Nonlinear Dynamics, Psychology, and Life Sciences, Vol. 11, Iss. 3, July, 2007, pp. 309-331
@2007 Society for Chaos Theory in Psychology & Life Sciences


Nonlinear Analysis of Digital Images and Doppler Measurements for Trophoblastic Tumor

Valeriy Orel, Academy of Medical Sciences, Kiev, Ukraine
Tatyana Kozarenko, Academy of Medical Sciences, Kiev
Konstantin Galachin, Academy of Medical Sciences, Kiev
Andriy Romanov, Academy of Medical Sciences, Kiev
Alexander Morozoff, Academy of Medical Sciences, Kiev

Abstract: Cancer can be viewed as a complex adaptive system. Complex adaptive systems can be described mathematically by nonlinear (chaos) theory including asymmetry, fractal structure and autocorrelation factor. Taking into consideration spatial irregularity and heterogeneity of internal structures of tumor cells, we examined deterministic chaos of trophoblastic tumor for organ, cellular, molecular levels on digital images and their Doppler measurements of blood flow. The digital images were tested by evaluation of contours deformation level and quantitative heterogeneous pattern. The suggested algorithm for estimation of spatial chaos in digital medical image is based on calculation of the skew and the spread parameters, fractal dimension and autocorrelation function. Ultrasound images demonstrated higher values of the skew parameter for the uterus of choriocarcinoma patients than hydatidiform mole and healthy individuals. The registered changes in nonlinear dynamics of uterine artery blood flow are tending to diminish deterministic chaotic process in choriocarcinoma. Nonlinear analysis of cell images for chorionic villi and tumor supressor gene p16 evidenced the tendency of increase in spatial chaos for patients with choriocarcinoma. The concept of deterministic chaos is hierarchical for the host during trophoblastic disease.

Keywords: trophoblastic tumor, deterministic chaos, digital image