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Research Papers

Computational Modeling and Analysis of Murmurs Generated by Modeled Aortic Stenoses

[+] Author and Article Information
Chi Zhu

Department of Mechanical Engineering,
Johns Hopkins University,
3400 N. Charles Street,
Baltimore, MD 21218
e-mail: czhu19@jhu.edu

Jung-Hee Seo

Department of Mechanical Engineering,
Johns Hopkins University,
3400 N. Charles Street,
Baltimore, MD 21218
e-mail: jhseo@jhu.edu

Rajat Mittal

Department of Mechanical Engineering,
Johns Hopkins University,
3400 N. Charles Street,
Baltimore, MD 21218
e-mail: mittal@jhu.edu

1Corresponding author.

Manuscript received July 27, 2018; final manuscript received February 3, 2019; published online March 5, 2019. Assoc. Editor: Ching-Long Lin.

J Biomech Eng 141(4), 041007 (Mar 05, 2019) (12 pages) Paper No: BIO-18-1344; doi: 10.1115/1.4042765 History: Received July 27, 2018; Revised February 03, 2019

In this study, coupled hemodynamic–acoustic simulations are employed to study the generation and propagation of murmurs associated with aortic stenoses where the aorta with a stenosed aortic valve is modeled as a curved pipe with a constriction near the inlet. The hemodynamics of the poststenotic flow is investigated in detail in our previous numerical study (Zhu et al., 2018, “Computational Modelling and Analysis of Haemodynamics in a Simple Model of Aortic Stenosis,” J. Fluid Mech., 851, pp. 23–49). The temporal history of the pressure on the aortic lumen is recorded during the hemodynamic study and used as the murmur source in the acoustic simulations. The thorax is modeled as an elliptic cylinder and the thoracic tissue is assumed to be homogeneous, linear and viscoelastic. A previously developed high-order numerical method that is capable of dealing with immersed bodies is applied in the acoustic simulations. To mimic the clinical practice of auscultation, the sound signals from the epidermal surface are collected. The simulations show that the source of the aortic stenosis murmur is located at the proximal end of the aortic arch and that the sound intensity pattern on the epidermal surface can predict the source location of the murmurs reasonably well. Spectral analysis of the murmur reveals the disconnect between the break frequency obtained from the flow and from the murmur signal. Finally, it is also demonstrated that the source locations can also be predicted by solving an inverse problem using the free-space Green's function. The implications of these results for cardiac auscultation are discussed.

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Figures

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Fig. 1

(a) Schematic of the modeled aorta and r, ϕ, and s represent the radial, azimuthal, and streamwise directions and (b) schematic of the modeled thorax (Fig. 1(a)) is adapted from Ref. [9]).

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Fig. 2

Instantaneous azimuthal vorticity (ωϕD/Vin) on the frontal plane as well as instantaneous streamwise vorticity (ωsD/Vin) on the cross section of the modeled aorta with 75% stenosis. Arrow (A): small recirculation zone, arrow (B): large recirculation zone, and arrow (C): starting position of the periodic shear layer vortex shedding. This figure is adapted from Ref. [9].

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Fig. 3

(a) Summary of the source locations on the anterior surface of all three cases. The arrows at θ=70 deg, 60 deg, and 55 deg point to the source locations for AS=50%, 62.5% ,and 75%, respectively, and (b) distribution of pressure fluctuation intensity along the anterior surface, where the peak locations are identified as murmur sources and are highlighted in (a) with arrows. This figure is adapted from Ref. [9].

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Fig. 4

(a) Spectrum of the pressure fluctuation at the source location of 50% case and (b) spectra of wall pressure fluctuations for AS=50%, 62.5%, and 75% at the source locations indicated in Fig. 3. Here the frequency is renormalized by the jet velocity (Vj) and jet diameter (Dj). The vertical dash line at Stj=0.93 indicates the break frequency from flow simulation. The solid lines in (a) show the slope of the spectrum calculated by the linear regression. These figures are adapted from Ref. [9].

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Fig. 5

Instantaneous wave pattern inside the modeled thorax with 75% stenosis demonstrated by the velocity contour. Frontal plane plots the velocity along the major axis (y direction) and the sagittal plane plots the velocity along the minor axis (x direction).

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Fig. 6

Temporal histories of the wall-normal velocity perturbation recorded at the four surface locations shown in Fig. 5 for 75% stenosis. The same range of the y-axis [−1×106, 1×106] is used to facilitate comparison of signal intensity at these four locations.

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Fig. 7

Spectra of the wall-normal acceleration at the four surface locations shown in Fig. 5 for 75% stenosis. The Strouhal number is defined as St=fD/cp.

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Fig. 8

Two-dimensional projection of the spectral energy of wall-normal acceleration on the anterior/posteriorsurface over the entire frequency band (I+II+III) for 75% case. The range of the contours is adjusted to best reflect the signal intensity in each case and the outline of the modeled aorta is included for clarity: (a) with shear modulus and (b) without shear modulus.

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Fig. 9

Two-dimensional projection of the spectral energy of wall-normal acceleration on the anterior/posteriorsurface over different frequency bands for 75% case with shear modulus included in the model. The range of the contours is adjusted to best reflect the signal intensity for each frequency range and the outline of the modeled aorta is included for clarity: (a) frequency band I, (b) frequency band II, and (c) frequency bandIII.

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Fig. 10

Two-dimensional projection of the spectral energy of wall-normal acceleration on the anterior/posteriorsurface over the low-frequency band I. A black diamond symbol is plotted in the same spatial location in Figs. 9(a) and 10 to facilitate comparison: (a) 50% and (b) 62.5%. Shear modulus is included in both models.

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Fig. 11

Spectra of the wall-normal acceleration on the epidermal surface of the modeled aorta. The signals are collected at the same spatial location indicated by the diamond symbol. The Strouhal number is defined as St=fD/cp.

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Fig. 12

Spectra of the wall-normal acceleration on the epidermal surface of the modeled aorta renormalized using jet velocity (Vj) and jet diameter (Dj). The signals are collected at the same spatial location indicated by the diamond symbol. Here, the vertical dash line represents Stj=0.93.

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Fig. 13

Illustration of the forward problem using the free-space Green's function. The solid squares are the point sources located on the aortic wall, and the solid circle represents the target point on the epidermal surface of the thorax.

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Fig. 14

Spectra of the wall-normal acceleration calculated from the free-space Green's function. The location at which these signals are calculated and the scaling of the Strouhal number are the same as Fig. 11.

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Fig. 15

Spectra calculated from individual point source (black squares in Fig. 13) at selected angle θ for 75% case. The location at which these signals are calculated and the scaling of the Strouhal number are the same as Fig. 11.

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Fig. 16

Illustration for the source localization problem using free-space Green's function. The square patch is the plane where source location is evaluated, and it is discretized into a 5×5 grid. The solid circles on the skin surface represent the 4×4 sensor array.

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Fig. 17

Source localization using free-space Green's function for 75% case on the square patch shown in Fig. 16. The diamond symbol represents the same spatial location as in Fig.9(a).

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