Robert Stepien

Simple fractal method of assessment of histological images for application in medical diagnostics.

We propose new method of assessment of histological images for medical diagnostics. 2-D image is preprocessed to form 1-D landscapes or 1-D signature of the image contour and then their complexity is analyzed using Higuchis fractal dimension method. The method may have broad medical application, from choosing implant materials to differentiation between benign masses and malignant breast tumors.

New method for analysis of nonstationary signals

Background Analysis of signals by means of symbolic methods consists in calculating a measure of signal complexity, for example informational entropy or Lempel-Ziv algorithmic complexity. For construction of these entropic measures one uses distributions of symbols representing the analyzed signal. Results We introduce a new signal characteristic named sequential spectrum that is suitable for analysis of the wide group of signals, including biosignals. The paper contains a brief review of analyses of artificial signals showing features similar to those of biosignals. An example of using sequential spectrum for analyzing EEG signals registered during different stages of sleep is also presented. Conclusions Sequential spectrum is an effective tool for general description of nonstationary signals and it its advantage over Fourier spectrum. Sequential spectrum enables assessment of pathological changes in EEG-signals recorded in persons with epilepsy.

Complexity of EEG‐signal in Time Domain ‐ Possible Biomedical Application

Human brain is a highly complex nonlinear system. So it is not surprising that in analysis of EEG‐signal, which represents overall activity of the brain, the methods of Nonlinear Dynamics (or Chaos Theory as it is commonly called) can be used. Even if the signal is not chaotic these methods are a motivating tool to explore changes in brain activity due to different functional activation states, e.g. different sleep stages, or to applied therapy, e.g. exposure to chemical agents (drugs) and physical factors (light, magnetic field). The methods supplied by Nonlinear Dynamics reveal signal characteristics that are not revealed by linear methods like FFT. Better understanding of principles that govern dynamics and complexity of EEG‐signal can help to find ‘the signatures’ of different physiological and pathological states of human brain, quantitative characteristics that may find applications in medical diagnostics.

SEM Image Analysis for Roughness Assessment of Implant Materials

We propose a new very simple method to determine roughness of a surface of an implant material from its scanning electron microscopy (SEM) image. For this purpose we have combined a preprocessing method that has been used in histopathology with fractal method used in nonlinear time series analysis. In the pre-processing step the image is transformed into 1-D signals (‘landscapes’) that are subsequently analyzed. Our method draws from multiple disciplines and may find multidisciplinary applications.

Biologically Inspired Models of Decision Making

We present two biologically inspired models, demonstrating how people make decisions – one, called Game of Choosing (GoC), demonstrates how promotion and autopromotion influence decision making, and second, called Chaosensology Model (ChS), demonstrates how emotions may influence logical decision making. Our results confirm what has been known in psycho-sociology since William James works.

New Fractal Methods for Diagnosis of Cancer

We have proposed two new fractal methods that may be helpful in diagnosis of cancer. To reduce computational complexity, 2-D images of tumors are firstly preprocessed following our methods to form 1-D sequences that are subsequently analyzed using Higuchi fractal dimension. The first method, Image Signature’s Fractal Dimension, is based on analysis of 1-D sequence called the signature of the tumour mass contour. The second method, Image Landscapes’ Fractal Dimension, is based on analysis of two 1-D sequences called the horizontal and vertical landscapes. Both methods are easy and quick and we demonstrated that they may be successfully applied in oncology to support pathologist’s diagnosis.

Econobiophysics - game of choosing. Model of selection or election process with diverse accessible information

We propose several models applicable to both selection and election processes when each selecting or electing subject has access to different information about the objects to choose from. We wrote special software to simulate these processes. We consider both the cases when the environment is neutral (natural process) as well as when the environment is involved (controlled process).

Chaotic Data Analysis and Hybrid Modeling for Biomedical Applications

We propose two methods of analysis of chaotic processes to be applied in sensory analysis. These methods may be used off-line in clinics e.g. for analysis of biosignals registered during sleep, or implemented into new sensor systems e.g. for drivers’ vigilance monitoring in real time; they may also be applied in new type of hybrid models of circulatory and respiratory systems.

Generating Heart Rate Variability - Application to Hybrid Modeling of Cardiorespiratory System

Since Heart Rate Variability (HRV) is an important indicator of patient’s health it is important to introduce HRV into the hybrid models of cardiorespiratory system. We decided to use Elman’s neural networks to generate off-line HRV signals of physiological and pathological patients, and we are working on application of this method on-line in our hybrid model. For analysis of the generated HRV and their comparison with input data we apply Higuchi’s Fractal Dimension method.