## Abstract

The monopole-source solution was used to calculate the three-dimensional complex acoustic pressure field for one-dimensional focused rectangular apertures in a medium having homogeneous acoustic and thermal properties. For each of six frequencies (1, 3, 5, 7, 9 and 12 MHz) and three focuses (f/1, f/2 and f/4), 33 rectangular aperture cases were investigated, for a total of 594 cases. For these focused field geometries, the three-dimensional temperature distribution was calculated using the bioheat transfer equation in homogeneous perfused media (attenuation = absorption: 0.3 dB/cm-MHz; perfusion length: 1.0 cm). For each of the 594 cases, the acoustic field was normalized to the derated spatial-peak temporal-average intensity (I_{SPTA.3}) of 720 mW/cm ^{2}, the maximum value condition allowed based on the U.S. Food and Drug Administration (FDA) regulatory limit for most diagnostic ultrasound (US) equipment. Using the normalized acoustic field, the axial temperature increase profiles and the maximum temperature increases (ΔT_{max}) were determined for each case. Also, from the normalized acoustic field, the unscanned-mode soft-tissue thermal index (TIS) for the rectangular sources was determined according to the procedures of the Standard for Real-Time Display of Thermal and Mechanical Indices on Diagnostic Ultrasound Equipment, commonly called the output display standard, ODS. The ΔT_{max}:TIS ratio of the 594 cases yielded a mean value of 0.22, a median value of 0.16, a maximum value of 1.04 and a minimum value of 0.039. For all but one of the cases, TIS was greater than ΔT_{max}. Also, two new unscanned-mode soft-tissue thermal indices (denoted TIS_{new(1)} and TIS _{new(2)}) were proposed. For new model 1, the ΔT_{max}: TIS_{new(1)} ratio yielded a mean value of 1.02, a median value of 1.01, a maximum value of 1.83 and a minimum value of 0.44. For new model 2, the ΔT_{max}: TIS_{new(2)} ratio yielded a mean value of 1.04, a median value of 0.99, a maximum value of 2.31 and a minimum value of 0.34. Further, both new models fit more closely to ΔT_{max} than does the ODS-determined TIS and have the potential of being easier for manufacturers to implement because only the source power and frequency need to be measured. (E-mail: wdo@uiuc.edu)

Original language | English (US) |
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Pages (from-to) | 965-972 |

Number of pages | 8 |

Journal | Ultrasound in Medicine and Biology |

Volume | 30 |

Issue number | 7 |

DOIs | |

State | Published - Jul 2004 |

## Keywords

- Output display standard
- Rectangular sources
- Thermal index

## ASJC Scopus subject areas

- Biophysics
- Radiological and Ultrasound Technology
- Acoustics and Ultrasonics