One way to accomplish this would be to section small samples of randomly oriented pieces of tissue and probe these sections with flat 2-D area probes ( Nyengaard and Gundersen, 1992 Løkkegaard et al., 2001) or by cutting the tissue in three orthogonal planes ( Kubíková et al., 2018). In order to avoid the problem related to the anisotropy of biological structures a number of techniques have been developed to ensure an isotropic interaction between probe and structural feature. Methodological biases of this type lead to estimates that systematically deviate from the true value regardless of the amount of sampling performed. One would prefer to avoid having to make any assumptions about the extent or existence of isotropy in biological tissue in order to avoid potential biases in the estimate that result from anisotropy. However, biological structures are seldom if ever isotropic structures. In this case, the orientation of the 2 dimensional area probe is not important. That is, the direction of its linear elements is equal in all three dimensions of space. This will be the case when the structural feature is truly isotropic. It is important to remember that this formula is applicable only when the linear structural feature has an isotropic interaction with the areal probe. Unlike the two dimensional Buffon problem, which involves the probability that a randomly thrown needle intersects a line on the floor, the space ball probe is based on the probability that a surface is hit by a line that is randomly oriented in 3D space. Briefly, it is based on a three dimensional version of the Buffon needle problem.
In spite of the simplicity of the formula, its' derivation is somewhat deep and the derivation and proof are presented in the original Smith-Guttman paper. Accordingly, the number of times that a linear structural feature ( Q) passes through a probe of known area ( A) is directly related to the length per unit volume ( L V) of the structural feature. The formula that relates measurements made on images to length ( Smith and Guttman, 1953) is simple and easy to apply (Equation 1). In this article, the use and application of a virtual isotropic surface probe that readily fulfills this requirement is described. Prior to the introduction of the space ball probe, stereological estimators of length were plagued by the requirement for an isotropic interaction between the area probes and linear features such as axons and capillaries. The stereological relationship formula for estimating length density, L V ^ = 2 Structural parameters of potential interest and for which quantitative studies of length have yet to be carried out include microtubules, involved in intracellular transport, and neuropil threads, an expression of Alzheimer's disease. These parameters can be used to evaluate brain hemodynamics ( Kubíková et al., 2018), tissue oxygenation ( Nikolajsen et al., 2015), and tissue repair ( Lee et al., 2005 McConnell et al., 2016) and ultimately used to develop therapeutic approaches to brain disorders. Examples using space ball probes include the length of dopaminergic axons, which can be related to the dopaminergic innervation and function of the striatum ( Li et al., 2016) the length of serotoninergic ( Liu et al., 2011) and cholinergic axons in cerebral cortex which can be related to cortical function ( Nikolajsen et al., 2011) and the length of astrocyte processes, which can be related to immune-reactivity ( McNeal et al., 2016). Journal of Microscopy, 206 (1), 54–64.Estimates of the length of cellular features can provide quantitative information about various biological functions. Stereological length estimation using spherical probes. The efficiency of systematic sampling in stereology and its prediction. The efficiency of systematic sampling in stereology-reconsidered. Gundersen, H.J.G., Vedel Jensen, E.B., Kieu, K., & Nielsen, J. : Variance due to systematic random sampling Variance due to systematic random sampling : Volume (grid X * grid Y * section thickness) (equation 2, 2002) by including that information in v (volume sampled). This equation eliminates the terms F2 (area-fraction) and F3 (thickness-fraction) used by Mouton et al.
Stereology spaceballs pdf#
Spaceballs for details about the probe or View/Print PDF