«Detection of coronary artery disease with an electronic stethoscope Schmidt, Samuel Publication date: Document Version Publisher's PDF, also known as ...»
3.3. Onset of murmurs The onset of murmurs is related to the geometry and the Reynolds number . In a straight tube unstable flow occurs at approximately Re=2300, but when the flow is hindered by an obstruction the critical Reynolds numbers are much lower. Flow can be classified in three states: laminar, disturbed and turbulent. In the disturbed flow fluctuations occur but the fluctuations are not fully irregular . Disturbed flow might cause murmurs, but the murmur intensity increases dramatically in the case of turbulent flow . Sacks et al. evaluated the relationship between Reynolds number, degree of stenosis and the onset of murmurs in the aorta of dogs . They found that turbulent flow was present when murmurs were observable. According to their study the Reynolds number which onsets murmurs could be estimated from the degree of the stenosis (⁄) where Reonset is the Reynolds number in the unobstructed part of the artery which onsets the murmurs. Therefore, murmurs will occur from a 50% stenosis if the Reynolds number exceeds 596 and murmurs will occur from a 75% stenosis if the Reynolds number exceeds 149. Even slow flow with a Reynolds number at 53 will cause a murmur in the case of 85% stenosis. In the estimated average case where the peak Reynolds number was 285 a 65% stenosis will cause murmurs. However, other factors such as the degree of pulsating flow and the shape of the stenosis affect the onset of murmurs . According to Young et al.
In contrast, a stenosis with a smooth transition from constriction to normal vessel diameter increases the Reonset with approximately 30% as compared with a sudden diameter change . Due to the large variations in flow, Reynolds number, anatomy and pulsation it is not possible to define exact degree of stenosis which will cause CAD murmurs.
1.3.4. Murmur characteristics As for the onset, the intensity of the murmurs is highly dependent on geometry and the Reynolds number. Two studies have used flexible tubes to study the relation between the power of the murmurs, Reynolds number and the degree of the stenosis [36, 37].
They both found a nonlinear relationship between the power of the murmurs, Reynolds
number and degree of stenosis:
(⁄) where Re is the Reynolds number in the unobstructed part of the vessel, K is a constant scaling factor related to artery wall properties, properties of the surrounding tissue and recording equipment. The intensity of murmurs is thus very sensitive to changes in both flow and the degree of stenosis. Since the coronary flow only decreases slowly as the degree of the stenosis increases, see Figure 4, the power of the murmurs will likely increase until a point close to 100% obstruction. In addition to the degree of the stenosis, the shape of the stenosis effects the intensity of the murmurs . Due to the large variation in physiological parameters it is difficult to estimate an absolute sound pressure for CAD murmurs, but a loose estimate can be made from experimental measurements of poststenotic wall pressure. Tobin et al. found the total poststenotic root mean square wall pressure to be 88.3 Pa, when the Reynolds number was 1500 and the stenosis degree was 68%. If this is rescaled to a Reynolds number at 285 the poststenotic root mean square wall pressure will be 1.64 Pa which correspond to a sound pressure at 98 dB (SPL).
The power spectrum of the murmurs is also related to the degree of the stenosis and the Reynolds number. The dominating component of the murmurs has a broad band character. The power spectrum of murmurs is typically characterized with a slight increase in power as frequency increases until a break frequency where the power rolls of , see Figure 6 which shows an experimentally obtained frequency spectrum of wall pressure in the post stenotic region.
Figure 6.1/3 octave spectrum of post stenotic wall pressure in an experimental tube .
Several studies have found that the break frequency is related to the Strouhal number  which describes the relation between frequency of vortex shedding, the flow velocity and the characteristic length. The break frequency of the murmurs has been
related to the average frequency of vortex shedding :
Where fb is the break frequency of frequency spectrum of murmur and u is the flow velocity in the stenosis. According to Jones et al. the Strouhal number can be estimated
from the degree of the stenosis and the Reynolds number :
(⁄) As an example, a 50% stenosis in a 3 mm artery with peak flow velocity at 30.45 m/s will generate a spectrum with a break frequency at 139 Hz. If the stenosis degree increases to 65% or 80% the break frequency will increase to respectively 375 Hz and 1738 Hz. This illustrates that the width of the murmur spectrum is strongly related to the stenosis degree.
In addition to the broad band component the power spectrum might contains narrow peaks. The peaks can be resonance frequencies of the artery wall or related to larger dominating vortices in the post stenotic region if turbulence is not fully developed .
Wang et al. modeled the left coronary artery tree with an electrical circuit model. He showed that a stenosis changed the resonance frequencies of the artery tree and that the turbulent flow excites these resonance frequencies . According to the model two resonance frequencies changed due to the stenosis, a high frequency component (150 Hz) increased in amplitude and shifted to higher frequencies. A second resonance frequency (100 Hz) shifted to a lower frequency and decreased in amplitude, see Figure 7. The modeling result was compared to recordings from CAD patients.
However studies of murmur from carotid arteries demonstrated that the surrounding tissue dampens the resonance frequency of the artery wall significantly . The presence of resonance frequencies in the CAD murmurs should therefore not be taken for granted.
Figure 7. Model of the influence of two different degrees of stenosis on the resonance frequencies of the left coronary artery tree .
Murmurs from the heart will be dampened by the chest wall. By the use of pressure catheter placed in the aorta in patients with an aorta stenosis and an accelerometer placed on the chest wall, Nygaard et al. found that the damping effect of the chest wall corresponds to a low pass filter with a cutoff frequency at approximately 26±12 Hz and an attenuation slope of 29±7.9 dB per decade , see Figure 8. At frequencies lower than the cutoff frequency the attenuation was 36±7.7 dB. Even though the low pass filter is a simplification of the complex transfer function of the chest wall the effect of the chest wall is that the high frequency part of the murmurs is attenuated significantly.
If the average attenuation across frequencies is estimated to 60 dB a loose estimate of the CAD murmur sound pressure at the chest wall is 38dB (SPL) if the poststenotic artery wall pressure corresponds to 98 dB as in the previous example where the stenosis degree was 68% and Reynolds number was 285. The detection of CAD murmurs are further complicated by the variation of the stenosis locations in the coronary artery tree, causing the distance and transfer function from the stenosis location to the recording spot to differ widely. Usually, prior studies placed the recording transducer in the 4th intercostal space at the left sternal border and a stenosis in the anterior part of the heart will thus be relatively close to the transducer.
Figure 9. Typical heart sound recording from a non-CAD female and the average diastolic power spectrum.
1.3.6. Summary of physiology and the signature of murmurs There is a large variation in the coronary flow and coronary anatomy. Typical coronary flow is likely to initiate murmurs in the case of a severe stenosis in major arteries, but the stenosis degree which is required for the onset of murmurs varies from subject to subject. Onset of murmurs does not necessarily means that the murmurs are powerful enough to be detected at the chest wall. However the power of the murmurs increase dramatically as the degree of the stenosis increases until a point close to total obstruction, thereby the likelihood of detecting the murmur increase as the stenosis degree increase until a high stenosis degree. The frequency spectrum of the murmurs is also very sensitive to the degree of the stenosis. The upper break frequency might range from approximately 140 Hz to more than 2000 Hz depending on the degree of the stenosis and the flow rate, but the effect of the chest wall can be seen as a low pass filter which might dampen out the high frequency part of the murmurs. The combination of a wide spread in physiological variables and mechanics which is very sensitive to small changes in these physiological variables makes the exacta acoustical response of a coronary stenosis unpredictable.
1.4. Prior art
The development of algorithms for detection of CAD from heart sounds is a small subdiscipline within the area of digital signal processing of heart sounds. A literature search identified 50 publication on the subject of signal processing methods for detection of CAD from heart sounds [41, 43-78, 78-90]. In addition Semmlow et Al.
publish a comprehensive review of the different methods and approaches used for heart sound based diagnosis of CAD .
Figure 10. Steps in a typical signal processing method for detection of CAD and examples of different approaches applied in each step.
A typical structure of algorithms for automatic interpretation of heart sounds includes three major steps: segmentation of the recording into intervals such as systoles and diastoles, extraction of one or more descriptive features and classification into diseases states. In CAD algorithms diastolic periods were typically identified either automatically, guided by ECG, or manually. Then characteristics were extracted from each diastolic period and averaged over several heart beats before classification into either CAD or non-CAD subjects. Figure 10 shows typical steps in algorithms for heart sound based diagnosis of CAD and summarizes different approaches from the existing literature.
1.4.1. Transducers As described in the section “Physiology and the signature of murmurs” the CAD murmurs are weak and non-audible. Therefore, a high sensitivity and a high signal to noise ratio is required for the acoustic transducer. Two main types of sensors are often used for recordings of heart sounds: air coupled microphone and accelerometers. The air coupled setup contains a microphone situated in a coupler house and the edges of the coupler house rest at the chest wall, see Figure 11. The recorded signal is proportional to the relative displacement of the skin enclosed by the coupler house . The advantage of the air coupled microphone is that the transducer’s impact on the chest wall is minimal and the construction is relative simple. The drawback is that the air coupled microphones is sensitive to background noise and that air has a poor impedance match with the chest wall. The air coupled microphone was used in several studies about CAD and heart sounds [48, 48, 68, 69, 69, 88-90].
Figure 11. Illustration of the air coupled microphone and the Accelerometer Accelerometers are often considered to be more robust against background noise , but the disadvantage is a mechanical load of the chest wall .