Second-order stereology of spatial fibre systems

Journal of Microscopy

Volumn 216, Issue 2, 2004, Pages 156-164

  Krasnoperov, R A ^a   Stoyan, D ^b  

^a Proxima Technology Ltd   (Russian Federation)

^b TU BERGAKADEMIE FREIBERG   (Germany)

Author keywords

Fibres; K function; Pair correlation function; Planar section; Second order stereology; Spatial distribution; Thyroid capillaries

Indexed keywords

CAPILLARITY; HIGH RESOLUTION TRANSMISSION ELECTRON MICROSCOPY; MICROCIRCULATION;

FIBER SYSTEMS; ISOTROPIC FIBERS; K-FUNCTION; PAIR CORRELATION FUNCTIONS; PLANAR SECTIONS; SECOND ORDERS; SECOND-ORDER STEREOLOGY; SPATIAL FIBERS; STEREOLOGY; THYROID CAPILLARY;

FIBERS;

ANIMAL TISSUE; ARTICLE; BLOOD VESSEL DIAMETER; CALCULATION; CAPILLARY; CORRELATION COEFFICIENT; FIBER; MATHEMATICAL MODEL; MEASUREMENT; NONHUMAN; PARAMETER; PRIORITY JOURNAL; RAT; STEREOLOGY; TECHNIQUE; THICKNESS; THYROID GLAND; TISSUE SECTION; TISSUE STRUCTURE; TRANSMISSION ELECTRON MICROSCOPY;

ANIMALIA;

EID: 7944233536     PISSN: 00222720     EISSN: None     Source Type: Journal    
DOI: 10.1111/j.0022-2720.2004.01407.x     Document Type: Article

References (33)

1. Adair, T.H., Wells, M.L., Hang, J. & Montani, J.P. (1994) A stereological method for estimating length density of the arterial vascular system. Am. J. Physiol. 266, H1434-H1438.
2. Bay, R.S. & Tucker, C.L., 3rd (1992) Stereological measurement and error estimates for three-dimensional fiber orientation. Polymer Eng. Sci. 32, 240-253.
3. Benes, V., Chadoeuf, J. & Kretzschmar, A. (1997) Properties of length estimation in spatial fibre models. Environmetrics. 8, 397-407.
4. Bishop, S.P., Powell, P.C., Hasebe, N., Shen, Y.T., Patrick, T.A., Hittinger, L. & Vatner, S.F. (1996) Coronary vascular morphology in pressure-overload left ventricular hypertrophy. J. Mol. Cell. Cardiol. 28, 141-154.
5. Cressie, N. (1991) Statistics for Spatial Data. J. Wiley & Sons, New York.
6. Cruz-Orive, L.M., Hoppeler, H.M., Mathieu, O. & Weibel, E.R. (1985) Stereological analysis of anisotropic structures using directional statistics. Appl Statist. 34, 14-32.
7. Eberhardt, C. & Clarke, A. (2001) Fibre-orientation measurements in short-fiber-glass composites. 1. Automated, high-angular-resolution measurement by confocal microscopy. Compos. Sci. Technol. 61, 1389-1400.
8. Elias, H. & Hyde, D.M. (1980) An elementary introduction to stereology (quantitative microscopy). Am. J. Anat. 159, 412-446.
9. Gokhale, A.M. (1990) Unbiased estimation of curve length in 3D using vertical slices. J. Microsc. 159, 133-141.
10. Gundersen, H.J.G. (2002) Stereological estimation of tubular length. J. Microsc. 207, 155-160.
11. Hennig, A. & Elias, H. (1964) Elliptical cylinders. Z. Wissen. Mikrosk. 66, 226-234.
12. Howard, C.V. & Reed, M.G. (1998) Unbiased Stereology. Three-Dimensional Measurement in Microscopy. BIOS Scientific Publishers, Oxford.
13. Krasnoperov, R.A. & Gerasimov, A.N. (2003a) Determination of size distribution of elliptical microvessels from size distribution measurement of their section profiles. Exp. Biol Med. 228, 84-92.
14. Krasnoperov, R.A. & Gerasimov, A.N. (2003b) Method for defining size distributions of objects approximated by elliptical cylinders. Patent on invention no. RU2219583. Filed 26.12.2000. Publ. 20.12.2003.
15. Krasnoperov, R.A. & Gerasimov, A.N. (2003c) Method for Stereological evaluation of object anisotropy. Patent on invention no. RU2211487. Filed 26.04.2001. Publ. 27.08.2003.
16. Krasnoperov, R.A., Grachev, S.V. & Gerasimov, A.N. (2001a) Elliptical microvessel sizes derived from measurement of size distributions of section profiles. FASEB J. 15, A119-A119.
17. Krasnoperov, R.A., Grachev, S.V. & Gerasimov, A.N. (2001b) Errors in measuring the section areas and the perimeters of microvessels from their electron and light microscopic profiles. Biophysics. 46, 505-511.
18. Kubínová, L., Janáček, J. & Krekule, I. (2002) Stereological methods for estimating geometrical parameters of microscopic structure by three-dimensional imaging. Confocal and Two-Photon Microscopy: Foundations, Applications, and Advances (ed. by A. Diaspro), pp. 299-332. Wiley-Liss, Inc., New York.
19. Mathieu, O., Cruz-Orive, L.M., Hoppeler, H. & Weibel, E.R. (1983) Estimating length density and quantifying anisotropy in skeletal muscle capillaries. J. Microsc. 131, 131-146.
20. Mattfeldt, T., Clarke, A. & Archengold, G. (1994) Estimation of the directional distribution of spatial fibre process using stereology and confocal laser scanning microscopy. J. Microsc. 173, 87-101.
21. Mattfeldt, T. & Mall, G. (1984) Estimation of length and surface of anisotropic capillaries. J. Microsc. 135, 181-190.
22. Møller, J. & Waagepetersen, R. (2003) Statistical Inference and Simulation for Spatial Point Process. Chapman & Hall/CRC. London.
23. Mouton, P.R., Gokhale, A.M., Ward, N.L. & West, M.J. (2002) Stereological length estimation using spherical probes. J. Microsc. 206, 54-64.
24. Odgaard, A., Jensen, E.B. & Gundersen, H.J. (1990) Estimation of structural anisotropy based on volume orientation. A new concept. J. Microsc. 157, 149-162.
25. Redon, C., Chermant, L., Chermant, J. & Coster, M. (1998) Assessment of fibre orientation in reinforced concrete using Fourier image transform. J. Microsc. 191, 258-265.
26. Ross, M.H., Romrell, L.J. & Kaye, G.I. (1995) Histology: a Text and Atlas. Williams & Wilkins, Baltimore.
27. Stoyan, D. (1984) Further stereological formulae for spatial fibre processes. Math. Operationsforsch. Statist. Series Statist. 15, 421-428.
28. Stoyan, D. (1985) Stereological determination of orientations, second-order quantities and correlations for random spatial fibre systems. Biometrical J. 27, 411-425.
29. Stoyan, D. & Stoyan, H. (1994) Fractals, Random Shapes and Point Fields. Methods of Geometrical Statistics. J. Wiley & Sons. Chichester.
30. Stoyan, H. & Stoyan, D. (1986) Simple stochastic models for the analysis of dislocation distributions. Physica Stat. Sol. A. 97, 163-172.
31. Stoyan, D., Kendall, W.S. & Mecke, J. (1995) Stochastic Geometry and its Applications. J. Wiley & Sons, Chichester.
32. Vogel, H.J., Weller, U. & Babel, U. (1993) Estimating orientation and width of channels and cracks at soilpolished blocks - a stereological approach. Geoderma. 56, 301-316.
33. Weibel, E.R. (1979/80) Stereological Methods, volumes 1 & 2. Academic Press, London.