Open Access

ARTICLE

Analytical Approach to Cell Geometry Description

P. Dabnichki¹, A. Zhivkov²

1 Department of Engineering, Queen Mary, University of London
2 Department of Mathematics, Sofia University, Bulgaria.

Computers, Materials & Continua 2005, 2(2), 97-104. https://doi.org/10.3970/cmc.2005.002.097

Abstract

A novel method for geometric reconstruction of smooth pseudo-rotational objects based on elliptic functions is developed. Based on the apparatus of theta functions analytical expressions for the main geometric invariants are derived. Reconstruction of asymmetric and irregular objects is illustrated. The advantages of the proposed technique lay in the following: i) reconstruction is computationally very fast and would allow a qualitative change in the current research practices, i.e. real-time monitoring and analysis of the responses of large cell samples ii) the accuracy of the method is very high and can be flexibly varied iii) the method allows quantitative analysis as demonstrated by the derived analytical representation for the main geometric invariants. Potential applications to existing experimental techniques and fundamental theoretical issues in mathematical models in cell physiology are briefly discussed.

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