Filipczyński L, Kujawska T, Wojcik J
Department of Ultrasonics, Polish Academy of Sciences, Warsaw.
Ultrasound Med Biol. 1993;19(8):667-79. doi: 10.1016/0301-5629(93)90073-w.
Transient solution of the thermal conductivity equation for the three-dimensional case of the Gaussian ultrasonic focused beam was derived and applied for cases relevant to medical ultrasonography. Quantitative results for the case of a homogeneous medium with constant values of thermal coefficients and constant absorption as well as for the two-layer tissue model used in obstetrics were presented for various diagnostic probes used in ultrasonography. The possible effects of perfusion and nonlinear propagation were neglected. The results obtained are in agreement with results of other authors when considering the steady-state and the infinitely short insonation time. The computations show the influence of the insonation time on the temperature elevation, thus making it possible to introduce its value as a factor in limiting the possible harmful effects in ultrasonography. This has been shown in diagrams presenting the temperature distribution along the beam axis of 6 different diagnostic probes for various insonation times and demonstrating the corresponding temperature decrease when limiting the insonation time to 5 and 1 min. For instance, the highest temperature elevation (for probe number 1, see Table 1) decreases 2.6 and 5 times with respect to the steady-state temperature when the insonation time equals 5 and 1 min, respectively.
推导了高斯超声聚焦束三维情况下热传导方程的瞬态解，并将其应用于医学超声检查相关的情况。给出了热系数恒定且吸收恒定的均匀介质情况以及产科中使用的双层组织模型在各种超声诊断探头下的定量结果。忽略了灌注和非线性传播的可能影响。在考虑稳态和无限短的声照射时间时，所得结果与其他作者的结果一致。计算结果显示了声照射时间对温度升高的影响，从而使得有可能将其值作为限制超声检查中可能有害影响的一个因素。这已在图表中得到展示，这些图表呈现了6种不同诊断探头在不同声照射时间下沿波束轴的温度分布，并表明当将声照射时间限制为5分钟和1分钟时相应的温度降低情况。例如，当声照射时间分别等于5分钟和1分钟时，最高温度升高（对于探头1，见表1）相对于稳态温度分别降低了2.6倍和5倍。
