K. Mahoney et al., Comparison of modelled and observed in vivo temperature elevations inducedby focused ultrasound: implications for treatment planning, PHYS MED BI, 46(7), 2001, pp. 1785-1798
Two numerical models for predicting the temperature elevations resulting fr
om focused ultrasound heating of muscle tissue were tested against experime
ntal data. Both models use the Rayleigh-Sommerfeld integral to calculate th
e pressure field from a source distribution. The first method assumes a sou
rce distribution derived from a uniformly radiating transducer whereas the
second uses a source distribution obtained by numerically projecting pressu
re field measurements from an area near the focus backward toward the trans
ducer surface. Both of these calculated ultrasound fields were used as heat
sources in the bioheat equation to calculate the temperature elevation in
vivo. Experimental results were obtained from in vivo rabbit experiments us
ing eight-element sector-vortex transducers at 1.61 and 1.7 MHz and noninva
sive temperature mapping with MRI. Results showed that the uniformly radiat
ing transducer model over-predicted the peak temperature by a factor rangin
g from 1.4 to 2.8, depending on the operating mode. Simulations run using t
he back-projected sources were much closer to experimental values, ranging
from 1.0 to 1.7 times the experimental results, again varying with mode. Th
us, a significant improvement in the treatment planning can be obtained by
using actual measured ultrasound field distributions in combination with ba
ckward projection.