Download Complex rhythmic processes are typical for living organisms

Gdańsk, September 25th, 2006
Complexity Measures of Heart Rate Variability
CompHRV
- data analysis and modeling
Complex rhythmic processes are typical for living organisms. The human cardiovascular system is
a paradigmatic source of the fundamental physiological rhythm - the heart rate, and is controlled by
several neural and hormonal mechanisms. Blood pressure and electrocardiogram (ECG) are the
easiest measures of signals originating in the cardiovascular system. The continuous ECG can be
transformed into a discrete signal of normal beat-to-beat cardiac periods, called NN-intervals. It has
been demonstrated that NN-intervals fluctuate in a complex manner: they show the long-range
temporal autocorrelations, multifractal scaling properties, and share characteristics of a physical
system in a critical state.
The variation in NN series is termed the heart rate variability (HRV). The HRV represents the most
promising marker in recognition of the relationship between the autonomic nervous system and
cardiovascular mortality. The heart rate is raised by slow acting sympathetic activity and decreased
by fast acting parasympathetic (vagal) activity. The balance between the effects of the sympathetic
and parasympathetic nervous systems is believed to be reflected in the beat-to-beat changes of the
fundamental cardiac cycle.
The ECG is the most commonly prescribed examination by physicians for their patients. The 24hour ECG Holter monitoring provides information on electrical activity of a heart during a long
time. Therefore there is a vast amount of data and research on HRV is conducted in many
scientific centers. This strong interest resulted in implementing the methods to medical routine.
In 1996 results were collected in a paper published in European Heart Journal 17 ( in pages 354381): Heart rate variability. Standards of measurement, physiological interpretation, and clinical
use, prepared as Task Force of The European Society of Cardiology and The North American
Society of Pacing and Elecrophysiology. However, two types of technical difficulties make the
analysis of HRV not as reliable as it could be. The first type of difficulties arises from the size of
the data sets. These sets are huge, hence dealing with them requires high skills in computer science.
The second type difficulty is related to the lack of stationary features in a single series what
strongly misleads standard tools. Careful pre-analysis of statistical properties of each series is
necessary.
Multifractal formalism is a proposition to determine statistical features of series by its scaling
properties. Scaling properties related to the long-range memory allow to estimate
interdependences in the system while singularity statistics provides insights into short-term
relations. Many types of real signals are investigated by multifractal analysis such as fully
developed turbulence, financial time series, load of network traffic and physiological signals. A
key issue in the classification and modeling of empirical data as well as in the analysis of the
physical mechanism producing scaling phenomena is the accurate measure of scaling exponents.
Existing methods are far from working as a black box. Therefore there is a pressing need
both to standardize existing estimators and to design new ones.
Multiplicative signal organization is associated with most of the phenomena where scaling
properties are observed. However, fractal dependences in the heart rate signals can also be related
to a critical dynamical state intrinsic to the heart because of the antagonistically acting systems
regulating heart beats. But the mechanism responsible for the complex heart dynamics is still being
discussed . The so-called open loop conditions, where parts of the control system are studied in
isolation, contributed significantly to better understanding of the physiology of cardiac control. A
number of mathematical models of short-term pressure control system has emerged as a result of
this approach. A fundamental hypothesis underlying mathematical modeling of HRV is that
changes in the cardiac rhythm can be associated with bifurcations in the model . Bifurcations in real
system can be understood as, for example, moving unhealthy rhythms into a normal one by
applying drugs. Since models of cardiovascular interactions are being debated, one is faced with
rather broad range of possible parametric models to consider. Models relating the three main
rhythms of human physiology: heart rate, blood pressure and respiratory are continuously verified
and improved.
Our research group successfully cooperates for last two years. The group consists of cardiologists
coordinated by Prof. dr hab. Andrzej Rynkiewicz from 1st Department of Cardiology of Medical
Academy of Gdańsk and physicists coordinated by dr hab. Danuta Makowiec, prof. UG, from
Institute of Theoretical Physics and Astrophysics of Gdańsk University.
So far by multifractal analysis of signals collected from carefully selected groups of patients
we could separate heart rates of healthy people from heart rates of people diagnosed with reduced
left ventricular systolic function. We also proposed new indicators (related to fractal statistics) of
HRV. Our results on HRV were published in following papers :
(1) A. Dudkowska , D. Makowiec, Physica A 336 (2004) 174-180: Sleep and wake phase of hart
beat dynamics by artficial insymmetrised patterns
(2) A. Dudkowska, D. Makowiec, Folia Cardiologica 12, suppl. D, (2005): Modeling of the human
cardiorespiratory system — the influence of the stochastic input
(3) A. Dudkowska, R.Gałąska, J. Wdowczyk-Szulc, A. Koprowski, D. Makowiec, A. Rynkiewicz,
Folia Cardiologica 12, suppl. D, (2005): Heart rate variability analysis by artificial insymmetrised
pattern
(4) D. Makowiec, R. Gałąska, A. Dudkowska, A. Rynkiewicz, M. Zwierz, Physica A 369, 632644 (2006) : Long-range dependencies in heart rate signals - revisited,
(5) D. Makowiec, A. Dudkowska, M. Zwierz, R. Gałąska, A. Rynkiewicz, Acta Phys.Pol B 37
1627-1639 (2006): Scale invariant properties in heart rate signals
and presented both to the medical audience by R. Gałąska ( MAG) on World Congress in
Cardiology in Barcelona, September 2006, and to physicists' audience by D.Makowiec (UG)
during Symposium on Marian Smoluchowski Symposium on Statistical Physics, Zakopane 2005.
There are two doctoral thesis being prepared ( R.Galąska, A.Dudkowska) which closely relate to
the project subject.