Nonlinear Biomedical Physics - Most accessed articles

Graph theoretical analysis of complex networks in the brain

Cornelis Stam — 2007-07-05T00:00:00Z

Since the discovery of small-world and scale-free networks the study of complex systems from a network perspective has taken an enormous flight. In recent years many important properties of complex networks have been delineated. In particular, significant progress has been made in understanding the relationship between the structural properties of networks and the nature of dynamics taking place on these networks. For instance, the 'synchronizability' of complex networks of coupled oscillators can be determined by graph spectral analysis. These developments in the theory of complex networks have inspired new applications in the field of neuroscience. Graph analysis has been used in the study of models of neural networks, anatomical connectivity, and functional connectivity based upon fMRI, EEG and MEG. These studies suggest that the human brain can be modelled as a complex network, and may have a small-world structure both at the level of anatomical as well as functional connectivity. This small-world structure is hypothesized to reflect an optimal situation associated with rapid synchronization and information transfer, minimal wiring costs, as well as a balance between local processing and global integration. The topological structure of functional networks is probably restrained by genetic and anatomical factors, but can be modified during tasks. There is also increasing evidence that various types of brain disease such as Alzheimer's disease, schizophrenia, brain tumours and epilepsy may be associated with deviations of the functional network topology from the optimal small-world pattern.

Fractional-calculus diffusion equation

Abdul-Wali Ajlouni — 2010-05-21T00:00:00Z

Background: Sequel to the work on the quantization of nonconservative systems using fractional calculus and quantization of a system with Brownian motion, which aims to consider the dissipation effects in quantum-mechanical description of microscale systems. Results: The canonical quantization of a system represented classically by one-dimensional Fick's law, and the diffusion equation is carried out according to the Dirac method. A suitable Lagrangian, and Hamiltonian, describing the diffusive system, are constructed and the Hamiltonian is transformed to Schrodinger's equation which is solved. An application regarding implementation of the developed mathematical method to the analysis of diffusion, osmosis, which is a biological application of the diffusion process, is carried out. Schrödinger's equation is solved. Conclusions: The plot of the probability function represents clearly the dissipative and drift forces and hence the osmosis, which agrees totally with the macro-scale view, or the classical-version osmosis.

Influence of very low doses of mediators on fungal laccase activity - nonlinearity beyond imagination

Elzbieta Malarczyk — 2009-09-04T00:00:00Z

Laccase, an enzyme responsible for aerobic transformations of natural phenolics, in industrial applications requires the presence of low-molecular substances known as mediators, which accelerate oxidation processes. However, the use of mediators is limited by their toxicity and the high costs of exploitation. The activation of extracellular laccase in growing fungal culture with highly diluted mediators, ABTS and HBT is described. Two high laccase-producing fungal strains, Trametes versicolor and Cerrena unicolor, were used in this study as a source of enzyme. Selected dilutions of the mediators significantly increased the activity of extracellular laccase during 14 days of cultivation what was distinctly visible in PAGE technique and in colorimetric tests. The same mediator dilutions increased demethylation properties of laccase, which was demonstrated during incubation of enzyme with veratric acid. It was established that the activation effect was assigned to specific dilutions of mediators. Our dose-response dilution process smoothly passes into the range of action of homeopathic dilutions and is of interest for homeopaths.

Editorial: Why Nonlinear Biomedical Physics?

Zbigniew Czernicki — 2007-07-05T00:00:00Z

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.

Research on the relation of EEG signal chaos characteristics with high-level intelligence activity of human brain

Xingyuan Wang — 2010-04-27T00:00:00Z

Using phase space reconstruct technique from one-dimensional and multi-dimensional time series and the quantitative criterion rule of system chaos, and combining the neural network; analyses, computations and sort are conducted on electroencephalogram (EEG) signals of five kinds of human consciousness activities (relaxation, mental arithmetic of multiplication, mental composition of a letter, visualizing a 3-dimensional object being revolved about an axis, and visualizing numbers being written or erased on a blackboard). Through comparative studies on the determinacy, the phase graph, the power spectra, the approximate entropy, the correlation dimension and the Lyapunov exponent of EEG signals of 5 kinds of consciousness activities, the following conclusions are shown: (1) The statistic results of the deterministic computation indicate that chaos characteristic may lie in human consciousness activities, and central tendency measure (CTM) is consistent with phase graph, so it can be used as a division way of EEG attractor. (2) The analyses of power spectra show that ideology of single subject is almost identical but the frequency channels of different consciousness activities have slight difference. (3) The approximate entropy between different subjects exist discrepancy. Under the same conditions, the larger the approximate entropy of subject is, the better the subject's innovation is. (4) The results of the correlation dimension and the Lyapunov exponent indicate that activities of human brain exist in attractors with fractional dimensions. (5) Nonlinear quantitative criterion rule, which unites the neural network, can classify different kinds of consciousness activities well. In this paper, the results of classification indicate that the consciousness activity of arithmetic has better differentiation degree than that of abstract.

Simulation study of autoregulation responses of peripheral circulation to systemic pulsatility

Federico Aletti — 2009-07-24T00:00:00Z

Background: This simulation study investigated potential modulations of total peripheral resistance (TPR), due to distributed peripheral vascular activity, by means of a lumped model of the arterial tree and a non linear model of microcirculation, inclusive of local controls of blood flow and tissue-capillary fluid exchange. Results: Numerical simulations of circulation were carried out to compute TPR under different conditions of blood flow pulsatility, and to extract the pressure-flow characteristics of the cardiovascular system. Simulations showed that TPR seen by the large arteries was increased in absence of pulsatility, while it decreased with an augmented harmonic content. This is a typically non linear effect due to the contribution of active, non linear autoregulation of the peripheral microvascular beds, which also generated a nonlinear relationship between arterial blood pressure and cardiac output. Conclusion: This simulation study, though focused on a simple effect attaining TPR modulation due to pulsatility, suggests that non-linear autoregulation mechanisms cannot be overlooked while studying the integrated behavior of the global cardiovascular system, including the arterial tree and the peripheral vascular bed.

Fractional modeling dynamics of HIV and CD4^+ T-cells during primary infection

A a Arafa — 2012-01-03T00:00:00Z

In this paper, we introduce fractional-order into a model of HIV-1 infection of CD4^+T cells. We study the effect of the changing the average number of viral particles N with different sets of initial conditions on the dynamics of the presented model. Generalized Euler method (GEM) will be used to find a numerical solution of the HIV-1 infection fractional order model.

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

Wlodzimierz Klonowski — 2007-07-05T00:00:00Z

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.

Discriminating between ADHD adults and controls using independent ERP components and a support vector machine: a validation study

Andreas Mueller — 2011-07-19T00:00:00Z

Background: There are numerous event-related potential (ERP) studies in relation to attention-deficit hyperactivity disorder (ADHD), and a substantial number of ERP correlates of the disorder have been identified. However, most of the studies are limited to group differences in children. Independent component analysis (ICA) separates a set of mixed event-related potentials into a corresponding set of statistically independent source signals, which are likely to represent different functional processes. Using a support vector machine (SVM), a classification method originating from machine learning, this study aimed at investigating the use of such independent ERP components in differentiating adult ADHD patients from non-clinical controls by selecting a most informative feature set. A second aim was to validate the predictive power of the SVM classifier by means of an independent ADHD sample recruited at a different laboratory. Methods: Two groups of age-matched adults (75 ADHD, 75 controls) performed a visual two stimulus go/no-go task. ERP responses were decomposed into independent components, and a selected set of independent ERP component features was used for SVM classification. Results: Using a 10-fold cross-validation approach, classification accuracy was 91%. Predictive power of the SVM classifier was verified on the basis of the independent ADHD sample (17 ADHD patients), resulting in a classification accuracy of 94%. The latency and amplitude measures which in combination differentiated best between ADHD patients and non-clinical subjects primarily originated from independent components associated with inhibitory and other executive operations. Conclusions: This study shows that ERPs can substantially contribute to the diagnosis of ADHD when combined with up-to-date methods.

Pulse Decomposition Analysis of the digital arterial pulse during hemorrhage simulation

Martin Baruch — 2011-01-12T00:00:00Z

Background: Markers of temporal changes in central blood volume are required to non-invasively detect hemorrhage and the onset of hemorrhagic shock. Recent work suggests that pulse pressure may be such a marker. A new approach to tracking blood pressure, and pulse pressure specifically is presented that is based on a new form of pulse pressure wave analysis called Pulse Decomposition Analysis (PDA). The premise of the PDA model is that the peripheral arterial pressure pulse is a superposition of five individual component pressure pulses, the first of which is due to the left ventricular ejection from the heart while the remaining component pressure pulses are reflections and re-reflections that originate from only two reflection sites within the central arteries. The hypothesis examined here is that the PDA parameter T13, the timing delay between the first and third component pulses, correlates with pulse pressure.T13 was monitored along with blood pressure, as determined by an automatic cuff and another continuous blood pressure monitor, during the course of lower body negative pressure (LBNP) sessions involving four stages, -15 mmHg, -30 mmHg, -45 mmHg, and -60 mmHg, in fifteen subjects (average age: 24.4 years, SD: 3.0 years; average height: 168.6 cm, SD: 8.0 cm; average weight: 64.0 kg, SD: 9.1 kg). Results: Statistically significant correlations between T13 and pulse pressure as well as the ability of T13 to resolve the effects of different LBNP stages were established. Experimental T13 values were compared with predictions of the PDA model. These interventions resulted in pulse pressure changes of up to 7.8 mmHg (SE = 3.49 mmHg) as determined by the automatic cuff. Corresponding changes in T13 were a shortening by -72 milliseconds (SE = 4.17 milliseconds). In contrast to the other two methodologies, T13 was able to resolve the effects of the two least negative pressure stages with significance set at p < 0.01. Conclusions: The agreement of observations and measurements provides a preliminary validation of the PDA model regarding the origin of the arterial pressure pulse reflections. The proposed physical picture of the PDA model is attractive because it identifies the contributions of distinct reflecting arterial tree components to the peripheral pressure pulse envelope. Since the importance of arterial pressure reflections to cardiovascular health is well known, the PDA pulse analysis could provide, beyond the tracking of blood pressure, an assessment tool of those reflections as well as the health of the sites that give rise to them.