Abstract Minimally-invasive cryosurgery is incapable of killing the tumor at the outer periphery of iceball, resulting in the inefficiency of tumor treatment. In this paper, we develop a new combined treatment of chemotherapy and cryotherapy (chemo-cryo) by injecting cold-responsive drug-loaded nanoparticles around the tumor before cryosurgery to enhance the treatment of deep-lying tumor. A macroscopic mathematical model is established for the first time, covering the cryosurgery, the release of anti-tumor drug (doxorubicin) from cold-responsive nanoparticles, and the drug transport in biological tissues. Therapeutic efficacy is evaluated in terms of the effective killing volumes of tumor and normal tissue, including cryosurgery killing and drug killing. Simulation results show that comparisons with cryosurgery alone demonstrate the advantage of chemo-cryo treatment in enhancing the therapeutic efficacy, given that the killing volume of normal tissue is lessened by 89.36% for the single-probe and 72.57% for the multi-probe in the case of complete tumor killing. The amount of doxorubicin released is determined by the holding time of cryoprobe, the sensitive temperature and initial concentration of drug-loaded nanoparticles, independent of doxorubicin diffusivity. Adjusting the holding time and the properties of nanoparticles and doxorubicin can augment the effective killing volume of tumor, but it is also accompanied by side effect on normal tissue, mainly manifested as drug killing. Results obtained can serve as the guideline to optimize chemo-cryo treatment regimens for deep-lying tumor.

中文翻译：

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联合冷冻手术和冷响应载药纳米粒子增强深部肿瘤治疗：数学模型

摘要 微创冷冻手术无法杀死冰球外围的肿瘤，导致肿瘤治疗效率低下。在本文中，我们通过在冷冻手术前在肿瘤周围注射冷响应载药纳米颗粒来开发一种新的化疗和冷冻疗法（chemo-cryo）联合疗法，以加强对深部肿瘤的治疗。首次建立了宏观数学模型，涵盖了冷冻手术、抗肿瘤药物（阿霉素）从冷响应纳米粒子的释放以及药物在生物组织中的转运。根据对肿瘤和正常组织的有效杀伤量来评估治疗效果，包括冷冻手术杀伤和药物杀伤。模拟结果表明，与单独冷冻手术相比，单探针对正常组织的杀伤量减少了 89.36%，多探针减少了 72.57%，证明了化学冷冻治疗在提高治疗效果方面的优势。完全杀死肿瘤的情况。阿霉素的释放量由冷冻探针的保持时间、敏感温度和载药纳米颗粒的初始浓度决定，与阿霉素的扩散性无关。调整纳米粒和阿霉素的保压时间和性质，可以增加对肿瘤的有效杀伤体积，但也伴随着对正常组织的副作用，主要表现为药物杀伤。获得的结果可以作为优化深部肿瘤化学冷冻治疗方案的指南。