1. Computation of Ultrasonic Pressure
Fields in Feline Brain
|Nazanin Omidi , Dr. Cecille Labuda , Dr.Charles C. Church| National Center for Physical Acoustics, Physics and Astronomy Department , The University of Mississippi
Contact: nomidi@go.olemiss.edu
Applications:
Diagnostic : Ultrasound Imaging
Therapeutic : Drug Delivery,
Focused Ultrasound Surgery
 Ultrasound : Sound at frequency higher than 20 KHz
 Typical range for biomedical ultrasound : 0.5- 10 MHz
 Simulate the acoustic pressure waveforms produced in the brains of
anesthetized felines by a spherically focused transducer at increasing
values of the source pressure amplitude at frequencies of 1, 3 and 9 MHz;
transducer focal length = 13 cm, diameter = 12.7 cm.
 Compute the corresponding intensities for the simulated focal pressure
waveforms at the location of the true maximum.
 Determine the time varying pressure waveforms for a water path and
integrate over a complete cycle to estimate the focal intensities assuming
linear propagation to correlate with the experimental data of Dunn et al’
(JASA 58:512-514).
 Determine computed waveforms using FDTD technique for nonlinear
propagation.
Simulate the focal
pressure
waveforms at the
real focus of the
transducer for a
series of source
pressure amplitude
and calculate the
corresponding
intensities using
equation:
𝐼 = 𝑝2
/2𝜌c/
2ρc
Step 1 Step 2
Compare the
computed
intensities with the
published
experimental data.
Step 3
Finite Difference Time Domain:
 Numerical Analysis technique
 Time domain method
 Grid based finite difference method
 Find approximation solution for PDE
 Discretize PDE to the space and time
 Find pressure evolution for entire system
 Dunn et al’ (JASA 58:512-514) showed a simple relation describes
the ultrasonic threshold for cavitation–induced changes in the
mammalian brain.
 The threshold acoustic intensities (I) for lesion formation at
frequencies of (f = 1, 3, 4, 4.5, 9 MHz) were found to be:
𝐼 =
𝑐 𝑓, 𝑇
𝑡
• I : Acoustic Intensity delivered to the site
• t: Time duration of the single acoustic exposure
• c : Weak function of frequency (f) and temperature (T)
A spherically focused transducer,
Focal length: 13-cm, Radius: 6.35-cm
r(j)
z (i)dr
dz : spatial grid size
 The linear theory successfully determines the focal intensities and the waveforms at low source pressures.
 The non-linear effect explains the behavior of the waveforms at higher source pressures in which the focal
pressure waveforms became increasingly distorted; similar results are obtained with increasing frequency.
 The peak positive and negative focal pressures are increased as source pressures increase.
 The simulated pressure and intensity waveforms at 3 MHz are much greater than 1MHz due to the sharper
focus at the higher frequency.
 There is a good agreement between pressure field measurement and calculations we made in water.
 There is a pretty much good agreement between our computed intensities and published experimental
data of Illinois university.
 Cavitation usually happens at the focus of the acoustic field (not always) and existence of cavitation are
increased by increasing frequency.
BC’S
Pressure field in z-axis
and r-axis
Project Overview
Introduction
Project Background
Simulation Space
FDTD Simulation
Experimental Setup
2a
f
Oscilloscope
Amplifier
Water filled tank
3D motorized
System
Wave generator
Hydrophone
Transducer-lens
Intensity Calculation
Simulation Results
Steady state positive peak pressure at 1MHz Steady state positive peak pressure at 3MHz
Intensity Simulation
Oscilloscope
Amplifier
Wave generator
3D motorized
system
Transducer-Lens
Hydrophone
Water filled
tank
Discussion and Conclusion
Calculate the time
varying pressure
waveforms, integrate
over one complete cycle
at different several
positions to find the
averaged intensity.
Observation
Measurement and
Calculation