Frequency, pulse length, and the mechanical index

Frequency, pulse length, and the mechanical
index
Charles C. Church
National Center for Physical Acoustics, The University of Mississippi, University, MS 38677
cchurch@olemiss.edu
Abstract: As currently defined, the mechanical index (MI) uses only two
parameters, peak rarefactional pressure and center frequency. The effect of
another important factor, the pulse length (LP), was investigated by numerical
computations for cavitation threshold (Pt) similar to the analytical work underlying
the MI. The effect of LP on Pt is small for the original threshold
criterion (maximum temperature, Tmax55000 K), but can be substantial for
the often-used criterion on maximum radius, Rmax52Ro . The potential for
bioeffects produced by purely mechanical means (Rmax) increases with LP ,
while those mediated by sonochemicals (Tmax) does not.
© 2005 Acoustical Society of America
PACS numbers: 43.35.Ei, 43.35.Wa, 43.80.Gx
Date Received: January 4, 2005 Date Accepted: April 12, 2005
1. Introduction
The mechanical index (MI) quantifies the likelihood that exposure to diagnostic ultrasound will
produce an adverse biological effect by a nonthermal mechanism. The MI is defined as the
estimated peak rarefactional pressure in vivo, pra , divided by the square root of the center
frequency of the beam. This formulation is based on an analytical solution for the radial motion
of air bubbles in water and blood obtained by Apfel and Holland,1 who determined the
approximate acoustic pressure amplitude required to cause a bubble to undergo inertial
cavitation, i.e., a large expansion followed by a rapid, violent collapse. Such a collapse can
radiate damaging shock waves and cause the gas within the bubble to attain a very high
temperature, 5000 K in the case of the MI, thereby producing large numbers of potentially
highly destructive free radicals. As currently defined, the MI uses only two of the many
parameters that characterize an acoustic field: peak rarefactional pressure and center frequency.
This work investigates the effect of another important parameter, pulse length, on the threshold
for inertial cavitation, and thus on the theoretical basis for the MI.
The ‘‘true’’ frequency response of cavitation thresholds has been a matter of some
discussion, particularly as it relates to the MI. Apfel and Holland’s analytical work1 suggested
that the threshold increased as frequency to the power 0.48 in water, and to the power 0.60 in
blood. The numerical simulations reported byS ˇ poner,2,3 performed assuming a sinusoidal pulse
within a Gaussian envelope but a lower maximum collapse temperature (Tmax51550 K),
indicated that the increase was linear with frequency. To investigate this discrepancy, the
relationship between acoustic frequency and the threshold for inertial cavitation is also
determined.
Several different theoretical criteria might be used to define the threshold for inertial
cavitation. For example, Flynn4 used a dynamic comparison between the inertial and pressure
components of the acceleration but showed that this is often approximately equivalent to Rmax
52Ro , i.e., the maximum radius equal to twice the equilibrium radius.An interesting dynamical
criterion equates the maximum collapse speed to the equilibrium speed of sound in the gas,
Umax5GMach1, since it is approximately the minimal value for Umax at which a shock wave
could be launched from the gas–liquid interface toward the center of the bubble,5,6 an event that
could be expected to produce significant thermal and nonthermal effects. The direct estimation
of internal temperature results in the two criteria already mentioned, Tmax51550 or 5000 K, used
Charles C. Church: Acoustics Research Letters Online [DOI: 10.1121/1.1901757] Published Online 24 June 2005
162 ARLO 6(3), July 2005 1529-7853/05/6(3)/162/7/$22.50 © 2005 Acoustical Society of America 162