1. Detection, segmentation and classification of heart sounds
Daniel Gill
Advanced Research Seminar
May 2004

2. Automatic Cardiac Signals Analysis
Problems :
Pre-processing and noise treatment.
Detection\segmentation problem.
Classification problem:
Feature extraction – waveshape & temporal information.
The classifier.

3. Outline Methods based on waveshape : - Envelogram
- Wavelet decomposition and reconstruction
- AR modeling
- Envelogram estimation using Hilbert
transform
Suggested method : Homomorphic
analysis
Suggested temporal modeling : Hidden Markov
Models

4. Heart beat, why do you miss when my baby kisses me ?
B. Holly (1957)

5. PCG Analysis We will concentrate mainly on S1 and S2.
We will discuss only methods which do not use external references (ECG, CP or other channels).
Most of the methods are non-parametric or semi-parametric (parametric models for the waveshape but non-parametric in the temporal behavior).
Suggestion for parametric modeling.

6. Features of PCG
The envelope of PCG signals might convey useful information.
In order to detect\segment\classify cardiac events we might need temporal information.

7. Segmentation Using Envelogram (S. Liang et al. 1997)
Use Shannon energy to emphasize the medium intensity signal.
Shannon Energy: E=-x2log(x2)

8. Segmentation Using Envelogram
The Shannon energy eliminates the effect of noise.
Use threshold to pick up the peaks.

9. Segmentation Using Envelogram
Reject extra peaks and recover weak peaks according to the intervals statistics.
Recover lost peaks by lowering the threshold

10. Segmentation Using Envelogram
Identify S1 and S2 according the intervals between adjacent peaks.

11. Segmentation Using Wavelet Decomposition and Reconstruction (Liang et al. 1997)
Use the frequency bands that contain the majority power of S1 and S2.
Daubechies filters at frequency bands :
a4 : 0-69Hz
d4 : Hz
d5 : 34-69Hz

12. Segmentation Using Wavelet Decomposition and Reconstruction
Use Shannon energy to pick up the peaks above certain threshold.
Identify S1 and S2 according to set of rules similar to those used in segmentation with envelograms.
Compare the segmentation results of d4, d5 and a4.
The choosing criterion : more identified S1s and S2s and less discarded peaks.

13. Segmentation Using Wavelet Decomposition and Reconstruction

14. AR modeling of PCG (Iwata et al. 1977, 1980)
Used narrow sliding windows (25ms) to compute 8th order AR model.
Features used : dominant poles (below 80Hz) and bandwidth.
Detected S1, S2 and murmurs.

15. Segmentation and Event Detection - Cons
Most of the methods are based on rules of thumb – no physical basis.
In most cases there is no parametric model of the waveshape and\or timing mechanism.
Not suitable for abnormal\irregular cardiac activity.
In case of AR model, there is still question of optimality : window size, order etc. In addition, there is no model for the timing mechanism of the events.
Heart sounds are highly non-stationary – AR model is very much inaccurate.

16. Suggested Methods Waveshape analysis – Homomorphic Filtering.
Temporal Model – (Semi) Hidden Markov Models.

17. Waveshape analysis - Homomorphic filtering
Express the PCG signal x(t) by
where a(t) is the amplitude modulation (AM) component (envelope) and f(t) is the Frequency modulation (FM) component.
Define

18. …
Thus
If the FM component is characterized by rapidly variations in time - apply an appropriate linear low-pass filter L.
we have
L is linear so :
By exponentiation :

19. AM envelopes
(a) Normal beat, (b) Atrial septal defect, (c) Mitral stenosis (d) Aortic insufficiency.

20. Identifying Peaks
A simple threshold was used to mark all the peak locations of the AM envelogram.
Suppose that two consecutive peaks are found at
and
We might have to reject extra peaks or recover lost peaks.

21. Extra peaks were rejected by the following rules:
if (splitted peak) if
choose
else choose
else choose (not splitted)

22. …
When an interval exceeds the high-level limit, it is assumed that a peak has been lost and the threshold is decreased by a certain amount. It is repeated until the lost peaks are found or a certain limit is reached.

23. Labeling
The longest interval between two adjacent peaks is the diastolic period (from the end of S2 to the beginning of S1).
The duration of the systolic period (from the end of S1 to the beginning of S2) is relatively constant

24. Labeling Thus Find the longest time interval.
Set S2 as the start point and S1 as the end point.
Label the intervals forward and backward.

25. Normal heart beat with the labels found

26. Homomorphic Filtering Pros
Provides smooth envelope with physical meaning.
The envelope resolution (smoothness) can be controlled.
Enables parametric modeling of the amplitude modulation for event classification (polynomial fitting ?).
Enables parametric modeling of the FM component (pitch estimation, chirp estimation ?)

27. Temporal Model – (Semi) Hidden Markov Model
HMM is a generative model – each waveshape feature is generated by the cardiological state of the heart.
HMM models have been already used for ECG signals.
The ECG state sequence obeys Markov property – each state is solely dependent on previous state.

28. HMM Formalism An HMM  can be specified by 3 matrices {P, A, B}:oT o1 ot
ot-1
ot+1 x1
xt+1 xT xt
xt-1
An HMM  can be specified by 3 matrices {P, A, B}:
P = {pi} are the initial state probabilities
A = {aij} are the state transition probabilities = Pr(xj|xi)
B = {bik} are the observation probabilities = Pr(ok|xi)

29. Generating a sequence by the model
Given a HMM, we can generate a sequence of length n as follows:
Start at state xi according to prob i
Emit letter o1 according to prob bi(o1)
Go to state xj according to prob aij
… until emitting oT 1 2 N … 1 1 2 N … 1 2 K … … 1 2 N … 2 2 2 N
b2o1 o1 o2 o3 oT

30. The three main questions on HMMs
Evaluation
GIVEN a HMM , and a sequence O,
FIND Prob[ O |  ]
Decoding
FIND the sequence X of states that maximizes P[X | O,  ]
3. Learning
GIVEN a sequence O,
FIND a model  with parameters , A and B that
maximize P[ O |  ]

31. Segmentation of ECG Using a Hidden Markov Model (L. Claveier et al.)
Purpose:
Segment ECG (12 parts);
Detect accurately P-wave, recognize cardiac arrhythmias.
Parameters:
Amplitude;
Slope.

32. Segmentation of ECG Using a Hidden Markov Model (Con.)
Possible state jumps of the HMM
Other jumps and states could be added to recognize various shapes of the P and T waves.

33. Segmentation of ECG Using a Hidden Markov Model (Con.)
Automatic segmentation of an ECG beat.
Automatic segmentation of a P-Wave

34. ECG segmentation using HSMM
N. Hughes et al. (2003) used HMM in a supervised manner.
Training signals were segmented and labeled by group of expert ECG analysts.
Used raw data and wavelet encoding.

35. Segmentation using HSMM - results

36. Conclusions
Homomorphic (or cepstral) analysis may provide parametric modeling of S1 & S2 and reduce significantly the dimension of the problem.
Parametric\probabilistic modeling like HMM (or HSMM) may provide robust segmentation of irregular cardiac activity.
It can make automatic classification easier.

37. Thank You !