Abstract
A method has been developed to approximate the volumes of cylindrical objects by slices. The method is based on an algebraic formula of circle. It allows to determine the thickness by width of the cylindrical object measured on the current and subsequent slices, which enables the morphometry of histological sections made with unequal pitch. The ‘‘cut cylinder’’ method is compared with other popular approximation methods: unilateral rectangles, trapezoids and reconstructions in the Amira software. A theoretical comparison of approximation methods revealed that an error of less than 5% can be achieved for the unilateral rectangle method with more than 11, and for the trapezoids’ method more than 6 slices. The ‘‘cut cylinder’’ algorithm allows to reproduce the contour of the cylindrical object in the most accurate way with a smaller number of slices - less than 6. In practical application of methods for round objects reconstructed by 6 histological sections with the equal pitch, the method of approximation by trapezoids gives a more accurate results and is easy to apply. In order to determine the thickness of the slice, the trapezoids’ method can be supplemented by a “cut cylinder” method, which contains a formula for determining the thickness of the slice by the width. The developed “cut cylinder” method allows to obtain data comparable to 3D-reconstruction in the Amira software (FEI, USA), however with a large dispersion for sections with equal pitch. #CSOC1120
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
References
Portero-Muzy, N., Arlot, M., Roux, J.-P., Duboeuf, F., Chavassieux, P., Meunier, P.: Evaluation and development of automatic two-dimensional measurements of histomorphometric parameters reflecting trabecular bone connectivity: correlations with dual-energy X-Ray absorptiometry and quantitative ultrasound in human calcaneum. Calcif. Tissue Int. 77, 195–204 (2005)
Yeh, S.A., Wilk, K., Lin, C.P., Intini, G.: In vivo 3D histomorphometry quantifies bone apposition and skeletal progenitor cell differentiation. Sci Rep. 8(1), 5580 (2018)
Revell P.A.: Quantitative methods in bone biopsy examination. In: Pathology of Bone. Springer, London (1986)
Jennane, R., Almhdie, A., Aufort, G., Lespessailles, E.: 3D shape-dependent thinning method for trabecular bone characterization. Med. Phys. 39(1), 168–178 (2012)
Stadlinger, B., Korn, P., Tödtmann, N., Eckelt, U., Range, U., Bürki, A., Ferguson, S., Kramer, I., Kautz, A., Schnabelrauch, M., Kneissel, M., Schlottig, F.: Osseointegration of biochemically modified implants in an osteoporosis rodent model. Eur. Cells Mater. 25, 326–340 (2013)
Dempster, D.W., Compston, J.E., Drezner, M.K., Glorieux, F.H., Kanis, J.A., Malluche, H., Meunier, P.J., Ott, S.M., Recker, R.R., Parfitt, A.M.: Standardized nomenclature, symbols, and units for bone histomorphometry: a 2012 update of the report of the ASBMR histomorphometry nomenclature committee. J. Bone Miner. Res. 28(1), 2–17 (2013)
Cocks, E., Taggart, M., Rind, F.C., White, K.A.: Guide to analysis and reconstruction of serial block face scanning electron microscopy data. J. Microsc. 270(2), 217–234 (2018)
Vasilyev, A.V., Volkov, A.V., Bolshakova, G.B., Goldstein, D.V.: Characteristics of neoosteogenesis in the model of critical defect of rats’ parietal bone using traditional and three-dimensional morphometry. Genes Cells 9(4), 121–127 (2014). in Russian
Vasilyev, A.V., Bolshakova, G.B.: The effect of dalarginum on the reparative regeneration of critical size calvarial defect in rats. Morphol. Newsl. 4, 11–18 (2014). in Russian
Allen, M.R., Burr, D.B.: Bone modeling and remodeling. In: Basic and Applied Bone Biology, 1st edn. Academic Press, Cambridge (2014)
Tapp, E.: Tetracycline labelling methods of measuring the growth of bones in the rat. J. Bone Joint Surg. Br. 48(3), 517–525 (1966)
Yuehuei, H.A., Kylie, L.M.: Handbook of Histology Methods for Bone and Cartilage, 1st edn. Humana Press, Totowa (2003)
Acknowledgments
The mathematical model “cut cylinder” was reviewed and approved by Marchuk Institute of Numerical Mathematics of the Russian Academy of Sciences (IVM RAS). Special gratitude is expressed to the specialist in the field of mathematical segmentation Dr. Alexander A. Danilov for his contribution to the correction and improvement of the method.
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2020 The Editor(s) (if applicable) and The Author(s), under exclusive license to Springer Nature Switzerland AG
About this paper
Cite this paper
Vasilyev, A.V., Bolshakova, G.B., Goldstein, D.V. (2020). The Method “cut cylinder” for Approximation Round and Cylindrical Shape Objects and Its Comparison with Other Methods. In: Silhavy, R., Silhavy, P., Prokopova, Z. (eds) Software Engineering Perspectives in Intelligent Systems. CoMeSySo 2020. Advances in Intelligent Systems and Computing, vol 1295. Springer, Cham. https://doi.org/10.1007/978-3-030-63319-6_5
Download citation
DOI: https://doi.org/10.1007/978-3-030-63319-6_5
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-030-63318-9
Online ISBN: 978-3-030-63319-6
eBook Packages: Intelligent Technologies and RoboticsIntelligent Technologies and Robotics (R0)