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Background: Recently, multifractal analysis based on generalized concepts of fractals has been applied to biological tissues composed of complex structures. Methods: Using digitized images of the maternal surface of 278 placentas, multifractal parameters were measured with a fractal analysis software. Results: The values of αmin, α(0), αmax and the degree of multifractality given by the αmax – αmin difference calculated from 278 placentas were 1.840 ± 0.068, 2.089 ± 0.034, 2.856 ± 0.128 and 1.017 ± 0.136, respectively. A significant decrease of αmin and as a consequence a significant increase in the degree of multifractality were observed according to gestational age. The α(0) value of the placenta complicated by pregnancy-induced hypertension (PIH) was significantly higher than that without PIH. The αmin and α(0) values of the placenta having intrauterine growth restriction (IUGR) were significantly higher than those without IUGR. On the other hand, the presence of chorioamnionitis did not change multifractal properties of the maternal surface of the placenta. Conclusion: The multifractal parameters may be objective indices of the heterogeneity or complexity of the macroscopic morphology of the maternal surface of the placenta. Multifractal analysis holds a promise for quantitatively evaluating physiological and pathological development of the placenta. Copyright © 2008 S. Karger AG, Basel [ABSTRACT FROM AUTHOR]

Background: Detrended fluctuation analysis (DFA) has recently been validated as an excellent method by which to analyze heart rate variability and distinguish healthy subjects from patients with various types of the cardiac nervous system dysfunction. Methods: One hundred and nineteen fetal heart rate (FHR) recordings obtained from healthy normal fetuses and 68 recordings obtained from small-for-gestational-age (SGA) fetuses were analyzed by DFA to examine gestational and pathologic changes of the scaling exponent, α. Results: In normal fetuses, a significant increase was observed in both the short-term (≤30 s) α1 and long-term (>30 s) α2 scaling exponents according to gestational age. The α1 values of SGA fetuses were not significantly different from those of healthy normal fetuses; however, the α2 values of the former group (0.955 ± 0.152) were significantly higher than those of normal subjects (0.887 ± 0.128; p = 0.001). Conclusion: The α2 exponent appears to be a sensitive probe for detecting subtle, and possibly important, changes that occur in fetuses with intrauterine growth restriction, and may be helpful in the early and noninvasive detection of placental insufficiency or incipient intrauterine growth restriction. The use of DFA techniques offers great promise for understanding FHR behavior. Copyright © 2007 S. Karger AG, Basel [ABSTRACT FROM AUTHOR]

Background: Decelerations of fetal heart rate (FHR) are the results of many pathophysiological factors that modulate the intrinsic rate of the heart. FHR change is a complex phenomenon and can be viewed as a type of nonlinear dynamic system. This paper presents a qualitative model of FHR decelerations based on catastrophe theory, especially to account for abrupt heart rate changes seen in variable decelerations. Methods: One of the elementary catastrophes, the cusp catastrophe, was used to model FHR changes seen in variable, late, and early decelerations. Results: Catastrophe theory describes typical variable decelerations as an abrupt response to a slowly changing force of attack (uterine contraction) and physiological defense. Because of its three-dimensionality and topological features, the cusp catastrophe model provides a qualitatively satisfying description of FHR decelerations. Conclusion: The organized complexity of living systems offers the best hope for the application of catastrophe theory. The nature of the elementary catastrophes will be essential knowledge in the mathematical analysis of biology. Copyright © 2006 S. Karger AG, Basel [ABSTRACT FROM AUTHOR]

Objective: A fractal is a shape made of parts similar to the whole in some way. The objective of this study was to determine whether surface growth patterns in endometrioid endometrial adenocarcinoma are fractal, and the mean fractal dimension differs according to histologic grades and depth of myometrial invasion. Methods: After the images of photographs of 120 resected uteri with endometrial cancers were digitized, the fractal dimensions of surface of tumors were measured using a fractal analysis software. Results: The mean fractal dimensions of surface growth patterns in G1, G2, and G3 adenocarcinoma were 2.318, 2.303, and 2.383, respectively. These values were significantly greater than the topological dimension of a surface (= 2). The value was significantly higher in G3 than in G2 (p = 0.03). And although not statistically significant, the value of G3 was greater than G1 (p = 0.10) and than (G1 and G2) group (p = 0.06). No significant difference nor tendency was found in the fractal dimension of the surface of the tumor according to depth of invasion. Conclusion: This study shows that the surface of endometrioid endometrial adenocarcinoma has a fractal structure, and the mean fractal dimension may differ according to histologic grades. Our report proposes a new way of looking at endometrial cancer pathology. We believe that fractal geometry gives insights into tumor morphology and becomes a useful tool for analyzing complex and irregular tumor growth patterns mathematically. [ABSTRACT FROM AUTHOR]