A study of latent heat effects in temperature proﬁles and lesion formation Jen-Chieh Wang a , Jay Shieh b , Ben-Ting Chen c , Chang-Wei Huang c,⇑ , Wen-Shiang Chen a,⇑ , Chuin-Shan Chen d a Department of Physical Medicine and Rehabilitation, National Taiwan University Hospital, Taipei, Taiwan, ROC b Department of Materials Science and Engineering, National Taiwan University, Taipei, Taiwan, ROC c Department of Civil Engineering, Chung Yuan Christian University, Chung Li, Taiwan, ROC d Department of Civil Engineering, National Taiwan University, Taipei, Taiwan, ROC article info Article history: Received 1 February 2013 Received in revised form 12 December 2013 Accepted 12 December 2013 Keywords: Focused ultrasound Thermal conﬁnement Denaturation Thermal dose Latent heat abstract The concept of thermal dose is widely adopted in the simulation of thermal therapies to estimate the for- mation of ablation lesions. However, such approaches typically use empirical assumptions, and treat the formation of a lesion as an end result from heating and not as a factor that could inﬂuence the temper- ature proﬁle. In this study, the forming of lesions during high-intensity focused ultrasound (HIFU) ther- apy is interpreted as a denaturation process involving an irreversible phase transformation, and is a critical factor inﬂuencing the evolution of the temperature proﬁle. Based on this notion and HIFU exper- iments performed on the pork tenderloin and egg white-based gel phantom, an important but often neglected phenomenon during the formation of the HIFU ablation lesion – referred to as the thermal con- ﬁnement – was revealed. The thermal conﬁnement, resulted from latent heat effects, exhibits features such as a substantial time delay in reaching maximum temperature around the ultrasound focal spot after turning off HIFU, and a lower-than-expected peak temperature attained during the ablation. A the- oretical model capable of predicting the thermal conﬁnement phenomenon and the changes in the tem- perature proﬁle associated with it was successfully constructed. In addition, a modiﬁed bioheat transfer equation with the effect of latent heat from denaturation was proposed. The simulated temperature pro- ﬁles further revealed the extent of the inﬂuence of the thermal conﬁnement is strongly dependent on the position relative to the ultrasound focal spot. Ó 2013 Elsevier Ltd. All rights reserved. 1. Introduction The adoption of the bioheat transfer equation [1] and thermal dose concept [2,3] for predicting the effect of high-intensity fo- cused ultrasound (HIFU) therapy has been well studied [4,5]. The procedure typically involves obtaining the temperature proﬁle (i.e., temperature history and distribution) by solving the bioheat transfer equation ﬁrst, followed by predicting the lesion size using the relationships of temperature and time. However, such an ap- proach has two major shortcomings: a crude expansion of the ori- ginal description of the thermal dose concept is commonly employed and the thermodynamic aspect of lesion formation and its effect on temperature proﬁle are often ignored. The original concept of thermal dose was that the effect of ther- mal therapy can be summarized by the relationship between the therapy acting time and the external temperature of the cells, i.e., therapy temperature [2,3]. In Dewey et al.’s experiments on heating Chinese hamster ovary (CHO) cells at different tempera- tures, information on the acting time t and acting temperature T of each heating case was collected and summarized. It was found that the ratio between the required treatment time for two differ- ent cases is equal to a certain constant R to the power of the tem- perature difference between the two cases. The relationship was deﬁned by Dewey et al. (1977) as: t 1 ¼ t 2 R ðT 1 T 2 Þ ð1Þ where subscripts 1 and 2 represent two different heating cases and constant R can be calculated by: R ¼ e DH=ð2TðTþ1ÞÞ ð2Þ where DH is the enthalpy or inactivation energy of the CHO cells. In fact, R should not be considered strictly as a constant, but as a tem- perature-dependent variable. Nevertheless, R was claimed by Dewey et al. to be 0.50 for the CHO cells in the temperature range 0017-9310/$ - see front matter Ó 2013 Elsevier Ltd. All rights reserved. http://dx.doi.org/10.1016/j.ijheatmasstransfer.2013.12.036 ⇑ Corresponding authors. Tel.: +886 3 2654206; fax: +886 3 2654299 (C.-W. Huang). Tel.: +886 2 23123456x67087; fax: +886 2 23832834 (W.-S. Chen). E-mail addresses: cwhuang@cycu.edu.tw (C.-W. Huang), wenshiang@gmail.com (W.-S. Chen). International Journal of Heat and Mass Transfer 71 (2014) 285–294 Contents lists available at ScienceDirect International Journal of Heat and Mass Transfer journal homepage: www.elsevier.com/locate/ijhmt