to be matched or correctly detected. The results were represented by recall (eq. 1) and precision (eq. 2). Recall represents the detection ratio of the real cells, and precision represents the correct ratio of the detected cells.

(1)
$recall=number of matching cellsnumber of manually labeled cells$

(2)
$precision=number of matching cellsnumber of automatically detected cells$

#### Vessel Tracing

The blood vessels were vectorized or traced as curved tubes, which are made up of 3D center lines and associated diameters. First, the coronal sections were filtered by a three-dimensional median filter with a size of 3 × 3 × 3 voxels. Secondly, the extracted image stacks were resliced tangentially, and the block-face correction was applied to enhance the local staining uniformity (Fig. 1e,f). Thirdly, an intensity transformation was applied to eliminate cells and tissue background, and only the blood vessels were retained and enhanced (Fig. 2a).

Figure 2.

Schematic representation of the iterative vessel tracing strategy. (a) The maximum intensity projection shows a small interconnected vascular network that includes big and small vessels. The scale bar is 50 μm. (b) Most of the blood vessels were traced (green) using NeuronStudio by the first seed. (c) The traced blood vessels were eliminated using a customized MATLAB program, and the remaining vessels were visualized by a maximum intensity projection. (d) The tracing results were manually edited using Amira, and the redundant branches were deleted to enhance the precision. (e) 3D reconstruction of the final result. The red and green vessels represent the first tracing and the post-tracing result, respectively.

Figure 2.

Schematic representation of the iterative vessel tracing strategy. (a) The maximum intensity projection shows a small interconnected vascular network that includes big and small vessels. The scale bar is 50 μm. (b) Most of the blood vessels were traced (green) using NeuronStudio by the first seed. (c) The traced blood vessels were eliminated using a customized MATLAB program, and the remaining vessels were visualized by a maximum intensity projection. (d) The tracing results were manually edited using Amira, and the redundant branches were deleted to enhance the precision. (e) 3D reconstruction of the final result. The red and green vessels represent the first tracing and the post-tracing result, respectively.

The blood vessels in layer IV of the barrel field were vectorized using 3D BrainCV (Wu et al. 2014). In brief, the images were first binarized, and morphological operations were applied to fill holes. Then, the tracing seeds were automatically localized at the center of the isolated regions that were identified using the pixel connectivity analysis. Subsequently, the blood vessels were identified with curved tubes based on the algorithm of voxel scooping (Rodriguez et al. 2009). Finally, the result was exported to a text file with an SWC format.

For an overview, the complete blood vessels of the barrel field in one brain were traced using a customized pipeline based on NeuronStudio (Wearne et al. 2005) (Fig. 2b). The tracing started from specific points inside the blood vessels, which were manually localized upon the maximum intensity projection (Supplementary Fig. 1a). Benefiting from the interconnectivity of blood vessels, most of the vessels can be traced by the first seed (Fig. 2e). The terminal branches with a length <10 μm were pruned to reduce the tracing error rate. Subsequently, the traced vessels were eliminated by filling black voxels to avoid perturbation (Fig. 2c). Then, the steps of enhancement and seeding were repeated to trace the remaining vessels until all the blood vessels were traced. Finally, the vectorized tracing results were imported to the Lineset Editor of Amira, and the error branches, which were identified by comparing the results with the original images, were manually deleted (Fig. 2d and Supplementary Fig. 1b). The final result was obtained by manual deletion (Fig. 2e).

The tracing results were verified qualitatively using Amira (Figs 2d, 3d, 4, and Supplementary Video 2). To perform the assessment quantitatively, we compared the traced vascular cross-sections with manually labeled cross-sections (Wu et al. 2014). The vascular intercross regions of the cortical slices, which ranged from the pial surface to the white matter, were manually labeled at an equidistant interval of 30 μm (Fig. 3e). The manually labeled results were used as a reference to evaluate the tracing results. The assessment results were represented by recall (eq. 3) and precision (eq. 4). The recall represents the tracing ratio among all the real blood vessels, and the precision represents the correct blood vessels among all the traced vessels. Moreover, the diameter was revised according to the area of the manually labeled regions (Fig. 3e).

(3)
$recall=number of overlap regionsnumber of manually labeled regions$

(4)
$precision=number of overlap regionsnumber of traced regions$

Figure 3.

Simultaneous visualization of cells and blood vessels and the assessment of vectorization. (a) The preprocessed coronal image with a thickness of 1 μm shows the cross-sections of the cells and the vessels in the barrel field. (b) The minimum intensity projection of the image stack in (a) with a thickness of 30 μm. The cortical layers of I–VI were labeled according to cellular density aggregation. The light blue arrows indicate the dense aggregated cells of the barrel walls. (c) The maximum intensity projection of the image stack in (a) with a thickness of 200 μm. The position of some of the penetrating vessels matches that of the barrel walls that are visible in (b). (d) Qualitative assessment of the vessel tracing. The traced center lines were superimposed on the maximum projection of the preprocessed images with a thickness of 100 μm. (e) Quantitative assessment of the vessel tracing. The regions indicated by the red circuits are cross-sections of the tracing result. The light green arrow indicates a spurious vessel, and the yellow arrows indicate blood vessels that were not traced. All the scale bars in (a–e) are 100 μm.

Figure 3.

Simultaneous visualization of cells and blood vessels and the assessment of vectorization. (a) The preprocessed coronal image with a thickness of 1 μm shows the cross-sections of the cells and the vessels in the barrel field. (b) The minimum intensity projection of the image stack in (a) with a thickness of 30 μm. The cortical layers of I–VI were labeled according to cellular density aggregation. The light blue arrows indicate the dense aggregated cells of the barrel walls. (c) The maximum intensity projection of the image stack in (a) with a thickness of 200 μm. The position of some of the penetrating vessels matches that of the barrel walls that are visible in (b). (d) Qualitative assessment of the vessel tracing. The traced center lines were superimposed on the maximum projection of the preprocessed images with a thickness of 100 μm. (e) Quantitative assessment of the vessel tracing. The regions indicated by the red circuits are cross-sections of the tracing result. The light green arrow indicates a spurious vessel, and the yellow arrows indicate blood vessels that were not traced. All the scale bars in (a–e) are 100 μm.

Figure 4.

3D reconstruction of the blood vessels in the barrel field. (a) The blood vessels were reconstructed by superimposing the vectorized result on a direct volume rendering. The size of the white bounding box is 1618 μm × 1082 μm × 870 μm. (b) An enlarged view of the orange box from (a) shows the vascular architecture near 2 barrels. The gray surfaces represent the barrel wall of C2 (left) and C3 (right). The size of the orange bounding box is 360 μm × 406 μm × 707 μm. The vascular diameter in (a and b) was color encoded by the color bar and was set to be half of the estimated value for clear comparison with the direct volume rendering. (c) An enlarged view of the yellow box from (b) shows the detailed local vascular architecture in layer IV. The traced center lines are represented by red curves in the direct volume rendering (white). The size of the yellow bounding box is 100 μm × 100 μm × 50 μm.

Figure 4.

3D reconstruction of the blood vessels in the barrel field. (a) The blood vessels were reconstructed by superimposing the vectorized result on a direct volume rendering. The size of the white bounding box is 1618 μm × 1082 μm × 870 μm. (b) An enlarged view of the orange box from (a) shows the vascular architecture near 2 barrels. The gray surfaces represent the barrel wall of C2 (left) and C3 (right). The size of the orange bounding box is 360 μm × 406 μm × 707 μm. The vascular diameter in (a and b) was color encoded by the color bar and was set to be half of the estimated value for clear comparison with the direct volume rendering. (c) An enlarged view of the yellow box from (b) shows the detailed local vascular architecture in layer IV. The traced center lines are represented by red curves in the direct volume rendering (white). The size of the yellow bounding box is 100 μm × 100 μm × 50 μm.

### Quantitative Analysis

Several statistical parameters that follow previous definitions (Lauwers et al. 2008; Weber et al. 2008; Tsai et al. 2009) were computed to quantify the 3D distribution of the cells and blood vessels (Wu et al. 2014). The cellular density was represented by the total number per unit volume, and the vascular density was represented by both the fractional volume and the total length per unit volume. Based on previous definitions (Lange and Halata 1979; Cassot et al. 2006), the blood vessels with a diameter of <9 μm were classified as microvessels, and the ones with a diameter of >9 μm were classified as big vessels. Moreover, the analysis results were corrected according to the estimated linear shrinkage of the brain sample (Wu et al. 2014).

## Results

### Vectorization and Reconstruction of Cells and Blood Vessels

To investigate the detailed architecture of the barrel cortex, we vectorized the individual cells and capillaries that covered the complete posteromedial barrel subfield in the left hemisphere of a mouse brain. We extracted the image stack according to a mouse brain atlas (Paxinos and Franklin 2001). Benefiting from our modified Nissl staining, both the cells and the capillaries could be distinguished simultaneously and clearly (Fig. 3a–c). The cells and blood vessels were vectorized and were digitally represented by spheres and curved tubes, respectively. The qualitative assessment illustrated that the centroids locate in the cells (Supplementary Video 1), and that the center lines locate in the blood vessels (Fig. 3d). For quantitative assessment, we manually marked 1371 cells and 1959 vascular cross-sections (Fig. 3e), which were used to compare to the vectorized results. As a result, we recalled 88.0% of the cells with a precision of 95.0% and 86.9% of the blood vessels with a precision of 91.7%. Moreover, the estimated vascular diameter was 89% of the manually labeled results.

To directly illustrate the vascular architecture in the barrel field, we reconstructed all the vectorized blood vessels (Fig. 4a,b). The barrels were identified and drawn according to the variation of the cell density in layer IV, which was illustrated by direct volume rendering (Fig. 5a and Supplementary Fig. 1d). Because the septal region is not obvious in the mouse brain (Petersen 2007), we combined the septal region with barrel walls and named the region the interbarrel septa/barrel wall according to a previous definition (Barrera et al. 2013). The reconstruction results directly show that the penetrating vessels preferentially locate in the region of interbarrel septa/barrel walls (Fig. 4b, and Supplementary Fig. 2 and Video 2). Figure 4c illustrates the detailed vascular architecture and the accurate tracing.

Figure 5.

Vascular architecture among barrels in layer IV. (a) A direct volume rendering of layer IV in the barrel field with a thickness of 250 μm at a cortical depth of approximately 570 μm. The standard nomenclature for the barrels that consist of rows A–E and arcs 1–5 was identified according to the variation in the cellular density. The large penetrating vessels are represented by the red dots scattered in the interbarrel septa/barrel wall. The medial–lateral and anterior–posterior axes are indicated. (b) The maximum intensity projection of the image in (a) shows the vascular architecture in layer IV. The scale bar is 200 μm. (c) 3D reconstruction of penetrating vessels and barrels. The barrel walls are represented by gray surfaces. The yellow and red penetrating vessels have branches that extend across neighboring barrels, and the greenish vessels do not. The size of the white bounding box is 1082 μm × 1681 μm × 150 μm. (d) The penetrating vessel manually labeled red in c shows branches that extend across to neighboring barrels (C3 and C4) and a nonneighboring barrel (C5). Note that the trunk of this penetrating vessel locates in the interbarrel septa/barrel wall, and some neighboring barrels (D2 and D3) are not supplied or drained by this penetrating vessel.

Figure 5.

Vascular architecture among barrels in layer IV. (a) A direct volume rendering of layer IV in the barrel field with a thickness of 250 μm at a cortical depth of approximately 570 μm. The standard nomenclature for the barrels that consist of rows A–E and arcs 1–5 was identified according to the variation in the cellular density. The large penetrating vessels are represented by the red dots scattered in the interbarrel septa/barrel wall. The medial–lateral and anterior–posterior axes are indicated. (b) The maximum intensity projection of the image in (a) shows the vascular architecture in layer IV. The scale bar is 200 μm. (c) 3D reconstruction of penetrating vessels and barrels. The barrel walls are represented by gray surfaces. The yellow and red penetrating vessels have branches that extend across neighboring barrels, and the greenish vessels do not. The size of the white bounding box is 1082 μm × 1681 μm × 150 μm. (d) The penetrating vessel manually labeled red in c shows branches that extend across to neighboring barrels (C3 and C4) and a nonneighboring barrel (C5). Note that the trunk of this penetrating vessel locates in the interbarrel septa/barrel wall, and some neighboring barrels (D2 and D3) are not supplied or drained by this penetrating vessel.

### Barrel-Specific Vascular Distribution

Compared with other cortical layers, the neurons in layer IV were activated the earliest, strongest, and most specifically by whisker stimulation (Woolsey et al. 1996; Vanzetta et al. 2004), which suggested that both the energy consumption and the blood supply among the barrels may be specific in layer IV. To evaluate this hypothesis, we examined the cellular and vascular distributions in layer IV specifically in the mouse brain (n = 5).

To directly observe the vascular distribution among the barrels, we extracted the images in layer IV and vectorized the blood vessels in the left hemisphere. Layer IV was localized by direct volume rendering, which shows the barrels based on cellular density variation in barrel hollows and the interbarrel septa/barrel wall (Fig. 5a and Supplementary Fig. 2). As a result, both the maximum intensity projection (Fig. 5b) and the 3D reconstruction (Fig. 5c,d) of layer IV in the barrel field directly revealed the vascular distribution among the barrels. A total of 224 penetrating vessels in the mouse brains (n = 5) were traced semiautomatically using NeuronStudio (Wearne et al. 2005; Fig. 5c and Supplementary Fig. 1a). By direct 3D reconstruction (Fig. 5c), we found that 75.1 ± 8.5% of the penetrating vessels in layer IV localize in the region of the interbarrel septa/barrel wall (n = 5; Supplementary Table 1). To examine whether this is a phenomenon of random distribution, we built a distance map of the septal region center (Supplementary Fig. 3) and randomly relocated the penetrating vessels within the barrel field (simulation time = 100, n = 1). Then, the biological distribution was compared with a random distribution, and a highly significant difference was found (P < 10−8, t-test).

Furthermore, we also observed that 30.0 ± 11.7% of the identified penetrating vessels had branches that stretched across neighboring barrels (n = 5; Supplementary Table 1). Moreover, 40.4 ± 7.7% of the identified penetrating vessels have nonuniform branching, which means that the branches of the penetrating vessels do not cover all the neighboring barrels (n = 5; Supplementary Table 1). For instance, a single representative penetrating vessel that is localized in the barrel septa was manually labeled section by section and reconstructed (Fig. 5d). It supplied blood to or drained blood from not only neighboring C3 and C4 but also a nonneighboring barrel of C5. Interestingly, no branch was found to stretch into neighboring D3 and D4.

To systematically analyze the detailed distribution variety of both big and small vessels, we computed the cellular and vascular density map in layer IV (Supplementary Fig. 4). As expected, cells clustered more densely in the barrel walls than in the barrel hollows (n = 1; Supplementary Fig. 4a). On preliminary analysis, the vascular length density map seemed to be mismatching with the barrels (Supplementary Fig. 4b). However, a detailed quantitative analysis suggested a potential matching (n = 5). We computed the length density of the microvessels and big vessels separately in both the barrel hollows and the interbarrel septa/barrel wall (Supplementary Table 2). The results showed that the length density of the big vessels in the region of the interbarrel septa/barrel wall overwhelms the density in the barrel hollows with a ratio of 3.07 ± 0.95, and the density of microvessels in the interbarrel septa/barrel wall is significantly lower than that in the barrel hollows with a ratio of 0.92 ± 0.03 (Fig. 6). To evaluate this observation statistically, we tested the hypothesis of uniform distribution (the density in the interbarrel/barrel wall equals that in the barrel hollows) by using a t-test, and the results show that the length densities of big vessels and microvessels are significantly nonuniformly distributed (P < 0.01).

Figure 6.

Density profiles of the cells and blood vessels inside the barrel hollows. The cellular density profiles were grouped by arcs (a) and rows (b). The microvascular length density profiles were also grouped by arcs (c) and rows (d). The cortical layers of layer IV in (a–d) were identified based on the cellular density profile (a and b).

Figure 6.

Density profiles of the cells and blood vessels inside the barrel hollows. The cellular density profiles were grouped by arcs (a) and rows (b). The microvascular length density profiles were also grouped by arcs (c) and rows (d). The cortical layers of layer IV in (a–d) were identified based on the cellular density profile (a and b).

### Similar Architecture of Barrels

To evaluate the similarity of the cellular and vascular architectures across barrels (Meyer et al. 2010), we compared the cellular and vascular density profiles along the radial cortical depth in the barrel field (n = 1). The barrels were grouped as either arcs or rows, and the cellular and vascular densities were computed inside the barrel hollows. The linear correlation values were measured using a two-tailed Spearman correlation coefficient with SPSS (SPSS, Inc.). The cellular density (Fig. 6a) (r > 0.81, P < 10−24) and the length density of the microvessels (Fig. 6c) (r > 0.88, P < 10−33) were not significantly different between the pairwise arcs of 1–5. The distribution of the cellular density (Fig. 6b) (r > 0.92, P < 10−41) and the microvascular length density (Fig. 6d) (r > 0.93, P < 10−44) were also not significantly different between the pairwise rows of A–E. In a word, the quantitative analysis reveals that the cellular and vascular distributions are significantly similar across the barrels.

## Discussion

The main findings are as follows: (1) the penetrating vessels in layer IV preferentially localize in the interbarrel septa/barrel wall, whereas microvessels cluster in the barrel hollows; (2) some branches of the penetrating vessels extend across the neighboring barrels and provide long distance blood supply or drainage; (3) some penetrating vessels supply blood to or drain blood from some but not all neighboring barrels. Moreover, we also demonstrated quantitatively that the cellular and vascular configurations in the barrel hollows are similar across barrels.

Traditional observations of the cellular and vascular distributions in layer IV were based on two-dimensional histology and optical imaging techniques with a limited imaging depth and resolution (Cox et al. 1993; Woolsey et al. 1996). Benefiting from the large-scale (Figs 4a and 5a) and high-resolution (Fig. 3a–c) imaging capability of MOST, our direct 3D reconstruction and quantitative analyses provided a more direct visualization and better precision of both the cellular and the vascular architectures. Moreover, the image processing successfully corrected the image distortion, and the vectorization of both the cells and the blood vessels was evaluated to be accurate both qualitatively (Figs 3d and 4, and Supplementary Videos 1 and 2) and quantitatively (Fig. 3e and Supplementary Video 1), which provides a solid foundation for further analysis.

Figure 3c illustrates the continuous small blood vessels with little breaks, which suggest that there is little collapse during sample preparation. Furthermore, the small amount of collapse could be considered evenly distributed without specific distribution among the barrels and should have little effect on our conclusion.

However, the techniques still have some limitations: (1) the brains must be removed from the skull and embedded in resin to ensure adequate hardness for robust thin sectioning; (2) the brain shrinkage may effect on the accuracy of quantitative analysis even though the linear shrinkage was estimated to correct the analysis results; and (3) the manual operations are labor-intensive and time consuming, which limits the sample number to be studied.

By direct 3D reconstruction and quantitative analyses, our results show that big penetrating vessels preferentially localize in the interbarrel septa/barrel wall, which is in agreement with previous observations of Woolsey and his colleagues (Cox et al. 1993; Woolsey et al. 1996), but differs from the results of Blinder et al. (2013). Blinder et al. (2013) localized the penetrating vessels in the pial surface (150 μm thick), which is not deep enough to reach layer IV (∼500 μm deep). The penetrating vessels were implicitly assumed to be perfectly straight and perpendicular to the pial surface, and the location of the superficial penetrating vessels was assumed to perfectly match the location in layer IV. Here we argue that even a small angle of deflection would greatly affect the results. Supplementary Figure 5 illustrates that the penetrating vessels could have a deflection of approximately 5.3 ± 3.5°, which may lead to a mismatch of approximately 46 μm. Considering that the size of the barrels is approximately 100 μm (Woolsey and Van der 1970; Fox and Woolsey 2008), a mismatch of 46 μm could move one penetrating vessel from the region of the interbarrel septa/barrel wall to the barrel centroid, which would lead to a conclusion of random distribution. Additionally, we noted that some penetrating vessels are not straight and may alter the mapping locations in layer IV. Furthermore, some penetrating vessels supply or drain only the superficial layers and do not penetrate to layer IV, which was considered to be a classification metric of penetrating vessels (Duvernoy et al. 1981; Weber et al. 2008). The penetrating vessels in the superficial layers may be erroneously mapped to layer IV by direct perpendicular matching (Blinder et al. 2013). In our results, the penetrating vessels were directly traced in layer IV without additional mapping. As a result, we found a great number of the penetrating vessels (75.1%) localized in the region of the interbarrel septa/barrel wall. The quantitative analysis results also showed a significant distribution bias. Thus, we argue that the penetrating vessels in layer IV of the barrel field preferentially localize in the region of the interbarrel septa/barrel wall, which suggests a barrel-specific distribution.

By quantitative analyses, our results suggested a slightly higher density of the microvessels in the barrel hollows than that in the interbarrel septa/barrel wall (Fig. 6c and Supplementary Table 2), which is also in agreement with the previous observations of Woolsey and his colleagues (Cox et al. 1993; Woolsey et al. 1996). Although Blinder et al. (2013) reported a highly interconnected network with a noncolumnar pattern, our results may still be consistent with theirs. In contrast to our vascular density, Blinder et al. (2013) examined the graph–theoretical connectivity of the capillary bed among the barrels. Our results suggest that the density of microvessels is slightly higher in the barrel hollows than that in the interbarrel septa/barrel wall. In such circumstances, the microvessels may still form a highly interconnected network.

According to our results, the specific distribution of big penetrating vessels and microvessels among barrels is consistent with their function. The ascending thalamocortical input from the ventral posterior medial nucleus clustered in the barrel hollows and formed a cluster of synapses (Logothetis and Pfeuffer 2004), which is highly energy demanding (Attwell and Laughlin 2001). Interestingly, similar vascular distribution patterns were also observed among the blobs of the visual cortex in both the squirrel monkey brain (Zheng et al. 1991) and the macaque brain (Keller et al. 2011). Thus, the columnar distribution pattern of big penetrating vessels and capillaries may potentially be common among the cortical columns of mammalian brains.

The widely used hemodynamic-based functional brain imaging, such as functional magnetic resonance imaging, measures blood volume, flow and oxygen saturation as a surrogate indicator of local neuronal activity, and generates a distorted map of neuronal activity (Gardner 2010). Previous studies showed that the stimulation of a single principle whisker could result in an instant corresponding neuronal activity and dilation of the capillaries (Sheth et al. 2004; Peppiatt et al. 2006), which concomitantly increases the blood supply (Petersen 2007; Alonso et al. 2008) in that whisker's corresponding barrel (Moskalenko et al. 1996; Yang et al. 1996). Blinder et al. (2013) also demonstrated that intrinsic optical signals follow columnar organizations. Thus, the functional brain imaging results are in good agreement with our anatomical results. Based on our observations, the clustering capillaries in barrel hollows may directly enhance the hemodynamic signals detected by functional brain imaging, which results in a barrel-specific functional activity map. The barrel-specific penetrating vessels may also regulate the barrel-specific blood flow at the level of branches. Therefore, our observations may provide an anatomical basis by which cortical columns can be distinguished using functional brain imaging (Kim et al. 2000; Sheth et al. 2004; Vanzetta et al. 2004; Gardner 2010; Blinder et al. 2013).

Furthermore, we found that some branches of penetrating vessels stretch into nonneighboring barrels. This lack of restriction to neighboring barrels suggests a potentially broad range of regulation. This observation may be consistent with the random model proposed by Blinder et al. (2013). Blinder et al. (2013) also found that the intrinsic optical signal returned to baseline approximately 2 barrels away, which is also consistent with our anatomical result. Regarding the hypothesis of vascular module (Woolsey et al. 1996), if they exist, our results suggested that the modules may be perfused or drained from a long distance by a penetrating vessel. It was reported that the dilation of penetrating vessels, which correspond to the stimulated barrel, could induce a large areal functional representation that includes nonneighboring barrels in an appropriate time range (Brett-Green et al. 2001; Masino 2003; Frostig et al. 2008). The structure observed in our study is consistent with these functional observations and provides anatomical support. In addition, we found that some penetrating vessels do not connect to all the neighboring barrels, which suggest an inhomogeneous functional representation. The evaluation of this inhomogeneity necessitates further detailed high-resolution functional imaging.

Our quantitative results of the vascular distribution at the whole mouse barrel cortex may help further understanding of the voltage sensitive dye experiments of the rodent cerebral cortex especially in whisker barrels in the last 20 years (Tanifuji et al. 1994; Kleinfeld and Delaney 1996; Petersen and Sakmann 2001; Lippert et al. 2007; Lustig et al. 2013). They may suggest that the cross-barrel branching of penetrating vessels related to initial activation which is focal in layer 4 but subsequently spreads horizontally in layers 2/3, and that the vertical distribution of microvessels and penetration vessels correlated to the whisker specific response that is confined to a single barrel but quickly, within 20 ms, spreads to adjacent barrels and beyond. We expect further correlated experiments and data analysis for better understanding of the brain function.

Moreover, we examined the detailed 3D cellular and vascular distribution in the barrel hollows across the complete cortical depth, which provides direct systematic evidence for the similarity hypothesis proposed by Meyer et al. (2010). The anatomical similarity among the barrels we found is reminiscent of the functional similarity of barrels. Every principal barrel in the barrel field connects with unique facial vibrissae and forms a major channel to collect information from the surrounding environment. The whisking and sensing function is similar among both the facial vibrissae and the barrels (Petersen 2007), and this anatomical similarity may be a fundamental basis of the functional similarity, which forms a bridge between the brain structure and function.

## Conclusion

The direct 3D reconstruction and quantitative analyses in layer IV of the barrel cortex show that the penetrating vessels preferentially locate in the interbarrel septa/barrel wall (75.1%) rather than the barrel hollows. The length density of microvessels in the interbarrel septa/barrel wall is lower than that in the barrel hollows with a ratio of 0.92. Among them, the branches of 59.6% of the penetrating vessels reach all neighboring barrels, whereas 40.4% only reach part of them. The branches of the other penetrating vessels extend beyond the neighboring barrels, which may provide cross-barrel blood supply or drainage. Furthermore, we found a highly similar architecture of cells and blood vessels among the barrels along the cortical depth. The above results demonstrated that the penetrating vessels and microvessels characterize a barrel-specific organization, whereas the branches of penetrating vessels do not, which suggests a much more complex vascular distribution pattern among cortical columns than before.

## Supplementary material

Supplementary material can be found at: http://www.cercor.oxfordjournals.org/.

## Funding

This work is supported by the National Natural Science Foundation of China (grant nos 81171067, 61102122, and 61121004), Ph.D. Programs Foundation of Ministry of Education of China (grant no. 20110142130006),Wuhan Sci-Tech Project (grant no. 2013010501010116), 985 project, and the seed project of WNLO.

## Notes

We thank T. Xu and S. Zeng for helpful discussions on the manuscript, B. Xiong, Y. Meng, and Y. Li for assistance with manual labeling. Conflict of Interest: The authors have declared that no competing interests exist.

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## Author notes

Jingpeng Wu and Congdi Guo contributed equally to this work.