Wlodzimierz Klonowski

Fractals in the Neurosciences, Part II Clinical Applications and Future Perspectives

It has been ascertained that the human brain is a complex system studied at multiple scales, from neurons and microcircuits to macronetworks. The brain is characterized by a hierarchical organization that gives rise to its highly topological and functional complexity. Over the last decades, fractal geometry has been shown as a universal tool for the analysis and quantification of the geometric complexity of natural objects, including the brain. The fractal dimension has been identified as a quantitative parameter for the evaluation of the roughness of neural structures, the estimation of time series, and the description of patterns, thus able to discriminate different states of the brain in its entire physiopathological spectrum. Fractal-based computational analyses have been applied to the neurosciences, particularly in the field of clinical neurosciences including neuroimaging and neuroradiology, neurology and neurosurgery, psychiatry and psychology, and neuro-oncology and neuropathology. After a review of the basic concepts of fractal analysis and its main applications to the basic neurosciences in part I of this series, here, we review the main applications of fractals to the clinical neurosciences for a holistic approach towards a fractal geometry model of the brain.

From conformons to human brains: an informal overview of nonlinear dynamics and its applications in biomedicine.

Methods of contemporary physics are increasingly important for biomedical research but, for a multitude of diverse reasons, most practitioners of biomedicine lack access to a comprehensive knowledge of these modern methodologies. This paper is an attempt to describe nonlinear dynamics and its methods in a way that could be read and understood by biomedical professionals who usually are not trained in advanced mathematics. After an overview of basic concepts and vocabulary of nonlinear dynamics, deterministic chaos, and fractals, application of nonlinear methods of biosignal analysis is discussed. In particular, five case studies are presented: 1. Monitoring the depth of anaesthesia and of sedation; 2. Bright Light Therapy and Seasonal Affective Disorder; 3. Analysis of posturographic signals; 4. Evoked EEG and photo-stimulation; 5. Influence of electromagnetic fields generated by cellular phones.

Everything you wanted to ask about EEG but were afraid to get the right answer.

We answer several important questions concerning EEG. We also shortly discuss importance of nonlinear methods of contemporary physics in EEG analysis. Basic definitions and explanation of fundamental concepts may be found in my previous publications in NBP. It is a magnificent feeling to recognize the unity of complex phenomena which appear to be things quite apart from the direct visible truth. Albert Einstein

Why Nonlinear Biomedical Physics

The two goals of Nonlinear Biomedical Physics are: firstly to show how nonlinear methods can shed new light on biological phenomena and medical applications and secondly to bridge the technical, mathematical, and cultural divides between the physical disciplines where these methods are being developed and the audience for their use in the biological and medical sciences.

Some computational aspects of the brain computer interfaces based on inner music

We discuss the BCI based on inner tones and inner music. We had some success in the detection of inner tones, the imagined tones which are not sung aloud. Rather easily imagined and controlled, they offer a set of states usable for BCI, with high information capacity and high transfer rates. Imagination of sounds or musical tunes could provide a multicommand language for BCI, as if using the natural language. Moreover, this approach could be used to test musical abilities. Such BCI interface could be superior when there is a need for a broader command language. Some computational estimates and unresolved difficulties are presented.

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.

Detection of Structural Features in Biological Signals

In this article structures in biological signals are treated. The simpler—directly visible in the signals, which still demand serious methods and algorithms in the feature detection, similarity investigation and classification. The major actions in this domain are of geometric, thus simpler sort, though there are still hard problems related to simple situations. The other large class of less simple signals unsuitable for direct geometric or statistic approach, are signals with interesting frequency components and behavior, those suitable for spectroscopic analysis. Semantics of spectroscopy, spectroscopic structures and research demanded operations and transformations on spectra and time spectra are presented. The both classes of structures and related analysis methods and tools share a large common set of algorithms, all of which aiming to the full automatization. Some of the signal features present in the brain signal patterns are demonstrated, with the contexts relevant in BCI, brain computer interfaces. Mathematical representations, invariants and complete characterization of structures in broad variety of biological signals are in the central focus.

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.

Non-equilibrium proteins

There exist no methodical studies concerning non-equilibrium systems in cellular biology. This paper is an attempt to partially fill this shortcoming. We have undertaken an extensive data-mining operation in the existing scientific literature to find scattered information about non-equilibrium subcellular systems, in particular concerning fast proteins, i.e. those with short turnover half-time. We have advanced the hypothesis that functionality in fast proteins emerges as a consequence of their intrinsic physical instability that arises due to conformational strains resulting from co-translational folding (the interdependence between chain elongation and chain folding during biosynthesis on ribosomes). Such intrinsic physical instability, a kind of conformon (Klonowski-Klonowska conformon, according to Ji, (Molecular Theories of Cell Life and Death, Rutgers University Press, New Brunswick, 1991)) is probably the most important feature determining functionality and timing in these proteins. If our hypothesis is true, the turnover half-time of fast proteins should be positively correlated with their molecular weight, and some experimental results (Ames et al., J. Neurochem. 35 (1980) 131) indeed demonstrated such a correlation. Once the native structure (and function) of a fast protein macromolecule is lost, it may not be recovered--denaturation of such proteins will always be irreversible; therefore, we searched for information on irreversible denaturation. Only simulation and modeling of protein co-translational folding may answer the questions concerning fast proteins (Ruggiero and Sacile, Med. Biol. Eng. Comp. 37 (Suppl. 1) (1999) 363). Non-equilibrium structures may also be built up of protein subunits, even if each one taken by itself is in thermodynamic equilibrium (oligomeric proteins; sub-cellular sol-gel dissipative network structures).