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Revista Colombiana de Obstetricia y Ginecología

Print version ISSN 0034-7434On-line version ISSN 2463-0225


JAVIER, Rodríguez et al. Mathematical diagnosis of fetal monitoring using the Zipf-Mandelbrot law and dynamic systems’ theory applied to cardiac physiology. Rev Colomb Obstet Ginecol [online]. 2006, vol.57, n.2, pp.88-99. ISSN 0034-7434.

Objective: developing a mathematical approach to fetal heart rate monitoring by applying Zipf-Mandelbrot law and 17 conceptions of dynamic systems’ health and illness to the appearance of Dynamical Components of the System (DCS) in the monitoring trace by evaluating the degree of complexity of DCS distribution. Design: this is a diagnostic concordance study based on applying the law of natural languages and physiological simplifications (based on the dynamical systems theory) to the DCS appearance of fetal heart rate (FHR) DCS for making diagnostic generalization. Material and methods: a set of one hundred monitoring tests from pregnant patients was evaluated and divided into two groups; group A consisted of 50 women having risk factors and group B by 50 women without them. Dynamic simplifications, selected prototypes and Zipf-Mandelbrot law (for characterizing the degree of complexity using all possible DCSs) were compared with the rest of the monitoring traces to differentiate between health and illness. Results: a healthy fetus’ cardiac dynamics have mathematical self-organization, characterized by its degree of complexity and the absence of pronounced inverted Dynamical Components of the System (piDCS). The disease is characterized by the lack of complexity, or the presence of one or more piDCS, or the presence of an inverted DSC (iDSC) equal to or higher than 20x40 associated with the appearance of other iDCS equal to or higher than 20x50, or by the lack of the group of DCSs having 15 and/or 20 beats per minute, or combinations of the diagnostic measurements. One out of two monitoring tests from group B and one out of six from group A returned an incorrect diagnosis (using conventional clinical parameters) according to the computed measurements. Conclusions: mathematical characterization of the monitoring traces led to objectively and reproducibly differentiating between health and illness in developing a clinical diagnosis.

Keywords : fetalwell-being; fetal monitoring; Zipf-Mandelbrot law; dynamic system components.

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