1.

Introduction

The perspective of imaging tubular structures associated with fibers,¹ vascular structures,² or roots³ is relevant in many biomedical contexts: development, tissue remodeling, physiology, etc. However, even if many studies have considered imaging local vessels, very few have tackled the complete reconstruction of very large volumes.^4–9 One motivation for aiming to perform such microvascular networks reconstruction is the modeling of blood perfusion^7–9 to decipher supracellular level organization from the analysis of the microvascular network^7,10 and to gain a global understanding of tissue structure/function physiology as opposed to local analysis at the cellular scale. Vascular structures provide nonlocal (graph-based) structural information, directly relevant to perfusion and metabolic exchanges, for which a tissue-scale computerized analysis can bring significant understanding to tissue functions. Going from fibers/tubular shapes in images to vascular tubes necessitates skeletonization processing. Many skeletonization methods have been proposed (cf., Refs. 11 and 12 for reviews) based on various techniques such as vessel enhancement filters, region-growing approaches, active contour centerline-based methods, stochastic frameworks using particle filters, and Markov marked point processes. Among these, homotopy preserving skeletonization methods provide very satisfactory results^10,13,14 when applied to isotropic voxels imaging such as x-ray tomography. Nevertheless, when dealing with nonisotropic imaging resulting from optical microscopy, one has to reconsider the entire set of workflow associated with image treatments to evaluate the reliability and sensitivity of the vessel’s segmentation.

One significant difficulty of LSFM is controlling illumination light scattering and absorption, whose effects can immensely degrade image quality in depth and widely depend on the shaping of the light sheet. Many techniques have been developed to compensate for laser light-sheet scattering, such as resonating mirror,¹⁵ multiview deconvolution,^16,17 structured illumination,¹⁸ and adaptive optics.¹⁹ Another important issue in LSFM is isotropic imaging because isotropic voxels are of tremendous assistance for reliable quantification and segmentation of spherical (e.g., cells and nucleus) or cylindrical (e.g., vessels and fibers) objects. Light-sheet fluorescence microscopy (LSFM) is an emerging and rapidly growing field where many variants are currently developed.^20,21 Currently, major efforts are applied to image large samples, in areas ranging from multicellular organoids/spheroids,¹⁷ whole organisms at the embryo level,^22,23 whole mount mammalian tissues,¹ and plants.^20,24 The segmentation of large vascular networks resulting from light-sheet imaging has rarely been performed and, to our knowledge, the quantification of the image analysis workflow accuracy associated with LSFM three-dimensional (3-D)-images applied to the blood vessel challenge has not been studied yet.

The aim of this contribution is to analyze the impact and benefits of multiview deconvolution LSFM for a reliable and quantitative 3-D reconstruction of fiber/vascular networks. We describe how large-field-of-view multiview LSFM imaging and deconvolution, performed on images acquired at low magnification, can be used to provide highly accurate reconstruction and segmentation of the entire vascular network of large tissue volumes. We focused our attention primarily on addressing the aspects related to multiview deconvolution and quality assessment of the resulting vascular segmentation.

2.

Materials and Methods

The imaging and analysis workflow follows steps given in Fig. 1(d). Tissue preparation and LSFM instrument are described in Sec. 2.1. Appendices B and C provide details about the registration and deconvolution steps.

Fig. 1

(a) Photography of a cleared mice inguinal adipose tissue. The red square indicates where LSFM imaging has been performed. (b) Illustration of a $1\text{-}{\mathrm{mm}}^3$ segmented and reconstructed vascular network sample corresponding to the square region shown in (a). The network is composed of about 42,000 segments, 22,000 bifurcations, and 1,063,000 segment elements. Segments are scaled and colored according to their estimated diameter (from cold color for small ones to hot color for large ones). (c) Schematic representation of the LSFM instrument showing, not at scale, the glass chamber, the Agarose block (in cyan) where the sample is embedded, the cylindrical lens (blue), and the slit to adjust the light-sheet geometry. (d) Flowchart of the imaging, postprocessing, and analysis workflow. (e) Maximum intensity projection ($150\text{-}\mu \mathrm{m}$ depth) of a small portion at full XY width (1 mm) of one view. (f) $X-Z$ profile of the centerline (dashed) in (e). (g) $X-Y$ and axial profile of a small vessel oriented in $X-Y$, axial profiles are represented perpendicular (A–B) and along the vessel axis (C–D). (h) Ratio of the Gaussian FWHM of $n=27$ vessels distributed across the width of the data sets (blue data points) to show consistent light-sheet geometry across the width of the image yielding an average isotropy of detection $X-Y$ versus $Z$ of about 6.25. The same ratio is measured on fluorescent beads and yields (red data points) 7.9 ($n=10$) in the center and 8.8 ($n=10$) on the edge of the image. Scale bars (g) and (h) $10\mu \mathrm{m}$. (i) Image of a glass fluorescent bead laterally and axially, scale bar $\mu \mathrm{m}$. (j) Closer view maximum intensity projection of an XY-plane of $100\mu \mathrm{m}$ $Z$-depth; scale bar: $40\mu \mathrm{m}$. (k) The vascular network visualized with tubular structures in Avizo (FEI) software extracted from (a) with four-views reconstruction; the color scale encodes vessel diameter. (l) Similarly, the vascular network extracted and compared for four-views and one-view data sets: shared segment elements are in blue, black segment elements are specific to the one-view-based network, and red segment elements are specific to the four-views-based network. The four-views network contains several segments elements important for the topology and the permeability (in red), which are not present in the one-view network; moreover, the one-view network contains artifact segment elements (in black), which do not contribute to the permeability of the vascular network.

2.3.

Vessel Segmentation and Skeletonization

Deconvolved images are thresholded and the resulting binary images are then used for network extraction. The spatial graph representing the vascular network is built up according to the vectorization of the binary image as described in Ref. 29. The vessels’ center lines are extracted with an appropriate homotopy preserving skeletonization method³⁰ used and described in Ref. 29. (Avizo^© FEI software has been used for visualization only, not for any of the hereby described image treatment.) Our experience with homotopy preserving skeletonization³⁰ (a special class of region-growing approach) has provided reliable and robust results.^10,14 The graph $G=(V,E)$ is then created, where $V$, the set of nodes, is extracted from the branching-voxel and end-voxel, and $E$, the set of edges, is extracted between connected node-voxels of the vessel skeleton. An edge is composed of a chain of center line voxels comprised between two nodes. In the following, we will refer to segment and segment element instead of edges and center line voxels as shown in Fig. 2(a). Vessel radii are estimated following Ref. 14: for each segment element and node, a sphere is expanded until 10% of its volume is left outside the vessel shape in the binary image. Figure 1(b) shows the network extracted from Fig. 1(a) with tubular-like visualization in Avizo^© FEI software.

Fig. 2

(a) Network notations and bifurcation angles definitions. (b) Illustration within one bifurcation of the skeletonization result. (c) Illustration of the comparison between two networks: the reference graph (in blue) is composed of segment element (small bullets) paired with the ones of the segmented graph in red. The pairing is materialized with gray cylinders, the diameter of which is scaled according to the associated pairing error using the minimum cost flow algorithm.

3.

Results

We performed light-sheet imaging of a fluorescently stained blood vessels network in cleared mouse adipose tissue, as shown in Fig. 1.

Two complementary strategies are possible for imaging vascular networks in large tissue volumes with LSFM: (i) using an axially confined light sheet (i.e., very thin) with tiled imaging of small FOVs or (ii) using an axially “thicker” light sheet at a large FOV. Depending on the detection system and its numerical aperture (NA), lateral resolution may be acceptable over a wide range of magnification to opt for the lowest number of tiles or FOVs, thereby avoiding extensive mosaic stitching. However, the axial extent of the light sheet required to homogeneously illuminate a large FOV may increase the anisotropy of detection in the XY-sheet plane versus the $Z$-direction, perpendicularly to the sheet plane. Higher magnification with thinner light-sheet illumination will bring more isotropic detection and would be a preferred instrumental choice. Nevertheless 3-D stitching may be challenging on whole mount organs, both for the intensity discontinuity between neighbors’ positions and for colinearity of light sheet. The required XY-movement may bring troublesome axial discontinuities in the data set. Ideally, imaging at the lowest magnification would save in acquisition complexity, time, and data storage. In the present contribution, we focus our interest on the image processing of the second strategy, for which multiview deconvolution can be used for the enhancement of image quality in large image data sets.^16,26

3.1.

Multiview Deconvolution

Figure 3(b) shows the resulting deconvolved images with the tuned parameter for the $n$-views configuration ($n\in [1:4]$). The intensity profiles plotted in Fig. 3(c) show how the voxel isotropy is improved considering that the transverse section of the vessel, where the profiles were extracted, should be circular. Note that the one-view deconvolution configuration delivers only an intermediate recovery of the $Z$-isotropy. Also, Fig. 3(c) (first, third, and fourth plots) displays one example of nonperfect centering of profiles following registration, which is further discussed at the end of Sec. 4. Finally, Figs. 3(b) and 3(c) show that the TV regularization perfectly prepares images for segmentation by favoring high gradient and homogeneous regions, so a simple thresholding of the intensity then provides an appropriate vessel segmentation.

Fig. 3

Improvement of the vascular network imaging isotropy from using multiview deconvolution. (a) Illustration of raw isotropic $128\mu {\mathrm{m}}^2$ orthogonal plans extracted at the same spot with four different views (imaging angles equal to $-45$, 0, 45, and 90 deg). Views at $-45$, 45, and 90 deg are registered based on view at 0 deg. (b) Illustration of the corresponding multiview deconvolved isotropic $128\text{-}\mu {\mathrm{m}}^2$ orthogonal plans obtained according to $n$-view configurations with $n=1$ (using view at 0 deg), $n=2$ (using views at 0 and 90 deg), $n=3$ (using views 0, 45, and 90 deg), and $n=4$ (using views $-45$, 0, 45, and 90 deg), $\mathrm{RLTV}\text{iteration}=25$, and $\mathrm{TV}=0.01$ (cf., Appendix C for more information). (c) $X$ (P1) and $Z$ (P2) intensity profiles extracted at the red-cross spot (XZ-plans) from the raw images [for the four angles in (a)] and the $n$-view deconvolved images [with $n$ from 1 to 4 in (b)].

3.2.

Accuracy on Ground Truth Data

Precision–recall curves for voxel matching and segment-element matching are plotted in Figs. 4(a) and 4(b) for the $n$-views configurations. Points of the curves are obtained by applying various threshold values to the deconvolved images resulting in binary images and then vascular graphs (Sec. 2.3). An ideal case would be a precision [i.e., the ratio of false positives (FP)] equal to the recall (i.e., the ratio of misses) and equal to 1 (i.e., no FP and no misses). From the two metrics, it is clear that four views outperform all other configurations in any cases. However, three views and two views provide close results, much better than the one-view configuration. Similar conclusions can be drawn from other ground truth data, showing a significant improvement from the $n=1$ view to a larger number of views ($n>1$).

Fig. 4

Left column: precision–recall (cf., Appendix A.1 for definitions) curves for (a) voxels matching and (b) segment-elements matching resulting from segmentation and network extraction, with optimal deconvolution parameters, of ground truth data set #1. Right column: comparison of several accuracy metrics resulting from our network segmentation workflow on three ground truth data sets according to $n$-views reconstructions. Parameters used (cf., Appendix C for more information): (c1) #1 $\mathrm{RLTV}\mathrm{it.}=30$ $\mathrm{TV}=0.001$, (c2) #2 $\mathrm{RLTV}\mathrm{it.}=35$ $\mathrm{TV}=0.001$, and (c3) #3 $\mathrm{RLTV}\mathrm{it.}=60$ $\mathrm{TV}=0.001$.

Figure 4(c) shows the complete set of accuracy metrics resulting from the segmentation of ground truth samples #1, #2, and #3 and for $n$-views configurations ($n\in [\mathrm{1,4}]$). For the three low-level metrics [voxel matching ($F$-score vox.), segment-element matching ($F$-score el.), and diameter error] as well as for the graph similarity, a clear trend stands out for the three samples: the best score, resp. the lowest error, is found for the four-views configurations and decreases, resp. increases, for the three views, two views, and finally reach the lowest score, resp. highest error, for the one-view configurations. Hence, here again, the one view ($n=1$) provides much lower results than $n>1$ regarding these metrics. It is interesting to mention that the diameter error from ground truth is, respectively, found equal to 35%, resp. 24%, for $n=1$, resp. $n=4$. This could appear quite accurate, but one has to bear in mind that perfusion is very sensitive to local vessel diameter, as given by the fourth power dependence of the local conductance. This is why the conductance error from ground truth is found much higher in whole sets. This is also why an accurate representation of vessels is a key methodological point for modeling tissues since a reliable quantitative estimate of conductance properties is a prerequisite for modeling. However, high-level accuracy metrics, i.e., the conductance and the permeability error, reveal a more mitigated trend. Concerning the conductance, the four-views configuration provided, again, the lowest error compared with the others for sample #2, which is not the case for samples #1 and #3, where no clear trend emerges. Concerning the permeability error, it is interesting to note that the lowest error results from the four-views configuration only for sample #3 (with a clear trend), whereas it remains unstable for samples #1 and #2.

3.3.

Synthetic Data

We take advantage of the synthetic network to monitor controlled degradation and evaluate how $n$-views perform on the network extraction regarding to the six accuracy metrics in the presence of increasing additive Gaussian noise [illustrated in Appendix D, Fig. 8(c)] and Poissonian noise. Figure 5(a) shows the $n$-views configuration score/error evolution for each metric according to Gaussian noise level [peak signal-to-noise ratio (PSNR)]. Similar results can be found in Fig. 5(b) for Poissonian noise distribution.

Fig. 5

Sensitivity of vascular network extraction to additive (a) Gaussian noise and (b) Poissonian noise evaluated using six different accuracy metrics on our synthetic network with $n$-views reconstructions ($n\in [\mathrm{1,4}]$) (cf., Appendix A for more information about metrics).

Again, a clear trend stands out for the three low-level metrics (the voxel matching $F$-score, the segment-element matching $F$-score, and the diameter error) as well as the high-level graph similarity: the four-views configuration outperforms the three others with highest score/similarity and resp. lowest error, whichever noise level applied. Similarly, three views outperform two views, and two views outperform one-view configuration. However, even if the conductance metric shows a similar hierarchy at a low noise level, it does not display a clear trend any more for noisy images. Concerning the permeability error, even if the curves are noisy, we found a similar trend as previously observed (cf., Sec. 3.2) for real data. One view gives the highest error and the three other configurations give much lower, but quite similar, errors with a slight advantage for four views. Hence, it is interesting to crop-up the statement that $n>1$ views are generally much better than one view for vascular network segmentation with a variable advantage of increasing the number of view $n$.

3.4.

Vascular Network Analysis of Biological Tissue

When applied at a large scale, the hereby proposed workflow allows the extraction of important structural properties of vascular networks. Figure 1(b) shows the vectorization of a $1\text{-}{\mathrm{mm}}^3$ subarea of the vascular network of the inguinal adipose tissue in mice. It reveals a particularly high vascular density [quantified in Fig. 6(b)] compared with other tissues such as brain¹⁴ or muscles. Figure 6 also shows characteristic bifurcation angles according to the convention defined in Fig. 2, as well as the segment length and segment-element radius distributions. Further statistics of interest, including several related to blood microcirculation in the tissue, are provided in Appendix G.

Fig. 6

Statistics of interest calculated on the vascular network extracted from the large mice tissue sample presented Fig. 1(b). (a) Bifurcation angles according to convention presented Figs. 2(a) and 2(b) relative local vascular volumic density (volume fraction of vessels) computed into $100\text{-}\mu \mathrm{m}$ voxels, (c) radius of segment elements, and (d) segment length. Vertical dashed lines represent mean values.

4.

Discussion

Optical imaging of large-scale volumes is not easily achievable with conventional optical microscopy. For high-resolution fluorescence data collection, confocal microscopy is still the gold standard. However, its ability to image in very large volumes will suffer drastic axial resolution degradation together with the working distance of the lens, which is required to target a specific depth. In general, the deeper the target is, the lower the NA is and, hence, the lower the axial resolution is. 3-D deconvolution techniques may somehow recover part of this resolution degradation; however, the typical deterioration of signal-to-noise ratio (SNR) at acute depth will not play in favor of this aim. Multiphoton microscopy, on the other hand, is typically limited to 1 mm in depth for in vivo experiments, and, even if sample clearing can improve this value, low NA lenses drastically reduce the efficiency of excitation of the technique. On the contrary, the accepted advantages of LSFM are to enable large working distances and high SNR and to offer sample mounting solutions (e.g., sample rotation) that are not accessible in conventional microscopy (e.g., confocal microscopy).

Here, we performed light-sheet imaging of a fluorescently stained blood vessels network in cleared mouse adipose tissue with enhanced anisotropic illumination (i.e., much worse axially) to probe the benefit for vessel segmentation of multiview fusion with deconvolution at low magnification range, and thereby show that high-accuracy blood vessel imaging can be performed without stringent conditions on the need for acquisition of tiled mosaics.

We estimate theoretically that the ratio between the objective lens lateral resolution (about $1.83\mu \mathrm{m}$ calculated for a $6.72\times$ magnification, in air, with an estimated NA of 0.2 and classical equation for full lateral extent $0.61\times$ wavelength/NA) and the light-sheet axial extent (set experimentally and measured in air to have a FWHM of about $20\mu \mathrm{m}$, cf., Sec. 2) gives an anisotropy factor of about 9.15. We confirmed this factor experimentally by reporting a characterization of optical resolution with glass beads, yielding from 7.9 to 8.8 [Fig. 1(i)]. Of note, we used glass fluorescent beads to enable imaging in BABB, providing a solution to the well-known problem of latex/polymer beads, which dissolve in this corrosive clearing medium. Finally, we empirically estimate this factor by measuring in the $X-Y$ and $Z$ diameters of the smallest vessels in our raw data sets to be around $6.25\pm -1.3\mu \mathrm{m}$ [cf., Fig. 1(h)], consistently lower because the smallest blood vessels are not subdiffraction objects for this range of magnification.

We were able to show that this factor can be reduced by multiview fusion to yield restored data with an anisotropy factor, i.e., the ratio between axial and lateral resolution, measured closer to 1 [as shown in Fig. 3(c)] even with only two views.

The aim of this contribution is to analyze and evaluate how multiview deconvolution improves the voxel isotropy in 3-D LSFM images for large-scale vascular network extraction. Vascular networks are extremely complex 3-D objects, for which an accurate evaluation of local structural properties is relevant to biological function. Hence, it is important to provide a systematic comparison of the influence of the multiview deconvolution steps and parameters on the subsequent reconstruction precision. Furthermore, the capabilities enabled by recent 3-D LSFM images at the centimeter scale open the road for the exploration of very large tissue volumes, for which a large light-sheet axial extent helps to acquire amounts of data. Our approach, therefore, consisted of working at low magnification to probe the ability to restore highly anisotropic illumination conditions with multiview deconvolution.

In conditions that are experimentally simple to set (at low magnification with air lenses), the potential for image improvement by multiview postprocessing is much larger than at high magnification as the starting anisotropy of XY-detection versus $Z$ illumination (i.e., light-sheet thickness) is greater, therefore, potentially simplifying the image acquisition procedure. Hence, there is a need for the evaluation of multiview deconvolution numerical costs and benefits for segmentation of large data/volume analysis.

We investigated six different metrics of interest for the analysis of low- to high-level structural properties of vascular networks. Using various ground truth data, we systematically quantified how structural, geometrical, and topological ingredients of vascular vessels are retrieved. First, we found that low-level metrics related to voxel, segment element, and diameter display a clear hierarchical quality response with the number $n$ of views, i.e., four views > three views > two views > one view. These results confirm the interest of multiview deconvolution procedures as they permit reaching high-confidence scores, as shown by PR curves of Figs. 4(a) and 4(b). Second, the results given by high-level metrics, especially the permeability, are found to be much less sensitive to the number of views. It shows a decreasing improvement, which could already be observed for low-level metrics in Figs. 4(a) and 4(b). This observation is related to the functional role of vascular networks. Even if, as previously mentioned, small structural local information, e.g., vessel diameters, are important to estimate accurately, they are not everywhere crucial to blood perfusion. When integrated into the network complexity, some vascular segments might not play an important role for perfusion [see Fig. 1(k), the segment difference between one view and four views segmentation]. This is why we found that a 100% error in conductance can translate into a 30% error only in permeability. Also, more interestingly, the progressing quality estimation of high-level metrics given in Fig. 4(c) does not show a clear hierarchical quality response when $n>1$. Since both computational and memory cost increase as $O(n)$, it is interesting to note that, above $n=2$, perfusion prediction resulting from multiview deconvolution might poorly improve from increasing the number of views. This trend is confirmed when considering progressive degradation in a synthetic network, shown in Fig. 5. In noisy situations, even low-level metrics display a much larger improvement from $n=1$ to $n=2$ than in a further number of view refinements.

The relevance of the presented segmentation workflow is shown in Fig. 6, where various vascular structural parameters have been reported on the analyzed fat tissue. The vessel radius histogram [Fig. 6(c)] displays a bell-shape Gaussian like curve, the mode of which corresponds to a capillary diameter of $7\mu \mathrm{m}$, close to what can be found in brain.¹⁴ The vessel length distribution [Fig. 6(d)] displays a Poissonian like behavior, whose mean length equal to $35\mu \mathrm{m}$ is two times shorter than the one found in brain.¹⁴ This feature illustrates the specificity of fat tissue where adipocytes are tightly vascularized, such that vascular segment length is comparable with their half perimeter. Furthermore, vascular volume fraction displays an average 4%, comparable with other tissues (e.g., brain and muscle) with distribution tails reaching values as large as 10%, as shown in Fig. 6(b). Finally, Fig. 6(a) shows the histogram of orientation angles as defined in Fig. 2(a). The orientation angle in red ${\varphi }_2$ displays a symmetrical distribution as opposed to the two other angles.³¹

Finally, let us now provide some elements for the usefulness and future extensions of the presented results. Since the exposed test cases (data, ground truth, and C++ code) are provided as supplementary material (supplementary materials data and code are available at: https://drive.google.com/file/d/1evXmG_x7TzL2yoqWa23qA7iJpWSjdZsF/view?usp=sharing), this contribution, using state-of-the-art processing, gives a first step toward quantitative vascular segmentation from LSFM imaging. Specific new methods associated with the image processing workflow, i.e., registration,³² deconvolution, segmentation,³³ and vectorization, might be interesting to explore in the future since they might help to improve the recovery of vascular properties. A detailed discussion of such possible extensions is obviously beyond the scope of this study. However, considering the registration step, we have explored the possibility of using nonrigid B-spline-based transformation.²⁵ Such nonrigid deformations require very careful parameter setting and are difficult to configure to reach a perfect alignment of views for each vessel, even considering local deformations sized to the vessel scale. Despite our efforts, we were not able to improve registration, while, at the same time, the computational cost was significantly increased.

5.

Conclusion

We analyze the quantitative segmentation of large microvascular networks from multiview LSFM images. Combining suitable multiview deconvolution and registration procedures, we addressed the question of vessel accurate segmentation and vascular network reliable 3-D reconstruction. We showed the benefit of increasing the number of angular views on image-based and structural metrics, confirming the convergence toward isotropic vessel reconstruction. However, considering higher-level metrics, associated with the network topology, lead us to temper the need for a large number of views. Using more than two views does not provide better results on perfusion oriented metrics. The presented results represent the first systematic quantitative evaluation of LSFM postprocessing workflow for reliable vascular network reconstruction. Knowing how much gain could be expected from a very large 3-D images data set and heavy posttreatment computation is of practical interest for future research. This is especially true for image-based quantitative modeling.

Finally, it is interesting to mention that, even if we mainly restrict our analysis to a cubic millimeter volume of tissue, the applicability of the imaging procedure has a much wider potential. As a matter of fact, the analyzed region is situated inside a much bigger layer into which the light-sheet penetrates (see Fig. 1). Hence, the range of accessible imaged volume is much wider, at least for high-quality clearing. Combining LSFM with a suitable image posttreatment workflow shows potential for centimeter tissue-scale analysis of vascular structures, at micron resolution, a perspective that deserves further investigation and effort.