### Introduction

By Darren Tran and Dr. Peter Mouton

Stereology is a design-based method prime for estimating first-order stereology parameters such as Volume (V), Surface area (SA), Length (L), and Number (N). This ensures that tissue analysis in fields including pulmonology, cardiology, and neuroscience is unbiased. However, the introduction of non-random error is often introduced in the tissue preparation stage leading to shrinkage and expansion of the tissue.

The most common method of analysis on this tissue is collecting data following all tissue processing, i.e., sectioning, staining, cover-slipping. However, some researchers have used methods of block advance (section thickness is taken from a partially processed tissue sample) rather than from the final processed tissue section. This leads to inconsistencies in study analyzing similar tissue section using stereology.

There is a quantitative basis for which stereology must be performed on after the completion of tissue processing because of the effects of block advance on total reference volume by the Cavalieri principle.

### Block Advance

Throughout tissue processing, tissue samples undergo a degree of volume change due to dying (agonal changes), perfusion or immersion fixation in dehydration agents (alcohol, aldehydes), and manual alterations in tissue volumes because of embedding, sectioning, staining, and cover slipping as required for tissue processing. In some studies, block advancing is performed where while the tissue is in a transitional form due to the volume changes by external manipulation, the volume of the reference space is taken.

For all tissue sections to be consistent, the only way to quantify reference volume of tissue in vivo is post-tissue processing; else, the researchers will be analyzing tissue of varying degree of processing leading to inconsistencies in the data. For example, brain tissue has a range of 60% to 70% between reference volume in vivo versus after final tissue processing.

Studies that are published in which stereology methods were used to obtain section volume will be assumed to follow the standard amount of shrinkage with estimation of total number of cells as the product of volume density (cells per unit volume) and the reference volume. To maintain accurate data for comparison with other published values, the final section thickness post-processing must be done to estimate reference volume as seen in Figure 1.

Figure 1: Systematic sections through an arbitrarily shaped volume

### The Cavalieri- Point Counting Method

The Cavalieri principle states that if two 3-D objects shave the same height and same cross-sectional area at every point along that height, they have the same volume.

To estimate total reference volume using the Cavalieri-point counting method Equation 1 is used:

In this equation, the product of the sum of points (∑P), area per point [a(p) in µm^{2}],the average section thickness in µm after all completion of all tissue processing(t), and the multiplier denoting sampling at every *k-th section* (k) yields the reference volume.

In the block advance method of using the Cavalieri-point counting method involving a transitional reference volume, Equation 2 is used which involves estimating a transitional reference volume (Vref) using block advance. A representation of this phenomenon is seen in Figure 2.

Figure 2: Two stacks of disks with the same volume demonstrating Cavalieri’s principle

### Disector Based Cell Counts

The effects of using block advance are seen in calculation of total cell number in equation 3.

Here in this equation, ∑*Q ^{–}* is the sum of objects counted using the optical disector; is the ratio of the section thickness (µm) to

*h,*the counting frame height in µm, at each cell counting location;

*asf*is the area sampling fraction [area disector frame (µm

^{2})/area x-y step (µm

^{2})]; and

*ssf*is the section sampling fraction (number sampled sections/total number of sections through the reference volume). The difference of using , thickness after tissue processing and the block advance method are similar to the Cavalieri Point counting method as they use the same parameters.

### Effects of using block advance in research

Figure 3: Results of Mouton et al with Cavalieri point counting (left) and cell number (right)

A study by Mouton et al explored the differences of tissue analysis with block advance and fully processed tissue samples as seen in Figure 3. The final section thickness (t-) was on average 10.5 ±0.4 μm (mean ± SD) as compared to the block advance (t^) of 40 um, for a z-axis shrinkage of ~ 74% from the tissue sectioning to the end of tissue processing. Similar trends were seen through calculation of reference volume using equations 1 and 2 and calculations of cell number using equation 3.

This affirms that possible tissue deformation occurs in many steps in the tissue processing scheme.

Figure 4: Schematic of progressive brain tissue deformation due to processing effects

As seen in Figure 4, post processing tissue shrinkage occurs through (A) in-vivo perfusion, (B) ex-vivo fixatives through immersion in hydrophobic reagents e.g., aldehydes, alcohol, acetone, (C) heating, paraffin embedding and freezing for tissue sectioning preparation, (D) tissue shrinkage following microtome sectioning, and finally (E) staining and cover-slipping tissue sections causing shrinkage.

Tissue processing-induced changes affect tissues variably; thus, the most practical method is to collect data after completion of all tissue processing. Uncertainty will be introduced when estimating other first-order stereological parameters such as surface area and length with data collected from a mixture of partially and completely processed tissue.

### What SRC Biosciences can do for you

Our Stereology Contract Research Organization (Stereology CRO) provides the most established option (since 1995) for stereology analysis with optional tissue processing for the global bioscience community. Under direct supervision of our Chief Scientific Officer (Dr. Peter R. Mouton), all tissue to be analyzed will be fully processed to ensure accurate and reproducible data.

Cited Works

[1] Mouton, P. R. (2002). *Principles and Practices of Unbiased Stereology: An Introduction for Bioscientists* (1st ed.). Johns Hopkins University Press.