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Abstract：
The application of local hyperthermia, particularly in conjunction with other treatment strategies (like chemotherapy and radiotherapy) has been known to be a useful means of enhancing tumor treatment outcomes. However, to our knowledge, there has been no mathematical model designed to capture the impact of the combination of hyperthermia and chemotherapies on tumor growth and control. In this study, we propose a nonlinear Partial Differential Equation (PDE) model which describes the tumor response to chemotherapy, and use the model to study the effects of hyperthermia on the response of prototypical tumor to the generic chemotherapeutic agent. Ultrasound energy is delivered to the tumor through High Intensity Focused Ultrasound (HIFU), as a noninvasive technique to elevate the tumor temperature in a controlled manner. The proposed tumor growth model is coupled with the nonlinear density dependent Westervelt and Penne\'s bio-heat equations, used to calculate the net delivered energy and temperature of the tumor and its surrounding normal tissue. The tumor is assumed to be composed of two species: drug-sensitive and drug-resistant. The central assumption underlying our model is that the drug-resistant species is converted to a drug-sensitive type when the tumor temperature is elevated above a certain threshold temperature. The \"in silico\" results obtained, confirm that hyperthermia can result in less aggressive tumor development and emphasize the importance of designing an optimized thermal dose strategy. Furthermore, our results suggest that increasing the length of the on/off cycle of the transducer is an efficient approach to treatment scheduling in the sense of optimizing tumor eradication.
摘要：
局部热疗的应用,特别是与其他治疗策略(如化疗和放疗)联合使用,已知是提高肿瘤治疗效果的有用手段.然而,根据我们的知识，目前还没有设计数学模型来捕获热疗和化疗联合治疗对肿瘤生长和控制的影响.在这项研究中,我们提出了一个描述肿瘤对化疗反应的非线性偏微分方程（PDE）模型，并利用该模型研究热疗对原型肿瘤对通用化疗药物反应的影响。超声能量通过高强度聚焦超声（HIFU）传递到肿瘤，作为一种非侵入性技术，以可控的方式提高肿瘤温度。所提出的肿瘤生长模型与非线性密度相关的Westervelt和Penne的生物热方程耦合，用于计算肿瘤及其周围正常组织的净递送能量和温度。假定肿瘤由两个物种组成：药物敏感和耐药。我们模型的核心假设是，当肿瘤温度升高到某个阈值温度以上时，耐药物种会转化为药物敏感型。获得的“计算机模拟”结果，确认热疗可导致较不积极的肿瘤发展，并强调设计优化的热剂量策略的重要性。此外，我们的结果表明,从优化肿瘤根除的意义上讲,增加换能器开/关周期的长度是治疗计划的有效方法.
