DOI: 10.1111/j.1365-2818.1981.tb01198.x. Resolution effect on the stereological estimation of surface and volume and its interpretation in terms of fractal dimensions

Resolution effect on the stereological estimation of surface and volume and its interpretation in terms of fractal dimensions

10.1111/j.1365-2818.1981.tb01198.x

Crossref journal-article

Wiley

Journal of Microscopy (311)

Abstract

SUMMARYEstimating surface and volume density of subcellular membrane systems at different magnifications yield different results. As the magnification is increased from × 18,000 to × 130,000 the estimates of surface density of endoplasmic reticulum and inner mitochondrial membranes increase by a factor of 3, whereas that for outer mitochondrial membranes increases only by 20%. The estimate of volume density of endoplasmic reticulum also increases by a factor of 3. No further increase is observed at magnifications above × 130,000 which is therefore called critical magnification. The findings are interpreted on the basis of the concept of fractals proposed by Mandelbrot, and the fractal dimensions of the membrane systems considered are estimated. This can lead to the derivation of resolution correction factors which permit measurements obtained at any magnification to be converted to estimates at critical magnification. These findings may explain, at least in part, the large discrepancy in the estimates of the surface of cytomembranes found in the literature.

Bibliography

Paumgartner, D., Losa, G., & Weibel, E. R. (1981). Resolution effect on the stereological estimation of surface and volume and its interpretation in terms of fractal dimensions. Journal of Microscopy, 121(1), 51â63. Portico.

Authors 3

D. Paumgartner (first)
G. Losa (additional)
E. R. Weibel (additional)

References 16 Referenced 112

10.1083/jcb.77.2.565
{'key': 'e_1_2_1_3_1', 'first-page': '409', 'article-title': 'The effect of optical resolution on the estimation of stereological parameters', 'volume': '431', 'author': 'Keller H.J.', 'year': '1976', 'journal-title': 'Proceedings of the Fourth International Congress on Stereology, Gaithersburg, U.S. Department of Commerce, National Bureau of Standards, Special Publications'} / Proceedings of the Fourth International Congress on Stereology, Gaithersburg, U.S. Department of Commerce, National Bureau of Standards, Special Publications / The effect of optical resolution on the estimation of stereological parameters by Keller H.J. (1976)
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10.1007/978-3-642-65492-3_1
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10.1016/S0344-0338(80)80137-3
{'key': 'e_1_2_1_9_1', 'first-page': '216', 'article-title': 'The influence of triiodothyronine and riboflavin deficiency on the rat liver with special reference to mitochondria. A morphologic, morphometric, and cytochemical study by electron microscopy', 'volume': '29', 'author': 'Reith A.', 'year': '1973', 'journal-title': 'Lab. Invest.'} / Lab. Invest. / The influence of triiodothyronine and riboflavin deficiency on the rat liver with special reference to mitochondria. A morphologic, morphometric, and cytochemical study by electron microscopy by Reith A. (1973)
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10.1083/jcb.17.1.208
Richardson L.F.(1961)Unpublished. Quoted from Mandelbrot(1977).
{'key': 'e_1_2_1_13_1', 'first-page': '609', 'article-title': 'Measurement of section thickness', 'volume': '1', 'author': 'Small J.V.', 'year': '1968', 'journal-title': 'Proceedings of the 4th European Conference on Electron Microscopy'} / Proceedings of the 4th European Conference on Electron Microscopy / Measurement of section thickness by Small J.V. (1968)
{'key': 'e_1_2_1_14_1', 'first-page': '743', 'article-title': 'Discussion on measurement of interlamellar spacing of pearlite', 'volume': '54', 'author': 'Underwood E.E.', 'year': '1961', 'journal-title': 'Trans. AIME.'} / Trans. AIME. / Discussion on measurement of interlamellar spacing of pearlite by Underwood E.E. (1961)
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10.1083/jcb.42.1.68

Dates

Type	When
Created	14 years, 1 month ago (Aug. 2, 2011, 12:33 p.m.)
Deposited	1 year, 9 months ago (Nov. 10, 2023, 10:13 a.m.)
Indexed	2 months, 1 week ago (June 25, 2025, 5:42 p.m.)
Issued	44 years, 8 months ago (Jan. 1, 1981)
Published	44 years, 8 months ago (Jan. 1, 1981)
Published Online	14 years, 1 month ago (Aug. 2, 2011)
Published Print	44 years, 8 months ago (Jan. 1, 1981)

Funders 0

None

BibTeX

@article{Paumgartner_1981, title={Resolution effect on the stereological estimation of surface and volume and its interpretation in terms of fractal dimensions}, volume={121}, ISSN={1365-2818}, url={http://dx.doi.org/10.1111/j.1365-2818.1981.tb01198.x}, DOI={10.1111/j.1365-2818.1981.tb01198.x}, number={1}, journal={Journal of Microscopy}, publisher={Wiley}, author={Paumgartner, D. and Losa, G. and Weibel, E. R.}, year={1981}, month=jan, pages={51–63} }

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