According to nonlinear dynamical system [10
], the dynamics of any physical or biological system can be quantified and described in terms of the motion of an attractor (e.g., strange or chaotic) and complexity indices of the reconstructed phase space. These concepts reflect some geometrical properties of the reconstructed phase space of the dynamical system under consideration, and these can be extracted. It is of great importance in the non linear analysis of a dynamical system the existence of low-dimension attractors and the estimation of the complexity indices D of the attractors [11
The difficulty of applying fractal mathematical processes to tumor biology is clear from the paucity of models that are useful to clinical practice. Tumors are nevertheless unstable systems, as illustrated by their heterogeneity in tumor genetics, aneuploidy, morphology, and growth patterns, for example. The change from cumulative minor genetic dysfunctions to catastrophic malignancy may thus have mathematical parallels. If tumors do exhibit chaotic properties, we may find them in the structural morphology of the whole tumor or its component parts, in the dynamic growth characteristics, in their patterns of behavior, or even in their response to therapy. It is the instability associated with a tumor (e.g., volume increase, invasion, or metastasis) rather than the existence of the tumor which kills. The restoration of stability or steady-state symbiosis of a tumor with its neighboring tissues may be an important objective in therapeutics.
By comparing the complexity indices it can be observed that there is a clear saturation value in large myomas and an absence of saturation value in small ones. Such a difference reflects an increase in the parameters (less organization, more chaoticity), which are needed in order to describe their dynamics. In terms of pathophysiology of myomas the observed difference which appeared in the biomagnetic recordings of the small myomas can be expressed as a distortion of the high rhythmicity and synchronization which characterized the large versus small myomas. It seems therefore that biomagnetic measurements with the use of non-linear analysis may prove to be a useful method in differentiating large and small myomas. It is true that biomagnetometry needs special equipment, a suitable prepared room and a good methodological knowledge for the employed methods, but once we have these requirements the method is rewarding. It is a non-invasive procedure, reliable, rapid and easy to interpret. Furthermore, it is totally harmless and well tolerated by women.
Our data suggest that biomagnetic measurements and nonlinear analyses are optimal procedures for assessing and differentiating uterine myomas.