Skip to main content

Advertisement

SpringerLink
Log in

Spatial Correlation Analysis of Isotropic Microvessels: Methodology and Application to Thyroid Capillaries

  • Published:
Annals of Biomedical Engineering Aims and scope Submit manuscript

Abstract

The study of relations between structural organization and functions of microcirculatory networks is a major aim of modern microangiology. Such a structural aspect of microvessels (MVs) as their spatial arrangement has substantial influence on their transport and other functional properties. This paper describes a methodology of spatial correlation analysis for isotropic blood and lymphatic MVs which is based on a stereological estimator of the pair correlation function [g 3D(r)] created recently by the authors for systems of elongated objects. The following main features of the methodology are presented: (i) interpretation of the shape of g 3D(r) curves, (ii) their quantitative description by numerical parameters, and (iii) limitations of the method arising from statistical requirements to MVs under investigation. The methodology is considered in the light of multilevel sampling designs, which are typical for biomedical morphology. The estimator with its methodological framework is applied to perifollicular blood capillaries in the adult rat thyroid. Related methods for studying the spatial arrangement of MVs are thoroughly discussed in the paper.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Figure 1.
Figure 2.
Figure 3.
Figure 4.
Figure 5.
Figure 6.
Figure 7.

Similar content being viewed by others

REFERENCES

  1. Antiga, L., B. Ene-Iordache, G. Remuzzi, and A. Remuzzi. Automatic generation of glomerular capillary topological organization. Microvasc. Res. 62:346–354, 2001.

    Article  PubMed  CAS  Google Scholar 

  2. Batra, S., K. Rakusan, and S. E. Campbell. Geometry of capillary networks in hypertrophied rat heart. Microvasc. Res. 41:29–40, 1991.

    Article  PubMed  CAS  Google Scholar 

  3. Bay, R. S., and C. L. Tucker, III. Stereological measurement and error estimates for three-dimensional fiber orientation. Polym. Eng. Sci. 32:240–253, 1992.

    Article  CAS  Google Scholar 

  4. Beard, D. A., and J. B. Bassingthwaighte. Modeling advection and diffusion of oxygen in complex vascular networks. Ann. Biomed. Eng. 29:298–310, 2001.

    Article  PubMed  CAS  Google Scholar 

  5. Bennett, R. A., R. N. Pittman, and S. M. Sullivan. Capillary spatial pattern and muscle fiber geometry in three hamster striated muscles. Am. J. Physiol. 260:H579–H585, 1991.

    PubMed  CAS  Google Scholar 

  6. Bentley, M. D., M. Rodriguez-Porcel, A. Lerman, M. H. Sarafov, J. C. Romero, L. I. Pelaez, J. P. Grande, E. L. Ritman, and L. O. Lerman. Enhanced renal cortical vascularization in experimental hypercholesterolemia. Kidney Int. 61:1056–1063, 2002.

    Article  PubMed  Google Scholar 

  7. Bosan, S., T. Kareco, D. Ruehlmann, K. Y. Chen, and K. R. Walley. Three-dimensional capillary geometry in gut tissue. Microsc. Res. Tech. 61:428–437, 2003.

    Article  PubMed  Google Scholar 

  8. Cerri, P. S., F. P. de Faria, R. G. Villa, and E. Katchburian. Light microscopy and computer three-dimensional reconstruction of the blood capillaries of the enamel organ of rat molar tooth germs. J. Anat. 204:191–195, 2004.

    Article  PubMed  Google Scholar 

  9. Eberhardt, C., and A. Clarke. Fibre-orientation measurements in short-fiber-glass composites. 1. Automated, high-angular-resolution measurement by confocal microscopy. Comp. Sci. Technol. 61:1389–1400, 2001.

    Article  Google Scholar 

  10. Flindt, R. Biologie in Zahlen. Stuttgart, New York: Fischer, 1985, p. 280.

    Google Scholar 

  11. Howard, C. V., and M. G. Reed. Unbiased Stereology. Three-Dimensional Measurement in Microscopy. Oxford: BIOS Scientific, 1998, p. 246.

    Google Scholar 

  12. Hubalkova, J., and D. Stoyan. On a qualitative relationship between degree of inhomogeneity and cold crushing strength of refractory castables. Cem. Concr. Res. 33:747–753, 2003.

    Article  CAS  Google Scholar 

  13. Itoh, J., A. Serizawa, K. Kawai, Y. Ishii, A. Teramoto, and R. Y. Osamura. Vascular networks and endothelial cells in the rat experimental pituitary glands and in the human pituitary adenomas. Microsc. Res. Tech. 60:231–235, 2003.

    Article  PubMed  Google Scholar 

  14. Juzkova, R., P. Ctibor, and V. Benes. Analysis of porous structure in plasma-sprayed coating. Image Anal. Stereol. 23:45–52, 2004.

    CAS  Google Scholar 

  15. Kayar, S. R., P. G. Archer, A. J. Lechner, and N. Banchero. The closest-individual method in the analysis of the distribution of capillaries. Microvasc. Res. 24:326–341, 1982.

    Article  PubMed  CAS  Google Scholar 

  16. Krasnoperov, R. A., and A. N. Gerasimov. Determination of size distribution of elliptical microvessels from size distribution measurement of their section profiles. Exp. Biol. Med. 228:84–92, 2003.

    CAS  Google Scholar 

  17. Krasnoperov, R. A., and A. N. Gerasimov. Stereological method of determining objects’ anisotropy. Patent on invention no. RU2211487. Filed April 26, 2001, Publ. August 27, 2003, p. 33.

  18. Krasnoperov, R. A., and D. Stoyan. Second-order stereology of spatial fibre systems. J. Microsc. 216:156–164, 2004.

    Article  PubMed  CAS  Google Scholar 

  19. Less, J. R., T. C. Skalak, E. M. Sevick, and R. K. Jain. Microvascular architecture in a mammary carcinoma: Branching patterns and vessel dimensions. Cancer Res. 51:265–273, 1991.

    PubMed  CAS  Google Scholar 

  20. Louis, P., and A. M. Gokhale. Computer simulation of spatial arrangement and connectivity of particles in three-dimensional microstructure: Application to model electrical conductivity of polymer matrix composite. Acta Mater. 44:1519–1528, 1996.

    Article  CAS  Google Scholar 

  21. Mattfeldt, T., H. Frey, and C. Rose. Second-order stereology of benign and malignant alterations of the human mammary gland. J. Microsc. 171:143–151, 1993.

    PubMed  CAS  Google Scholar 

  22. Mayhew, T. M. Second-order stereology and ultrastructural examination of the spatial arrangements of tissue compartments within glomeruli of normal and diabetic kidneys. J. Microsc. 195:87–95, 1999.

    Article  PubMed  CAS  Google Scholar 

  23. May-Newman, K., O. Mathieu-Costello, J. H. Omens, K. Klumb, and A. D. McCulloch. Transmural distribution of capillary morphology as a function of coronary perfusion pressure in the resting canine heart. Microvasc. Res. 50:381–396, 1995.

    Article  PubMed  CAS  Google Scholar 

  24. Minnich, B., H. Bartel, and A. Lametschwandtner. How a highly complex three-dimensional network of blood vessels regresses: The gill blood vascular system of tadpoles of Xenopus during metamorphosis. A SEM study on microvascular corrosion casts. Microvasc. Res. 64:425–437, 2002.

    Article  PubMed  Google Scholar 

  25. Murakami, T., T. Miyake, Y. Uno, A. Ohtsuka, T. Taguchi, and T. Sano. The blood vascular architecture of the rat thyroid gland: A scanning electron microscope study of corrosion casts. Arch. Histol. Cytol. 52:15–30, 1989.

    Article  PubMed  CAS  Google Scholar 

  26. Nunan, N., K. Wu, I. M. Young, J. W. Crawford, and K. Ritz. In situ spatial patterns of soil bacterial populations, mapped at multiple scales, in an arable soil. Microb. Ecol. 44:296–305, 2002.

    Article  PubMed  CAS  Google Scholar 

  27. Reed, M. G., and C. V. Howard. Stereological estimation of covariance using linear dipole probes. J. Microsc. 195:96–103, 1999.

    Article  PubMed  CAS  Google Scholar 

  28. Skorjanc, D., F. Jaschinski, G. Heine, and D. Pette. Sequential increases in capillarization and mitochondrial enzymes in low-frequency-stimulated rabbit muscle. Am. J. Physiol. 274:C810–C818, 1998.

    PubMed  CAS  Google Scholar 

  29. Steiniger, B., L. Ruttinger, and P. J. Barth. The three-dimensional structure of human splenic white pulp compartments. J. Histochem. Cytochem. 51:655–664, 2003.

    PubMed  CAS  Google Scholar 

  30. Stoyan, D. Stereological determination of orientations, second-order quantities and correlations for random spatial fibre systems. Biometrical J. 27:411–425, 1985.

    Article  Google Scholar 

  31. Stoyan, D., and H. Stoyan. Fractals, Random Shapes and Point Fields. Methods of Geometrical Statistics. Chichester, UK: Wiley, 1994, p. 389.

    Google Scholar 

  32. Stoyan, D., W. S. Kendall, and J. Mecke. Stochastic Geometry and its Applications. Chichester, UK: Wiley, 1995, p. 436.

    Google Scholar 

  33. Wyss, H. M., E. Tervoort, L. P. Meier, M. Muller, and L. J. Gauckler. Relation between microstructure and mechanical behavior of concentrated silica gels. J. Colloid Interf. Sci. 273:455–462, 2004.

    Article  CAS  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Proxima Technology Ltd., 20a-107, L. Tolstoy St., Pushkino, Moscow Region, 141206, Russia

    Renat A. Krasnoperov

  2. Institut für Stochastik, TU Bergakademie, 09596, Freiberg, Germany

    Dietrich Stoyan

Authors
  1. Renat A. Krasnoperov
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Dietrich Stoyan
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Renat A. Krasnoperov.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Krasnoperov, R.A., Stoyan, D. Spatial Correlation Analysis of Isotropic Microvessels: Methodology and Application to Thyroid Capillaries. Ann Biomed Eng 34, 810–822 (2006). https://doi.org/10.1007/s10439-006-9085-9

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10439-006-9085-9

Keywords

Search

Navigation