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ISIS Report 25/07/07
Physics of Organisms & Applications
The Heartbeat of Health
You can tell a person’s health from the way the heart beats, it is the complex
rhythm of the Quantum Jazz
of life, and mathematical physicists are learning how to decipher it. Dr.
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Complex music of the healthy heart
As regular as heartbeat,
right? Not exactly, scientists with a physical bent and penchant for number
crunching have been busy analysing the heartbeat for the past 20 years. They
talk about the ‘complexity of the heartbeat’ and how best to wrest signs of
dynamic order out of apparently random variability, which, they are convinced,
could tell doctors whether the person is healthy or not .
The apparent regularity
of the heartbeat conceals abundant variability, and contrary to common intuition,
the more healthy the heart, the more variable the beat (Fig. 1), and this
can be seen by recording how the interval between successive heartbeats changes
(see Box 1).
1. Which is the heartbeat of health?(Modified from )
Figure 1  contains
four heartbeat recordings, only one of which is from a healthy individual,
the other three are from people with severe heart disease. A and C, which
look quite regular, are from patients with severe congestive heart failure,
while D is from a subject with fibrillation of the atrium (see Box 1), which
produces a very erratic heartbeat. B is the record of the healthy heart, which
looks far from regular.
The most exciting
discovery about the healthy heartbeat is the rich mathematical structure underlying
the apparent variability that distinguishes it from arbitrary randomness;
in much the way that music can be distinguished from noise.
The healthy heart
beats to the complex rhythm of Quantum Jazz  (SiS 32), “the music of the organism dancing
life into being” (see also Quantum Jazz, The Tao
of Biology , SiS 34).
How the heart beats [5, 6]
The heart has four chambers:
two upper small ones called left and right atrium and two lower big ones
called left and right ventricle. A ‘pacemaker’ site, the sinoatrial (SA)
node located in the back wall of the right atrium, initiates the heartbeat.
Special cells in the SA node spontaneously generate spikes of electrical
discharge (action potentials) at a rate of about 100 per minute. This intrinsic
rhythm is strongly influenced by the autonomic (involuntary) nerves. The
vagus (parasympathetic) nerve brings the resting heart rate down to 60-80
beats/min, the sympathetic nerves speeds up the heart rate.
The action potential
generated by the SA node spreads throughout the upper heart chambers (atria),
depolarising them and causing them to contract. The electrical impulse meanwhile
travels to the lower chambers (ventricles) via the atrioventricular (AV)
node in the wall between the atria, where specialised conduction pathways
rapidly conduct the wave of depolarisation throughout the ventricles to
make them contract. It is very important for the depolarisation wave to
travel unimpeded and intact through the heart so that the contraction of
the heart chambers are coordinated to send blood efficiently to the lungs
and through to the rest of body. ‘Fibrillation’ of the heart occurs when
the depolarisation wave breaks up, and different parts of the heart contract
in a totally disorganised way, which can cause death if untreated immediately.
The giant electric
fields generated by the depolarisation and contraction of the atria, followed
by the ventricles are detected throughout the body, and can be recorded
with electrodes placed on the chest and the wrists and ankles. A continuous
record of successive heartbeats obtained in this way is referred to as the
electrocardiogram (ECG). It can be seen that the contraction of the ventricle
sends out the most prominent spike, and beat-to-beat interval (interval
between two heartbeats) is taken between these big spikes. Some instruments
can record these beat-to-beat intervals directly to form a continuous record
(see Fig. 1). It turns out that how the beat-to-beat interval changes with
time may tell us whether the individual is healthy.
In 1993, Eugene
Stanley and collaborators at Boston University in the United States published
a paper showing that while the heartbeat records from healthy people look
superficially very variable, there is a long-time correlation in the intervals
between beats in the healthy heart . For example, shorter intervals tend
to be followed by longer ones, and the effect occurs on a wide range of time
scales, from seconds to many hours. In contrast, heartbeat records from heart
disease patients look superficially much more regular, but were significantly
less correlated when analysed mathematically.
In other words, there was less dynamic order in the heart rhythm of those
afflicted with heart disease.
The importance of distinguishing healthy from unhealthy heart rhythms
There have been numerous studies aimed at extracting
the mathematical structures that characterize the rhythm of the healthy heartbeat,
in order to clearly distinguish it from the heart rhythms of people with heart
disease or at risk from heart disease . That is important not only for
diagnosis, but also for monitoring the patient’s recovery and response to
various drugs and treatments. And mathematics can help to accomplish this
non-invasively, with minimum intervention and risks. It is a bit like the
practitioner of traditional Chinese medicine who can diagnose illnesses of
the internal organs by feeling the quality of the patient’s pulse.
According to the
American Heart Association, 79.4 million American adults (1 in 3) are estimated
have one or more types of cardiovascular disease, of which 37.5 million are
aged 65 or older . Among them are overlapping categories of 72 million
with high blood pressure, 15.8 million with coronary heart disease, 7.9 million
with myocardial infarction (heart attack) and 8.9 million with chest pains.
Cardiovascular disease claims more lives each year than cancer, chronic lower
respiratory disease, accidents and diabetes mellitus combined. More importantly,
millions suffer from undiagnosed heart disease; the prevalence of undiagnosed
congestive heart failure is estimated to be approximately 20 million in the
Although there are some conventional tests for the diagnosis
of heart disease (several of them highly invasive), none can effectively predict
which patients are at risk of sudden death. New drugs and other treatments
continue to be developed to treat heart disease, but there are still no tests
that can rapidly evaluate how well the patient is responding to treatment,
and whether the risk of sudden death has been reduced or increased by the
treatment. Consequently, the efficacy of these treatments must be determined
empirically with slow, prospective-controlled studies that last for many years,
and even then are very difficult to extrapolate to individual patients.
The study of heart
rhythm was considered so important that the European Society of Cardiology
and the North American Society of Pacing and Electrophysiology formed a task
force to develop the standards of measurement, physiological interpretation
and clinical use of heart rate variability. The task force published their
findings in 1996 . In September 1999, under the sponsorship of the National
Center for Research Resources of the National Institutes of Health, Ary Goldberge
and colleagues at Harvard Medical School in Boston, USA inaugurated the Research
Resource for Complex Physiologic Signals available at http://circ.ahajournals.org/cgi/content/full/101/23/e215
[2, 11]. The PhysioNet Resource, as it came to be known, has three interdependent
components. The PhysioBank is a large and growing archive of well-characterized
digital recordings of physiologic signals from healthy subjects and from those
with a variety of conditions such as life-threatening cardiac arrhythmias,
congestive heart failure, sleep apnea (cessation of breathing during sleep),
neurological disorders and aging. PhysioToolkit is a library of open-source
software for physiological signal processing and analysis, detection of significant
events by using both classical techniques, and novel methods based on statistical
physics and non-linear dynamics. PhysioNet is an on-line forum for dissemination
and exchange of recorded biomedical signals and open-source software for analysing
Fractal heart rhythm
The typical heart rhythm data are time series of the interval between successive
heartbeats lasting from minutes to 24 hours. The length of the interbeat interval
changes from one interval to the next, fluctuating around a mean of about a
second (60 beats per minute). It conforms to the mathematical structure of
‘deterministic chaos’ in that the interbeat interval, though locally unpredictable,
is nevertheless globally confined in its variation within a ‘strange attractor’
in abstract mathematical ‘phase space’. That was not surprising, as the same
mathematical structures have been found in many natural and biological processes
 (The Excluded Biology, SiS 18). By
applying more and more sophisticated mathematical tools for signal processing,
researchers have been able to characterize the healthy heart rhythm quite precisely
[2, 8-11, 13-16].
A method widely used
to analyse a signal or time series is to estimate its power spectrum density - the signal’s relative
frequency content - assuming that the signal is made up of waves of different
frequencies. This is done by a Fourier Transform, which gives a spectrum of
many frequency peaks, the higher the amplitude of the peak the more that frequency
component contributes to the signal.
The healthy heart
rhythm typically shows that the contributions of different frequencies S(f) varies as the reciprocal of the frequency
S(f) ~ f
Plotting log S(f) against the log f will give a straight line with a slope
of -b, and this is referred to as 1/f scaling, characteristic of processes
that exhibit fractal dynamics.
Fractals are irregular
objects that have fractional dimensions in between the usual 1, 2, or 3, and
display ‘self-similarity’, in that they are made of subunits (and sub-units
of subunits many times over) that resemble the structure of the whole at many
different scales of magnification. Examples are branching trees, fern leaves,
and blood vessels.
Fractals describe not just geometric objects, but especially complex biological
processes that are correlated with one another.
For example, metabolic
rate B increases as body mass
M increases according to the
‘allometric’ relationship, B ~ Ma,
which has been known to apply famously across animal species from mouse to
elephants since 1932, but no one had a satisfactory explanation until Geoffrey
West from Los Alamos National Laboratory and James Brown at the University
of New Mexico, Albuquerque and colleagues showed how allometric scaling arises
from fractal structures  (No
System in Systems Biology, Biology’s
Theory of Everything, SiS
21), and indeed, implies fractals
Distinguishing healthy from unhealthy heart rhythms with fractal analysis
Fractal mathematics has
been applied successfully to signals such as the healthy heartbeat that fluctuates
across multiple time scales in similar ways. Typically, the larger the time
scale the bigger the fluctuation; and when the logarithm of the fluctuation
F(n) is plotted against the
logarithm of the time scale (in number of heartbeats) n, a straight line is obtained with slope
as indicative of scaling, or self-similarity:
F(n) ~ na
For this analysis, the time series is first ‘detrended’ to remove the underlying
local trend, i.e., it is smoothed to obtain a flat baseline for all times, before
computing the amplitude of fluctuations over different numbers of heartbeats,
from 2 to 10 000.
Applying the method to 30
datasets - each a 24 h record – from 18 healthy and 12 patients with congestive
heart failure, the Boston University and Harvard Medical School researchers
found that the data during wake hours scale linearly over two decades between
60 to 6 000 beat, with the average exponent aw~1.05 for the healthy group,
and 1.2 for the heart failure patients [11, 15]. For the sleep data, a smaller
average exponent as
~ 0.85 was found for the healthy and 0.95 for the heart failure group. When
the data points of the time series were shuffled (to destroy the intrinsic
dynamic order), they all gave a slope of 1.5 as characteristic of random walk
fluctuations or Brownian motion, which has no long-term correlation.
The researchers also analysed 17 datasets from six cosmonauts during long-term
orbital flight on the Mir space station under zero gravity and high stress activity.
Each dataset contained continuous records of 6h under both sleep and wake conditions.
For all cosmonauts, the scaling exponents were nearly the same as those found
for the healthy terrestrial group: aw~1.04
for the wake phase and as~0.82 for the sleep phase. The individual record
of a subject from each group is illustrated in Figure 2.
2. Plots of fluctuation against number of heartbeats (a) a healthy individual,
(b) a cosmonaut, (c) a patient with heart failure, and (d) a randomised (shuffled)
time series of the healthy individual. (Modified from .)
There are many scaling
exponents on the heartbeat data capable of distinguishing between health and
disease, and the scaling properties also vary with age, but the changes are
different from those associated with heart failure.
of the healthy heart rhythm can be demonstrated most clearly with a mathematical
procedure called ‘wavelet transform’, which estimates the differing spectrum
of frequencies contributing to the changing signal at different time scales
(see Fig. 3). The horizontal axis is time corresponding to about 1 700 heartbeats.
The vertical axis is the scale of analysis increasing from 5 to about 300
s. The brighter colours indicate larger values of the wavelet amplitudes,
corresponding to large heartbeat fluctuations. The white tracks represent
the maximum wavelet transform lines, which exhibit a tree-like self-similar
structure. So magnifying a portion of the upper panel corresponding to 200
beats on the horizontal axis and about 5 to 75 s on the vertical axis results
in a structure (middle panel) resembling the whole. In contrast, the wavelet
analysis of the times series from a patient with sleep apnea over 1 500 heart
beats and 5 to 200 s (bottom panel) shows the loss of the self-similar structure
over multiple timescales exhibited by the healthy heart (top panel).
Figure 3. Wavelet analysis of heartbeat times series
from a healthy subject (top and middle panel) and a patient with sleep apnea
(bottom panel). See main text for details (modified from ).
Multifractal heart rhythm
The analyses of heartbeat time series described so far
assumes that the signal is stationary, i.e., it remains the same over time.
But it is clear from casual inspection of the time series (Fig. 1B) that the
heartbeat signal is not stationary, and hence, the scaling exponents may differ
at different times. In other words, the heart rhythm may be multifractal ,
rather than monofractal, and requires many exponents to fully characterize
Furthermore, the multifractal
exponents of the healthy heart rhythm, h,
are not independent of one another. The heartbeat series of 18 healthy subjects
(both daytime and night-time) individually and as a group yielded multifractal
exponents with fractal dimensions close to 1.0 distributed continuously over
a broad range 0<h<0.3 centred at h~0.125 (Figure 4, black curve), suggesting
that the fluctuations in the heartbeat exhibits anticorrelated behaviour (0<h<0.5
corresponds to anticorrelated behaviour; h=0.5 corresponds to uncorrelated
behaviour, while h>0.5 correspond to correlated behaviour). In contrast,
the time series from patients with congestive heart failure showed a clear
loss of multifractality (Fig. 4, grey curve), with the exponents distributed
over a much narrower range centred at h~0.22 (closer to 0.5 compared to the
4. Fractal dimension versus multifractal (Hurst) exponent for the heartbeat
records of healthy subjects compared with those of patients with congestive
heart failure (see main text).
The significance of these
findings is best described by the comment of the researchers  that the
healthy heartbeat is “more like a symphony than a solo performance.”
The heart is not a solo player in the quantum jazz of life
The heart is not a solo
player in the quantum jazz of life [3, 4]. Instead, it is in symphony with all other players, intermeshing and syncopating
with their varied rhythms, reflecting the correlations and couplings in a
system that is quantum coherent
in the ideal. It is the rhythm of the organism dancing life into being, in
which every single player is freely improvising and yet keeping in tune and
in step with the whole.
The coupling between heart and other rhythms is quite precise, extending to
phase correlations among all the body rhythms, which is why shuffling the heartbeat
time series results in the loss of the exquisite hidden dynamic order that includes
precise phase correlations. An unhealthy heart, by contrast, is no longer intercommunicating,
but falls back onto its own intrinsic rhythm, like a very boring person who
keeps saying the same things, not listening or responding to anyone else, which
is why its heartbeat appears superficially more regular, while the dynamic hidden
order is destroyed.
The study of heart rate variability looks so promising that patents have been
granted recently on mathematical procedures for  “diagnosing heart disease,
predicting sudden death, and analysing treatment response.”
Looking further ahead, this minimally invasive/intervention approach may be
just the paradigm change we need in medicine to deliver health to the nation
safely and effectively, based on an intellectually rigorous holistic perspective
that’s nevertheless centred on the individual organism. Read the next article
in the series Happiness
is a Heartbeat Away  (SiS 35).