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Theoretical and experimental derivation of the function relating the size distribution of spherical particles in a volume element to that obtained from images of sections taken through it

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Summary

The mathematical formulation of three classes of theories concerning the problem outlined in the title of this study was critically assessed and experimentally evaluated. It was found that only one class of the theories describes the relation between the distribution of particles in a volume element to that observed in sections through this volume in a satisfactory way. The errors in the remaining two classes could be traced and the corrections made after a mathematically rigorous analysis brought these theories to comply with a model which, as we could prove experimentally, deserves a high level of confidence.

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References

  1. Bach, G.: Über die Größenverteilung von Kugelschnitten in durchsichtigen Schnitten endlicher Dicke. Z. wiss. Mikr.64, 265–270 (1959).

    Google Scholar 

  2. Coupland, R. E.: Determining sizes and distribution of sizes of spherical bodies such as chromaffin granules in tissue sections. Nature (Lond.)217, 384–388 (1968).

    Google Scholar 

  3. Covey-Crump, P. A. K.: Statistical analysis of granule size in the granular cells of the magnum of the hen oviduct. Quart. J. exp. Physiol.65, 233–237 (1970).

    Google Scholar 

  4. Kendall, M. G., Moran, P. A. P.: Geometrical probability. London: Charles Griffin & Co., Publishers 1963.

    Google Scholar 

  5. Komenda, S., Perinova, V., Bayer, A.: Die mikroskopische Bestimmung der Größenverteilung von Kugelelementen, die zufällig in gewisser Umwelt verstreut sind. Biometr. Z.11, 73–91 (1969).

    Google Scholar 

  6. Lenz, F.: Zur Größenverteilung von Kugelschnitten. Z. wiss. Mikr.63, 50–56 (1956).

    Google Scholar 

  7. Lenz, F.: Die Bestimmung der Größenverteilung von in einem Festkörper eingebetteten kugelförmigen Teilchen mit Hilfe der durch einen ebenen Schnitt erhaltenen Schnittkreise. Optik11, 524–527 (1954).

    Google Scholar 

  8. Lodin, Z., Navratil, E., Podlaha, M.: A study of the statistical distribution of the volumes of cellular nuclei and its relation to the statistical distribution of their projection areas. Čs. Morfol.11, 145–151 (1963).

    Google Scholar 

  9. Wicksell, S. D.: The corpuscle problem. Biometrika17, 84–99 (1925).

    Google Scholar 

  10. Zeipel, H. von: Catalogue de l'amas globulaire Messier 3. Annales observ. Paris25, 1–46 (1906).

    Google Scholar 

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Authors and Affiliations

  1. Département de Biophysique, Faculté de Médecine, Université de Sherbrooke, Canada

    Marcel Bélanger & Wolf D. Seufert

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  1. Marcel Bélanger
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  2. Wolf D. Seufert
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Additional information

Supported by a grant from the Medical Research Council of Canada.

In partial fulfillment of the requirements for obtention of the degree of a Master of Science. Supported by a Studentship from the Medical Research Council of Canada.

Scholar of the Medical Research Council of Canada.

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Bélanger, M., Seufert, W.D. Theoretical and experimental derivation of the function relating the size distribution of spherical particles in a volume element to that obtained from images of sections taken through it. Biophysik 9, 39–63 (1972). https://doi.org/10.1007/BF01293479

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  • DOI: https://doi.org/10.1007/BF01293479

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