MicroCT Vascular Network Analysis Program: Development, Validation and Comparison to Manufacturer Software.

Abstract

Bone repair’s dependence on angiogenesis makes accurately measuring vascular networks of great importance to orthopaedic researchers. A three-dimensional imaging modality like microcomputed tomography would better capture these networks than histology. There are commercially available programs to analyze vessel networks in three dimensions, but these may be too costly for laboratories. Alternatively, μCT trabecular software could be used but may not be appropriate. The goal of this project was to develop a vascular network analysis protocol based on freely or commonly available software and compare its performance to that of a μCT trabecular analysis software. The protocol developed, called Vascular Network Analysis or VNA, relies on two modules in Fiji ImageJ and a custom MATLAB program. We validated the software and compared it to a μCT trabecular analysis program (MicroCT) using in silico models of increasing complexity and differing homogeneity. In general, VNA outcomes were significantly different from true values, but most were within an acceptable percent error (<10%). VNA and MicroCT performed almost identically for volume but significantly differently for average vessel diameter. For the homogenous models, the average diameters differed only slightly, but were starkly different for the heterogeneous models. In the most heterogeneous system, the microCT software overestimated average diameter by about 650% from true. VNA was within 1% of true for the same model. In conclusion, we have developed a program to analyze vascular networks from microCT scans which is easily accessible, insensitive to network homogeneity, and of higher accuracy compared to a μCT trabecular analysis software.

Introduction

It is well established that angiogenesis and osteogenesis have a very close, yet not fully understood relationship.¹ Bone formation during repair is highly dependent on vascularization to provide progenitor cells, nutrients, oxygen, and waste removal. There is also significant cross-talk between vascular and osteogenic cells.^2,3 This interdependency has been demonstrated across the bone repair spectrum in drill hole defects,⁴ stress fractures,^5,6 distraction osteogenesis,^7,8 complete fractures,^4,9–11 and segmental bone defects,⁴ where inhibiting or encouraging angiogenesis has a correlative effect on bone formation. Thus, adequately characterizing vascular networks is of great interest when investigating fracture repair or segmental bone defect reconstruction.

Historically, vasculature has been assessed using histology. Histological analysis allows quantitative measurements like vessel density and area as well as differentiation of different vessel types or maturity. However, because histology is a two-dimensional modality, it is very prone to sectioning bias and does not capture the entire vascular network within a volume of interest. A three-dimensional approach, like micro computed tomography (μCT), could provide more accurate and complete vasculature characterization. It would not only capture the entire network in a region but also allow additional measurements for comparison, such as total volume and total network length.

An additional benefit is that μCT is already widely used in orthopaedic research to measure the size, structure, and density of bone in three-dimensions. All μCT systems have validated manufacturer software producing morphological outcomes like total volume, bone volume, mean trabecular thickness, and mean trabecular spacing. Since trabecular bone morphology is similar to that of a vascular network, some studies have directly used μCT manufacturer’s software to generate data about the vascular network following perfusion with a contrast agent.^12,13 Some of the bone outcomes are clearly analogous (i.e. bone volume for vessel volume, trabecular thickness for vessel thickness) while some are less clearly related (i.e. normalized trabecular number for vessel number, voxel diameter distribution for vessel diameter distribution). However, some desired metrics like vessel network length or branching have no analogous output. Also, it is unclear if the algorithms used for bone analysis are appropriate for vascular networks. There are some commercially available software packages, such as Amira, for analyzing vascular networks, but these may be too expensive for academic research applications – especially if this is not going to be a routine measurement for a particular lab.

This project’s main objective was to create an analysis protocol based on freely available or commonly used academic software to generate vascular data from μCT scans. We hypothesized that a protocol customized for vascular network analysis would perform significantly better than software developed specifically for trabecular bone analysis.

Methods

Protocol Overview.

The protocol we developed, called Vascular Network Analysis (VNA), is broken down into three sequential modules: 1) Volume Skeletonization, 2) Skeleton Processing, and 3) Measurement Consolidation. Modules 1 and 2 are performed by separate plugins in ImageJ’s Fiji (NIH, Bethesda, MD), an open source image processing software package, with some minor custom alterations (see supplemental data). The final module, Measurement Consolidation, is a custom MATLAB script (MathWorks, Natick, MA) written specifically for this project. MATLAB licenses are provided by most universities. The modified ImageJ Fiji plugin, MATLAB files, and a detailed user manual can be accessed at github.com/McBrideGagyiLab/VNA. The process takes an input of either .DCM or .TIF slices of the original 3D scan. If exported from the μCT in grayscale format, the images should be cropped and thresholded so that the vessels of interest are segmented from other structures and binary. We prefer to use the manufacturer’s software to segment the vessels and output these as binary .DICOMS. The first module reduces the segmented volume to a 1 pixel wide skeleton. The second module breaks that skeleton into individual branches and outputs a list with each branch’s length and midpoint, the latter being our modification. The final module takes in the generated list and the original segmented slices. It removes any artifact branches (i.e. noise - branches less than 3 voxels in length), calculates the total vessel volume, finds the maximal vessel diameter near the vessel mid-point, and consolidates all of the data to be output. In the end, the user is given a file with the total vessel volume (VV), total vessel length (VL), number of branches (BN), average vessel diameter (V.Dia), vessel diameter standard deviation (V.Dia.StDev), individual vessel lengths, and individual vessel diameters. The standard deviation could be used as a measure of homogeneity (or heterogeneity).

Validation.

We first validated the software using computationally created vessel models. This provided known ‘true’ values for comparison. Four simple, single-tree models were made in Fusion360 (Autodesk, San Rafael, CA) with 31 to 35 branches ranging in length from 181 to 965 μm and in diameter from 32 to 150 μm (Table 1, Figures 1 and S1). Each simple tree was replicated 2, 4, 8, or 16 times in either random or uniform orientations to test the accuracy of VNA under increasing complexity (Figure 1). Each model was output from Fusion 360 as a .STL file, which is only a surface mesh. The mesh was converted to an image stack of the solid volume at 10 μm resolution using the VOXELISE function in MATLAB.¹⁴ Each image stack was run through the VNA modules. All of the outputs were compared with the known input (i.e. true values) from the computational models both as absolute values and as a percent error from true. Post-hoc analysis was done to locate any false additional branches and group them by motifs.

Table 1.

Model Uses and Parameters

Model	Diameter Distribution Type	Use	Number of Trees	Number of Branches	Branch Length Range (μm)	Branch Diameter Range (μm)	Total Vessel Volume (mm3)	Total Network Length (mm)	Average Diameter (μm)	Diameter Standard Deviation (μm)
Simple 1 – 1 Tree	Homogeneous	Validation	1	35	304 to 898	60 to 150	0.151	19.12	104.0	27.2
Simple 2 – 1 Tree	Homogeneous	Validation	1	35	395 to 965	90 to 150	0.204	23.88	110.6	17.1
Simple 3 – 1 Tree	Homogeneous	Validation	1	31	253 to 520	80 to 120	0.065	12.20	88.4	10.9
Simple 4 – 1 Tree	Homogeneous	Validation	1	31	181 to 826	32 to 60	0.016	14.24	37.8	7.3
Simple 1 – 16 Tree Random	Homogeneous	Validation & MicroCT Comparison	16	560	304 to 898	60 to 150	2.416	305.92	104.0	26.9
Simple 2 – 16 Tree Random	Homogeneous	Validation & MicroCT Comparison	16	560	395 to 965	90 to 150	3.264	382.08	110.6	16.9
Simple 3 – 16 Tree Random	Homogeneous	Validation & MicroCT Comparison	16	496	253 to 520	80 to 120	1.040	195.25	88.4	10.8
Complex 1	Homogeneous	MicroCT Comparison	1	97	272 to 1,190	75 to 125	0.406	65.45	94.9	11.9
Complex 2	Homogeneous	MicroCT Comparison	1	101	216 to 982	60 to 100	0.196	50.94	75.8	9.4
1000 μm	Heterogeneous	MicroCT Comparison	1	98	189 to 1,192	70 to 130 and 1000	4.278	40.90	125.4	20.4
750 μm	Heterogeneous	MicroCT Comparison	2	100	233 to 929	80 to 200 and 750	3.980	57.13	194.2	20.8
500 μm	Heterogeneous	MicroCT Comparison	3	99	402 to 1,043	50 to 150 and 500	1.899	65.16	138.3	13.6

Figure 1. Example of Simple Model Replication.

To validate the VNA protocol, 4 simple in silico models were created in an AutoCAD program. These simple models were then copied and pasted in either a uniform or random orientation to test how the program handled larger models and increased complexity

Comparison to μCT Manufacturer’s Software.

First, 5 homogeneous models were used to compare VNA’s accuracy to our μCT manufacturer’s bone analysis software. The first 3 models were the previously used 16-tree, random orientation simple models (496–560 branches, same range of lengths and diameters). The final 2 were newly created, more complex 1-tree models with 97 to 101 branches ranging in length from 216 to 1,190 μm and in diameter from 60 to 125 μm (Table 1, Figure S2). The models were converted to image stacks using the same VOXELISE function and resolution as before. After voxelization, the image stacks were converted to DICOMs in ImageJ and loaded onto the μCT server as new ‘scans’ (μCT35, ScanCo, Switzerland). The scans were directly analyzed with the manufacturer’s trabecular bone analysis software (MicroCT). In parallel, new DICOM stacks were generated from the scans, downloaded from the μCT server, and analyzed with the VNA protocol. While in theory the uploaded and downloaded DICOMS should be identical, the additional DICOMS were generated to ensure that the volumes/DICOMS being analyzed by both software packages were as identical as possible and to replicate real use. Because MicroCT does not provide all of the same measurements, only a subset of the VNA measurements were compared (Table 2). For the vessel diameter distributions, the quartiles for each dataset were determined. However, MicroCT’s thickness text file is not a list of every voxel’s assigned diameter value, making determining the exact cutoff difficult. The file is a count of how many pixels fall into each size bin. Thus, for these data sets the quartiles were determined by interpolation.

Table 2.

Analogous Outputs of the MicroCT and VNA

Vascular Network Analysis	MicroCT Software
Vessel Volume (VV)	Bone Volume (BV)
Average Vessel Diameter (V.Dia)	Average Trabecular Thickness (Tb.Th)
Vessel Diameter Standard Deviation (V.Dia.StDev)	Trabecular Thickness Standard Deviation (Tb.Th.SD)
Vessel Diameter Distribution (Normalized)	Trabecular Thickness Voxel Distribution (Normalized)

Finally, there were some concerns that MicroCT’s trabecular thickness algorithms may not work well in a highly heterogeneous system like vasculature. To test this possibility, three heterogeneous complex models were created for comparison. Each model contained one or more trees, each with a dominating main branch (i.e. 1 branch with a 1,000 μm main vessel, 2 branches with 750 μm main vessels, and 3 branches with 500 μm main vessels, Figure 2). The total number of branches in each model ranged from 98–100 with all the smaller branches being of a similar size and length as the homogenous models (233 to 1,192 μm in length, 50 to 200 μm in diameter, Table 2). The same outcomes were used for comparison.

Figure 2. Complex Heterogeneous Models.

To test how the VNA and microCT manufacturer’s software handled highly heterogenous systems, three in silico models were created. Each had 1 to 3 dominating vessels with approximately 100 much smaller branches within the ranges used for the homogeneous models (70 to 200 μm Diameters).

Statistics. Validation Tests.

Ideally the data for all tree numbers would have been tested together. However, since 1-tree random was not a possible configuration and led to an unbalanced data set, the data for the 1-tree model data was analyzed separately from the 2- to 16-tree data. First the 1-tree models’ VNA outcomes were compared to the true values using paired t-tests for each outcome. In parallel, the percent error for each outcome was tested using a one-sample t-test with a hypothesized mean of zero. This provided an initial measure of VNA’s accuracy.

For the 2- to 16-tree models, each outcome was first compared using repeated measures ANOVA considering all tree numbers together (main effect: tree number – 2 vs 4 vs 8 vs 16, repeated effect: orientation – true vs uniform vs random). If both factors and their interaction were significant, as was the case for BN and VL, the data was separated by tree number to evaluate the significance of orientation within each tree number level (Table S1 and S2). For these outcomes, orientation was viewed as the more important and interesting variable than tree number. It is obvious that non-normalized outcomes like the total number of branches would increase with increasing trees. Orientation is the measure of accuracy and the focus of this experiment. A repeated measures ANOVA was completed on the segregated data for each tree number (repeated effect: orientation). If that was significant, then pair-wise comparisons between orientations for that tree number were done using paired t-tests to determine which data sets were significantly different from each other.

If only orientation was significant, which was the case for VV, V.Dia, and V.Dia.StDev, the data from all trees was pooled within each orientation to determine the significance of orientation. A repeated measures ANOVA was completed on the pooled data (repeated effect: orientation). If that was significant, then pair-wise comparisons between orientations on the pooled data were done using paired t-tests to determine which data sets were significantly different from each other. All data is shown as mean and standard deviation.

Statistics. MicroCT Comparisons.

For VV, V.Dia, and V.Dia.StDev homogeneous μCT comparisons, first a repeated measures ANOVA was used (repeated factor: software – true vs VNA vs MicroCT). If this was significant, then pair-wise comparisons were done with paired t-tests. For the quartiles, first a repeated measures ANOVA was done (main factor: quartile – minimum, 25%, 50%, 75%, maximum, repeated factor: software). Both factors and their interaction were significant, so to determine the significance of the software (i.e. accuracy), the data was separated by quartile and each quartile’s data was tested with a repeated measures ANOVA (repeated factor: software). If that was significant, then pair-wise comparisons on the segregated data were done with paired t-tests. The heterogeneous results were either almost identical to the homogenous models or highly skewed. So, no formal testing was done for these models, but each model is presented individually rather than as a grouped mean. All data other is shown as mean and standard deviation.

Results

Validation.

For the 1-tree models, VNA reported more vessels (BN) with significantly smaller VL and V.Dia than the true values. VV was smaller but not significant (p=0.069). VV, BN, VL, and V.Dia percent errors were also significant. V.Dia.StDev was slightly, but not significantly, lower than the true values by either absolute or percent error. The average percent errors for VV, VL, V.Dia were all within 7.5% of the true values and consistently under value, which we felt was within an acceptable range (Figure 3). The additional branches were always located at branch points within the models (Figures 4 and S1, 8 branch points and 15 extra branches between all models). Some were located where a single branch split into 3 or more branches (5 of 8 branch points, accounting for 6 of 15 extra branches). Rather than splitting directly into 3 or 4 branches, it first split into 1 or 2 short adaptor branches that then split into 2 (Figure 4B¹). This added one extra branch to the V.Dia and VL calculations. Less frequently (3 of 8 branch points), a lateral branch would form between 2 new branches, making that joint a triangle rather than a ‘y’ (Figure 4B²). This type of error affected the total branch number much more because it added three extra branches (9 of 15 extra branches). In either motif, macroscopically the joint looked correct. The errors were only visible upon detailed inspection.

Figure 3. Simple Model Results.

In general, the VNA results were statistically different from the true values. However, the percent errors were within an acceptable range for all outcomes except branch number (BN). Also, VNA results remained consistent even with increasing tree number and complexity

Figure 4. Skeletonization Errors.

(A) Original in silico model for Simple Model 2. (B) All extra branches occurred at junction points. Dots indicate extra branches. (B1) Some occurred where 3 or more branches diverged and a small adaptor branch was created adding 1 extra branch. (B2) Others occurred where 2 or more branches diverged and a lateral branch was falsely created. This type of error added 3 extra branches.

When the volume and complexity were increased by replicating the single trees 2, 4, 8, or 16 times in a uniform or random orientation, there were few differences between the two orientations but both were often different from true (lower for VV, VL, and V.Dia, higher for BN) (Figure 3). As expected, BN and VL proportionally increased with significant interaction between tree number and orientation. VV also increased proportionally, but neither the tree number nor the interaction term was significant. V.Dia and V.Dia.StDev, which are already normalized, remained constant with increasing tree number. For all outcomes, there were significant differences attributable to orientation (Tables S1 to S3). VV was similar between uniform and random orientations, but both were significantly lower than true. For BN, uniform and random orientations were similar to each other for all tree numbers. The p-value for all uniform/random BN comparisons to true were less than 0.10, but less than 0.05 only for random at 2 trees and uniform at 4 trees. For VL, uniform and random were similar to each other and both different from true at all branch numbers except 8. At 8 branches, all three groups were different from each other. V.Dia was similar to VL. Uniform and random were similar and both were significantly lower than true. V.Dia.StDev was different between all three groups.

Comparison – Homogenous.

VV and V.Dia.StDev were the same between all three groups (true vs VNA vs MicroCT). In contrast, V.Dia was significantly different between all three groups with MicroCT being the lowest and VNA the intermediate (Figure 5, Table S4). For the diameter distributions (Figure 6, Tables S5 to S6), the minimum, 50^th percentile, 75^th percentile, and maximum were significantly different between all three groups. Interestingly, the minimum diameter found by MicroCT was 10 μm for all models, the exact same size as a single voxel. MicroCT’s quartiles, and thus distribution, were shifted to lower values (to the left), while the VNA quartiles were closer to the true values, but still significantly lower.

Figure 5. Complex Homogeneous Model Results.

VNA and MicroCT reported vessel volumes (VV) and average standard deviations (V.Dia.StDev) similar to true values. Average vessel diameter (V.Dia), however, was better measured by VNA, which was still significantly different than true.

Figure 6. Complex Homogenous Diameter Distribution.

For the homogenous models, MicroCT always reported vessels just a few voxels in diameter, which significantly shifted the minimum, 50th percentile, and 75th percentile to lower values, although this did not qualitatively affect the overall histogram shape. VNA quartiles were also significantly lower than true values but closer than MicroCT values.

Comparison – Heterogeneous.

Similar to the homogenous models, VV was identical for both software programs and slightly lower than the true value. V.Dia.StDev was similar for 2 of the 3 models, although resulted in very different percent errors (Figure 7). Similar to the homogenous models, the MicroCT always resulted in more error, although in these cases it was a very large overestimation that was proportional to the largest vessel diameter. In all three cases, V.Dia was much closer to the dominating vessels’ diameter than the true average of the ~100 smaller vessels (Figure 7). This resulted in extremely large percent errors and great shifting of the histograms to larger values (to the right, Figure 8). As the dominating vessels’ diameters decreased to that of the other vessels, the percent error decreased.

Figure 7. Complex Heterogeneous Model Results.

As with the homogenous models, vessel volumes (VV) were measured almost identically and very close to true. Average vessel diameter (V.Dia) was greatly different between the two software packages. MicroCT’s averages were very close to the dominating vessel diameters, which resulted in very large percent errors.

Figure 8. Complex Heterogeneous Model Histograms.

Qualitatively, the true and VNA vessel distributions were fairly similar. On the other hand, MicroCT’s distributions were highly weighted towards the dominating vessels.

Discussion

The purpose of this project was to create and validate a method to analyze μCT scans of vascular networks based on free or commonly available software. The system we developed was based on two modules from ImageJ’s Fiji software with slight modifications and a custom MATLAB script. Fiji is free to anyone, and MATLAB is commonly provided by universities.

Overall, our protocol was fairly accurate for the in silico models tested. Most of the measured parameters had errors within an acceptable range (<10%), except for branch number. Also, measurements were rarely affected by vessel orientation. The skeletonization process, which simplifies the volume into a 1 voxel-wide representation for segmentation into branches, sometimes created very short extra branches at branch points. While not ideal, these additional branches did not greatly perturb any other outcomes despite their dependence on the branch segmentation step. The extra branches were always very small and did not add much to the overall network length calculation regardless. Also, in many cases, they were just an incorrect subdivision of a single, larger branch’s overall length. Thus, they did not increase the calculated network length. Had the branch been properly seen as one structure, the measurement would have been the same as when subdivided to a small extra branch and the larger correct branch. On the other hand, this did lead to unreal vessel diameters being added to the histograms and factored into the average. However, because these were typically at junction points, the magnitudes of those additional diameters were close to that of the bulk and did not drastically change the vessel distributions or averaged vessel diameter. Volume was completely unaffected, because the algorithm for that outcome is not related to the skeletonization process. Whether similar skeletonization errors will occur with in vivo samples is difficult to predict. It will depend highly on vessel architecture and needs further examination.

The other main outcomes, VV, VL, and V.Dia, had a fairly consistent negative error. While some of this is certainly due to the VNA algorithms, we think part of this error may actually be due to edge effects during the voxelization process. All the ‘true’ values were taken from the model parameters in Autodesk Fusion 360. The model was then output as an .STL file, which is a 3-dimensional surface mesh, and then made into a solid, voxelized volume using MATLAB. Essentially, the models went from analog to digital. While this process typically has little effect on areas that are clearly within or outside the rendered volumes, there are always edge or partial volume effects. Voxels at the edge of the object, which are only partially within the mesh boundaries, must be assigned as either space or solid. This loss of partially filled pixels at the vessel surfaces could easily explain part of the underestimations in volume, length, and diameters. Since these periphery losses occur before processing with VNA (or the microCT software) begins, the true error from the software may be far less. μCT scans themselves are susceptible to this phenomenon when representing a contiguous object like a bone in digitized format, so it is an issue that will be present in real application.

Comparing the VNA and MicroCT results for the complex in silico models demonstrated why new software was needed for characterizing vasculature. First, MicroCT was not designed to measure all important parameters for assessing angiogenesis (e.g. VL). Second, while VV was calculated almost identically, VNA demonstrated a much higher accuracy in V.Dia than MicroCT. This was especially true in the highly heterogeneous networks. For the vessel diameters, this is due to the different algorithms used by the two software packages. VNA is structurally based, where each branch gets an equal weight. The average is calculated as:

$$V.Dia=\frac{1}{n_b}\sum d_{\mathit{\text{branch}}}$$ (1)

where n_b is the number of branches and d_branch is the diameter of each individual branch. The microCT software uses a sphere fitting method, where each voxel is assigned a value equal to the diameter of the largest sphere that contains itself and still fits within the structure.^13,15 Therefore, the average thickness is calculated as:

$$V.Dia=\frac{1}{n_v}\sum d_{\mathit{\text{voxel}}}$$ (2)

where n_v is the number of voxels and d_voxel is the diameter of the largest sphere that contains that voxel (i.e. the diameter value assigned to that voxel). As demonstrated in the heterogeneous histograms (Figure 8) and in the example (Figure 9), since larger objects contain more voxels, they have a larger weight in the average thickness calculation. This method is completely appropriate for calculating trabecular or cortical bone thicknesses where the goal is to know what size structures most of the bone material is located in, and the networks are fairly homogenous. One would not want an errant piece of ectopic bone being weighted the same as the main cortical structure. However, this approach is not necessarily correct for vessel diameters especially when the networks are highly heterogeneous. Furthermore, the sphere fitting method used by MicroCT erroneously “finds” more larger and smaller vessel diameters because voxels at vessel bifurcation points or near vessels ends are included in the calculation. The former are fitted to spheres larger than the individual vessels they join, while the latter are fitted to very small spheres. In the end, this creates errors that are non-uniform from sample to sample and highly distorts the resulting histograms. Calculating each branch’s diameter at the midpoint and then averaging them avoids this error and makes VNA a better tool for researchers to characterize vascular networks by their diameter. However, VNA is still sensitive to errors if individual branches are erroneously partitioned into multiple vessels.

Figure 9. Explanation of Algorithm Differences.

The great differences in the VNA and MicroCT average diameter (V.Dia) calculations are due to the underlying algorithms. VNA is structurally based and counts each branch equally in the averaging. The MicroCT software is voxel based and calculates the average of all the voxels’ assigned diameter values. Thus larger vessels end up being weighted more heavily.

Implementing our VNA software or a similar program is more limited by our current technologies than the accuracy of the programs themselves. Our current contrast agents are not ideal. The agent most commonly used for ex vivo microCT imaging in orthopaedics is the commercially available product MICROFIL (Flow Tech Inc, Carver, MA). While it has many excellent features like maintaining morphology during curing, the radiopacity is very similar to that of bone, so it is not feasible to segment the two tissues in the same volume of interest of a single scan. Two scans must be done pre- and post-decalcification and registered. This is not an issue for volumes lacking bone. Other post-mortem contrast agents are on the market or are reported in the literature, but seem to be either too costly or technically challenging to gain regular use. Of greater import is that vessels could be unmeasured, orphaned, or cut into multiple branches by inadequate contrast agent filling or using a scanning resolution larger than the vessel diameter. For our studies in rat hind limbs, the samples themselves are too large to scan at an adequate resolution to capture very small vessels. The smallest resolution we can use on these samples is 10 μm and capillaries are typically on the order of 5 to 10 μm. Either issue, poor infilling or poor resolution, would not greatly affect the outcomes if the microCT manufacturer’s software were used, but would cause vessels to be double (or more) counted using VNA.

There are some additional things to consider when using VNA to analyze microCT scans. First, BN is very sensitive to errors and probably not to be trusted or reported, although the other measures are either not dependent on or not as sensitive to this error and could be reported with confidence. Second, the protocol as a whole is not highly sophisticated. However, it was meant to be an easily accessible tool for most researchers, which we feel we achieved. When running on a typical desktop, the user may run into memory issues since the scans themselves are quite large, although we were able to run the protocol on our largest data set of over 2.83*10⁸ voxels. Access to computers with higher computing power will alleviate this issue. Finally, noisy data will add branches. While some measures are in place to limit noise effects (i.e. excluding branches 1–2 voxels in length), every effort should be made to have a ‘clean’ scan. This can be done by increasing the integration time, averaging scans, or doing additional preprocessing to reduce noise.

In conclusion, we have developed an easily accessible software protocol to analyze vascular networks from microCT scans, VNA, that performs overall better than the μCT manufacturer’s software that was developed for bone. Both measure equivalent volumes, and the microCT manufacturer’s software performs well enough for vessel diameters when the networks are relatively homogenous, although the vessel diameter distributions may need increased scrutiny. The μCT software could be combined with the first two VNA modules to get some additional outcomes (i.e. VL). However, our VNA protocol does well in either homogenous or heterogeneous systems and provides the additional outcomes automatically. As a field, we need to work on developing better contrast agents that easily and completely fill the vascular network, while also being far more radiopaque than bone. Thus, information about bone and vessels could be collected from a single scan with minimal sample processing. We also expect the accuracy of both programs to increase as imaging and basic computational technology improve.

Supplementary Material

Supp FigS1

Figure S1. One-tree base models and their skeletonized versions. Dots identify extra branches.

Supp figS2

Figure S2. Complex Homogeneous Models. The top panel are three of the sixteen-tree random models used in the validation studies. The final two are more complex one-tree models used only for the VNA/MicroCT comparisons.