Stereology ANHB3313 Prof. Stuart Bunt (based on web site written by Lutz Slomianca See also

What is Stereology? Think about your stereo set at home or stereo images. They are not called "stereo" because there are two speakers or two pictures. They are called "stereo", which is derived from the Greek word for a "geometric object", because they try to recreate sounds or objects in space. Stereology tries to recreate or estimate the properties of geometrical objects in space (anything from a whole rat to a nerve cell). Applying stereological methods to tissue or organ section allows us to estimate the geometrical properties of the objects contained in the sections.

Quantification of Histology Need to describe different tissues Need to describe abnormalities Qualitative terms –Large, many, few, darker, lighter –“Durian are quite large” Quantitative terms –Number, area,volume,length,time

Quantification of Histology Need to describe different tissues Need to describe abnormalities Qualitative terms –Large, many, few, darker, lighter –“Durian are quite large” Quantitative terms –Number, area,volume,length,time –Durian are about the size of your head –40cm long, one litre in volume

Other Variables Other “dimensions” –Randomness/order –Rough/Smoothness –Alignment –Colour

Sampling Too many cells! Need to know your tissue,ordered,random,aligned,shapes Need to know what you want to measure Need to know the accuracy required Need to know misleading factors Need to know the errors in your measurements

Sampling We can only create a representative sample if 1. we have access to the entire structure or population. 2. we can recognize and/or define the entire structure or population. 3. all parts of the structure or population have the same chance to contribute to our sample.

Full Access If we do not have full access, our statements can only be valid for the parts of the structure or population that we have access to. Sometimes it will still make sense to investigate this part and sometimes it will not. If it still makes sense to us, we will have to argue for it.

Ability to Define or Identify If we are interested in a population of cells, and if we have the entire organ which contains these cells, then we have access to the entire population. We still have to recognize the cells. If we cannot define and/or recognize the structure or population, we either have to limit us to the parts we can define or we have to accept that we include parts of other structures or populations which we are not interested in.

Specific labels used to identify structures –Antibodies –DNA/RNA tags –Radioactive probes –Specific fluoro labels –Etc. Or shape etc.

All parts have the same chance of being sampled. If we cannot make sure that all parts of the structure or population contribute equally to our measurements, our statements will only be valid (1) if we know how well each part was represented in our measurements and (2) if we adjust our final statement for the unequal representation. In practice, this is often impossible to do. If it is possible, it usually requires a lot of work and, of course, we will have to argue for it.

Sampling Random independent samples

Uniform Random Systematic Samples U.R.S.

Difficulties with non-random objects

Sections are parts of 3D objects Assumptions needed about 3D structure 15 blue nuclei? 14 red nuclei? (actually 9 and 13) Assumption based models pre 1990?

Design based methods points (0 dimensions)can be used to measurevolumes (3 dimensions) lines (1 dimension)areas (2 dimensions) areas (2 dimensions)lengths (1 dimension) volumes (3 dimensions)numbers (0 dimensions) Use the fact that a section is a 3D block of tissue albeit very thin in one dimension

The Estimation of Volumes using Points (Cavalieri Estimator) First, imagine a rectangular grid. Next, we place points at each of the intersections of the grid lines and associate one of the rectangular areas formed by the grid with each point. By associating one area with a point located at each intersection we will cover the entire area of the grid. Each point actually "represents" an area. That means that we can estimate the area occupied by an object in the section by placing a grid of points on the section and counting the points which fall onto the object.

Overprojection Imagine an opaque sphere in a section which is thick enough to contain the entire sphere. Looking at the section the sphere will look like a circle. If we measure the area of the circle and multiply it be the thickness of the section we end up with the volume of a cylinder instead of the volume of a sphere - a very large overprojection error.

Thinner sections reduce the error If we divide the sphere over an increasing number of sections, the error will get smaller and smaller (A and B, overestimate in red). If we could cut infinitely thin sections the error would disappear.

Sampling can reduce errors The sampling of sections (urs, of course) can further reduce the error. When we sample, we want the underestimates (green; top samples in C) to balance the overestimates (green; bottom samples in C). The error that remains is an "overestimate of the underestimates" (red; top samples in C).

Essentially, estimating numbers with volumes is just the reverse of estimating volumes with points. But matters get a little complicated by the fact that we rarely are interested in counting true 0-dimensional points. Instead we want the numbers of biologically interesting objects. Somehow we need to convert objects into points, which means we have to do 2 or 3 things.

We have to identify something in our object which has a fixed numerical relation to the object and which can be clearly identified in the object. For example, if we would want to count intact, healthy humans we could count heads (1/object) or eyes (2/object) - hairs wouldn't work.

Sometimes the object itself is countable but sometimes it isn't. Blood cells, as nicely defined and physically separated objects, are directly countable. Neurons, with their complex shapes interdigitating in nervous tissue, are difficult to define in routine sections and are usually not directly countable. The nucleus of cells is usually well defined in routine sections, and there is only one of them in most cells types. The nucleus, as an easily recognizable unit with a fixed numerical relation to the object it represents, is usually the "something" that is counted.

We have to associate a point, i.e. something that "is there" only once in our section(s), with the object that we are going to count. That we see a nucleus in the section is not unique for the nucleus. Even a small nucleus may be present in multiple sections if our sections are very thin. Even if our sections are very thick, a few nuclei will have been split between sections and will be present in two sections. "Finding" that unique point of a sectioned object was actually the big breakthrough. In a series of sections, an object will only once be visible for the first time. The number of objects in a certain volume of e.g. an organ will, on average, correspond to the number of objects which become visible for the first time in a sample of that volume.

Estimation of Numbers using Volumes In a series of sections, an object will only once be visible for the first time. The number of objects in a certain volume of e.g. an organ will, on average, correspond to the number of objects which become visible for the first time in a sample of that volume.

Estimation of Area using lines Imagine a space - let's say a room in the basement. Now imagine an area in this space - let's say a sheet hanging to dry in the room. Now imagine some weird person shooting arrows in random directions in this room. How many times will the arrows pierce the sheet? Well, it depends on the size of the sheet and the number of shots. If we count the number of holes in the sheet and if we know the area of the sheet we can actually estimate the length of the paths flown by the arrows or, vice versa, if we count the number of holes in the sheet and know the length of the paths flown by the arrows we can estimate the area of the sheet. Or in scientifically more appropriate terms: The number of intersections (holes in the sheet) of lines (flown by the arrows) with a surface (of a sheet) is directly proportional to the length of the lines and the area of the surface.

Computer “Arrows” In fact we use a computer to put virtual lines through our section. Use fairly thick sections and a computer controlled microscope in the Z axis (up and down) Computer puts a dot on the section and moves it laterally as you focus up or down to make a “line”.