Higher order solitary solutions to the meta-model of diffusively coupled Lotka-Volterra systems.

A meta-model of diffusively coupled Lotka-Volterra systems used to model various biomedical phenomena is considered in this paper. Necessary and sufficient conditions for the existence of nth order solitary solutions are derived via a modified inverse balancing technique. It is shown that as the highest possible solitary solution order n is increased, the number of nonzero solution parameter values remains constant for solitary solutions of order n > 3 . Analytical and computational experiments are used to illustrate the obtained results.

The characterization of the transit through the anaerobic threshold based on relationships between RR and QRS cardiac intervals.

This paper aims to develop a novel computational technique for the detection of the transit through the anaerobic threshold. This technique uses only cardiac intervals derived from the electrocardiogram and is based on algebraic relationships between RR and QRS intervals. Electrocardiograms are measured during the load and the recovery processes. Algebraic relationships between cardiac intervals are used not only to identify the anaerobic threshold but also to characterise individual features of the person during the transit through the threshold. The ratio between carbon dioxide and oxygen in the exhaled air is used to validate the results. The algebraic relationship between cardiac intervals serves as a stand-alone indicator for both the determination of the anaerobic threshold and the characterization of the performance of the person during the load and the recovery processes.

New approach for visualization of relationships between RR and JT intervals.

This paper presents the concept of perfect matrices of Lagrange differences which are used to analyze relationships between RR and JT intervals during the bicycle ergometry exercise. The concept of the perfect matrix of Lagrange differences, its parameters, the construction of the load function and the corresponding optimization problem, the introduction of internal and external smoothing, embedding of the scalar parameter time series into the phase plane-all these computational techniques allow visualization of complex dynamical processes taking place in the cardiovascular system during the load and the recovery processes. Detailed analysis is performed with one person's RR and JT records only-but the presented techniques open new possibilities for novel interpretation of the dynamics of the cardiovascular system.