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Blood Capillary Length Estimation from Three-Dimensional Microscopic Data by Image Analysis and Stereology

Published online by Cambridge University Press:  14 May 2013

Lucie Kubínová*
Affiliation:
Department of Biomathematics, Institute of Physiology, Academy of Sciences of the Czech Republic, Vídeňská 1083, 14220 Prague, Czech Republic
Xiao Wen Mao
Affiliation:
Department of Radiation Medicine, Loma Linda University, Loma Linda, CA 92354, USA
Jiří Janáček
Affiliation:
Department of Biomathematics, Institute of Physiology, Academy of Sciences of the Czech Republic, Vídeňská 1083, 14220 Prague, Czech Republic
*
*Corresponding author. E-mail: [email protected]
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Abstract

Studies of the capillary bed characterized by its length or length density are relevant in many biomedical studies. A reliable assessment of capillary length from two-dimensional (2D), thin histological sections is a rather difficult task as it requires physical cutting of such sections in randomized directions. This is often technically demanding, inefficient, or outright impossible. However, if 3D image data of the microscopic structure under investigation are available, methods of length estimation that do not require randomized physical cutting of sections may be applied. Two different rat brain regions were optically sliced by confocal microscopy and resulting 3D images processed by three types of capillary length estimation methods: (1) stereological methods based on a computer generation of isotropic uniform random virtual test probes in 3D, either in the form of spatial grids of virtual “slicer” planes or spherical probes; (2) automatic method employing a digital version of the Crofton relations using the Euler characteristic of planar sections of the binary image; and (3) interactive “tracer” method for length measurement based on a manual delineation in 3D of the axes of capillary segments. The presented methods were compared in terms of their practical applicability, efficiency, and precision.

Type
Biological Applications
Copyright
Copyright © Microscopy Society of America 2013 

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References

Bjaalije, J.G. (2002). Localization in the brain: New solutions emerging. Nat Rev Neurosci 3, 322325.CrossRefGoogle Scholar
Borgefors, G. (1984). Distance transformations in arbitrary dimensions. Comput Vision Graph 27, 321345.CrossRefGoogle Scholar
Čapek, M., Janáček, J. & Kubínová, L. (2006). Methods for compensation of the light attenuation with depth of images captured by a confocal microscope. Microsc Res Tech 69, 624635.CrossRefGoogle ScholarPubMed
Čebašek, V., Eržen, I., Vyhnal, A., Janáček, J., Ribarič, S. & Kubínová, L. (2010). The estimation error of skeletal muscle capillary supply is significantly reduced by 3D method. Microvasc Res 79, 4046.CrossRefGoogle Scholar
Cruz-Orive, L.M. & Howard, C.V. (1991). Estimating the length of a bounded curve in three dimensions using total vertical projections. J Microsc 163, 101113.CrossRefGoogle Scholar
Dorph-Petersen, K.-A., Nyengaard, J.R. & Gundersen, H.J.G. (2001). Tissue shrinkage and unbiased stereological estimation of particle number and size. J Microsc 204, 232246.CrossRefGoogle ScholarPubMed
Favre, C.J., Mancuso, M., Maas, K., McLean, J.W., Baluk, P. & McDonald, D.M. (2003). Expression of genes involved in vascular development and angiogenesis in endothelial cells of adult lung. Am J Physiol Heart Circ Physiol 285, 19171938.CrossRefGoogle ScholarPubMed
Gokhale, A.M. (1990). Unbiased estimation of curve length in 3D using vertical slices. J Microsc 159, 133141.CrossRefGoogle Scholar
Gundersen, H.J.G. (1986). Stereology of arbitrary particles. A review of unbiased number and size estimators and the presentation of some new ones, in memory of William R. Thompson. J Microsc 143, 345.CrossRefGoogle ScholarPubMed
Gundersen, H.J.G. (2002). Stereological estimation of tubular length. J Microsc 207, 155160.CrossRefGoogle ScholarPubMed
Gundersen, H.J.G., Jensen, E.B.V., Kiêu, K. & Nielsen, J. (1999). The efficiency of systematic sampling in stereology—Reconsidered. J Microsc 193, 199211.CrossRefGoogle ScholarPubMed
Howard, C.V., Reid, S., Baddeley, A. & Boyde, A. (1985). Unbiased estimation of particle density in the tandem scanning reflected light microscope. J Microsc 138, 203212.CrossRefGoogle ScholarPubMed
Huang, C.X., Qiu, X., Wang, S., Wu, H., Xia, L., Li, C., Gao, Y., Zhang, L., Xiu, Y., Chao, F. & Tang, Y. (2013). Exercise-induced changes of the capillaries in the cortex of middle-aged rats. Neuroscience 233, 139145.CrossRefGoogle ScholarPubMed
Janáček, J., Čebašek, V., Kubínová, L., Ribarič, S. & Eržen, I. (2009). 3D visualization and measurement of capillaries supplying metabolically different fiber types in the rat extensor digitorum longus muscle during denervation and reinervation. J Histochem Cytochem 57, 437447.CrossRefGoogle Scholar
Janáček, J., Kreft, M., Čebašek, V. & Eržen, I. (2012). Correcting the axial shrinkage of skeletal muscle thick sections visualized by confocal microscopy. J Microsc 246, 107112.CrossRefGoogle ScholarPubMed
Janáček, J. & Kubínová, L. (2010). Variances of length and surface area estimates by spatial grids: Preliminary study. Image Anal Stereol 29, 4552.CrossRefGoogle Scholar
Kochová, P., Cimmermann, R., Janáček, J., Witter, K. & Tonar, Z. (2011). How to asses, visualize and compare the anisotropy of linear structures reconstructed from optical sections? A study based on histopathological quantification of human brain microvessels. J Theor Biol 286, 6778.CrossRefGoogle ScholarPubMed
Kreczmanski, P., Schmidt-Kastner, R., Heinsen, H., Steinbusch, H.W.M., Hof, P.R. & Schmitz, C. (2005). Stereological studies of capillary length density in the frontal cortex of schizophrenics. Acta Neuropathol 109, 510518.CrossRefGoogle ScholarPubMed
Kubínová, L. & Janáček, J. (2001). Confocal microscopy and stereology: Estimating volume, number, surface area and length by virtual test probes applied to three-dimensional images. Microsc Res Tech 53, 425435.CrossRefGoogle ScholarPubMed
Kubínová, L., Janáček, J., Karen, P., Radochová, B., Difato, F. & Krekule, I. (2004). Confocal stereology and image analysis: Methods for estimating geometrical characteristics of cells and tissues from three-dimensional confocal images. Physiol Res 53(Suppl 1), S47S55.CrossRefGoogle ScholarPubMed
Kubínová, L., Janáček, J. & Krekule, I. (2002). Stereological methods for estimating geometrical parameters of microscopic structure by three-dimensional imaging. In Confocal and Two-Photon Microscopy: Foundations, Applications and Advances, Diaspro, A. (Ed.), pp. 299332. New York: Wiley-Liss Inc. Google Scholar
Kubínová, L., Janáček, J., Ribarič, S., Čebašek, V. & Eržen, I. (2001). Three-dimensional study of the capillary supply of skeletal muscle fibers using confocal microscopy. J Muscle Res Cell Motil 22, 217227.CrossRefGoogle ScholarPubMed
Kubínová, L., Mao, X.W., Janáček, J. & Archambeau, J.O. (2003). Stereology techniques in radiation biology. Radiat Res 160, 110119.CrossRefGoogle ScholarPubMed
Larsen, J.O., Gundersen, H.J.G. & Nielsen, J. (1998). Global spatial sampling with isotropic virtual planes: Estimators of length density and total length in thick, arbitrarily orientated sections. J Microsc 191, 238248.CrossRefGoogle ScholarPubMed
Mattfeldt, T., Mall, G., Gharehbaghi, H. & Moller, P. (1990). Estimation of surface area and length with the orientator. J Microsc 159, 301317.CrossRefGoogle ScholarPubMed
Mattfeldt, T., Möbius, H.-J. & Mall, G. (1985). Orthogonal triplet probes: An efficient method for unbiased estimation of length and surface of objects with unknown orientation in space. J Microsc 139, 279289.CrossRefGoogle ScholarPubMed
Meyer, F. (1992). Mathematical morphology: From two dimensions to three dimensions. J Microsc 165, 528.CrossRefGoogle Scholar
Moreau, P. & Ronse, C. (1996). Generation of shading-off in images by extrapolation of Lipschitz functions. Graph Models Image Proces 58, 314333.CrossRefGoogle Scholar
Mouton, P.R., Gokhale, A.M., Ward, N.L. & West, M.J. (2002). Stereological length estimation using spherical probes. J Microsc 206, 5464.CrossRefGoogle ScholarPubMed
Ndode-Ekane, X.E., Hayward, N., Gröhn, O. & Pitkänen, A. (2010). Vascular changes in epilepsy: Functional consequences and association with network plasticity in pilocarpine-induced experimental epilepsy. Neuroscience 166, 312332.CrossRefGoogle ScholarPubMed
Pawley, J.B. (Ed.) (2006). Handbook of Biological Confocal Microscopy, 3rd ed. Berlin: Springer.CrossRefGoogle Scholar
Santaló, L.A. (1976). Integral Geometry and Geometric Probability. Reading, MA: Addison-Wesley.Google Scholar
Sheppard, C.J.R. & Török, P. (1997). Effects of specimen refractive index on confocal imaging. J Microsc 185, 366374.CrossRefGoogle Scholar
Štencel, M. & Janáček, J. (2006). On calculation of chamfer distance and Lipschitz covers in digital images. In Proc S4G, Lechnerová, R., Saxl, I. & Beneš, V. (Eds.), pp. 517522. Prague: Union of Czech Mathematicians and Physicists.Google Scholar
Sterio, D.C. (1984). The unbiased estimation of number and sizes of arbitrary particles using the disector. J Microsc 134, 203231.CrossRefGoogle ScholarPubMed
Triggs, B. & Sdika, M. (2006). Boundary conditions for Young-van Vliet recursive filtering. IEEE T Signal Proces 54, 23652367.CrossRefGoogle Scholar
Wan, D.-S., Rajadhyaksha, M. & Webb, R.H. (2000). Analysis of spherical aberration of a water immersion objective: Application to specimens with refractive indices 1.33–1.40. J Microsc 197, 274284.CrossRefGoogle Scholar
Weibel, E.R. (1979). Stereological Methods, Vol.1. Practical Methods for Biological Morphometry. London: Academic Press.Google Scholar
Young, I.T. & van Vliet, L.J. (2002). Recursive Gabor filtering. IEEE T Signal Process 50, 27982805.CrossRefGoogle Scholar
Zakiewicz, I.M., van Dongen, Y.C., Leergaard, T.B. & Bjaalije, J.G. (2011). Workflow and atlas system for brain-wide mapping of axonal connectivity in rat source. PLoS One 6, e22669. CrossRefGoogle Scholar