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 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.

Influence of the distensibility of large arteries on the longitudinal impedance: application for the development of non-invasive techniques to the diagnosis of arterial diseases

Wassila Sahtout — 2012-04-16T00:00:00Z

Background: This study shows that the arterial longitudinal impedance constitutes a hemodynamic parameter of interest for performance characterization of large arteries in normal condition as well as in pathological situations. For this purpose, we solved the Navier-Stokes equations for an incompressible flow using the finite element analysis method and the Arbitrary Lagrangian Eulerian (ALE) formulation. The mathematical model assumes a two-dimensional flow and takes into account the nonlinear terms in the equations of fluid motion that express the convective acceleration, as well as the nonlinear deformation of the arterial wall. Several numerical simulations of the blood flow in large vessels have been performed to study the propagation along an arterial vessel of a pressure gradient pulse and a rate flow pulse. These simulations include various deformations of the wall artery leading to parietal displacements ranging from 0 (rigid wall) to 15% (very elastic wall) in order to consider physiological and pathological cases. Results: The results show significant changes of the rate flow and the pressure gradient wave as a function of aosc, the relative variation in the radius of the artery over a cardiac cycle. These changes are notable beyond a critical value of aosc equal to 0.05. This critical value is also found in the evolution of the longitudinal impedance. So, above a variation of radius of 5%, the convective acceleration, created by the fluid-wall interactions, have an influence on the flow detectable on the longitudinal impedance. Conclusions: The interpretation of the evolution of the longitudinal impedance shows that it could be a mean to test the performance of large arteries and can contribute to the diagnosis of parietal lesions of large arteries. For a blood vessel with a wall displacement higher than 5% similar to those of large arteries like the aorta, the longitudinal impedance is substantially greater than that obtained in the absence of wall displacement. This study also explains the effects of convective acceleration, on the shape of the decline of the pressure gradient wave and shows that they should not be neglected when the variation in radius is greater than 5%.

On consciousness, resting state fMRI, and neurodynamics

2010-06-03T00:00:00Z

Background: During the last years, functional magnetic resonance imaging (fMRI) of the brain has been introduced as a new tool to measure consciousness, both in a clinical setting and in a basic neurocognitive research. Moreover, advanced mathematical methods and theories have arrived the field of fMRI (e.g. computational neuroimaging), and functional and structural brain connectivity can now be assessed non-invasively. Results: The present work deals with a pluralistic approach to "consciousness'', where we connect theory and tools from three quite different disciplines: (1) philosophy of mind (emergentism and global workspace theory), (2) functional neuroimaging acquisitions, and (3) theory of deterministic and statistical neurodynamics – in particular the Wilson-Cowan model and stochastic resonance. Conclusions: Based on recent experimental and theoretical work, we believe that the study of large-scale neuronal processes (activity fluctuations, state transitions) that goes on in the living human brain while examined with functional MRI during "resting state", can deepen our understanding of graded consciousness in a clinical setting, and clarify the concept of "consiousness" in neurocognitive and neurophilosophy research.

Econobiophysics - Game of Choosing. Model of Selection or Election Process with Diverse Accessible Information

Wlodzimierz Klonowski — 2011-09-05T00:00:00Z

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).

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.

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.

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.

New method for analysis of nonstationary signals

Robert Stepien — 2011-06-22T00:00:00Z

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.

Hilbert-Huang versus morlet wavelet transformation on mismatch negativity of children in uninterrupted sound paradigm

Fengyu Cong — 2009-02-02T00:00:00Z

Background: Compared to the waveform or spectrum analysis of event-related potentials (ERPs), time-frequency representation (TFR) has the advantage of revealing the ERPs time and frequency domain information simultaneously. As the human brain could be modeled as a complicated nonlinear system, it is interesting from the view of psychological knowledge to study the performance of the nonlinear and linear time-frequency representation methods for ERP research. In this study Hilbert-Huang transformation (HHT) and Morlet wavelet transformation (MWT) were performed on mismatch negativity (MMN) of children. Participants were 102 children aged 8–16 years. MMN was elicited in a passive oddball paradigm with duration deviants. The stimuli consisted of an uninterrupted sound including two alternating 100 ms tones (600 and 800 Hz) with infrequent 50 ms or 30 ms 600 Hz deviant tones. In theory larger deviant should elicit larger MMN. This theoretical expectation is used as a criterion to test two TFR methods in this study. For statistical analysis MMN support to absence ratio (SAR) could be utilized to qualify TFR of MMN. Results: Compared to MWT, the TFR of MMN with HHT was much sharper, sparser, and clearer. Statistically, SAR showed significant difference between the MMNs elicited by two deviants with HHT but not with MWT, and the larger deviant elicited MMN with larger SAR. Conclusion: Support to absence ratio of Hilbert-Huang Transformation on mismatch negativity meets the theoretical expectations, i.e., the more deviant stimulus elicits larger MMN. However, Morlet wavelet transformation does not reveal that. Thus, HHT seems more appropriate in analyzing event-related potentials in the time-frequency domain. HHT appears to evaluate ERPs more accurately and provide theoretically valid information of the brain responses.