Biomedical Engineering Reference

In-Depth Information

6

Numerical Modeling for Simulation

and Treatment Planning of

Thermal Therapy: Ultrasound

6.1 Introduction ...............................................................................................................................95

6.2 Models of Ultrasound Propagation ........................................................................................95

Rayleigh-Sommerfeld Integral • Rectangular Radiator Method • Fast Near-Field

Method • Angular Spectrum Approach • Nonlinear Ultrasound Propagation • Software

Programs • Intensity and Power Calculations

6.3 Thermal Modeling and Treatment Planning ......................................................................105

Bioheat Transfer Model • Thermal Dose Calculations • Thermal Therapy Planning

6.4 Summary ...................................................................................................................................116

References .............................................................................................................................................116

Robert J. McGough

Michigan State University

6.1 Introduction

Rayleigh-Sommerfeld integral or with expressions that are

closely related to the Rayleigh-Sommerfeld integral, where

each approach has an associated numerical accuracy, computa-

tion time, and algorithmic complexity. These numerical mod-

els are applicable to the three transducer geometries that are

most often encountered in thermal therapy, namely the circu-

lar piston, the rectangular piston, and the spherical shell. Other

pressure simulations include nonlinear propagation effects,

especially when higher intensities are generated by a focused

ultrasound transducer or a large aperture phased array. Some

of these numerical models for linear and nonlinear ultrasound

propagation are implemented in publicly available software.

After the pressure is computed with one of these numerical

models, power depositions are also calculated for subsequent

bioheat transfer simulations.

Pressure fields generated by single and multiple element transducers

are routinely simulated during the initial design of an ultrasound

applicator and also throughout the subsequent characterization

and optimization of power depositions, temperature distributions,

and thermal doses produced by these thermal therapy applicators.

Numerical models describe the diffraction of ultrasound produced

by single transducers, fixed-phase multiple transducer configura-

tions, and ultrasound phased arrays. Nonlinear effects are also

incorporated into some of these numerical models. The resulting

power deposition then provides the input to the bioheat transfer

equation. Temperatures are computed for most applications, and

thermal doses are also calculated, especially for simulations of abla-

tion therapy. In more advanced models, the effects of intervening

tissue heating are considered, beamforming algorithms are evalu-

ated, and more complicated issues such as patient anatomy and tis-

sue inhomogeneities are also included. Patient treatment planning

then combines several of these models in an effort to optimize the

temperature distribution or thermal dose in the tumor while spar-

ing sensitive normal tissues.

6.2.1 rayleigh-Sommerfeld Integral

The Rayleigh-Sommerfeld integral is the most common model

for linear ultrasound propagation in simulations of thermal

therapy. The numerical formulas derived from the Rayleigh-

Sommerfeld integral superpose contributions from a point

source surrounded by a rigid baffle radiating into an infinite

half-space. The frequency-domain Green's function describing

the contribution from each point source is
e
−
jkR
/(2π
R
), where

the 2π in the denominator indicates a baffled point source

radiating into an infinite half-space (as opposed to 4π in the

denominator, which indicates an unbaffled source radiating in

6.2 Models of Ultrasound propagation

Simulated pressures generated by ultrasound applicators

are often computed with a linear propagation model. These

numerical models capture the effects of diffraction in the

near-field region. Pressures are typically calculated with the

95