FAQ

Frequently Asked Questions

These are the top questions asked by users requesting support for either Neurolucida or Stereo Investigator. Have a look through the list before contacting technical support. It might save you some time.

Should I use m=0 or m=1?

The sampling process has two considerations. The first is the value of interest, be it cell counts or any other geometric quantity. The second issue is to get an idea of how good the estimate is. The latter is done by estimating the CE. Basically, you guess what the value is and then guess how good the first guess was.

All CE estimates are model based and the CE method published by Gundersen is no exception. The m=0 and m=1 results differ in some arcane mathematical descriptions that relate the collected samples to a model of the object from which the samples were obtained. The authors decided that most biological tissue has characteristics that are described by the m=1 results. This is not always true. If there are any sharp cutoffs in the data, then the m=0 results are the appropriate results to use. Notice that the decision to use m=0 or m=1 is made outside of the obtained samples.

The easiest way to understand the difference is to consider an example of sampling in which the m=0 result is appropriate. Suppose that the samples come from something that has a triangular graph. A triangular graph is 0 until it ramps up in a straight line segment and suddenly plummets back to 0. (Please excuse my lack of knowledge of proper biological terms.) The volume of the chambers of a heart can approximate a triangular graph when the heart is sectioned perpendicular to its long axis. Near the tip of the heart the chambers are small and so is the cross sectional area. Sections closer to the top of the heart show increasing area until the end of the chambers is reached. Suddenly the area drops to 0.

Sudden cutoffs are uncommon in biological tissues. That is why m=1 is recommended and usually used today. The SI software computes both, because it is not possible to know from the samples which method is appropriate.

Kieu et. al. have published a paper in which they examine the samples, assuming that there are enough, to see which method is appropriate. The general idea is to see how smooth the samples appear to be.

Stereo Investigator calculates the CE estimates with both smoothness class equations: m=0 and m=1. m=1 is the newer method, and is recommended.

In short, the m=0 CE equation was the original CE estimate developed for use with the optical fractionator (see Gundersen and Jensen, 1987).

In 1999, Gundersen et. al. published a new paper referenced below, which reconsiders the CE issue and recommended estimating the CE with the m=1 smoothness class. The authors determined that biological tissues are best described by the m=1 class.

If you want to compare your results with older papers published using the pre-1999 CE estimate, you may want to use the m=0 smoothness class for a more direct comparison.

For a full explanation, please refer to the paper “The efficiency of systematic sampling in stereology – reconsidered” by H.J.G. Gundersen, E.B.V. Jensen, K. Kieu & J. Nielsen, Journal of Microscopy Vol. 193, Pt 3, March 1999, pp. 199-211.

Are variable tissue thicknesses
problematic?

Question

I have found that the amount of tissue shrinkage between experiments really varies, leaving me with a final thickness between 10 and 18um, depending on the experiment. I am unsure about whether or not to maintain the height of my counting brick, even if it means using a 5um counting brick for an 18um thick section. Is it acceptable to change the counting brick height between experiments, as long as it is maintained between different samples within an experiment? Any advice would be greatly appreciated. Thanks!

Discussion

Just as a point of clarification I assume you mean the height of the optical disector when you say the counting brick height. The optical disector is usually bounded by guard zones on top and bottom so that only the middle portion of the tissue is used in counting.

The original thickness of the tissue is not given here, but for the purposes of discussion I can assume that the material was cut at 30 microns. If that is the case, then a final section thickness of 10 microns means that the tissue has shrunk to 33% of its original thickness and 18 microns means that the tissue shrunk to 60% of it’s original thickness. An optical disector height of 5 microns in the 10 micron tissue is really a 15 micron high optical disector in the original tissue. In the 18 micron tissue the 5 micron optical disector is an 8 micron high optical disector.

I mention this because I want to point out that in a sense the optical disector height is changing between animals. This is reflected in the varying height sampling fraction values.

It is perfectly fine to change the sampling parameters between specimens. What does not work out is changing them in the middle of an organ. Not only is it okay to change the sampling parameters, it is also the smart thing to do. Beginning with the very first specimen knowledge is learned about how many counts are made. If only 50 counts are made then it is likely that the estimate is not that good. If the counts total to 1000 then it is likely that the estimate is must better than it actually needs to be. In other words, too much work was done. Going on to the next animal, sampling parameters are adjusted to bring the number of counts to a usable level – say 150 to 250.

In the case given here, a check of section thickness up front can be used to select sampling parameters appropriate for specimens. A short disector may require the use of more sampling sites to get enough counts. Smaller grid step sizes produces more sampling sites. A taller disector may be able to use larger gird stepping sizes to reduce the number of sampling sites and still count enough cells.

You may want to take a look at the CE formulas. Understanding all of the nitty gritty is not necessary. Notice that the equations are based on the counts and not on the sampling parameters themselves. The results from different specimens can be compared even though the sampling parameters differ.

There are other considerations if the tissue has varying thickness within the sections. Please ask again if this is an issue.

If you have a significant variation of tissue section thickness, then this will effect the accuracy of the estimation of total cell number when using the standard Optical Fractionator.

If you are using Stereo Investigator, I would suggest that you utilize the number-weighted variation of the Optical Fractionator. This technique requires that you measure the section thickness at each sampling site. Then the measured section thickness is used in the results calculation to make a more accurate estimate of total cell number.

A good paper that covers this topic is: K.-A. DORPH-PETERSEN, J. R. NYENGAARD AND H. J. G. GUNDERSEN, Tissue shrinkage and unbiased stereological estimation
of particle number and size,
Journal of Microscopy, Vol. 204, Pt 3, December 2001, pp. 232±246.

Is the Optical Fractionator really unbiased?

Questions

Is the Optical Fractionator really assumption free and unbiased?
There are a number of people who claim that the Optical Fractionator is not really assumption free and unbiased. They cite Benes and Lange, TINS 2001. Any comments?

Discussion

The term assumption free has been debated for a number of years. The term is used to indicate that the method does not make any of the following assumptions: size, shape, orientation or distribution of the objects. Of course, many assumptions are made as have been clearly stated in the articles describing these techniques. One assumption is that the researcher is able to understand what is being viewed in the microscope. Another assumption is that the researcher is able to measure the thickness of the sections.

Is stereology unbiased? The answer is yes. The TINS 2001 articles was written by Schmitz and Hof and refers to an article by Benes and Lange. Benes and Lange claim that the user must use very large counting frames. Schmitz and Hof dispute this. Benes and Lange also think that differential compression along the z-axis can bias the results. This is true. The issue is to determine how much of the z is being sampled. The number weighted section thickness addresses this issue. Please see Karl-Anton Dorph-Petersen et al, (J of Microscopy 1998).

It appears that there is some confusion between bias and accuracy. An unbiased estimate is one in which the average of all of the estimates is the true value. This is good since more work improves the result. Biases cannot be filtered out of the data. Biases do not cancel out. An accurate estimate is one that is close to the true answer. An accurate estimate might be a biased estimate. If that is the case, it means doing more work makes it impossible to find the true answer.

In summary, the beauty of the Optical Fractionator is that it provides an unbiased estimate of particles regardless of size, shape, orientation, or distribution of the particles being counted.

Using the Optical Fractinator in non-uniform cell distributions

Question

Can the Optical Fractionator be used to obtain accurate results with non-uniform cell distribution? There seems to be concern among some people that the Optical Fractionator does not yield accurate results unless the cell distribution is uniform.
Can the Optical Fractionator be used to obtain accurate results with non-uniform cell distribution?

Discussion

By non-uniform distribution I assume you are referring to a distribution that is not uniformly random. It has been suggested in the literature that stereological procedures such as the Optical Fractionator provide inaccurate results unless the particles being counted are distributed in a uniformly random manner. It is important to differentiate the two parts of the problem. Part 1 is getting an unbiased value. This is very important since it means that the more data that is collected, the better the results. Part 2 is getting an estimate of how good the answer is. This is where the CE comes into play.

The estimated number is not affected by the distribution of the cells. The estimation of the number of cells is not dependent on any argument that the particles are distributed in any fashion. On the other hand, the CE estimations are affected. This is to be expected. This simply says that the distribution of the particles together with the manner in which the particles were sampled could lead to poor estimates. This is true for all estimation techniques. Estimation does not mean exact determination. There is always some random error in the results.

The CE estimations available for the Optical Fractionator are all model based. This means that they are not unbiased. It is always possible to construct a population that will cause the CE estimations to fail. This does not mean that the population estimate is biased. The Matheron technique (aka Gundersen CE) has a model that the number of particles per section changes slowly across sections. A graph of the number of particles vs sections is a plot of points. The model assumes that connecting the points is a rough approximation of the actual curve. A population that violates this is a population of thin bands of cells and the section are taken parallel to these thin bands. The actual curve plummets to zero between the points. Sectioning perpendicular to the bands does not have this sampling problem that leads to a poor CE estimation. In either case, the population estimate is unbiased.

In summary, the accuracy of the Optical Fractionator is estimated by the CE and that is why it an important value.

Optical Fractinator or Nv:Vref?

Questions

Most people now use the Optical Fractionator probe. Is there any reason to do the Nv:Vref probe? I realize that the Optical Fractionator is immune to tissue shrinkage issues. Are there some case where Nv:Vref should be used?

Discussion

There are two basic techniques used to estimate the number of cells when using thick sections. The first technique that was developed is known as Nv*Vref. The idea is that the numerical density of cells is estimated and that density is multiplied by the reference volume to estimate the number of cells. The newer technique is the Optical Fractionator. The Optical Fractionator estimates the number of cells in a single step. That is why the technique is preferred today. Doing a single estimation instead of two estimations is more efficient.

The Nv*Vref method does have its uses. The Optical Fractionator must be able to sample a known fraction of the tissue. That isn’t always possible.

Consider the problem of counting cells and the Optical Fractionator places counting frames where the tissue is missing. During the preparation process part of the tissue was torn off. There might be cells to count, but the counting frame falls over missing tissue. Or suppose that the sampling technique results in the tissue of interest, but it is not possible to determine how much of the region of interest was sampled. There is no way to apply the Optical Fractionator unless the fraction of tissue sampled is known.

The Nv*Vref provides an unbiased estimate of the number of cells if it is possible to estimate the reference volume and every cell still has an equal chance of being counted. So if loss of tissue is a random process then this technique is unbiased. If the sampling used for density estimates is random then the technique is unbiased. Bias is introduced if the sample is always taken in the center of the region of interest. Then the edges of the regions have 0 chance of being used.

It is important to remember that every stereological technique has its requirements. In some experiments some of the requirements for a commonly used technique may not be met. If that is the case, take a look at other techniques that estimate the same quantity to see if the requirements can be met there. The broad range of experimental conditions has led to a number of solutions – pick the one that meets your needs.

Section Thickness and the Physical Disector

Questions

My cells are about 40 um in diameter.
Are my 6 um sections ok to count these cells?
Is there a rule about how thick sections can be in relation to the size of the cell to count with the physical disector? The reason I ask this question is that I have seen in papers where people cut their tissue 3um thick for doing the physical disector. This would twice the number of sections that I have now. I want to be as efficient as possible by using as few sections as I can, but I don’t want to cut my sections too thick in order to be useful.

Discussion

The physical disector uses what a stereologists calls a section. A section is a very thin piece of tissue that approximates a plane. In mathematics a plane is infinitely thin. It isn’t possible to create such a section. What is important is that the tissue is cut thin enough to be considered a plane.

So just what is infinitely thin for all practical purposes? Imagine a plane passing through the tissue. Now imagine that the tissue disappears except where the plane touches the tissue. The result is a flat, infinitely thin image. The disector uses two such planes. The planes have to be parallel. The planes pass through the tissue and in a sense collect two images. The images have to be close enough so that all of the changes between the two images can be inferred from the images. This means that objects can be connected to each other if they are part of the same object. It also means that profiles that are not part of the same object can be understood to be separate particles. If it is possible to reconstruct the contents of the missing volume from the two images, then the two images can be thought of as representing a volume.

A 3D probe that is used to count must have at least 3 dimensions. That is what a disector provides if the conditions are met. The volume is the interval between the two planes. The volume’s contents are inferred from the information on the 2 planes.

The physical disector counts tops. To do this the planes must be close enough so that no particle being counted can fall between the planes. If particles could lie between the planes then the counts would be undercounts, since there are more particles there than would be sampled.

Another problem occurs when the planes are not infinitely thin. One particle might end and another particle might begin within the same tissue. These particles are stacked one above the other.

A reasonable rule of thumb is to use sections that are 1/3 the smallest dimension of the particles being counted (Gundersen 1986). This supposes that counting is done on a pair of sections of this thickness. For larger objects it is possible to use two thin sections that are not sequential sections.

In the situation that is described here it may be possible to use sections that are not sequential. The sections are thinner than 1/3 the height of the smallest objects being counted. The important issue is whether or not it is possible to understand the changes between the pair of sections used in the physical disector. Using sequential sections may not be optimal. It may turn out that the sections are so close that few tops are encountered. This means that few counts are generated and that means many section pairs must be used. This is not an efficient way to count.

A study that uses thicker sections is described in the Journal of Microscopy, Vol 197, January 2000, pp 36-45. This study uses 50 micron sections. The graph on page 41 illustrates the effects of various section thickness values on the number of counts that are generated. The graph clearly shows that 50 micron sections is the most efficient way to section material. As was asked before, so just what is infinitely thin for all practical purposes? In this article the answer is 50 microns.

What does "Account for Missing Section/Add Probe for Missing Section" do?

The add probe for missing section option is a way of telling the software what to do when a section is missing. The information from a particular section is identified as missing. It is just as possible that the work has not been done. The software is unable to differentiate between a partially completed sterological study and missing data without formally stating that a section is missing.

The unbiased method of handling the situation is to apply the fractionator principle. This is valid as long as the missing section is a random event.

One alternative to the fractionator principle is to model. A model might assume that the value at the missing section is the mean of the values of the two neighboring sections. Modeling is biased. This means that the mean of the results is no longer guaranteed to be the correct answer.

Modeling is often justified by stating it is more representative of the data. That’s nice to say, but is it true? Modeling is rarely tested.

A good example of getting into trouble is to model the area of a missing section in a Cavalieri estimator by taking the mean of areas of the neighboring sections. Sounds simple and sounds good. In fact, this overestimates the area in all cases except when the object has the same cross section everywhere. That’s right. Unless the object is trivial, the answer is guaranteed to be wrong.

I don’t want to take the time to demonstrate it here. I suggest that some simple experimentation is tried to see that this is true.

The point is that simple glowing claims such as, “is a better representation,” must be proven mathematically. The math demonstrates that the fractionator principle is the proper method to use.

Can I use the nucleator on saggital sections?

Question
I would like to use the nucleator to measure the volume of the cells that I count in an optical fractionator. From reviewing the stereology literature I see that the nucleator can be used on isotropic or vertical sections. What about sagittal sections? Any help would be appreciated.

Discussion

The nucleator is a technique that can be used to estimate paticle volume. As with all stereological techniques there is a requirement that the probe and the objects interact with some degree of randomness. The word probe refers to the geometric shape interacting with the objects of interest. In the case of the nucleator the probe is a straight line. This straight line represents a random line in the 3D world. Since the tissue is normally sectioned, the possible choices for the 3D line are restricted. Within the section the orientation of the line is restricted to the angles from 0 to 180 degrees.

So how can all of the possible lines that might have run through the original tissue be represented? The answer is that the sections must be cut with random orientation.

A sagittal section is a preferred orientation. Using these sections it is not possible to run any 3D line through the particles being measured. This isn’t a problem if the particles appear the same here as they do in all other section orientation.

This doesn’t mean that the particles have to be spheres. Banana shaped particles work too as long as they are randomly oriented. The problem is that it is difficult to tell if the particles are randomly oriented.

The strict answer to the question is that sagittal sections cannot used. On the other hand, sagittal sections can be used if it is proved that the particles are randomly oriented. Verifying the random orientation of the particles is much more difficult than estimating their volume. The most demanding issue is that this check must be done in all experiments because what is true in the control tissue may not be true in the experimental tissue.

If random selection is broken at any point in the process, “all bets are off.”

How Do I Handle Missing Sections?

Problem

I have had several occasions where for one reason or another the section that I should use for counting is missing. What should I do in this case? Skip the section? Use another section? Any insight would be appreciated.

Solution

The important issue here is why the section cannot be used in counting. If the reason is random, then there are stereologically sound methods of using the samples despite the missing section. A dropped section, a section ruined during slicing, a section that did not stain properly are possible random causes. All that matters is that the section is not dismissed for preferential reasons. Such reasons might be that the section had very little of the region of interest on it, or the cells were too crowded to make counting easy. Removing a section for random reasons is similar to applying the fractionator principle. Suppose there are 6 sections. Roll a die and a number from 1 to 6 is chosen at random. Remove that section. Now the remaining 5 sections represent 5/6 of the original. Therefore, an unbiased estimate of the original quantity is the estimate from the 5 sections divided by the sampling fraction which is 5/6.

An important consideration is that although the result is unbiased, the variance has been increased.

If the sections are well spread out it is also possible to substitute a neighboring section. Suppose every 15th section is being used. If it is available, then use the 14th or 16th section as a substitute. Report this substitution in the results. This technique may be more difficult to justify if every other section is being used.

The colors of a live image on a monitor do not match the view of the image through the oculars

Problem

When I look at a live inage on a monitor, the colors don’t match what I see through the oculars. For example, I see orange and dark purple on the monitor, but pink and bright purple through the oculars.

Resolution

If your setup allows you to remove the IR filter from the path, you may have forgotten to return the filter to the path.

If this does not solve the problem, please contact Support.