Evaluating atrial fibrillations through strange attractors dynamics.

Nonlinear dynamics is nowadays widely employed in the study of biological phenomena. In such context, taking into account that abnormal heart rhythms display chaotic behaviours, in our opinion, the specific attractor dynamics can constitute a method for evaluating various cardiac afflictions. By using mathematical procedures specific to nonlinear dynamics we devise a new method for evaluating atrial fibrillations. Using data from ECG signals, we construct strange attractors corresponding to the phase space, specific to the analyzed signals. We show that their dynamics reflect abnormal heart rhythms. The skewness and kurtosis values are in accordance with pulse rate distributions from histograms of the analyzed signals. The Lyapunov exponent has positive values, close to zero for normal heart rhythm and with values over one order of magnitude higher in the case of fibrillation crises, highlighting a chaotic behavior for cardiac muscle dynamics. All the employed statistical parameters were calculated for a total of 5 cases (ECG signals) and statistical correlations were made using Python programming language. The presented results show that by applying nonlinear dynamics methods for analyzing the heart electrical activity we can obtain valuable information regarding fibrillation crises.

Multifractality through Non-Markovian Stochastic Processes in the Scale Relativity Theory. Acute Arterial Occlusions as Scale Transitions.

By assimilating biological systems, both structural and functional, into multifractal objects, their behavior can be described in the framework of the scale relativity theory, in any of its forms (standard form in Nottale's sense and/or the form of the multifractal theory of motion). By operating in the context of the multifractal theory of motion, based on multifractalization through non-Markovian stochastic processes, the main results of Nottale's theory can be generalized (specific momentum conservation laws, both at differentiable and non-differentiable resolution scales, specific momentum conservation law associated with the differentiable-non-differentiable scale transition, etc.). In such a context, all results are explicated through analyzing biological processes, such as acute arterial occlusions as scale transitions. Thus, we show through a biophysical multifractal model that the blocking of the lumen of a healthy artery can happen as a result of the "stopping effect" associated with the differentiable-non-differentiable scale transition. We consider that blood entities move on continuous but non-differentiable (multifractal) curves. We determine the biophysical parameters that characterize the blood flow as a Bingham-type rheological fluid through a normal arterial structure assimilated with a horizontal "pipe" with circular symmetry. Our model has been validated based on experimental clinical data.

Theoretical model for the diclofenac release from PEGylated chitosan hydrogels.

Controlled drug delivery systems are of utmost importance for the improvement of drug bioavailability while limiting the side effects. For the improvement of their performances, drug release modeling is a significant tool for the further optimization of the drug delivery systems to cross the barrier to practical application. We report here on the modeling of the diclofenac sodium salt (DCF) release from a hydrogel matrix based on PEGylated chitosan in the context of Multifractal Theory of Motion, by means of a fundamental spinor set given by 2 × 2 matrices with real elements, which can describe the drug-release dynamics at global and local scales. The drug delivery systems were prepared by in situ hydrogenation of PEGylated chitosan with citral in the presence of the DCF, by varying the hydrophilic/hydrophobic ratio of the components. They demonstrated a good dispersion of the drug into the matrix by forming matrix-drug entities which enabled a prolonged drug delivery behavior correlated with the hydrophilicity degree of the matrix. The application of the Multifractal Theory of Motion fitted very well on these findings, the fractality degree accurately describing the changes in hydrophilicity of the polymer. The validation of the model on this series of formulations encourages its further use for other systems, as an easy tool for estimating the drug release toward the design improvement. The present paper is a continuation of the work 'A theoretical mathematical model for assessing diclofenac release from chitosan-based formulations,' published in Drug Delivery Journal, 27(1), 2020, that focused on the consequences induced by the invariance groups of Multifractal Diffusion Equations in correlation with the drug release dynamics.