Castillo-Montiel E, Chimal-Eguía J C, Tello J Ignacio, Piñon-Zaráte G, Herrera-Enríquez M, Castell-Rodríguez A E
Laboratorio de Modelación y Simulación, Centro de Investigación en Computación, Instituto Politécnico Nacional, Av. Juan de Dios Bátiz, Esq. Miguel Othón de Mendizábal, Del. Gustavo A. Madero, México City, 07738, México.
Departamento de Matemática Aplicada a las Tecnologías de la Información y las Telecomunicaciones, E.T.S.I. Sistemas Informáticos, Universidad Politécnica de Madrid, Ctral. de Valencia. Km. 7, Madrid, 28031, Spain.
Theor Biol Med Model. 2015 Jun 9;12:11. doi: 10.1186/s12976-015-0007-0.
The immunotherapy using dendritic cells (DCs) against different varieties of cancer is an approach that has been previously explored which induces a specific immune response. This work presents a mathematical model of DCs immunotherapy for melanoma in mice based on work by Experimental Immunotherapy Laboratory of the Medicine Faculty in the Universidad Autonoma de Mexico (UNAM).
The model is a five delay differential equation (DDEs) which represents a simplified view of the immunotherapy mechanisms. The mathematical model takes into account the interactions between tumor cells, dendritic cells, naive cytotoxic T lymphocytes cells (inactivated cytotoxic cells), effector cells (cytotoxic T activated cytotoxic cells) and transforming growth factor β cytokine (T G F-β). The model is validated comparing the computer simulation results with biological trial results of the immunotherapy developed by the research group of UNAM.
The results of the growth of tumor cells obtained by the control immunotherapy simulation show a similar amount of tumor cell population than the biological data of the control immunotherapy. Moreover, comparing the increase of tumor cells obtained from the immunotherapy simulation and the biological data of the immunotherapy applied by the UNAM researchers obtained errors of approximately 10 %. This allowed us to use the model as a framework to test hypothetical treatments. The numerical simulations suggest that by using more doses of DCs and changing the infusion time, the tumor growth decays compared with the current immunotherapy. In addition, a local sensitivity analysis is performed; the results show that the delay in time " τ", the maximal growth rate of tumor "r" and the maximal efficiency of tumor cytotoxic cells rate "aT" are the most sensitive model parameters.
By using this mathematical model it is possible to simulate the growth of the tumor cells with or without immunotherapy using the infusion protocol of the UNAM researchers, to obtain a good approximation of the biological trials data. It is worth mentioning that by manipulating the different parameters of the model the effectiveness of the immunotherapy may increase. This last suggests that different protocols could be implemented by the Immunotherapy Laboratory of UNAM in order to improve their results.
利用树突状细胞（DCs）对不同类型癌症进行免疫治疗是一种此前已探索过的诱导特异性免疫反应的方法。这项工作基于墨西哥国立自治大学（UNAM）医学院实验免疫治疗实验室的研究成果，提出了一种针对小鼠黑色素瘤的DCs免疫治疗数学模型。
该模型是一个五延迟微分方程（DDEs），它代表了免疫治疗机制的简化视图。该数学模型考虑了肿瘤细胞、树突状细胞、初始细胞毒性T淋巴细胞（未激活的细胞毒性细胞）、效应细胞（激活的细胞毒性T细胞）和转化生长因子β细胞因子（TGF-β）之间的相互作用。通过将计算机模拟结果与UNAM研究小组开展的免疫治疗生物学试验结果进行比较，对该模型进行了验证。
对照免疫治疗模拟得到的肿瘤细胞生长结果显示，肿瘤细胞群体数量与对照免疫治疗的生物学数据相似。此外，将免疫治疗模拟得到的肿瘤细胞增加量与UNAM研究人员应用的免疫治疗生物学数据进行比较，误差约为10%。这使我们能够将该模型用作测试假设治疗方法的框架。数值模拟表明，与当前的免疫治疗相比，通过使用更多剂量的DCs并改变输注时间，肿瘤生长会衰减。此外，还进行了局部敏感性分析；结果表明，时间延迟“τ”、肿瘤的最大生长速率“r”和肿瘤细胞毒性细胞速率的最大效率“aT”是最敏感的模型参数。
通过使用这个数学模型，可以利用UNAM研究人员的输注方案模拟有无免疫治疗情况下肿瘤细胞的生长，从而很好地逼近生物学试验数据。值得一提的是，通过操纵模型的不同参数，免疫治疗的有效性可能会提高。这最后一点表明，UNAM免疫治疗实验室可以实施不同的方案以改善其结果。
