Oscillatory phenomena in the brain activity and their synchronization are frequently studied using mathematical models and analytic tools derived from nonlinear dynamics. In many experimental situations, however, neural signals have a broadband character and if oscillatory activity is present, its dynamical origin is unknown. To cope with these problems, a framework for detecting nonlinear oscillatory activity in broadband time series is presented. First, a narrow-band oscillatory mode is extracted from a broadband background. Second, it is tested whether the extracted mode is significantly different from linearly filtered noise, modelled as a linear stochastic process possibly passed through a static nonlinear transformation. If a nonlinear oscillatory mode is positively detected, further analysis using nonlinear approaches such as the phase synchronization analysis can potentially bring new information. For linear processes, however, standard approaches such as the coherence analysis are more appropriate and provide sufficient description of underlying interactions with smaller computational effort. The method is illustrated in a numerical example and applied to analyze experimentally obtained human EEG time series from a sleeping subject.
- MeSH
- Biological Clocks physiology MeSH
- Time Factors MeSH
- Electroencephalography methods MeSH
- Humans MeSH
- Models, Neurological MeSH
- Brain physiology MeSH
- Nonlinear Dynamics MeSH
- Signal Processing, Computer-Assisted MeSH
- Sleep physiology MeSH
- Spectrum Analysis MeSH
- Check Tag
- Humans MeSH
- Publication type
- Journal Article MeSH
- Research Support, Non-U.S. Gov't MeSH
This study was aimed to analyse the lower limb kinematics during the change of direction (COD) performance with the dominant (DL) and non-dominant (NDL) leg using linear (traditional kinematics) and nonlinear (Self Organising Map-based cluster analysis) approaches. Three 5-0-5 COD performances with the DL and three with the NDL were performed by 23 (aged 21.6 ± 2.3 years) collegiate athletes. No significant difference was observed between the COD duration, and approach speed of DL and NDL. Significantly greater ankle abductions, knee and hip external rotations were identified in COD with DL, compared to NDL (p < .001, d > 0.8). Self Organising Maps portrayed a completely different coordination pattern profile during change of direction performance with the DL and NDL. The cluster analysis illustrated similar inter-individual coordination patterning when participants turned with their DL or NDL. No visible relationship was observed in the cluster analysis of the lower limb joint angles and angular velocities. Outcomes of this study portrayed that coordination patterning (combination of joint angles and the rate of change of angles) could portray the movement patterning differences in different tasks, while a sole investigation on the joint angles or angular velocities may not reveal the underlying mechanisms of movement patterning.
- MeSH
- Leg * physiology MeSH
- Biomechanical Phenomena MeSH
- Lower Extremity * physiology MeSH
- Functional Laterality * physiology MeSH
- Ankle physiology MeSH
- Humans MeSH
- Young Adult MeSH
- Motor Skills * physiology MeSH
- Nonlinear Dynamics MeSH
- Movement physiology MeSH
- Cluster Analysis MeSH
- Athletic Performance * physiology MeSH
- Check Tag
- Humans MeSH
- Young Adult MeSH
- Male MeSH
- Female MeSH
- Publication type
- Journal Article MeSH
Fröhlich model describes emission of electromagnetic field in the interior of biological cells by oscillating polar units, now mostly identified with microtubule filaments. Central element of this theory is the system of rate equations for the quantum occupancy numbers n i of collective oscillation modes. These equations describe both linear and nonlinear properties of the system; presence of the latter can lead to condensation of the incoming energy into the lowest frequency mode - a phenomenon deemed to be of major importance for cell's biochemistry, because the excited mode can engage in chemical reactions while the major part of the system remains near the equilibrium, not exposed to energetic stress. This paper explores, using a simple model, the influence of strong static electric field created by mitochondria flanking the microtubules on nonlinear interactions and, in turn, on occupancy numbers. The computed results show that simultaneous presence of both sufficient metabolic pumping and adequately elevated static electric field is necessary for the full unfolding of the hallmark properties of the Fröhlich model. It is suggested that cancer-related mitochondrial dysfunction leading to metabolic transformation has additional adverse effect mediated by diminution of static fields which in turn reduces the nonlinear processes in the Fröhlich systems, essential for energy condensation in the fundamental mode.
Peak shapes in electrophoresis are often distorted from the ideal Gaussian shape due to disturbing phenomena, of which the most important is electromigration dispersion. For fully dissociated analytes, there is a tight analogy between nonlinear models describing a separation process in chromatography and electrophoresis. When the velocity of the separated analyte depends on the concentration of the co-analyte, the consequence is a mutual influence of the analytes couples, which distorts both analyte zones. In this paper, we introduce a nonlinear model of electromigration for the analysis of two co-migrating fully dissociated analytes. In the initial stages of separation, they influence each other, which causes much more complicated peak shapes. The analysis has revealed that the two most important phenomena-the displacement and the tag-along effects-are common both for nonlinear chromatography and electrophoresis, though their description is partly based on rather different phenomena. The comparison between the nonlinear model of electromigration we describe and the numerical computer solution of the original continuity equations has proven an almost perfect agreement. The predicted features in peak shapes in initial stages of separation have been fully confirmed by the experiments.
Practically all experimental measurements related to the response of nonlinear bodies that are made within a purely mechanical context are concerned with inhomogeneous deformations, though, in many experiments, much effort is taken to engender homogeneous deformation fields. However, in experiments that are carried out in vivo, one cannot control the nature of the deformation. The quantity of interest is the deformation gradient and/or its invariants. The deformation gradient is estimated by tracking positions of a finite number of markers placed in the body. Any experimental data-reduction procedure based on tracking a finite number of markers will, for a general inhomogeneous deformation, introduce an error in the determination of the deformation gradient, even in the idealized case, when the positions of the markers are measured with no error. In our study, we are interested in a quantitative description of the difference between the true gradient and its estimate obtained by tracking the markers, that is, in the quantitative description of the induced error due to the data reduction. We derive a rigorous upper bound on the error, and we discuss what factors influence the error bound and the actual error itself. Finally, we illustrate the results by studying a practically interesting model problem. We show that different choices of the tracked markers can lead to substantially different estimates of the deformation gradient and its invariants. It is alarming that even qualitative features of the material under consideration, such as the incompressibility of the body, can be evaluated differently with different choices of the tracked markers. We also demonstrate that the derived error estimate can be used as a tool for choosing the appropriate marker set that leads to the deformation gradient estimate with the least guaranteed error.
- MeSH
- Models, Biological * MeSH
- Biomechanical Phenomena MeSH
- Biomedical Engineering * MeSH
- Humans MeSH
- Mathematical Concepts MeSH
- Stress, Mechanical MeSH
- Nonlinear Dynamics MeSH
- Animals MeSH
- Check Tag
- Humans MeSH
- Animals MeSH
- Publication type
- Journal Article MeSH
- Research Support, Non-U.S. Gov't MeSH
During phonation, the respiratory, the phonatory, and the resonatory parts of the voice organ can interact, where physiological action in one subsystem elicits a direct effect in another. Here, three major subsystems of these synergies are reviewed, creating a model of voice subsystem interactions: (1) Vocal tract adjustments can influence the behavior of the voice source via nonlinear source-tract interactions; (2) The type and degree of vocal fold adduction controls the expiratory airflow rate; and (3) The tracheal pull caused by the respiratory system affects the vertical larynx position and thus the vocal tract resonances. The relevance of the presented model is discussed, suggesting, among others, that functional voice building work concerned with a particular voice subsystem may evoke side effects or benefits on other subsystems, even when having a clearly defined and isolated physiological target. Finally, four seemingly incongruous historic definitions of the concept of singing voice "support" are evaluated, showing how each of these pertain to different voice subsystems at various levels of detail. It is argued that presumed discrepancies between these definitions can be resolved by putting them into the wider context of the subsystem interaction model presented here, thus offering a framework for reviewing and potentially refining some current and historical pedagogical approaches.
- MeSH
- Models, Anatomic * MeSH
- Biomechanical Phenomena MeSH
- Respiration * MeSH
- Phonation * MeSH
- Vocal Cords anatomy & histology physiology MeSH
- Voice Quality * MeSH
- Humans MeSH
- Nonlinear Dynamics * MeSH
- Airway Resistance MeSH
- Systems Integration * MeSH
- Trachea anatomy & histology physiology MeSH
- Vibration MeSH
- Singing * MeSH
- Check Tag
- Humans MeSH
- Publication type
- Journal Article MeSH
- Review MeSH
