Title: A Computational Model for Sound Propagation in the Human Lung
1A 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
2Ultimate 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
3Motivation
- 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.
4Integrated lung sounds simulation approach
5Current 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.
6Sound Propagation Equation
- Inhomogeneous Wave Equation (original form)
- Inhomogeneous Wave Equation (alternate form)
7Fluid 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.
8Sound 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.
9Numerical 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.
10Some 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
11Sound Absorption
- Inhomogeneous Wave Equation is modified by adding
a first order attenuation term that models sound
absorption in the lung tissues
12Verification 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.
13Parallel 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.
14Parallel Implementation (contd.)
Thirteen-Point Stencil
15Sound 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.
16Thorax cross-section from Visible Human CT Data
17Sound 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.
18Sound Propagation using pulse source
- Simulated pressure field at a mid horizontal
section using - a 128 x 128 x 128 grid
19Sound propagation animation
20Simulated 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
21Power spectrum for sinusoidal source
22Power Spectrum for Pulse Source
23Summary 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.
24Ongoing 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.