The high frequency dielectric constant of poly-adenine (poly-A) was measured between 1 MHz and 1 GHz. The purpose of these experiments was to investigate the state of water molecules that are bound to the charged groups of the poly-A molecule. Analysis of the data using the Maxwell's mixture equation revealed the dielectric constant of bound water higher than we expected. Using Onsager's internal field in Debye's equation, we calculated the dielectric constant of water in the vicinity of a charged ion. The result of this computation demonstrates that the dielectric constant of bound water is much smaller than the normal value only in the immediate proximity of charged ions (within 2 A). The dielectric constant increases rapidly to the normal value as the distance increases from 2 to 4 A. This observation indicates that charged sites of polyions have only short range interactions with the surrounding water molecules. However, this conclusion pertains only to rotary diffusion of bound water since dielectric measurement is unable to detect translational diffusion.
The main purpose of the present work is the definition of a fully automatic procedure for correlation dimension (D(2)) estimation. In the first part, the procedure for the estimation of the correlation dimension (D(2)) is proposed and tested on various types of mathematical models: chaotic (Lorenz and Henon models), periodical (sinusoidal waves) and stochastic (Gaussian and uniform noise). In all cases, accurate D(2) estimates were obtained. The procedure can detect the presence of multiple scaling regions in the correlation integral function. The connection between the presence of multiple scaling regions and multiple dynamic activities cooperating in a system is investigated through the study of composite time series. In the second part of the paper, the proposed algorithm is applied to the study of cardiac electrical activity through the analysis of electrocardiographic signals (ECG) obtained from the commercially available MIT-BIH ECG arrhythmia database. Three groups of ECG signals have been considered: the ECGs of normal subjects and ECGs of subjects with atrial fibrillation and with premature ventricular contraction. D(2) estimates are computed on single ECG intervals (static analysis) of appropriate duration, striking a balance between stationarity requisites and accurate computation requirements. In addition, D(2) temporal variability is studied by analyzing consecutive intervals of ECG tracings (dynamic analysis). The procedure reveals the presence of multiple scaling regions in many ECG signals, and the D(2) temporal variability differs in the three ECG groups considered; it is greater in the case of atrial fibrillation than in normal sinus rhythms. This study points out the importance of considering both the static and dynamic D(2) analysis for a more complete study of the system under analysis. While the static analysis visualizes the underlying heart activity, dynamic D(2) analysis insights the time evolution of the underlying system.
Cardiac morbidity and mortality increases with the population age. To investigate the underlying pathological mechanisms, and suggest new ways to reduce clinical risks, computational approaches complementing experimental and clinical investigations are becoming more and more important. Here we explore the possible processes leading to the occasional onset and termination of the (usually) non-fatal arrhythmias widely observed in the heart. Using a computational model of a two-dimensional network of cardiac cells, we tested the hypothesis that an ischemia alters the properties of the gap junctions inside the ischemic area. In particular, in agreement with experimental findings, we assumed that an ischemic episode can alter the gap junctions of the affected cells by reducing their average conductance. We extended these changes to include random fluctuations with time, and modifications in the gap junction rectifying conductive properties of cells along the edges of the ischemic area. The results demonstrate how these alterations can qualitatively give an account of all the main types of non-fatal arrhythmia observed experimentally, and suggest how premature beats can be eliminated in three different ways: a) with a relatively small surgical procedure, b) with a pharmacological reduction of the rectifying conductive properties of the gap-junctions, and c) by pharmacologically decreasing the gap junction conductance. In conclusion, our model strongly supports the hypothesis that non-fatal arrhythmias can develop from post-ischemic alteration of the electrical connectivity in a relatively small area of the cardiac cell network, and suggests experimentally testable predictions on their possible treatments.
A preliminary analysis of the Lyapunov spectru,m determination from a time-series with the Jacobian-based approach is presented. The method has been tested on the Lorenz attractor obtaining good Lyapunov exponents estimate, then it has been applied to the study of ECG signals coming from MIT-BIH Arrhythmia Database. W e obtained almost always a positive first exponent confirming the chaotic nature of the electrical heart activity measured from surface ECG. However, Lyapunov spectrum estimate is often influenced by the choice of some working parameters. The main purpose of this work is to gain insights on the influence of such working parameters on results.
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