Application of Linear Stochastic Models in the Investigation of the Effects of Parkinson’s Disease on the Cop Time Series

The primary objective of this study was to use linear stochastic modeling approach to investigate parameters which may be sensitive enough to detect and quantify the changes in postural instability (PI) related to the progression in Parkinson’s disease (PD). Data collected in a previous study were analyzed in the current study. Participants with mild PD (n=13), moderate PD (n=10) and age range match healthy controls (HC, n=21) were instructed to stand in a comfortable self-selected natural stance on a force platform in both eyes open (EO) and eyes closed (EC) conditions. The foot-floor reaction forces were used to calculate the center of pressure (COP) time series. This COP time series was fitted by two different linear stochastic models: 1) an autoregressive (AR), and 2) an autoregressive moving average (ARMA) model. The postural control system was modeled as an inverted pendulum to describe pure body mechanics and a proportional, derivative and integral (PID) strategy was assumed for balance regulation. Swiftness, damping and stiffness parameters were extracted from the AR model. Natural frequency and damping ratio were extracted from the ARMA model. The statistical analysis (ANOVA) of these parameters revealed significant differences in stiffness and swiftness parameters between the HC and moderate PD population in the EO condition. These three parameters showed trends with progression of PD. The swiftness parameter showed decreasing mean values as PD severity increased, indicating that PD caused slower reactions to small deviations from equilibrium when compared to healthy controls. The mild and moderate PD, compared to HC, demonstrated by higher mean values of stiffness, suggesting a more rigid control strategy. The analysis of damping parameter revealed that the PD, compared to HC, may have a reduced ability to attenuate sway velocity during quiet stance as indicated by lower mean values of damping parameter and damping ratio. The natural frequency did not show significant trends in EO condition, but revealed an increasing trend with progression of PD. This could indicate that the PD could have larger number of deviations of COP from equilibrium. The analysis of effect of condition (EO, EC) revealed significant differences in all the five parameters. The stiffness, damping parameter and damping ratio had higher mean values for EO, compared to the EC condition, indicating the vital role that the visual feedback plays in detecting small perturbations from equilibrium leading to a better posture regulation in EO condition. The swiftness parameter and natural frequency indicated higher mean values in EC, compared to the EO condition, suggesting that the various sensory cues might be weighted differently in EO and EC conditions. Future studies should investigate the sensitivity of these calculated parameters to changes in PI in PD using a larger sample size and longer duration of trials. Also the variations in these parameters in response to dynamic tasks such as gait initiation and balance recovery should be considered in future studies

Quaternion-based complexity study of human postural sway time series

A multidimensional approach for the study of the center of pressure (CoP) was selected. During the work the dataset was characterized recurring to algorithms taken from Chaotic and Stochastic time series analysis. The effects of the visual and cognitive components were addressed to allow a proper modelization of the data in the complex and quaternion domains

Resistance Training Exercise Program for Intervention to Enhance Gait Function in Elderly Chronically Ill Patients: Multivariate Multiscale Entropy for Center of Pressure Signal Analysis

Falls are unpredictable accidents, and the resulting injuries can be serious in the elderly, particularly those with chronic diseases. Regular exercise is recommended to prevent and treat hypertension and other chronic diseases by reducing clinical blood pressure. The “complexity index” (CI), based on multiscale entropy (MSE) algorithm, has been applied in recent studies to show a person’s adaptability to intrinsic and external perturbations and widely used measure of postural sway or stability. The multivariate multiscale entropy (MMSE) was advanced algorithm used to calculate the complexity index (CI) values of the center of pressure (COP) data. In this study, we applied the MSE & MMSE to analyze gait function of 24 elderly, chronically ill patients (44% female; 56% male; mean age, 67.56±10.70 years) with either cardiovascular disease, diabetes mellitus, or osteoporosis. After a 12-week training program, postural stability measurements showed significant improvements. Our results showed beneficial effects of resistance training, which can be used to improve postural stability in the elderly and indicated that MMSE algorithms to calculate CI of the COP data were superior to the multiscale entropy (MSE) algorithm to identify the sense of balance in the elderly

Fractal Physiology and the Fractional Calculus: A Perspective

This paper presents a restricted overview of Fractal Physiology focusing on the complexity of the human body and the characterization of that complexity through fractal measures and their dynamics, with fractal dynamics being described by the fractional calculus. Not only are anatomical structures (Grizzi and Chiriva-Internati, 2005), such as the convoluted surface of the brain, the lining of the bowel, neural networks and placenta, fractal, but the output of dynamical physiologic networks are fractal as well (Bassingthwaighte et al., 1994). The time series for the inter-beat intervals of the heart, inter-breath intervals and inter-stride intervals have all been shown to be fractal and/or multifractal statistical phenomena. Consequently, the fractal dimension turns out to be a significantly better indicator of organismic functions in health and disease than the traditional average measures, such as heart rate, breathing rate, and stride rate. The observation that human physiology is primarily fractal was first made in the 1980s, based on the analysis of a limited number of datasets. We review some of these phenomena herein by applying an allometric aggregation approach to the processing of physiologic time series. This straight forward method establishes the scaling behavior of complex physiologic networks and some dynamic models capable of generating such scaling are reviewed. These models include simple and fractional random walks, which describe how the scaling of correlation functions and probability densities are related to time series data. Subsequently, it is suggested that a proper methodology for describing the dynamics of fractal time series may well be the fractional calculus, either through the fractional Langevin equation or the fractional diffusion equation. A fractional operator (derivative or integral) acting on a fractal function, yields another fractal function, allowing us to construct a fractional Langevin equation to describe the evolution of a fractal statistical process. Control of physiologic complexity is one of the goals of medicine, in particular, understanding and controlling physiological networks in order to ensure their proper operation. We emphasize the difference between homeostatic and allometric control mechanisms. Homeostatic control has a negative feedback character, which is both local and rapid. Allometric control, on the other hand, is a relatively new concept that takes into account long-time memory, correlations that are inverse power law in time, as well as long-range interactions in complex phenomena as manifest by inverse power-law distributions in the network variable. We hypothesize that allometric control maintains the fractal character of erratic physiologic time series to enhance the robustness of physiological networks. Moreover, allometric control can often be described using the fractional calculus to capture the dynamics of complex physiologic networks

Theory and application of time-frequency analysis to transient phenomena in electric power and other physical systems

textThis dissertation provides a new theoretical scheme of signal processing: cross time-frequency analysis. The proposed cross time-frequency analysis is applied to various types of real-world signals and systems in order to verify the feasibility and applicability of the proposed theory. The application of time-frequency analysis is focused on electric power and other physical systems. Unfortunately, classical Fourier-based methodologies and power quality indices are not directly applicable for the assessment and localization of transient power quality phenomena. Hence, in this dissertation, application of time-frequency analysis is discussed for the assessment and localization of transient power quality events. Through the use of joint time and frequency localized “energy” distributions, a set of time-frequency based transient power quality indices are presented and applied to real-world disturbance signals. Also, a solution for the spatial localization of transient disturbances is presented. It rests upon calculating a time and frequency localized “phase difference” via cross time-frequency analysis. By evaluating the phase difference of voltage and current at the time and frequency of interest and at different spatial points, one can identify the direction of transient disturbance energy flow in order to pinpoint the location of the transient disturbance source. In addition, applications of time-frequency theory have been extended to various types of real-world physical signals and systems. A new reflectometry methodology, time-frequency domain reflectometry, is proposed and demonstrated with experimental results. Also, cross time-frequency analysis has been utilized for the characterization of ocean wave group propagation, and applied to transient postural sway signals to identify the effects of aging and sensory systems on human postural control systems.Electrical and Computer Engineerin