The Method “cut cylinder” for Approximation Round and Cylindrical Shape Objects and Its Comparison with Other Methods

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. © 2020, The Editor(s) (if applicable) and The Author(s), under exclusive license to Springer Nature Switzerland AG.

Vasilyev A.V. 1, 2 , Bolshakova G.B. 3 , Goldstein D.V.4
  • 1 Central Research Institute of Dental and Maxillofacial Surgery, Timur Frunze St., 16, Moscow, 119021, Russian Federation
  • 2 Peoples’ Friendship University of Russia, Medical Institute, Miklukho-Maklaya St., 6, Moscow, 117198, Russian Federation
  • 3 Research Institute of Human Morphology, Tsyurupy St., 3, Moscow, 117418, Russian Federation
  • 4 Research Centre for Medical Genetics, Moskvorechye St., 1, Moscow, 115478, Russian Federation
Ключевые слова
Approximation; Critical-size defect; Morphometry; ‘‘cut cylinder’’ method
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