Spectral Decomposition of the Flow and Characterization of the Sound Signals through Stenoses with Different Levels of Severity

Abstract

Treatments of atherosclerosis depend on the severity of the disease at the diagnosis time. Non-invasive diagnosis techniques, capable of detecting stenosis at early stages, are essential to reduce associated costs and mortality rates. We used computational fluid dynamics and acoustics analysis to extensively investigate the sound sources arising from high-turbulent fluctuating flow through stenosis. The frequency spectral analysis and proper orthogonal decomposition unveiled the frequency contents of the fluctuations for different severities and decomposed the flow into several frequency bandwidths. Results showed that high-intensity turbulent pressure fluctuations appeared inside the stenosis for severities above 70%, concentrated at plaque surface, and immediately in the post-stenotic region. Analysis of these fluctuations with the progression of the stenosis indicated that (a) there was a distinct break frequency for each severity level, ranging from 40 to 230 Hz, (b) acoustic spatial-frequency maps demonstrated the variation of the frequency content with respect to the distance from the stenosis, and (c) high-energy, high-frequency fluctuations existed inside the stenosis only for severe cases. This information can be essential for predicting the severity level of progressive stenosis, comprehending the nature of the sound sources, and determining the location of the stenosis with respect to the point of measurements.

Keywords: atherosclerosis; break frequency; frequency spectral analysis; proper orthogonal decomposition; sound source localization; stenosis; turbulent pressure fluctuations.

Figure 1

A sectional view of the flow domain. Flow is from left to right. The figure is out of scale, and the dimensions are in mm.

Figure 2

Experimental setup of Laser Doppler Anemometry (LDA) axial velocity measurements for a constricted pipe representing arterial stenosis.

Figure 3

Validation of computational fluid dynamics (CFD) results of 92% stenosis at Re = 1600 with the LDA measurements.

Figure 4

Mean Pressure on the arterial wall in the post-stenotic region.

Figure 5

Mean axial velocity at six different locations (1D to 6D) downstream of stenosis for all severity cases.

Figure 6

Pressure fluctuations on the arterial wall and root-mean-square (RMS) of pressure fluctuations on the middle cross-section of the flow domain showing the concentration and high-energy fluctuation through and downstream of the stenosis.

Figure 7

Point of maximum excitation in the post-stenotic region by analyzing (a) RMS of pressure fluctuations on the wall and (b) turbulent kinetic energy (TKE) on the stenosis centerline.

Figure 8

For all severity cases: (a) Sound pressure level (SPL) variation at different frequencies of acoustic pressure and (b) exponential increase in RMS of pressure fluctuations and mean axial velocity with an increase in stenosis severity.

Figure 9

Acoustic spatial-frequency map of the post-stenotic region for all severity cases.

Figure 10

For 87% stenosis: (a) frequency content of the flow, (b) isosurfaces of proper orthogonal decomposition (POD) mode 1 of RMS of acoustic pressure, (c) snapshot of high-energy fluctuations for different frequency ranges and the bandwidth of 1000–1400 Hz.