Biomedical Engineering Reference
In-Depth Information
(a)
(b)
FIGURE 6.9
Simulated multiple focus intensity patterns produced by a 2D cylindrical section array: (a) Axial plane and (b) focal plane. (After
E. S. Ebbini and C. A. Cain,
Int. J. Hypertherm.
, 7, 6, 1991.)
patterns generated by the sector vortex array. The multiple focus
patterns produced by mode scanning, which typically consist of
two or four discrete focal spots in a single focal plane, are also
consistent with the planar symmetry of the phased array.
Although multiple focusing increases the size of the heated
volume relative to a single focus, most multiple focus patterns
cover only a fraction of the tumor volume. To heat the entire
tumor, several single and/or multiple focus patterns are needed,
but optimally distributing the foci among several beam patterns
is a challenging problem. One approach solves the bioheat trans-
fer equation for any number of single focus (or multiple focus)
patterns and defines a transfer matrix that describes the tem-
perature generated by each focal pattern at each control point
(McGough et al. 1992). After the temperatures are specified
at each of these control points, a least-squares solution that
describes the power weighting of each focal pattern is obtained.
Another heating strategy defines a spiral focal point trajectory
and generates approximately uniform temperatures in a circu-
lar region (Salomir et al. 2000). This is achieved in two steps,
where therapeutic temperatures in the interior of the circular
region are established with the spiral scan pattern, and then the
temperature is maintained with a circular scan that focuses the
ultrasound on the edge of the circular region.
The overlapping energy contributions generated by several
beam patterns, each with multiple foci, are optimized in the
tumor and in sensitive normal tissues with waveform diversity
beamforming (Zeng et al. 2010). Waveform diversity calculations
minimize a cost function with constraints using semi-definite
