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.

局部热疗的应用，特别是与其他治疗策略（如化学疗法和放射疗法）的结合，已经被认为是增强肿瘤治疗结果的有用手段。然而，据我们所知，还没有数学模型设计来捕获热疗和化学疗法的结合对肿瘤生长和控制的影响。在这项研究中，我们提出了一个非线性偏微分方程（PDE）模型，该模型描述了肿瘤对化学疗法的反应，并使用该模型研究了热疗对原型肿瘤对通用化疗药的反应的影响。超声能量通过高强度聚焦超声（HIFU）传递到肿瘤，这是一种非侵入性技术，可控地升高肿瘤温度。拟议的肿瘤生长模型与依赖于非线性密度的Westervelt和Penne的生物热方程相结合，用于计算肿瘤及其周围正常组织的净传递能量和温度。假定该肿瘤由两种物质组成：药物敏感和耐药。我们模型所依据的主要假设是，当肿瘤温度升高到某个阈值温度以上时，耐药菌便会转变为对药物敏感的菌种。获得的“ in silico”结果表明，热疗会导致较不积极的肿瘤发展，并强调设计最佳热剂量策略的重要性。此外，