Graduate School in Nonlinear Science

Sponsored by the Danish Research Academy

MIDIT                               OFD                           CATS
Modelling, Nonlinear Dynamics       Optics and Fluid Dynamics     Chaos and Turbulence Studies
and Irreversible Thermodynamics     Risø National Laboratory      Niels Bohr Institute and 
Technical University of Denmark     Building 128                  Department of Chemistry
Building 321                        P.O. Box 49                   University of Copenhagen 
DK-2800 Lyngby                      DK-4000 Roskilde              DK-2100 Copenhagen Ø
Denmark                             Denmark                       Denmark

Multipole Description of Complex Systems Applied to Heart Rate Variability

J. Levitana,d, M. Lewkowicza, N. Pozanovb, and Y. Ashkenazya,b

(a) Dept. of Physics, College of Judea and Samaria, Ariel, Israel
(b) The Research Inst., College of Judea and Samaria, Ariel, Israel
(c) Dept. of Physics, Bar-Ilan University, Ramat-Gan, Israel
(d) Dept. of Physics, The Technical University of Denmark, Lyngby, Denmark

MIDIT-seminar 463

Thursday September 2, 1999, 14.00 h
at MIDIT, IMM Building 305, room 027


We present a geometrical description of a two-dimensional plot of data points in terms of a gravitational multipole expansion where every data point is assigned a unit mass. The monopole moment represents the number of data points; the gravitational dipole moment is arranged to be zero by choosing the origin in the center of mass. The gravitational quadropole moment measures the deviation from a circular, disc-like, distribution of data points. These quadropole moments, calculated for the principal axes, offer a unique description of the mass distribution. The method is applied to the detrended time series created from R-R intervals obtained from a set of 32 individuals whose state of cardiac function is well known. The method succeeds to separate between individuals with normal and abnormal cardiac function. Finally the method is applied to some well-known attractors.