Estimation of scaling index on space records of cell proliferation in the developing central nervous system
by
Jorge Mazzeo
Institute of Biomedical Engineering, Buenos Aires University and Interdisciplinary Group in Theoretical Biology, Favaloro University, Argentina
Coauthors: Melina Rapacioli (Interdisciplinary Group in Theoretical Biology, Favaloro University, Argentina) Santiagoo Duarte (IBCYN, School of Medicine, Buenos Aires University, Argentina) Carlos D’Attellis (Interdisciplinary Group in Theoretical Biology, Favaloro University, Argentina) Vladimir Flores (Interdisciplinary Group in Theoretical Biology, Favaloro University and IBCYN, School of Medicine, Buenos Aires University, Argentina)

vflores@favaloro.edu.ar

The dynamics of neuroepithelial cell proliferation in the chicken tectum opticum is analyzed using a model within the framework provided by the theory of stochastic point processes. Spatial signals of cell proliferation consisting of numerical sequences of intermitotic intervals were recorded under microscopic observation. The main goal of this work is to determine the possible existence of some kind of correlation or dependency between proliferating cells. The central hypothesis is that, if proliferating cells behave interactively, such interactions should impart some kind of dependency or memory on the signals representing the spatial organization of the proliferative activity. Additionally, appropriate methods of signal analysis should provide information about the spatial range of such interactions.

The analyses were performed by means of standardized algorithms designed to characterize the dynamics of numerical sequences by computing the scaling index of the stochastic processes. Among these methods, the Hurst index (one of the earliest proposed), the Detrended Fluctuation Analysis, the Fano Factor, the Power Spectral Density and the Dispersional Analysis were applied in this study.

Many authors [1],[2],[3] have pointed out that some of these methods are sensitive to non-stationarities. To overcome these pitfalls, elimination (remotion) of global trends is recommended [4] to transform the signal into a stationary sequence.

Here we analyze inaccuracies in scaling index estimation that, paradoxically, appear because of global trends removal.

This study was realized on artificial series, synthesized with defined statistical parameters, and also on spatial records of cell proliferation. We propose some methodological guidelines which are relevant to our specific field of research.

[1] Kun Hu, Plamen Ch. Ivanov1, Zhi Chen, Pedro Carpena, H. Eugene Stanley, “Effects of Trends on Detrended Fluctuation Analysis”, arXiv:physics/0103018 v4 14 May 2001

[2] M. Ignaccolo, P. Allegrini, P. Grigolini, P. Hamilton, B. J. West, “Scaling in Non-stationary time series I”, arXiv:physics/0301057 v1 22 Jan 2003

[3] Zhi Chen, Plamen Ch. Ivanov, Kun Hu, H. Eugene Stanley, “Effect of Nonstationarities on Detrended Fuctuation Analysis”, arXiv:physics/0111103 v2 15 Apr 2002

[4] Trang Dinh Dang and Sándor Molnár, “On the Effects of Non-Stationarity in Long-Range Dependence Tests”, El. Eng. Vol. 43, No. 4, Pp. 227–250, 1999

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Date received: April 30, 2008