MORPHOMETRY

Morphometry vs. Stereology

Stereology is generally defined as the procedure of deriving 3-dimensional information from measurements on 2-dimensional images. Morphometry can be defined as the quantification of structural features when the 3-dimensional structure is understood.

It is important to always keep in mind that when viewing sections in the light microscope or the Transmission Electron Microscope that the structures are actually three dimensional and that a particular 2-dimensional view can arise from more than one 3-dimensional structure. The simplest example is the observation in a section (or polished surface of a solid) of a circular structure. This can arise from sectioning a cylindrical, spherical, elliptical or irregular structure. Attempts to quantify aspects of the 3-dimensional structure require understanding of that structure, either to determine what equations to use, or to know whether the observations are representative, or both.

Consider that simple circular profile. If you wanted to use it to calculate the surface to volume ratio of the structure sectioned, it would be simple in the case of a cylindrical structure (where all circular sections will be the same size), but difficult in the case of a spherical structure, where the profile size in the section depends on the position of the section in relation to the centre of the sphere. The problem becomes even more complex in the case of irregular structures.

Basic Measurements

Consider a basic question related to this drawing:
Outlines

The green outlines are representative of some structure of interest in a section outlined by the black box. One of the most basic questions that can be asked is: what is the area of the outlines?
It comes in several forms:

What is the area of each outline?
What is the total area of all outlines?
What fraction of the section area is enclosed by the outlines?

Although these questions appear the same, operationally the first can be much more involved than the other two. (Consider for example how the question of the area of an outline is to be answered if the outline is partly outside the edge of the section.)

Two distinctly different approaches

There are a number of methods that can be used to answer these questions, but they separate into two classes:

Techniques where the boundary of the structure must be precisely defined
Techniques involving approximations where the ability to precisely locate the boundary is frequently not critical.

Precise techniques

A remarkably simple way to answer the area questions if the information is on paper (a drawing or a micrograph) is to use a pair of scissors to cut out the areas, and weigh the cutouts. If the paper is of uniform thickness, the weight will yield the area quite accurately. This is an accepted method, though not commonly used now. However it illustrates the principle well. To get the result the observer must be able to follow the edge of each area unequivocally and every bit of edge must be processed.

There are related techniques which are less destructive of micrographs.

A mechanical device called a planimeter can measure the area within an area traced by an observer moving its stylus around the perimeter. (These devices are hard to locate now.)
An observer can trace the edge of areas on a micrograph using a computer peripheral called a graphics tablet. A small signal emitted from a special pen is detected by the tablet, so the path of the pen can be recorded.
Digitised images displayed on a computer screen can be traced with a pointer controlled with a mouse, joystick or touch screen.
Image analysis performed by computer may be able to detect the position of the boundaries of interest and follow them. (This is different to methods based on detection of features of the area within the boundary that may thereby define the area.) These methods generally require some effort on the part of the observer, even if only to monitor the outcome.

These methods suffer from common problems:

They fail completely, or at best become inaccurate, when part of the boundary is ill defined
they can be quite time consuming
observer fatigue is likely to lead to significant departures of the traced boundary from the real one with consequent inaccuracies

though the more computerised techniques may reduce the labour.

Approximation techniques

Methods which do not suffer from the above problems (some of which lead to inaccuracy) but which can produce consistent approximations represent attractive alternatives to the labour intensive approaches.

A simple example is to consider the outline question. Imagine if the outlines were drawn on a paper with a square grid.

The question of the area of each outline can be addressed with the total area of squares that predominantly lie in the outlines. While this is obviously an approximation, it will often be quite an acceptable one. In this case, you would probably answer "four" for the left outline. The top and bottom of these four are not completely in outline, but some of the outline occupies parts of adjacent squares, so the errors tend to average out.

This approach is an example of a collection of approximation methods referred to as Point Counting Morphometry.

Feedback