A Computational Model for Sound Propagation in the Human Lung

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A Computational Model for Sound Propagation in
the Human Lung
Chandru Narasimhan and Kumar Mahinthakumar North
Carolina State University Richard C. Ward and
Kara L. Kruse Oak Ridge National Laboratory
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Ultimate Goals

• Develop a suite of high resolution supercomputer
  models for simulating normal breath sounds in the
  human lung.
• Perform a frequency domain analysis to identify
  dominant frequencies that are propagated to the
  chest wall.
• Couple with a sound generation model based on a
  CFD model of airflow through lung airways
• Develop an integrated model for the simulation of
  normal breath sounds.
• Synthesize normal breathing sounds from computed
  acoustic pressure fields at the chest wall.
• Validate with existing breath sounds data

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Motivation

• The ability to computationally simulate normal
  breath sounds will lead to a greater
  understanding of how breath sounds are generated
  and propagated in the human lung.
• This is a long-standing problem that has not yet
  been solved due to previous limitations in
  computational power and lack of adequate model.
• Our ultimate goal is utilize powerful parallel
  computers combined with the use of sophisticated
  models to solve this long standing problem.
• This will ultimately lead to a powerful
  analytical tool for pulmonary diagnosis based on
  ascultation.
• An understanding of predominant frequencies that
  are propagated to the chest wall will lead to
  better design of stethoscopes and other tools.

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Integrated lung sounds simulation approach
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Current Status

• A parallel supercomputer model for sound
  propagation has been developed and tested using
  the Visible Human CT data in the human thorax -
  This will be the focus of this presentation.
• An existing supercomputer model for fluid flow is
  being tested for simulating air flow through lung
  airways on going work.
• The computer model for sound generation near
  future work.

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Sound Propagation Equation

• Inhomogeneous Wave Equation (original form)
• Inhomogeneous Wave Equation (alternate form)

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Fluid Flow Equations

• The three-dimensional Navier-Stokes equations
  will provide the flow field for the sound
  generation component
• p(x,t) pressure field, u(x,t) velocity field,
  x spatial coordinate vector, t time, and ?
  density of air.

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Sound Generation Equation

• Sound generation from turbulent vortices
  described by Lighthills equation

pa(x,t) acoustic pressure. c0 speed of sound
in air. For convenience, summation notation is
used in the right hand side source term with i,j
1,2,3, where u1,u2,u3 and x1, x2, x3 are the
x,y,z components of the velocity vector u and the
spatial coordinate vector x respectively.
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Numerical Approximation for Sound Propagation
Wave Equation

• 3-D central finite-differences
• Explicit time-stepping
• Time step constraint
• Original Form Equation
• 4th order in space for pressure and 2nd order in
  space for density
• Alternate Form Equation
• 2nd order in space for both pressure and density
• Alternate form is more stable for heterogeneous
  media with a large number of time steps.

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Some Sound Propagation Issues

• Numerical stability for heterogeneous media
• The original sound propagation equation exhibited
  numerical instability for large number of
  timesteps
• Problem resolved by alternate sound propagation
  equation and Interpolation of CT data for higher
  resolution
• Sound absorption
• Implemented using a linear attenuation term
• Boundary conditions
• A completely reflecting boundary condition (pa
  0) at the chest wall current implementation
• Absorbing boundary condition at the chest wall
  planned in the near future

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Sound Absorption

• Inhomogeneous Wave Equation is modified by adding
  a first order attenuation term that models sound
  absorption in the lung tissues

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Verification Exercises

• Verification of the sound propagation model was
  performed using analytical solutions for a
  bell-shaped pulse source in a homogeneous medium.
• Very good agreement was obtained between
  analytical and numerical solutions.

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Parallel Implementation

• 1-D Domain decomposition using MPI (message
  passing interface) library
• Options implemented for asynchronous and
  persistent communication modes
• Parallel I/O using the MPI-IO library
• Input Visible Human CT data
• Output pressure field
• Specific performance tuning for the IBM SP (180
  4-CPU Nighthawk II nodes) at ORNL but also tested
  on the Origin 2400 at NCSC.

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Parallel Implementation (contd.)
Thirteen-Point Stencil
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Sound Sources

• A single bell-shaped pulse at the center of the
  thorax as an initial condition.
• A sinusoidal wave at the center of the thorax as
  a continuously driving source (boundary
  condition).
• Acoustic pressure derived from a fluid flow
  simulation in the airway regions of the thorax
  future work.

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Thorax cross-section from Visible Human CT Data
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Sound propagation using pulse source
(a)
(b)
(c)
(d)
Sound wave propagation in the human lung using
the Visible Human data. A single horizontal
cross-section near the mid chest area is shown.
(a) CT data for a horizontal section of the human
torso, (b) Initial artificial pulse source,
Acoustic pressure field (c) at time 0.25 ms,
(d) at time 0.5 ms. Equation (3) is used in the
simulations.
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Sound Propagation using pulse source

• Simulated pressure field at a mid horizontal
  section using
• a 128 x 128 x 128 grid

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Sound propagation animation
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Simulated lung sounds near body surface for
sinusoidal source
64 x 64 x 208
128 x128 x 208
Pressure vs Time
Sinusoidal Source 780 Hz
Power Spectrum
Sinusoidal Source 1560 Hz
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Power spectrum for sinusoidal source
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Power Spectrum for Pulse Source
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Summary and Conclusions

• A parallel supercomputer model has been developed
  for sound propagation through the human lung.
• The model serves as a good analysis tool for
  investigating dominant frequencies that are
  propagated to different locations on the chest
  wall.
• Preliminary results indicate that the dominant
  frequencies are in the 100 Hz to 50 kHz range.
• Preliminary results also indicate that more sound
  is propagated to the right anterior part of the
  chestwall corroborating experimental observations.

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Ongoing and Future Work

• Incorporating sound generation from airflow
• First test with artificial flow field.
• Couple with fluid flow code.
• Extend parallelization from 1-D to 3-D domain
  decomposition.
• Validate with experimental observations.
• Frequency domain.
• Time domain.
• Synthesized sound.