Quantifying Branching Density in Rat Mammary Gland Whole-mounts Using the Sholl Analysis Method

All animal use and procedures for this study were approved by the NIEHS Laboratory Animal Care and Use Committee and conducted in an Association for Assessment and Accreditation of Laboratory Animal Care-accredited facility.

1. Excise Mammary Glands

1. Pre-label all slides using a xylene-proof method (pencil works best). Cover them with mounting solution at the end to preserve the label.
2. Euthanize the animal by an Institutional Animal Care and Use Committee-approved method.
3. After euthanasia, place the animal on its back on a dissecting board (Figure 1). Stretch and pin down all four limbs, with the rear limbs forming an inverted V (holding pins or small-gauge needles work well).
4. Spray the abdomen liberally with 70% ethanol to keep hair out of the mammary sample.
5. Using forceps, pull up the abdominal skin at the midline and make a small incision with dissecting scissors, being careful not to puncture the peritoneum.
   1. Beginning at the incision, cut the skin up to the neck region and then distally to the front limb. Cut down to the inguinal region and then distally to the first joint of the rear limb on the same side; this incision usually separates mammary glands 5 and 6. Avoid cutting the peritoneum.
   2. Pull back the skin with the attached mammary fat pad using forceps, gently separating it from the peritoneum using the blunt end of dissecting scissors. Separate as far dorsally as possible to fully expose the 4^th and 5^th inguinal mammary glands on the underside of the skin; pin the skin to the dissecting board (Figure 2).
   3. Gently grasp the mammary tissue of the 5^th gland with the rounded side of curved forceps and slowly trim the gland away from the skin, being careful not to nick the gland or the skin.
   4. Continue to trim, moving dorsally until the 4^th and 5^th glands have been completely lifted from the skin. Ensure that the nipple region is removed with the rest of the gland, as this serves as the starting point for the Sholl analysis. Cut the mammary tissue away from the body where it is attached at gland 4.
6. Once the gland is removed from the animal, spread it evenly on an electrostatically charged, 25 mm x 75 mm x 1 mm microscopy slide, with the side that was adjacent to the skin facing down.
   NOTE: For glands from older or lactating animals, a 51 x 75 x 1 mm slide may be required.
7. While wearing gloves, gently squeeze out any air bubbles. Cover the gland with a plastic paraffin film and another microscope slide and compress the gland to adhere it to the slide.
   NOTE: A 50 mL conical tube filled with water serves as a suitable weight. The amount of time required to adhere to the slide depends on the thickness of the gland. Thin, postnatal day (PND) 4 glands should be compressed for a minimum of 30 min, while thicker, adult glands may require as much as 2-5 h.

2. Prepare Mammary Whole-Mounts

1. Prepare the carmine alum solution at least 24 h in advance, as it requires boiling and refrigeration.
   1. Dissolve 1 g of carmine alum and 2.5 g of aluminum potassium sulfate (AlK(SO₄)₂·12H₂O) in 500 mL of distilled water and boil for 20 min in a 1-L flask. Bring the final volume to 500 mL using distilled water.
   2. Filter the solution through filter paper under a vacuum and refrigerate for storage.
      NOTE: Carmine alum solution can be reused but should be discarded when the color begins to fade.
2. Prior to fixation, peel the paraffin film off the gland, being careful not to pull the gland off the slide. Place the slide(s) in a glass slide-staining jar and immerse in fixative (100% ethanol, chloroform, and glacial acetic acid in a 6:3:1 ratio) for 12-48 h, depending on the thickness of the glands.
3. Pour off the fixative and soak the glands in 70% ethanol for 15 min. Gradually rehydrate the glands by pouring out 1/3 of the ethanol solution and replacing it with distilled water. Soak for 5 min. Repeat this process three times.
4. After the final rinse, pour off all the ethanol/water solution and replace it with 100% distilled water. Soak the glands for 5 min.
5. Pour off the distilled water and immerse the glands in the carmine alum solution. Stain the glands for 12-24 h, depending on the thickness.
   NOTE: The glands cannot be over-stained, but the staining time for multiple batches should be the same, so that the staining intensity is the same.
6. Pour off the carmine alum solution and rinse the glands in 100% distilled water for 30 s. Gradually dehydrate the glands by soaking them in 70% ethanol for 15 min, 95% ethanol for 15 min, and 100% ethanol for 20 min.
7. Clear the glands of fat by soaking them in xylene for 12-72 h, depending on the thickness.
   NOTE: The glands should be translucent (clear). If any opaque (whitish) areas remain, continue soaking in xylene until translucent. If lactating or otherwise very thick glands are being stained and cleared, the xylene may need to be replaced once to fully clear the glands.
8. Mount the slides with a xylene-based mounting medium by pipetting enough medium to just cover the gland. Add a coverslip, ensuring that no air bubbles form.
9. Allow the slides to dry. As the mounting medium dries, it will contract under the coverslip, and it may be necessary to add additional mounting medium. Once no additional medium is required, allow the slides to dry completely; this may take 2-3 weeks.
10. Once the slides are completely dry, any residual mounting medium can be removed with a cotton swab and a small amount of xylene. Be careful not to use too much xylene, as this can dissolve the mounting medium and loosen the coverslip. If this happens and air bubbles collect under the coverslip, the coverslip should be removed in xylene and the mounting process should be repeated.

3. Prepare Whole-mount Images for Analysis

1. Capture images of whole-mounts (Figure 3) using a macroscope or dissecting microscope and a digital camera with the appropriate software.
   NOTE: While any magnification that captures the entire glandular epithelium can be selected, it is imperative to capture all whole-mount images that will be compared to each other at the same magnification.
2. Download ImageJ software (or FIJI software)⁶.
3. Open the mammary whole-mount image in ImageJ by clicking "File" → "Open." Select the Freehand tool and trace around the glandular epithelium. Select "Edit" → "Clear Outside."
   1. Remove the lymph nodes by tracing around the node and using the Freehand tool and "Edit" → "Cut."
4. Separate the color channels by selecting "Image" → "Color" → "Split Channels." Select the channel with the best contrast, typically the blue channel.
   NOTE: An RGB image consists of a stack of the red, green, and blue components of that image. This action separates these components into three 8-bit grayscale images.
5. Subtract the background by selecting "Process" → "Subtract Background." Choose the desired parameters and then click "Preview" to preview the changes.
   NOTE: "Subtract Background" removes smooth, continuous backgrounds. Additionally, "Process" → "Filters" → "Unsharp Mask" can be used to create contrast.
6. Choose one of the following methods for automatically removing noise: despeckle or remove outliers.
   NOTE: ImageJ offers a third method for automatic noise removal: remove NaNs. However, the remove NaNs command is not applicable since it uses 32-bit images, and the current method uses 8-bit images.
   1. Remove noise using the despeckle command by selecting "Process" → "Noise" → "Despeckle."
      NOTE: This is equivalent to adding a median filter, which replaces each pixel with the median value in its 3 × 3 neighborhood.
   2. Remove noise using the remove outliers command by selecting "Process" → "Noise" → "Remove Outliers."
      NOTE: This process replaces a pixel with the median of the pixels in the immediate surroundings if it deviates from the median by more than a certain value (the threshold).
7. Remove any remaining noise manually (Figure 4).
   1. Open a copy of the original image and use this as a guide for what is and what is not noise. Click the double-red-arrow button at the far right of the toolbar. Select the Drawing Tools; the Drawing Tool buttons will now appear in the toolbar.
   2. Click the Eraser tool. Adjust the eraser diameter by right-clicking the Eraser tool button. Hold the left mouse button to erase noise.
      NOTE: Only one session of erasing can be undone. Once the left mouse button is released and clicked again, the previous erase cannot be undone.
8. Adjust the threshold by selecting "Image" → "Adjust" → "Threshold." Move the sliders to adjust the minimum (upper slider) and maximum (lower slider) threshold values until an adequate depiction of the gland is achieved.
   NOTE: Setting the threshold value segments grayscale images into features of interest and background.
   1. Click Apply. If necessary, remove additional noise at this point by following steps 3.6.1 and 3.6.2.
9. Reconstruct the portions of the glandular epithelium that were removed by thresholding and noise removal (Figure 5).
   1. Conduct image reconstruction carefully and on a minimal basis to maintain the integrity of the original image. Refer to the original image for a reference as to what is and what is not epithelium.
   2. Click the Spray Can tool (on the toolbar with the Drawing Tools). Adjust the spray diameter and rate by right-clicking on the Spray Can tool button. Carefully fill in missing sections of gland by clicking or holding down on the left mouse button.
10. Create a skeletonized image of the gland for conducting the Sholl Analysis. Ensure that the thresholded image is binary by selecting "Process" → "Binary" → "Make Binary."
    1. If the image is white on a black background, select "Process" → "Binary" → "Options" and uncheck "Black Background." Skeletonize the image by selecting "Process" → "Binary" → "Skeletonize."
       NOTE: This repeatedly removes pixels from the edges of the binary image until it is reduced to a single-pixel-wide shape.
    2. Dilate the image one time by selecting "Process" → "Binary" → "Dilate."
       NOTE: This fills in gaps created by thresholding and skeletonizing by adding pixels to the edges of the binary image.
11. Save the image by selecting "File" → "Save As." Select an image type (typically jpeg), enter the filename, and click "OK."
12. Check the accuracy of the skeletonized image by overlaying the skeletonized image onto the original image (Figure 6).
    1. Create an overlay by opening both the original image and the skeletonized image. Select "Image" → "Overlay" → "Add Image." In the "Add Image" dialog box, select the skeleton image from the "Image to Add" dropdown menu and set the opacity at 30%.
    2. Save the image of the skeleton image overlaid onto the original by selecting "File" → "Save As." Select an image type, enter the file name, and click "OK."

4. Conduct the Sholl Analysis

1. Open a skeleton image and make the image binary by selecting "Process" → "Binary" → "Make Binary."
   1. Prior to setting the magnification scale, measure the number of pixels/mm using a micrometer for the magnification at which the images were captured.
   2. Set the measured magnification scale by selecting "Analyze" → "Set Scale." Enter the number of pixels/mm. Set the "Known Distance" and the "Pixel Aspect Ratio," both to 1. Enter "mm" for the "Unit of Length" and check "Global" (maintains the same scale for each image).
2. Determine the ending radius (enclosing radius) for the Sholl analysis by drawing a line from the start of the primary duct (center of analysis) to the most distal point of the glandular epithelium (Figure 7).
   1. Use the line drawing tool in the toolbar to draw a line between the points of interest. Press the "M" key to take a measurement and note that a results window will open.
      NOTE: The value in the "Length" column is the length of the line in mm. This value will be automatically entered as the Ending Radius when setting the Sholl parameters. The Sholl plugin will use the starting point of the line as the center of the centric rings.
3. Running the Sholl Analysis.
   1. Run the analysis by selecting "Plugins" "Advanced Sholl Analysis;" a parameter window will appear.
   2. Set the Starting Radius in "I. Definition of Shells" to 0.00 mm; the length of the line measured in step 4.2 will automatically be entered as the "Ending Radius."
   3. Set the "Radius Step Size" to 0.1 mm.
      NOTE: The radius step size determines the number of rings (effectively the number of iterations); a smaller step size will increase the number of rings, while a larger step size will decrease the number of rings. The radius cannot be set too small, although an excessively small radius will result in an unnecessarily large number of rings. However, it can be set too large, which will create fewer rings and subsequently underestimate the true number of intersections. Refer to Stanko et al. (2015) for further information on determining the step size.
   4. Set the "# Samples" to 1 and the "Integration" to "Mean" in "II. Multiple Samples per Radius."
   5. Set the "Enclosing radius cutoff" to 1 and check "infer from starting radius" for the "# Primary branches" in "III. Descriptors and Curve Fitting."
      NOTE: "Fit profile and compute descriptors" and "Show fitting details" can be checked as desired.
   6. Check "Linear" and select "Best fitting degree" in "Profiles Without Normalization;" check "Most informative." Select "Area for Normalized Profiles" in "IV. Sholl Methods."
   7. Check "Create Intersections Mask" in "V. Output options" to create a heat map of the intersections (optional).
   8. Click "Cf. Segmentation" to generate a preview window of the image with rings to confirm the area of analysis.
4. Click "OK" to run the analysis.

5. Measuring the MEA

1. Measure the MEA by tracing the shortest distance around the epithelial tree (Figure 8).
   1. In ImageJ with the skeleton image of the gland open, click the Polygon tool. Click on a point on the perimeter of the epithelial tree to begin the polygon, move around the perimeter of the gland, and click to add a line segment.
   2. When the entire epithelial area has been circumvented, double-click to close the polygon. Press the "M" key to open a results window; the value in the "Area" column is the MEA.
2. In cases where the glandular epithelium has extended beyond the lymph node, subtract the lymph node area (LNA) from the MEA when calculating the branching density.
   1. Measure the LNA by tracing the lymph node in the same manner as the epithelial tree and pressing "M."
      NOTE: The LNA must be subtracted from the MEA in these cases because the lymph node prevents the analysis from counting intersections within the LNA. When the epithelium has not reached the lymph node, the LNA is zero.

6. Reporting Data

1. Report values for the enclosing radius, MEA, N, k, and branching density.
   NOTE: The enclosing radius is determined in step 4.2 and the MEA is determined in step 5.1.
   1. Run the analysis to generate a Sholl results window.
      NOTE: The reported N is the value for the sum inters. The reported k is the value for the Sholl regression coefficient (semi-log). The Sholl analysis will return a value for k over any measured region of the glandular epithelium. To obtain an accurate value for k over the full epithelium, the ductal ends must be present.
   2. Modify the Sholl analysis for the mammary gland by using the output value for N to calculate the branching density (the fundamental endpoint of this method). Calculate the branching density using the formula N/(MEA-LNA) and report the value as N/mm².