Non-linear reaction-diffusion models of turbulence
and chaos in active media: Theory, computer
simulation and applications in Cardiology and
Cardiovascular Circulation

Prof. Sh. Einav and Dr. Victor Kardashov
Department of Biomedical Engineering, Tel-Aviv University

The main purpose of the proposal is the development of the coupled analytical and signal processing tools, implementing real-time interactive analysis and monitoring of the main cardio-vascular parameters. The parameters include: Heart Rate Variability (HRV), Heart Potential Rate, Pulse Pressure Variability (PPV). By using of these parameters the Degree of Correlation of Heart Beatings and Pressure Pulses have determined. The main idea of our approach is to use new modification of nonlinear reaction-diffusion equations, including the main electro-physiological and hemodynamical parameters, for description of the Heart Potential and Pressure Pulse propagation for every pulse. Obtained sequence of equations, coupled with signal processing of the real ECG and Pressure Pulse Signal, allow construction of the complex of time series, describing a real-time dynamics of the parameters, associated with Autonomic Neural System, Heart Sensibility, Heart Potential Velocity and etc. Our preliminary results on computer analysis of these time series indicate that it is feasible approach to visual monitoring and analysis of the above-mentioned cardiovascular parameters. It may be used for computer assisted control of the cardiovascular system during surgery and prediction of acute cardiovascular events by use of long time monitoring of the ECG and Pulse Pressure. On the other hand, the analysis of interactive dynamics of these time series by using of the modern concepts of nonlinear dynamics is suggested as possible software for implementing of non-invasive, computer assisted system for early recognition and diagnostics of acute cardio-vascular disorders such as Atrial and Ventricular Fibrillation, Coronary Artery Disease, Mio-Cardiac Ischemia, Congestive Heart Failure, Endothelial Dysfunction, Obstructive Sleep Apnea, and etc.

1) Proposed system may be used for real time visual monitoring of HRV and PPV for preventing and early diagnosis of different types of arrhythmia and pulse instability.
2) After clinical validation it may be used in clinical practice together with conventional medicine for recognition of early symptoms of acute heart failure, hypertension, ischemia, infarction and patients stress conditions;
3) Coupled HRV and PPV automatic monitoring may be used for treating of control system for drug administration on cardio-vascular and neural diseases and neural stresses.
4) Direct monitoring of autonomic nervous system conditions and associated parameters may be useful for implementing of early diagnostics and optimal therapy strategy treating of such diseases as Obstructive Sleep Apnea and Familial Dysautonomia.
5) The approach appears to be particularly promising for application in combination with analysis of so called "Abnormal intra-QRS potentials" that developed as a new electrical index for predicting arrhythmic events.