Function approximations to accelerate 3-D beam predictions for thermal dose calculations

Dustin E. Kruse, Chun Yen Lai, Mario Hlawitschka, Katherine W. Ferrara

Research output: Chapter in Book/Report/Conference proceedingConference contribution

1 Scopus citations


Robust and safe control of tissue heating requires predictions of beam location, temperature and thermal dose in order to optimize the spatial and temporal distribution of acoustic power. Such calculations are computationally intensive, and our objective is to identify methods to speed up such calculations. Monochromatic beam prediction relies heavily on complex exponentials. We have identified a fast 4th order approximation for the evaluation of a complex exponential using a reduced-complexity polynomial that minimizes absolute error to a maximum of 0.001 over -π to π, and we quantified the effects of the approximation on beam intensity and total acoustic power (TAP) for a 128 physical element transducer array. We demonstrate that ultrasound beam predictions are accelerated by 13x using a fast approximation to evaluate complex exponentials compared to standard libraries. The approximation was optimized to minimize error in TAP, the relevant quantity for thermal diffusion-limited heating. The resulting error in TAP was found to be less than 8×10-4%, and the error in intensity was found to be less than 3×10-2% as compared to full precision calculations. The same methodology may be applied to other beam prediction algorithms to speed their execution at a relatively minor degradation in accuracy.

Original languageEnglish (US)
Title of host publicationProceedings - IEEE Ultrasonics Symposium
StatePublished - 2009
Event2009 IEEE International Ultrasonics Symposium, IUS 2009 - Rome, Italy
Duration: Sep 20 2009Sep 23 2009


Other2009 IEEE International Ultrasonics Symposium, IUS 2009


  • Complex exponential approximation
  • Mild hyperthermia
  • Sine-cosine approximation
  • Thermal dose
  • Ultrasound beam prediction

ASJC Scopus subject areas

  • Acoustics and Ultrasonics


Dive into the research topics of 'Function approximations to accelerate 3-D beam predictions for thermal dose calculations'. Together they form a unique fingerprint.

Cite this