chaos and fractals in heart rate
Dirk Hoyer
Institut fuer Pathologische Physiologie
Klinikum der Friedrich Schiller Universitaet
07740 Jena
tel. 03541-635944
i...@hpux.rz.uni-jena.de
Dimitris Kugiumtzis
In article <370n47$6...@hpux.rz.uni-jena.de>, i...@rz.uni-jena.de (Dirk Hoyer) writes:
>My work deals with nonlinear analysis of heart rate but also
>respiration and EEG. We found perhaps finite Correlation dimensions
>in HR but also 1/f fractal like behavior. My problem is to distuinguish
>between deterministic (regular or chaotic) and stochstic characteristics
>in the time series. We found CD and positive leading Lyapunov Exponets
>inticating deterministic chaos.
>But stochastic signals with 1/f power spectra have also such properties.
>Who has some ideas or remarks with regard to distuinguisch chaotic and
>stochastic, also fractal properties.
>Our results seem to be useful for the classification of pathological
>situations. I would like to improve the theoretical basis.
Very interesting posting. I would like to add some comments to it.
This problem does not concern only ECG or EEG but more or less any
application to data that seem to be random at first look.
The whole problem in the analysis is related to the presence and
the type of noise (that can be assumed equivalently as high
dimensionality of the underlying system):
- Measurement noise: When the underlying deterministic
system is not essentially corrupted by noise then it should be
possible to discriminate determinism from randomness assuming
sufficient length of the time series and observability restrictions
to the measured variable. BUT, when it is and when it is not
"essentially corrupted"? I believe this has to do with the
acceptable SNR (Signal to Noise Ratio), i.e. that the amplitude
of noise is not large enough to mask the system dynamics.
- Dynamic noise: In the presence of such noise I would assume
that the system is stochastic (deterministic part + noisy part
direct the evolution of the system).
The analysis of physiological data so far indicates exactly this,
i.e. the noise is not simply due to measurement but intrinsic to
the system.
I appreciate any comments to this.
Dimitris
=====================
dimi...@ifi.uio.no
tl :+47 22852464
fax:+47 22852401
Dimitris Kugiumtzis
Dept of Informatics
Pb 1080 Oslo,Norway
=====================
Louis M. Pecora
Kugiumtzis) wrote:
For a deterministic test I would recommend the recent work by Danny Kaplan
and variations on the same themes by Salvino and Cawley:
1. D. T. Kaplan, "Exceptional events as evidence for determinism," Physica
D 73,
38-48, 1994.
2. D. T. Kaplan and L. Glass, "Direct Test for Determinism in a Time
Series,"
Phys. Rev. Lett. 68, 427, 1992.
3. L. Salvino and R. Cawley, "Smoothness means good embedding," Phys. Rev.
Lett.
(sorry don't have exact volume,but it's recent), 1994.
4. L. Salvino and R. Cawley, "Statistical Test for 'Smooth Dynamics' in
Embedded
Time Series," Phys. Rev. Lett. 73, 1091, 1994.
I'm also working on the problem and I've come up with a set of statistics
to test for specific mathematical properties of time series: continuity,
injectivity, differentiability (smoothness), etc. These are more refined
than above and you can decide which you want to use as your test for
determinism:
(1) close points in present means close points in future (continuity)
(2) close points in present means close, linearly realted points in future
(differentiability -- smooth dynamics)
(3) close points in future mean close points in past (injectivity -- this
is not determinism, but more like retrodiction)
(4) close points in future and past are in one-to-one correspondence (this
is similar to what mathematicians call a homeomorphism--Note: this is *not*
the same as (1); it is actually (1) and (2) combined)
(5) close points in future and past are in one-to-one, linear
correspondence (this is similar to what mathematicians call a
diffeomorphism)
Well, you get the idea. Depends on what level of determinism you want to
talk about. However, you can distinguish from white noise or colored noise.
My own work will probably be submitted for publication within the month (If
you send me your address, I'll send a preprint when ready). But I highly
recommend above reference 1. for a good start on these issues. It's the
first work that I know of that generates a statistically sensible test
that's close to a mathematical definition of determinism. It's also very
readable.
--
Lou Pecora
code 6341
Naval Research Lab
Washington, DC 20375
pec...@zoltar.nrl.navy.mil
/* My comments are my own and do not represent the views of the
U.S. Navy. They rarely agree with me anyway. */
READ NEWS
Datadvocat
pec...@zoltar.nrl.navy.mil (Louis M. Pecora) writes:
re availability of preprint
I'd appreciate a copy of this as well:
Frank Funderburk
CCGA
Hopkins/Bayview Research Campus
Box 5261
Baltimore, MD 21224
Thanks in advance.
Dan Winter
and at Heart Math Institute, doing power series spectral analyses
of ECG at moments correlated to emotion.
What we see consistently is that the fourier transform or
frequency signature of harmonics contained in the Heart
electricities become dramatically ordered or coherent
replicably during compassion or love. (between approx 0-40hz)
In response to my suggestion, they also published a measure
of increased braiding or ordering in test tube DNA specifically
in the presence of this ordered EKG field. I have also measured
significant increased order and entrainment in the
charge envelope around nearby plants and trees in response
to what is apparently a heart become a phonon laser.
(Spectrum analysis of capacitive accelerometrics in a technique
similar to Bentov ."Stalking the Wild Pendulum".)
My suggestion re: fractality in ECG is this..
The model which I teach at international conferences on coherent emotion
is:
The heart solves the problem of chaos by using a PARTICULAR KIND
of phase coherence in it's musical harmonic content. When the
wave lengths contained in the heart's beat fit together in a
RECURSIVE GEOMETRY ARRAY, then informationally the heart benefits
from a spin path to the zero point. (cf zero point energy research, cf the
mechanism of phasec onjugate mirroring in non linear optics).
I have found the geometry of the wave lengths present in the heart beat
to fit patterns based on 2, square root of 2, and on square root of
phi (Golden Mean)..
Essentially this means the heart in coherent emotion learns to
fabricate electrical spider webs which permit recursion/fractality/
nestedness/ self-embeddedness.
Since our model is that phase coherence in glandular electricities
is the mechanism where glands input immune system/ and braid
DNA.. it appears this phonon laser from the glands called emotion/
optimizes in the geometry of fractality.
Lest we fail to leap in where angels fear to tread here,
I will also comment, that it is my conclusion that
onset electrical recursion in pressure systems like
heart and brain electricities is the onset of self-awareness.
More info on the data acquisition techniques avail.
book: 440pp
"Alphabet of the Heart" $22
2 hr film:
"Accessing the Alphabet of the Heart" $17
Dan Winter
Crystal Hill Multimedia
9411 Sandrock Rd
Eden, NY 14057
implosi...@gmail.com
www.HeartsRing.com
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Pic att'd
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