1.

Introduction

Peripheral neuromodulation is a growing area of research that involves the application of external stimuli to modulate nerve activity.¹ Although these methods have been applied to treat various disease conditions, the effectiveness of these therapies has been limited. For instance, vagus nerve stimulation (VNS) is a clinically approved therapy to treat conditions such as drug-resistant epilepsy,² depression,³ and obesity.⁴ However, therapeutic efficacy with this method is just moderate, with 50% of patients seeing a significant ($>50\%$) reduction in seizure frequency after 1 year of implantation.⁵ In addition, several trials involving VNS therapy have failed to reach clinical endpoints.^6,7 We find that computational modeling approaches can aid researchers to test various interface designs and identify ideal stimulation parameters (pulse amplitude, width, duty cycle, etc.); these could serve to improve fiber selectivity and thereby increase therapeutic efficacy. However, these models require accurate anatomical information about human nerve morphology since the latter significantly affects optimal stimulation parameters.⁸ Therefore, there is a need for methods that enable visualization and mapping of human peripheral nerves to improve computational models, providing a deeper understanding of nerve responses to neuromodulation therapies and enhancing treatment outcomes.

While prior studies have described the macroscopic connectivity of peripheral nerves in detail, reports on the arrangement of fibers within fascicles along the length of the nerve have been limited thus far.^9–11 The analysis is also challenging in nerves such as the vagus, which can be over 40 cm in length in adults.¹⁰ We are developing image acquisition and analysis methods to track groups of fibers along the length of a peripheral nerve to determine how they split, merge, and coincide with other fiber tracts.

To image peripheral nerves at fiber resolution, several methods have been proposed. The gold standard methods to image nerve anatomy involve electron microscopy (EM), including transmission EM for two-dimensional (2D) imaging of thin sections and serial block-face EM for three-dimensional (3D) imaging.^12,13 Advances in multiphoton and super-resolution microscopy methods have also been described to image peripheral nerves with and without labels.¹⁴ However, these systems are appropriate for very small volumes and are technically complex and expensive. Diffusion MRI approaches have been developed to image white matter tracts in the human brain in vivo.^15–17 These methods are also being used clinically to evaluate various peripheral nerve injuries, including traumatic lesions¹⁸ and chronic neuropathies.¹⁹ Recent preclinical advances have made these methods suitable for microscopic imaging of ex-vivo tissues as well, including mouse brain²⁰ and postmortem human spinal cord.²¹ However, resolution and contrast in routine diffusion MRI datasets limit direct visualization of fiber structure within peripheral nerves, thereby requiring additional validation methods. Micro-CT using a conventional x-ray source with appropriate tissue staining has been used to image nerve structure ex vivo.^11,22 These methods have shown that some nerves (e.g., vagus¹⁸) have more fascicle branching than previously appreciated. However, this technique is limited to the visualization of nerve fascicles rather than nerve fibers. To address these technical challenges, we have developed a serial block-face imaging system based on the microscopy with ultraviolet surface excitation (MUSE) technique.^23,24 MUSE is based on the use of fluorescent stains, possibly complemented by absorbing stains for additional contrast, excited using short-wavelength (280-nm range) ultraviolet light that penetrates only $\sim 10$ to $20\mu \mathrm{m}$ below the surface of tissue specimens.²⁵ This simplifies the setup by obviating the need for alternative and more complex optical sectioning methods, as in confocal microscopy. The application of MUSE in a serial block-face imaging setup permits imaging of samples across extended depths and has been described in previous reports.^24,26–29

In our approach, referred to as 3D-MUSE, nerve samples are first stained with an absorptive dye to delineate structures of interest and then counterstained with an ultraviolet fluorescent dye (commonly rhodamine), followed by dehydration and embedding into resin blocks for section and imaging. We adopted a previously published method for whole-mount staining of nerves in cadaver tissues called Sihler’s staining.³⁰ 3D-MUSE is suitable for imaging embalmed human cadaver nerves.

3D-MUSE datasets of peripheral nerve tissues can be analyzed with tractography methods to build a map of the underlying fiber organization, which could be a step toward building a connectome for the peripheral nervous system. Although imaging methods based on light microscopy do not commonly have sufficient resolution to clearly resolve all nerve fibers (e.g., unmyelinated fibers can be under $0.5\mu \mathrm{m}$ in diameter), tractography methods can still be used to estimate fiber orientation. The methods assume that the underlying displacement field is smooth and estimate flow vectors by analyzing a small neighborhood around each pixel. The flow vectors serve as a proxy for fiber displacements and can be used to build a tractogram starting from a defined set of seed points. Similar methods to estimate the orientation of fiber groups have been applied in a wide range of datasets, including diffusion MRI,¹⁷ microscopy,³¹ and OCT.³² In the context of processing diffusion MRI data, several tractography toolkits are publicly available, including Diffusion Toolkit,³³ Slicer DMRI,³⁴ DSI Studio,³⁵ and DIPY.³⁶ However, these software tools are made to work with modality-specific datasets (e.g., diffusion-weighted images acquired at various gradient strengths). Modifying them to work with microscopy data is not straightforward, suggesting the need to create a dedicated software tool. In addition, there is an opportunity to create a specialized solution for peripheral nerves with their long-axis geometry and fascicles surrounded by fiber-free epineurium.

In this work, we developed a software package, NerveTracker, to visualize and track groups of nerve fibers in 3D-MUSE datasets. The software is implemented as a multi-threaded application in Python and is built on top of the Qt and VTK libraries. The software utilizes either optic flow or structure tensor algorithms to determine local fiber orientation. Tracking is initialized by color-seeding each group of fibers within a specific slice of a 3D stack. Tracking follows the orientation field in either direction along the stack. The resultant set of streamlines (referred to as a tractogram) can be interactively visualized and edited. Using deep learning, we segmented fascicle regions and anatomically constrained streamlines to stay within the mask. Novel metrics to measure the correspondence of a tractogram with ground truth fascicle (groups of fibers) segmentation as well as similarity values for comparing two tractograms are used. Example results are shown.

2.

Image Analysis Methods

3.

Software Features

NerveTracker allows automated analysis of nerve tracts in 3D-MUSE images of peripheral nerves. The workflow outlining the software is presented in Fig. 1. In the upcoming text, we describe software features in greater detail, but some of the main features are summarized here:

Fig. 1

Workflow of the proposed software, NerveTracker, to visualize and track groups of nerve fibers in 3D-MUSE datasets. The software takes the image stack, manually delineated ROIs on the first slice, and image metadata as input; runs the chosen tractography algorithm; and provides interactive visualization and editing tools for the generated tractogram.

The software is written in Python and uses Qt v5.0 (Riverbank Computing, England, United Kingdom) for its GUI implementation and Visualization Toolkit 9.2 (VTK, Kitware Inc., Clifton Park, New York, United States) for 3D visualization. Upon initialization, appropriate file paths to the image stack and mask are provided. Imaging parameters such as pixel size, section thickness, and number of images in the stack are provided by means of a dialog window or a pre-defined XML file. The expected format and fields in the XML file are provided in Appendix A. The parameters of the tractography algorithm are set as desired and the flow estimation algorithm can be run in either direction of the stack. Using the UI, individual visualization elements (image slice, streamlines, cluster centroids, etc.) can be added to or removed from the visualization window as desired.

We implemented NerveTracker to provide simple image visualization for large (10 GB and greater) 3D-MUSE image volumes. The software currently supports 2D grayscale images in PNG format. We note that our method can routinely generate datasets that exceed system memory. For example, considering a 12-megapixel camera sensor and a single tile, 4000 image slices at 8-bit pixel depth would take up $\sim 50\mathrm{GB}$ of space. To reduce memory requirements on the user’s computer, the software does not read all images into memory. Instead, a virtual stack is created by reading only the requested 2D image slice from the disk at any time. This approach allows us to significantly reduce memory requirements during visualization. The tractogram and an arbitrary image slice can be viewed at the same time.

The software also considers memory constraints when running the tractography analyses. Since the optic flow method computes flow between two frames at a time, images can be loaded into memory directly. However, the structure tensor approach requires a 3D volume as input to estimate flow at each voxel. Since loading the full stack would not be possible in computers with limited memory, we process the stack one volume chunk at a time to ensure that the program does not request memory beyond available RAM. The number of slices in a processed chunk is provided as input along with other imaging metadata. Individual chunks are created with overlap, which is computed based on the user-defined neighborhood and noise scale parameters. This ensures consistency in vector calculations at pixels near the edge of a chunk.

The starting coordinates of the generated streamlines are initialized from the user-provided binary mask. A connected-components analysis is run to identify individual ROIs from the annotated image. Next, for each connected component, a list of all pixel coordinates inside the component is created. The list is randomly permutated, and seed points are selected starting from the first index in the list until the desired sampling density is reached. The default sampling density is set to 1 seed per 100 pixels and has a maximum value of 1 seed per pixel. We ensure that the seed point coordinates are the same between runs by setting the same seed value to the random generator before permuting the list. This allows an accurate comparison of tractograms generated with varying algorithm parameters.

Interactive editing of generated streamlines is achieved using the vtkContourWidget class, allowing the user to either create new streamlines or delete unwanted streamlines. Furthermore, the user can provide a corresponding stack of fascicle masks to constrain the tractography result. Since peripheral nerve fibers are always contained within fascicles, tracking of streamlines can be terminated if the tracts exit the provided fascicle mask. In addition, streamlines can be clustered using the Quickbundles algorithm, developed for diffusion MR datasets. Our implementation directly uses the DIPY Python package³⁶ where this functionality is readily available.

4.

Results

Tractography results are presented on two representative 3D-MUSE datasets. The datasets include a human cervical vagus nerve (sample 1) and a branch of the tibial nerve (sample 2). Both samples were sectioned at $3\mu \mathrm{m}$ thickness and imaged either with $0.9\mu \mathrm{m}$ pixel spacing (sample 1) or $0.74\mu \mathrm{m}$ pixel spacing (sample 2). Images are collected using a 12-megapixel camera, with image sizes of $4000\times 3000\text{pixels}$. Further details on sample preparation and imaging system specifications are provided in Appendix B. A total of 1500 images were collected for sample 1, and 900 images were collected for sample 2, giving $\sim 16$ and 10 GB after conversion to grayscale, respectively. We found that the nerve in sample 2 covered approximately half of the image field of view; thus, an additional cropping step was applied to reduce the image size to around $2200\times 2400\text{pixels}$.

To verify that the tractography output matches the spatial organization of fiber groups in the image stack, we created ground truth segmentations on select slices and computed the ${\text{Dice}}_{\text{norm}}$ metric. For sample 1, we manually traced the outline of fibers in a particular fascicle on the first image slice. A flythrough video of the stack along with the segmentations overlaid is shown in Video 1, MP4, 53.0 MB [URL: https://doi.org/10.1117/1.JBO.29.7.076501.s1]. We consider four slices at equally spaced intervals along the stack and overlay the manual tracing as an orange mask [Figs. 2(a)–2(d)]. From these segmentations, we found that this group of fibers merged with other fascicles and eventually split across two fascicles when they reached the last image of the stack [Fig. 2(d)]. In Figs. 2(e)–2(h), the result of the tractography analysis using the optic flow method is overlaid on the raw images for comparison. The tractography analysis is found to match the ground truth segmentation to a large extent when tracking both in the forward (Fig. 2) and backward (Fig. S1 in the Supplementary Material) directions. A similar analysis was performed for sample 2 as well. The mean ${\text{Dice}}_{\text{norm}}$ values across all bundles for both samples are provided in Table 1. We find that this metric is always above 0.66 and has a mean value over 0.75. In addition, we find that the structure tensor approach seems to perform better on both datasets compared with the optic flow analysis. Along with the quantitative analysis, we qualitatively verified that the tractogram is consistent with respect to the imaging data for sample 2. In this sample, a group of fibers are outlined as they exit one fascicle and enter another [Figs. 3(a)–3(e)]. In Fig. 3(f), we selectively visualize streamlines initiated from the fascicle of interest and identify the branching event, with a group of streamlines exiting from the bundle, corresponding to the image data. Video 2 demonstrates interactive visualization of this event in the software by moving across the image stack and viewing from various camera angles.

Fig. 2

Correspondence between manual segmentation of fiber bundles and tractography results on select slices from sample 1. (a)–(d) Fibers within a select fascicle were outlined as a group and visualized with an orange mask as an overlay. These fibers were found to split into two separate fascicles at the last slice of the stack, shown in panel (d). (e)–(h) Tractography with optic flow analysis initiated at the first slice ($z=0\mathrm{mm}$) generates streamlines that resemble the manual segmentation result. The ${\text{Dice}}_{\text{norm}}$ metric for the orange streamlines was 0.88, 0.88, and 0.81 at $z=1.5$, 3, and 4.5 mm, respectively. Scalebars indicate $500\mu \mathrm{m}$.

Table 1

Dicenorm values measuring overlap between ground truth segmentation of fiber bundles and tractograms at intermediate slices in the stacks (1/3rd, 2/3rd, and at the end of the stack).

Fig. 3

Tractography methods on 3D-MUSE data can detect the movement of fiber groups from one fascicle to another. (a) 3D-MUSE image slice (green channel, contrast adjusted) from sample 2, illustrating several large fascicles. We consider this slice to be at $z=0\mu \mathrm{m}$ for the purpose of this illustration. (b) Close-up view of the ROI outlined by the white box in panel (a). (c)–(e) Images at different $z$ depths in the image stack, all cropped at the same ROI. A group of fibers can be identified moving from the fascicle below to the fascicle on top, indicated by a dashed outline. (f) 3D visualization of the tractogram generated by structure tensor analysis shows a split in the fiber groups (black arrow) corresponding to this moving group of fibers. Scalebars correspond to $500\mu \mathrm{m}$ in panel (a) and $100\mu \mathrm{m}$ in panels (b)–(e). (Video 2, MP4, 24.1 MB [URL: https://doi.org/10.1117/1.JBO.29.7.076501.s2])

To further identify differences in the output of the two tractography approaches, we performed both qualitative and quantitative comparisons of the generated streamlines. In Fig. 4, we visualize streamlines generated both from optic flow and structure tensor analysis on sample 1. Comparing all streamlines in Figs. 4(a) and 4(f), we did not identify any significant differences. However, since the generated tractograms are dense due to a large number of streamlines (nearly 15,000), we show streamlines originating from individual fascicle bundles arranged by decreasing fascicle areas in Figs. 4(b)–4(e) and 4(g)–4(j). The overall structure of the streamlines was found to be similar across all fascicles. We computed the ${\mathrm{MCN}}_{\text{dist}}$ metric between the two tractograms and found it to be around $49\mu \mathrm{m}$, indicating good similarity since it is less than 2% of any dimension of the image stack. The results were comparable when a similar analysis was done for sample 2, as shown in Fig. S2 in the Supplementary Material. The ${\mathrm{MCN}}_{\text{dist}}$ metric between the optic flow and structure-tensor-based tractograms for this sample was found to be around $100\mu \mathrm{m}$ (less than 6% of any dimension of the stack). Parameters used in the optic flow and structure tensor analyses are provided in Appendix C. In terms of computation time on 1500 slices at a $4000\times 3000$ image size, generating the tractograms took around 14 min for the optic flow analysis and 18 min for the structure tensor approach.

Fig. 4

Comparison of tractogram results generated from optic flow (a)–(e) and structure tensor (f)–(j) analysis. To aid the visualization of dense tractograms (a), (f), tracts originating from individual fascicles or ROIs are rendered with unique colors. This allows selective visualization of individual bundles, as shown in panels (b)–(e) and (g)–(j) for the optic flow and structure tensor approaches, respectively. We find that both methods provide visually similar results on both datasets.

We tested whether downsampling our datasets would have a significant effect on the generated tractograms. We took the image stacks acquired at $3\mu \mathrm{m}$ image slice thickness and dropped one or three slices in between to effectively create stacks at 6 and $12\mu \mathrm{m}$ image slice thickness. Alternatively, images were downsampled in-plane ($XY$) by a factor of 2 or 3. We computed the mean ${\text{Dice}}_{\text{norm}}$ metric as described previously and show the mean value across intermediate slices in Table 2. We found that the overlap metrics for the downsampled stacks and the baseline stack are similar ($\sim 2\%$ to 9% change). We also computed the ${\mathrm{MCN}}_{\text{dist}}$ between the tractograms from the downsampled and baseline stacks and found that these values also indicate high similarity (Table 3).

Table 2

Quantifying changes in tractogram accuracy with respect to changes to image properties.

Table 3

MCNdist values (in μm) provide a measure of similarity between two tractograms.

Post-processing operations on generated streamlines include streamline clustering to create representative streamlines. Although the software allows the user to specify a seed point sampling density as well as an opacity value for the rendered streamlines, these settings may not be ideal for visualization. For example, in Figs. S3(a)–S3(c) in the Supplementary Material, reducing the seed point sampling density yields a less dense tractogram but could miss tracking some regions within fascicles in the image. Similarly, images in Figs. S3(d)–S3(f) in the Supplementary Material show the effect of varying opacity. A visualization with 10% streamline opacity does not provide significant improvements compared with higher values, and further reductions would reduce the overall visibility of the streamlines. Instead, by applying a clustering algorithm on the streamlines (Quickbundles), the user can get a compact representation of the tractogram both in terms of visualization as well as file size. The result of applying the clustering algorithm to a tractogram is shown in Fig. S4 in the Supplementary Material. The clustering algorithm is also used during the computation of the ${\mathrm{MCN}}_{\text{dist}}$ metric to compare two tractograms.

In addition, the software provides a few streamline editing tools to the user. Streamlines can be edited by drawing a contour over a specific image slice and choosing to either create new streamlines or delete existing streamlines as shown in Video 3, MP4, 68.5 MB [URL: https://doi.org/10.1117/1.JBO.29.7.076501.s3] and Video 4, MP4, 27.3 MB [URL: https://doi.org/10.1117/1.JBO.29.7.076501.s4], respectively. In terms of automated editing, the user can provide fascicle masks for each image in the stack as described in Figs. 5(a) and 5(b). The software can use these masks to remove streamlines that exit the fascicle regions. This process is referred to as anatomically constrained tractography (ACT),⁴⁵ and the results on two image slices from sample 1 are shown in Fig. 5(c). We implement a method for automatic fascicle segmentation with a 2D U-net network separately, outside the current software package. The results of running the segmentation algorithm on the image stack from sample 1 are shown in Video 5.

Fig. 5

Deep-learning-based image segmentation pipeline for segmenting fascicles and epineurium regions in 3D-MUSE images. Since the method can generate many 2D slices, manual annotation of each slice is time-consuming. Thus, we segment a few slices in the stack (1 out of 100) and train a model to subsequently segment all slices in the stack. (a) U-net architecture used in this work, (b) training and testing strategy employed in this work, and (c) modifications to tractography result when using the segmentation masks. Video 5 shows a flythrough video of the segmentation result for this dataset. Images in panel (b) were created with BioRender. Scale bars in panels (a) and (c) indicate 500 and $30\mu \mathrm{m}$, respectively. (Video 5, MP4, 21.5 MB [URL: https://doi.org/10.1117/1.JBO.29.7.076501.s5])

5.

Discussion and Conclusion

To our knowledge, this is the first study demonstrating microscopic tractography on human peripheral nerves. This has been made possible by our new software (NerveTracker), which tracks groups of nerve fibers in 3D-MUSE images. Below, we review the algorithms and results and describe some future directions.

We proposed a metric based on the Dice coefficient to measure the accuracy of the tractograms compared with manual ground truth segmentations of fiber groups. We obtain point clouds at each 2D slice in the tractogram and convert them into a binary mask to compute a Dice overlap metric with the ground truth segmentations. We found that the ${\text{Dice}}_{\text{norm}}$ metric was greater than 0.75 on average, for both the optic flow and structure tensor approaches on both datasets. Since a Dice score of 1 indicates perfect correspondence, the values obtained here show that the tractograms are reasonably accurate. Sample 2 was found to have higher ${\text{Dice}}_{\text{norm}}$, possibly due to better contrast from the large diameter fibers in the tibial nerve. We also identified that the tractograms were robust to changes in pixel size and section thickness when evaluated with the ${\text{Dice}}_{\text{norm}}$ metric. We identified that the tractograms retain their accuracy at both 6 and $12\mu \mathrm{m}$ image slice thickness. This indicates that instead of capturing an image of the block face after every $3\mu \mathrm{m}$ slice, the system could skip imaging a few slices and still provide suitable tractograms. This approach could substantially reduce overall imaging time. A similar result was also found with downsampling in plane by a factor of 2 and 3, suggesting that a reduction in system magnification (leading to requiring fewer image tiles) may be possible. Alternate distance-based metrics acting on point clouds (e.g., chamfer distance⁴⁶) could also be considered in future studies.

We found that both methods for estimating fiber orientation generated visually similar tractography results. However, from the ${\text{Dice}}_{\text{norm}}$ metric, structure tensor gave somewhat better results than optic flow. This is reasonable since the structure tensor approach takes several image slices into consideration when estimating flow vectors, as compared with the optic flow approach, which tracks points from one image frame to the next. In addition, since the optic flow algorithm was run with a window size of 50 pixels at two resolution levels (i.e., the original resolution and 2× downsampling), the largest field seen by the algorithm was $100\times 100\text{pixels}$ at the original resolution. Considering an average fiber diameter of $\sim 5\mu \mathrm{m}$, this field may hold up to 20 fibers. However, fiber groups that branch out from a fascicle may be smaller than the window; thus, structures outside the branching fiber bundle and still inside the window could influence the flow calculations.

Deep learning-based image segmentation methods were successfully applied to segment fascicles and epineurium in the cross-sectional nerve images. Since a single 3D-MUSE stack can contain over 1000 2D images, manual annotation of the slices is time consuming and not readily feasible. We adopted a strategy of selectively labeling every 100th slice within a stack, trained a network on those slices, and predicted segmentations for all slices in the stack. This approach is suitable since we observe significant variation in staining intensity and contrast across samples due to the nature of whole-mount staining. We are continuing to test other suitable network training strategies as well as newer model architectures.⁴⁷ We created methods in NerveTracker to take such segmentations as input and restrict streamlines to stay within the fascicle regions, thereby ensuring biologically feasible tracts. The segmentations can also be used to generate accurate anatomical mesh models for computational modeling studies of neuromodulation.⁴⁸

Data from complementary imaging methods can be incorporated with our microscopic tractograms. For example, information on fiber type (afferent versus efferent) could be accessed by suitable immunohistochemistry methods on thin sections.⁴⁹ By combining such complementary information of fiber types on the tractogram, it would be possible to create a more functionally relevant map of the nerve. Similarly, by incorporating EM, it should be possible to identify the distribution of both myelinated and unmyelinated fibers within a peripheral nerve cross-section. Analyses can also be extended to imaging modalities having a lower resolution, but larger field of view. For example, microscopic tractography could help us further understand fascicular organization as seen in micro-CT.¹¹ Similarly, our approach could be complementary to lower-resolution diffusion MRI tractography. It could provide validation for higher-resolution diffusion MRI as they continue to develop the technology.

Some extensions to our methods are possible. Further tests are required to determine if our approach can be extended to higher-resolution micro-CT or light-sheet datasets. We are encouraged in this regard as others have reported promising results using the structure tensor approach on such data.^38,50 Alternatively, deep learning-based methods such as FlowNet and MMFlow have been proposed for the task of object tracking in video sequences. It should be possible to implement and test these methods in a straightforward manner with NerveTracker. We have currently implemented lightweight visualization of graphical tractograms and individual image slices. Given the large data sizes ($\sim 100\mathrm{GB}$), routine 3D rendering of 3D-MUSE image data would be difficult. A promising method for handling large data is formats that store data at multiple resolutions (e.g., Zarr). We could include volumetric visualizations of such datasets when the core VTK library supports them in future software releases. When the VTK library supports volume rendering options for such file formats, we could include them in future software releases.

In summary, this work presents a software toolkit for visualizing and tracking fiber groups in block-face microscopy datasets. We found that 3D-MUSE allows volumetric imaging of peripheral nerves, and the software presented here can generate useful insights from this relatively new imaging approach. The software is written in Python and is thus easily customizable if new features are to be added. The software currently supports fast visualization of 2D image slices and implements two flow estimation algorithms and several postprocessing and analysis methods on the generated tractograms. The computation time for the tractography analyses was found to be reasonable (around 15 min for generating streamlines on a dataset of 1500 images), suggesting the suitability of the methods to process larger datasets. Interactive streamline editing tools include both automated and manual correction of streamlines. The software presented here can be used as an alternative to track objects or features of interest in 3D image stacks, without the need for explicitly segmenting them on each slice.

6.

Appendix A

The image metadata file should contain the following fields:

An example XML metadata file is provided below.

<?xml version="1.0"?>

<root>

 <pixel_size_xy name="0.9"/>

 <image_slice_thickness name="3"/>

 <image_type name=".png"/>

 <num_images_to_read name="1000"/>

 <step_size name="64" />

</root>

7.

Appendix B

Nerve tissues were prepared for 3D-MUSE imaging using a whole-mount staining and embedding approach, similar to the protocol described in our previous work.²⁴ First, samples were stained with Ehrlich’s hematoxylin (12.5% $v/v$ in DI water) to create absorptive contrast to nerve fibers and nuclei. To allow the stain to completely diffuse into the tissue, samples were left in the staining solution on a rocker for 4 days. Next, they were dehydrated through the increasing concentrations of ethanol (30%, 50%, 70%, 80%, 90%, and 100%, 4 h each). Rhodamine B was included in the last ethanol step (0.25% $w/v$) to create a contrast with hematoxylin. Subsequently, samples were placed in Glycol methacrylate (GMA) monomer for 1 day and followed by GMA infiltration solution for 2 days. Finally, they were placed in an embedding mold and polymerized by adding an initiator to the infiltration solution. The hardened blocks were trimmed and mounted on plastic chucks, making them suitable for sectioning on the microtome. The imaging system consisted of an infinity-corrected microscope with a Nikon objective (either 4×/0.13 NA or 5×/0.14 NA), tube lens (Thorlabs, Newton, New Jersey, United States, TTL-100-A), and a CMOS camera [Teledyne FLIR (Wilsonville, Oregon)]. The light source consisted of a UV light source (Thorlabs, M280L4) mounted on the imaging system to provide oblique illumination.

8.

Appendix C

Unless otherwise specified, parameters used in the optic flow analysis are as follows. The window size was set to 50 pixels, and the number of resolution levels was set to 2. Prior to running the optic flow analysis, a Gaussian blur with a standard deviation ($\sigma$) of 2 pixels was applied to the images to reduce noise in the gradient computation. Similarly, the parameters used in the structure tensor analysis were a neighborhood scale of 5 pixels and a noise scale of 1 pixel. Images were down-sampled in $XY$ by the closest integer factor to create near-isotropic voxels ($2.7\times 2.7\times 3\mu \mathrm{m}$ for sample 1 and $2.96\times 2.96\times 3\mu \mathrm{m}$ for sample 2) prior to computing the structure tensor.