how to determine isotropy of sample

I am trying to measure the volume of neurons in coronal MTL sections. The nucleator probe is not isotropic, neither are my sections. Is there a way to determine if these pyramidal neurons are isotropic? I have seen some papers published that state they assumed isotropy of the neurons but did not offer an explanation.

Dear emwillia:
Thank you for writing. I am glad you are thinking about the orientation of the objects whose volume you are estimating. It is true that if some combination of the probe (the Nucleator probe) and the sample (neurons) does not ensure isotropy of interaction between the probe and the sample, then you may come up with biased estimates. In other words, if the cell is for instance a pyramidal cell, and you are always sectioning it down it’s long axis, you would overestimate the volume. If you take isotropic sections ( it means that you have randomized the orientation of your sample, usually by embedding the pieces of tissue in a sphere of embedding material, and rolling it randomly along the lab bench to come up with the orientation for sectioning. To be able to ‘read’ the anatomy of the sample a little better, you can choose a vertical direction and take vertical sections ( In this case the tissue block is positioned with its vertical direction perpendicular to the sectioning blade, and the block is ‘spun’ randomly by picking a degree between one and 360. Then for the probe a special type of line segment called a cycloid ( is used that is oriented with respect to the vertical section. Taking isotropic or vertical sections is probably the best way to make sure that no orientation of the probe and sample interaction is favored, the surest way to safeguard against sectioning in such a way causes bias towards overestimating or underestimating the volume.
Anatomists do not usually look forward to taking isotropic or vertical sections because it can make anatomical landmarks difficult to identify. Many times people, either because they don’t know about it or because they decide not to, will not take isotropic or vertical sections. If preferential sections are used, rather than saying you have an unbiased estimate, it may be better to graph the results in a histogram (number of cells on the Y axis and volume estimate on the X axis) and let people know that you used preferential sections ( instead of isotropic or vertical, and that may have caused bias (see first paragragh:
Of course, and to get to your question, you can somehow prove that your particles are either isotropic themselves or that they are arranged in an isotropic way. The former has been addressed for various brain cells (Schmitz, C., Schuster, D., Niessen, P. and H. Korr (1999) No Difference between Estimated Mean Nuclear Volumes of Various Types of Neurons in the Mouse Brain Obtained on either Isotropic Uniform Random Sections or Conventional Frontal or Sagittal Sections, J. of Neuroscience Methods, 88, pp. 71 – 82.) and the latter for cortical cells in layers in the cerebrum (Oster, S., Christoffersen, P., Gundersen, H. J., Nielsen, J.O., Pakkenberg, B. and C. Pedersen (1993) Cerebral Atrophy in AIDS: a Stereological Study, Acta Neuropathol., 85, pp. 617 -622.). The way this is done is to run the same experiment twice once with preferential sections and once with either isotropic or vertical. If you get the same results, it shows there was no need to take the vertical or istotropic section.

I hope you find this answer helpful and please feel free to comment with any further questions.