Trends in Neurosciences
TechniquesStereological methods for estimating the total number of neurons and synapses: issues of precision and bias
Section snippets
Fundamental approaches to making estimates of total number
There are two fundamental approaches used to estimate the total numbers (est N) of neurons or synapses in a neural structure that are currently in wide use. The first is a two step process that involves the estimation of both the volume of the structure, est V(ref), and the volume density, est NV, of either the neurons or synapses9. The product of the two is an estimate of total number: est V(ref)×est NV=est N. (This approach was first used by Pakkenberg and Gundersen10 to make estimates of the
Assumption-based and design-based counting techniques
Stereological techniques for counting objects embedded in a bounded matrix that must be sectioned in order to observe the objects, such as neurons and synapses, can be divided into two general categories. (Here, the term stereology is used in its classical sense as a body of mathematical methods that relate global quantities, which include volume, surface area and length, and also object number, to measurements obtainable on sections of the structure27, 29.) The first of these categories
Sources of biases in estimation procedures
Until recently, assumption-based counting techniques have been used in most studies that have involved estimates of neuron and synapse number. As described in more detail below, these techniques for counting have potential sources of bias that are not present with the new generation of counting methods that involve direct counting with disectors36 or other 3D counting probes (see Box 1). Counting-related bias remains one of the major points of contention in the debate. Should design-based
Determinations based on direct counts of serially reconstructed objects
When counting objects in serially reconstructed material (Fig. 1A), one sequentially examines the sections in the series, determines which sectional profiles belong to the same object and gives the same cardinal number to sectional profiles from the same object36. This process essentially reduces the number of sectional profiles associated with each object to a zero dimensional parameter (point) or number that is based on the physical continuity of the sectional profiles. With this technique,
Indirect counting techniques based on geometrical assumptions
The principles that underlie the most fundamental indirect technique for determining the number objects in a volume of tissue, NV, are based on the relationship between the number of profiles of objects per unit area of the sections, QA, the caliper height of the objects in a direction normal to the plane of the section, H, and the thickness of the sections, h: NV=QA/(H+h) (Ref. 28). Notably, this technique requires either determinations (based on serial reconstructions) or assumptions about H,
Direct counting with disectors
The disector counting technique eliminates the potential biases associated with assumption-based methods because it involves the direct counting of objects in a defined volume of a structure. In a similar way to the methods of counting of serially reconstructed objects, this method does not depend upon information about the geometry of the objects. The conditions that must be met for its application are the same as those that apply to making counts of serial reconstructions (as described above).
Methodological and observer biases
The potential methodological biases that are inherent in assumption-based counting techniques are essentially calibration errors, similar to those encountered when reading a thermometer that has unknowingly been displaced from its scale. (Other sources of methodological biases can arise from improper calibration of the imaging system.) In order to distinguish between different types of methodological biases, the term geometrical biases will be used subsequently to refer to the potential
Design-based versus assumption-based stereological methods
The major limitation of assumption-based approaches to counting is the difficulty that is associated with obtaining accurate information about the size, shape and orientation of the objects being counted6. This information is necessary in order to derive the height factor used in the equations for indirect counting techniques, mentioned previously. In biological structures, objects are seldom, if ever, oriented randomly or of a uniform size and shape. The accuracy of the assumptions about the
Practical issues
One of the more crucial aspects of the debate about counting methods has focused on practical issues. These include questions about whether or not the geometrical biases can have a significant effect on the results of a study3, 41 and whether or not assumption-based counting is more readily performed and requires less expensive equipment4, 8. Although these issues fall outside the main aims of this article, it should be noted that there is empirical evidence that the biases can be significant36
The precision of stereological estimates
As mentioned at the beginning of this review, estimates must be unbiased and have a sufficient amount of precision to be useful. This review also aims to promote a better understanding of the concept of the precision of an estimate or estimation procedure. There has been a considerable amount of confusion in the literature about the difference between the unbiasedness and the precision of estimates. This is partly due to the use of the expressions ‘consistency’, ‘precision’, ‘accuracy’,
Unbiased versus precise
From the examples given, it is possible to appreciate the distinction between the unbiasedness of an estimate and the precision of an estimate (variance in statistical terms). As already mentioned, an estimation procedure can be defined as unbiased if it on average gives the true number. In order for it to be unbiased, both the sampling of sections and the sampling of objects (rules for counting) have to be unbiased. In the examples given here, systematic, uniformly random, sampling of sections
Concluding remarks
The precision of an estimate and the degree to which it is biased are two separate aspects of an estimate (Fig. 6). The degree to which an estimate is biased by either the non-representative sampling of sections or possible geometrical biases, associated with assumption based counting techniques, is difficult, if not impossible, to evaluate and correct. The probability than an estimate of synapse or neuron number reflects the true value is increased when design-based sampling and counting
References (49)
Neurocytology
(1996)- et al.
Acta Neuropathol.
(1997) - et al.
Anat. Rec.
(1991) - et al.
Neurosci. Lett.
(1997) - et al.
Neuroscience
(1993) - et al.
J. Appl. Physiol.
(1962) J. Neurol. Neurosurg. Psychiatry
(1991)- et al.
J. Comp. Neurol.
(1997) - Gundersen, H.J.G. et al. J. Microsc. (in...
Prog. Neurobiol.
J. Comp. Neurol.
J. Neurobiol.
J. Neuropathol. Exp. Neurol.
J. Neurocytol.
Am. J. Physiol.
J. Neurosci. Methods
J. Comp. Neurol.
Acta Pathol. Microbiol. Immunol. Scand.
J. Microsc.
J. Microsc.
J. Neurotrauma
J. Comp. Neurol.
Acta Neuropathol.
Cited by (756)
Flavonoids of Phoenix dactylifera L. ameliorates mercury-toxicity on the kidney of Wistar rats. A biochemical, morphological and molecular approach
2024, Pharmacological Research - Modern Chinese MedicineThe assessment of neuronal plasticity following sciatic nerve injuries in rats using electron microscopy and stereological methods
2024, Journal of Chemical Neuroanatomy