1. Noninvasive Detection of Coronary Artery Disease John Semmlow and John Kostis Laboratory for Noninvasive Medical Instrumentation Rutgers University and Robert Wood Johnson Medical School

2. Noninvasive Detection of Coronary Artery Disease Basic Approaches 1) Electro cardiogram (ECG) Techniques: Resting ECG, Exercise ECG (Stress test), cardio-integram. 2) Flow-based Techniques: Thallium 201 myocardial scintigraphy (Thallium stress test), Pharmacoloical stress imaging, gated blood pool scanning 3) Direct Imaging Techniques: Positron emission tomography (PET), Magnetic reasonance imaging (MRI), Digital subtraction angiography, computer-assisted tomography (CAT) 4. Wall Motion: Stress ecochardiology, apex cardiology, cardiokymography, seismocardiography. 5) Acoustic method.

3. Signal Detector Editing/ Diastolic Window Classifier Signal Diastolic Signal Disease Vector Disease State Signal Processing Algorithms

4. Preprocessing S2 Detection Find Diastolic Window Edit Data Spectral Estimation (FFT) Model-Based Analysis Save Data Software Processing Components

5. S2S1 Diastolic Window

6. FFT Spectra Averaged spectra of the diastolic portion of 10 heart cycles from a normal and diseased patient. Normal Diseased Frequency

7. Short-Term Fourier Transform (Spectogram) where w(t-τ) it is the window and t slides the window across the function. In discrete form:

8. Time-Frequency Limitation To increase time resolution you need a shorter window A shorter window decreases the frequency resolution This leads to a time-frequency uncertainty:

9. Response of the Short-Term Fourier Transform Step-change in Frequency

10. Chirp Signal Linear increase in frequency with time

11. STFT Response to a Chirp

12. To overcome time-frequency limitations of STFT, there are two different approaches: Cohen class of distributions: Wigner-Ville, Choi-Williams and many others. These are all based on the “instantaneous autocorrelation function. Time-scale approaches: The Wavelet Transform

13. The Wavelet Transform There are two basic type of Wavelet Transform: The Continuous Wavelet Transform (CWT). Similar to the STFT except scale is changed. The Discrete Wavelet Transform (DWT). Also known as the Dyadic Wavelet Transform. Non-redundant, used bilaterally, best described with filter banks

14. Continuous Wavelet Transform Recall the Short Term Fourier Transform In the STFT a family of windowed, harmonically related sinusoids ‘slides’ across the signal function, x(τ). In the CWT, the family is a series of functions at different scales (sizes) that slide across the signal function Where: a scale the function and b does the sliding.

15. Wavelet Functions A wide variety of functions can be used as long as they are finite. For example, the Morlet Wavelet is a popular function

16. The Morlet Wavelet at Four different scales. The wavelet at a = 1, is the baseline, or “mother” wavelet

17. Different scales (values of a) produce a different time-frequency trade-off. Δω Δt = constant

18. CWT to a step change in frequency

19. Cohen’s Class of Distributions Basic equation: While this equation is quite complicated, it breaks down into three components. Two dimensional filter Instantaneous autocorrelation function Sinusoids that take the Fourier Transform

20. Wigner-Ville Distribution The Wigner-Ville Distribution has now filter so it consists only of the Fourier Transform of the instantaneous autocorrelation function. In discrete notation: where R x (n,k) is the instantaneous autocorrelation function

21. Instantaneous Autocorrelation Function In the regular autocorrelation function, time is integrated out of the result, so is is only a function of the shift. In the instantaneous autocorrelation function, no integration is performed and time remains in the function. The function becomes a function of both time and shift R(t,τ).

22. Cosine Wave

23. Cosine wave Double frequency

24. Wigner-Ville to a chirp function (analytic signal)

25. Wigner-Ville to a step change in frequency (analytic signal). Note the cross products