Heart Diseases Problem Diagnosis

1
Heart Diseases Problem Diagnosis
We discuss here wavelet methods to determine
characteristics point of ECG signal, its
compression, detection of its abnormalities,
characterization of heart rate variability
through the study of ECG signal, and probe a
variety of arrhythmias.
The Electrocardiogram
Muscular contraction is associated with
electrical changes known as depolarization. The
electrocardiogram (ECG) is measure at the body
surface and results from electrical changes
associated with activation first of the two small
heart chambers, the atria, and then the two
larger heart chambers, the ventricles.
2
Figure 1 A schematic of ECG exhibiting normal
sinus rhyhum
3
ECG timing, distortions and noise
Producing an algorithm for the detection of the P
wave, QRS complex and T wave in an ECG is a
difficult problem due to the time varying
morphology of the signal subject to physiological
conditions and the presence of noise.
Recently, a number of wavelet-based techniques
have been proposed to detect these features.
Senhadji et al compared the ability of wavelet
transform based on three different wavelets
(Daubechies, spline, and Morlet) to recognize and
describe isolated cardiac beats. Sahambi et al
used a first-order derivative of the Gaussian
function Figure 2(a) as a wavelet for the
characterization of the ECG waveforms.
4
They used modulus maxima-based wavelet analysis
to detect and measure various parts of the
signal, especially the location of the onset and
offset of the QRS complex and P and T waves.
Note that for an anti-symmetric wavelet, such
as the first derivative of the Gaussian, dominant
peaks in the signal correspond to zero crossings
in the wavelet transform. (For symmetric
wavelets, dominant peaks in the signal correspond
to extrema in the transform plot.) One of the ECG
signals they analyzed, together with its wavelet
transform at four consecutive scales, is shown in
Figure 2(b).
5
The maxima and minima of the wavelet-transformed
signal are used to determine the location and
width of the QRS complex. This is shown in the
lower two plots of the figure 2(b) containing,
respectively, the signal and its corresponding
wavelet transform at the largest scale. The
vertical lines above the ECG signal at the top of
the plot show the location of the QRS complex
determined from the zero crossings of the modulus
maxima of the transformed signal.
6
Figure 2
7
Figure 3
8
A Healthy Heart is a Fractal Heart
Feature Detection Heart Trouble
9
When you go to the doctors office one of the
first thing they do is jot down your blood
pressure and pulse rate. According to Ary
Goldberg of Harvard University, they might do
well to include another number your heratbeats
fractal dimension
Goldberg spoke on the role of fractal dynamics in
physiology at the SIAM 2003 Annual Meeting, held
June 16-20 in Montreal. Careful analysis of
heartbeat time-series could give cardiologists
new diagnosis tools in the battle against heart
disease. Similar analysis of brain waves and
stride length in walking could give researchers
new insights into such conditions as epilepsy and
Parkinsons disease.
The heart is part of a large feedback system
whose dynamics are non-linear, non-stationary,
and multi-scale Goldberger observes. As
mathematicians well know, even simple nonlinear
rules can lead to complex behavior
10
and the rules the heart are hardly simple. Its
an incredibly complicated system, Goldberg says.
Consequently, the healthy heartbeat is one of
the most complex signals in nature.
All this runs counter to the view of the regular
sinus rhythm the comforting lub-dub we all
associate with stress-free existence-as the gold
standard of cardiology. To be sure, you dont
want your heart beating erratically, as in Don
the first page quiz That patient has a
condition known as atrial fibrillation. But
neither do you want a steady or sinusoidally
varying pulse rate of the types shown in A and C
those are from patients with severe congestive
heart failure. The healthy heart rate is the one
shown in B. Goldberg and colleagues, notably
C.-K. Peng of Harvard, and Eugene Stanley and
Plamen Ivanov of Boston University, have
developed a number of methods for analyzing
heart-beat and other physiologic data.
11
One is a method they call detrended fluctuation
analysis (DFA). The basic idea is to calculate
the average amount of fluctuation over bins of
different sizes-that is, the root means square
deviation between the signal and its trend in
each bin-and then plot the result as a function
of bin size. Remarkably DFA for a healthy heart
form an almost perfect line of slope 1- a
hallmark of Fractal behavior. (Its characteristic
of whats called 1/f noise and indicates the
presence of long-range correlations in the
signal. White and brown noise, by contrast,
tend to line up with slopes of 0.5 and 1.5,
respectively.)
If all hearts produced slope -1 plots, the
finding would be intriguing but not clinically
valuable. Goldbergers group has not found that
to be the case, how ever Recordings from the
people with diseased hearts and from elderly
people show marked departures from slope-1
straightness. This indicates a loss of complexity
in the heartbeat as a result of illness or aging.
12
The difference between healthy and diseased heart
signal is even more striking in a multi-fractal
analysis. The signal from a beating shows signs
of being a multifractal, which means that it is
characterized by a range of exponents, of which
the DFA slope is only the first.
Indeed, a wavelet-based analysis of a healthy
heart shows non-zero Fratcal dimension over a
broad range of exponents, whereas the same
analysis from a subject with congestive heart
failure has a much more restricted range.
You actually see very reproducible degradation
of the Fractal scaling pattern, Goldberg says.
That also raises the possibility that there are
diagnostics and prognostic uses-besides
application-of some of these newer monitoring
techniques.
13
Peng, Goldberger, and Madalena Costa of the
University of Lisbon have devised another
application technique, called multi-scale
entropy, which measures the complexity of
physiologic signal like the heartbeat and
demonstrates a consistent loss of information
with aging and disease.
Their paper on the technique appeared last year
in Physical Review Letters.
For fractals and other complexity-related
measures to reach the bedside will require close
collaboration among researchers from different
disciplines, Goldberger stresses. In particular,
he says physiologists are not used talking
about Fractals and nonlinear mechanisms and
complex systems, although they deal with those
every day.
14
The concept of homeostasis-the idea that
organisms strive to maintain an ideal steady has
been a staple of physiology for the last seventy
years and still has strong appeal. The fractal
patterns observed by Goldberger and colleagues
indicate an adaptive variability, so that they
dont locked into one mode of behavior.
Progress in the field will also depend on
researchers having ready access to data. Data
that are generated in an intensive care unit may
be of huge interest of people who have been
looking at complex systems in a very different
guise, Goldberg points out. Toward that end, his
group has set up physioNet (www.phsionet.org),
with funding from National Center of Research
Resources of the National Institutes of Health.
Its like a GenBank for physiology, Goldberger
says. It allows people around the world to look
at data sets that they otherwise wouldnt have
access to.
15
PhysioNet includes an archive of physiologic data
sets, such as the Fan-tasia Database EKG and
respiration records of 40 adults (20 young and 20
elderly) who spent two hours watching the
classical Disney film. It also provides a toolkit
of open-source software, plus a discussion site,
tutorials, publications, and set of challenges
for all comers.
Golberger is enthused by the possibilities.
Once theres good data and a communications
network, then anything and every thing can
happen, he says The potential for discovery is
enormous.
16
(No Transcript)
17
Time Series Challenge Opening the 2003 SIAM
Annual Meeting with an invited talk titled
Fractal Dynamics in Health and Their Breakdown
with Disease and Aging, Ary Goldberger of Beth
Israel Deaconess Medical Center and Harvard
Medical School showed the audience these four
rate recordings and invited them to choose the
one they would most like to have. As hands went
up for each possibility, Goldberger pointed out
that only one was from a healthy patient the
other three came from people at risk of some
thing really bad. (When he presented the same
challenge to medical people, he said , a
cardiologist was among those who made the worst
possible choice.) Which one would you hope to
have?
18
Contribution of the Wavelet Analysis to the
Non-Invasive Electro-cardiology 
19
Today, various digital-signal-processing methods
are applied to the ECG to identify, extract and
analyze the different ECG signal components. In
this large set of signal-processing tools, a new
technique called wavelet transformation appears
to be a promising method describing time and
frequency characteristics of ECG waves. Here we
present an overview of the wavelet technique
applied to the area of quantitative
electro-cardiology without describing
mathematical details of the wavelet theories.
20
In the first place some rationale for the
utilization of new ECG processing tools are
discussed. In the second place will describe the
contribution of the wavelet transformation in
quantitative electro-cardiology. This
technique will be discussed and compared to the
classical techniques using time-domain and
frequency-domain measurements
21
The frequency representation of a signal can be
obtained using different techniques including the
Fourier transformation, and the autoregressive
method. The most frequently used in
electro-cardiology is the Fast-Fourier
Transform (FFT) that is able to decompose any
temporal signal (theoretically this signal should
be deterministic and periodic) in an infinite set
of sinusoid functions. This set of sinusoid
functions is then represented in the frequency
space using the amplitude and the phase of each
of these functions. The FFT thus provides a link
between the time representation of a signal (in
seconds) and the frequency representation (in
Hertz or cycle/second).
22
As the digitized ECG is a finite signal, its
boundaries are usually abrupt. These abrupt cuts
of the signal make it discontinuous. This
introduces a smearing (decrease and spread) of
all the estimated frequency peaks. In order to
avoid this, the calculation of the FFT is applied
to the windowed ECG. The windowing aims to
smoothly decrease the boundary of the ECG signal
to zero, removing its discontinuity. The
limitation of this approach is that windowing
reduces the frequency resolution and therefore
lowers the quality of the estimation of the ECG
signal frequencies
23
Another unavoidable limitation of the Fourier
transformation for the ECG analysis is that this
technique does not provide insight into exact
location of frequency components in time. The
frequency content of the ECG varies in time the
QRS complex is a high frequency wave whereas the
T wave contains low-frequency components.
Therefore, the need for an accurate description
of the ECG frequency contents according to their
location in time is essential. Utilization of
time-frequency representation in quantitative
electrocardiology is thus justified. This kind
of representation provides insight into three
dimensions of the ECG signal the time, the
frequency and the amplitude (figure 1)
24
Figure 1 Time-frequency domain represents a
combination of time-domain and frequency-domain
characteristics of the ECG signal
25
Among these various time-frequency
transformations, the wavelet transformations also
called time-scale transformations, is gaining a
particular interest in quantitative
electro-cardiology.
26
Figure 2 The wavelet-coefficient calculation is
illustrated using a set of analyzing wavelet from
the Mexican hat wavelet and the ECG signal from
a healthy subject. The analyzing wavelets are
first multiplied by the ECG signal. Then the
wavelet coefficients are calculated using the
area under the resulting curves. The area values
are then plotted in the time-scale domain
providing the three-dimensional representation of
the signal.
27
Thus, when the wavelet analyzes slow waves as the
T wave, longer wavelets are needed and frequency
resolution is good. Whereas with rapid waves,
like the QRS complex, shorter wavelets provide
better signal time description time-resolution
is good but frequency resolution is poor. As a
microscope can focus on specific details of a
slide, the wavelet shape can be adapted to focus
the analysis on specific components of the ECG.
28
Increasing use of computerized ECG processing
systems requires effective ECG data compression
techniques which aim to enlarge storage capacity
and improve methods of ECG data transmission over
phone and internet lines. The wavelet
compression methods described in 1992 provide a
robust technique suited for detecting and
removing redundancy in the signal. The few
publications available on this topic suggest that
the ECG data compression using wavelets could
decompose the ECG without any redundancy and
provide high compression ratio and high quality
reconstruction of ECG signal. According to
these preliminary reports, wavelet-based
compression seems to be more efficient than the
classical compression methods.
29
One of the crucial steps in the ECG analysis is
to accurately detect the different waves forming
the entire cardiac cycle. Some studies aim to
design effective methods for detection and
classification of ECG waves. For instance, Li et
al. developed a wavelet-based classification
method that correctly identifies 99.8 of ECG
waveforms from the MIT/BIH arrhythmia database.
Some authors have also shown that the wavelets,
configured following a wavelet network, provide
efficient extraction for discriminating between
normal and abnormal cardiac pattern. Even if many
algorithms have already been defined for ECG
pattern recognition, the wavelet transformation
seems to offer a new approach worth
investigating, especially in areas of limited
performance of current techniques, like P and
T-wave recognition.
30
The wavelet technique has also been used for the
evaluation and monitoring of ischemic ECG
changes. Mac Leod et al. used wavelet technique
for identification of the ECG changes resulting
from acute coronary artery occlusion and
reperfusion observed during PTCA procedure.
This study demonstrates that the wavelets are
able to identify specific detailed time-frequency
components of ECG signal, which are sensitive to
transient ischemia and eventual restoration of
electrophysiological function of the myocardial
tissue.
The FFT method, frequently used to evaluate heart
rate variability (HRV), has inevitable
limitations related to spectral leakage caused by
abrupt changes at the boundary of the HRV signal.
In addition, FFT introduces inconsistent spectral
components of the tachogram
31
Because the efficiency of the time-domain
late-potential detection is limited to the
terminal portion of the QRS complex and is also
affected by inaccuracies of QRS-end detection,
frequency-domain methods have been investigated
The HRECG analysis is the field of research most
actively seeking to benefit from the wavelet
signal-processing technique. In 1989, Meste et
al. applied for the first time, the wavelet
transform to 5 KHz sampled ECGs. Subsequently,
they used the Meyer wavelet for the detection of
the late potentials. The first quantitative
analysis of the HRECG using wavelet
transformation was described by Dickhaus et al.,
who identified significant differences in HRECG
between post-infarction patients with ventricular
tachycardia and healthy subjects.
32
A different approach was used by Shinnar and
Simson who examined the local scaling behavior of
the ECG wavelet transformation. Patients without
ventricular tachycardia produced ECG wavelet
transformation with relatively constant slope,
while patients prone to ventricular tachycardia
produced ECG wavelet transformation with
multifractal behavior. Morlet et al. designed a
wavelet-based method for the detection of
irregular structure, or singularities in the
HRECG, consisting of an algorithm for tracking
the evolution of the so-called local maxima of
the wavelet transform across scales. This
method is based on the detection, the connection
and the acknowledgment of the connected maxima as
signal singularities.
33
It provides an increase in sensitivity and
specificity for detecting late potentials in
comparison with the results from the time-domain
approach. Couderc et al. and Rubel et al.
reported studies using non-redundant
wavelet-decomposition of the HRECG for the
accurate description of the time-frequency
components of late potentials without the need of
QRS-endpoint localization.
However, no specific wavelet techniques have yet
demonstrated a clinically relevant advantage (of
wavelet) over the classical Simson's method for
late potential detection. The major contribution
of the wavelet to late potential detection is
that the wavelets also seem to be able to detect
abnormal intra-QRS potentials. An example of
wavelet transformation of HRECG is presented in
the figure 3. This approach is of particular
value in the detection of late potentials in
patients with anterior infarction and those with
bundle branch blocks.
34
Figure 3 Examples of redundant wavelet
transformations of the vector magnitude from two
post-infarction patients without (left panel) and
with (right panel) sustained ventricular
tachycardia. The two vertical lines mark the
onset and the offset of the unfiltered QRS
complex. The ellipse emphases the time-frequency
area with abnormal high-frequency components
between 89 and 230 Hz and between 80 and 130 ms
after the onset of the QRS complex.
35
The wavelet ECG quantifiers could thus be a new
alternative to time-domain analysis of the
repolarization segment, especially for diagnosing
the long QT syndrome in patients with borderline
QT duration and for quantifying heterogeneity of
repolarization44.
Time-domain analysis of the ECG is the simplest
approach for detecting and quantifying the
different ECG waves. However, efficacy of this
approach is often limited by the inaccurate
definition of ECG wave endpoints (end of the QRS,
T wave location). More complex signal-processing
tools, i.e. simultaneous time and frequency
domain techniques, were developed to provide more
accurate representation and identification of the
ECG potentials.
36
The wavelet transformation is a new promising
technique in non-invasive electrocardiology
providing improved methods for late-potential
detection, HRV analysis and evaluation of the
repolarization segment abnormalities. The
benefit of the wavelet transformation lies in its
capacity to highlight details of the ECG signal
with optimal time-frequency resolution. Since the
application of wavelet transformation in
electrocardiology is relatively new fields of
research, many methodological aspects (choice of
the mother wavelet, values of the scale
parameters) of the wavelet technique will require
further investigations in order to improve the
clinical usefulness of this novel signal
processing technique. Simultaneously diagnostic
and prognostic significance of wavelet techniques
in various fields of electrocardiology needs to
be established in large clinical studies.
37
Feature Detection Heart Trouble
38
Here we shall described a standard method for
detecting feature within a complicated signal.
This method, known as correlation, is a
fundamental part of Fourier analysis. We shall
describe here some of the ways in which wavelet
analysis can be used to enhance the basic
correlation method for feature detection.
Lets begin by examining feature detection for ID
signals. Feature detection is important in
seismology, where there is a need to identify
characteristics features that indicate, say,
earthquakes tremors within a long seismological
signal. Or, in an electrocardiogram (ECG), it
might be necessary to identify portions of the
ECG that indicate an abnormal heartbeat.
39
(No Transcript)
40
At the top of the Figure (1) we show a simulated
ECG, which we shall refer to as signal C. The
feature that we wish to locate within signal C is
shown in the middle of Figure (1) this feature
is meant to simulate an abnormal heartbeat. It
is, of course easy for us to visually locate the
abnormal heartbeat within the Signal C, but that
is a far cry from an algorithm that a computer
could use for automatic detection.
As noted above, the standard method used for
feature detection is correlation. The correlation
of a signal f with a signal g, both having
lengths of N values, will be denoted by (fg). It
is also a signal of length N, and its kth value
(fg)k is defined by
41
In order for the sum in (1) to make sense, the
signal g needs to be periodically extended, i.e.,
we assume that for each k. When
computing the correlation (fg), the signal f is
the feature that we wish to detect within the
signal. Usually the signal f is similar to the
abnormal heartbeat signal shown in the middle of
Figure (1), in the sense that the values of f are
0 except near the central portion of the signal.
This reduces the distortion that results from
assuming that g is periodic. We will describe
their use in feature detection
The rationale behind using the correlation (fg)
to detect the location of f within g is the
following. If a portion of g matches the form of
the central portion of f where the significant,
non-zero values are concentrated - then for a
certain value of k, the terms in (1) will all be
squares.
42
This produces a positive sum which is generally
larger than the sums for the other values of
(fg). In order to normalize this largest value
so that it equals 1, we shall divide the values
of (fg) by the energy of f. That is, we denote
the normalized correlation of f with g by (fg),
and the kth value of (fg) is
where
43
We can show that under the right conditions, the
maximum value for ltfggt is approximately 1.
As an example of this ides we show at the bottom
of Figure (1) the graph of the squares of the
positive values of the normalized correlation
ltfggt for the abnormal heartbeat and Signal C.
Notice how the maximum for this graph clearly
locates the position of the heartbeat with in
Signal C.
The value of this maximum is 1, thus proving the
following simple criterion for locating an
abnormal heartbeat if a normalized correlation
value is near 1, then an abnormal heartbeat is
probably present at the location of this value.
We have ignored the negative values of normalized
correlation because a negative value of ltfggt
indicates a preponderance of oppositely signed
values, which is a clear indication that the
values of f and g are not matched.
44
The squaring serves to emphasize the value near
1. It is not necessary , but produces a more
easily interpretable graph a graph for which
the maximum value near 1 more clearly stands out
from smaller values.
Notice that there are smaller peaks in the bottom
graph of Figure (1) that mark the locations of
the normal heartbeat in Signal C. These smaller
peaks are present because the abnormal heartbeat
was created by forming a sum of a normal
heartbeat plus a high frequency noise term.
Consequently, these peaks reflect a partial
correspondence between the normal heartbeat term
and each of the normal heartbeats in signal C.
We shall now describe a wavelet based method for
suppressing these peaks in the detection signal
resulting from the normal heartbeats. While this
may not be necessary for the case of Signal C, it
might be desired for other signals.
45
Each normal heartbeat in Signal C has a spectrum
that has significant values only for very low
frequencies in comparison to high frequency
oscillations that are clearly visible in the
abnormal heartbeat. Our method consists,
therefore, of subtracting away an averaged signal
from Signal C.
As we know in the previous section, the higher
the level k of the averaged signal Ak , the
nearer to zero are the low frequencies which make
up the non-zero values of the averaged signals
spectrum . Hence by subtracting away
from Signal C an averaged signal Ak for high
enough k, we can remove the low frequency values
from the spectrum, of f that rise from the normal
heartbeat.
46
For example at the top of Figure 1(b) we show the
signal that is the difference between Signal C
and its fourth averaged signal A4. Comparing this
signal with signal C we can see that the normal
heratbeats have been removed, but there is till a
residue corresponding to the abnormal heartbeat.
In the middle of Figure 1(b) we show the signal
graph of all the squares of positive values of
the normalized correlation of the middle signal
with the top signal . This signal clearly locates
the position of the abnormal heartbeat, at the
same location as before, but without the
secondary peaks for the normal heartbeats.