Abstract: Methods of contemporary mathematical physics such
as chaos theory are useful for analyzing and understanding the
behavior of complex biological and physiological systems. The three
dimensional model of HIV/AIDS is the basis of active research since
it provides a complete characterization of disease dynamics and the
interaction of HIV-1 with the immune system. In this work, the
behavior of the HIV system is analyzed using the three dimensional
HIV model and a chaotic measure known as the Hurst exponent.
Results demonstrate that Hurst exponents of CD4, CD8 cells and
viral load vary nonlinearly with respect to variations in system
parameters. Further, it was observed that the three dimensional HIV
model can accommodate both persistent (H>0.5) and anti-persistent
(H
Abstract: Many systems in the natural world exhibit chaos or non-linear behavior, the complexity of which is so great that they appear to be random. Identification of chaos in experimental data is essential for characterizing the system and for analyzing the predictability of the data under analysis. The Lyapunov exponents provide a quantitative measure of the sensitivity to initial conditions and are the most useful dynamical diagnostic for chaotic systems. However, it is difficult to accurately estimate the Lyapunov exponents of chaotic signals which are corrupted by a random noise. In this work, a method for estimation of Lyapunov exponents from noisy time series using unscented transformation is proposed. The proposed methodology was validated using time series obtained from known chaotic maps. In this paper, the objective of the work, the proposed methodology and validation results are discussed in detail.
Abstract: Analysis of blood vessel mechanics in normal and
diseased conditions is essential for disease research, medical device
design and treatment planning. In this work, 3D finite element
models of normal vessel and atherosclerotic vessel with 50% plaque
deposition were developed. The developed models were meshed
using finite number of tetrahedral elements. The developed models
were simulated using actual blood pressure signals. Based on the
transient analysis performed on the developed models, the parameters
such as total displacement, strain energy density and entropy per unit
volume were obtained. Further, the obtained parameters were used to
develop artificial neural network models for analyzing normal and
atherosclerotic blood vessels. In this paper, the objectives of the
study, methodology and significant observations are presented.