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Open AccessArticle

Mixed-Unit Lattice Approach for Area Determination of Cellular and Subcellular Structures

Department of Mathematics, Elwood John Glenn, Elwood, NY 11731, USA
Appl. Sci. 2019, 9(24), 5267; https://doi.org/10.3390/app9245267
Received: 14 November 2019 / Revised: 29 November 2019 / Accepted: 30 November 2019 / Published: 4 December 2019
(This article belongs to the Section Applied Biosciences and Bioengineering)
Even small changes in the dimensions of cellular and subcellular structures can inform an ongoing disease. An increase in glomerular dimensions is associated with kidney disease and can predict glomerulosclerosis, whereas an increase in the size of fluid-filled renal cysts is predictive of end-stage polycystic kidney disease. In the absence of set formulae to define the area of curvilinear irregular regions, such as glomeruli and cysts, the method of counting unit squares is used. Nonetheless, as infinitesimally small as the unit square may be, this 2D space-filling method still underestimates the area of a curvilinear region. Developed herein is a mixed-unit lattice approach that represents an improvement over the existing method for estimating the areas of cellular and subcellular structures. In test cases comprising images of glomeruli and renal cysts, this method outperformed the conventional unit-squares method, and may form the foundation for refining the current method used by most types of software for estimating the area of irregular curvilinear regions. View Full-Text
Keywords: area; glomeruli; cysts; irregular; curvilinear; unit; mixed; lattice area; glomeruli; cysts; irregular; curvilinear; unit; mixed; lattice
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Narayan, R. Mixed-Unit Lattice Approach for Area Determination of Cellular and Subcellular Structures. Appl. Sci. 2019, 9, 5267.

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