dePillis2013 - Mathematical modeling of regulatory T cell effects on renal cell carcinoma treatment

Mathematical modeling of regulatory T cell effects on renal cell carcinoma treatment

Lisette dePillis 1, , Trevor Caldwell 2, , Elizabeth Sarapata 2, and Heather Williams 2,
1.

Department of Mathematics, Harvey Mudd College, Claremont, CA 91711
2.

Harvey Mudd College, Claremont, CA 91711, United States, United States, United States

Abstract

We present a mathematical model to study the effects of the regulatory T cells (Treg) on Renal Cell Carcinoma (RCC) treatment with sunitinib. The drug sunitinib inhibits the natural self-regulation of the immune system, allowing the effector components of the immune system to function for longer periods of time. This mathematical model builds upon our non-linear ODE model by de Pillis et al. (2009) [13] to incorporate sunitinib treatment, regulatory T cell dynamics, and RCC-specific parameters. The model also elucidates the roles of certain RCC-specific parameters in determining key differences between in silico patients whose immune profiles allowed them to respond well to sunitinib treatment, and those whose profiles did not.
Simulations from our model are able to produce results that reflect clinical outcomes to sunitinib treatment such as: (1) sunitinib treatments following standard protocols led to improved tumor control (over no treatment) in about 40% of patients; (2) sunitinib treatments at double the standard dose led to a greater response rate in about 15% the patient population; (3) simulations of patient response indicated improved responses to sunitinib treatment when the patient's immune strength scaling and the immune system strength coefficients parameters were low, allowing for a slightly stronger natural immune response.
Keywords: Renal cell carcinoma, mathematical modeling., sunitinib, immune system, regulatory T cells.

调节性T细胞对肾细胞癌（Renal Cell Carcinoma, RCC）治疗影响的数学建模

Lisette dePillis 1, , Trevor Caldwell 2, , Elizabeth Sarapata 2, 和 Heather Williams 2,
1. 哈维玛德学院数学系，克莱尔蒙特，加利福尼亚州91711
2. 哈维玛德学院，克莱尔蒙特，加利福尼亚州91711，美利坚合众国

摘要

本研究构建数学模型，用以探究调节性T细胞（regulatory T cells, Treg）对舒尼替尼（sunitinib）治疗肾细胞癌（Renal Cell Carcinoma, RCC）的影响。舒尼替尼可抑制免疫系统的天然自我调节机制，使免疫系统的效应组分能够更长时间地发挥功能。本数学模型以de Pillis等人2009年提出的非线性常微分方程（ordinary differential equation, ODE）模型为基础，新增了舒尼替尼治疗、调节性T细胞动力学以及肾细胞癌特异性参数模块。本模型还阐明了部分肾细胞癌特异性参数在区分两类计算机模拟患者时的作用：一类患者的免疫特征可使其对舒尼替尼治疗产生良好应答，另一类则无此应答效果。

本模型的模拟结果可复现舒尼替尼治疗的临床结局，具体如下：
（1）遵循标准给药方案的舒尼替尼治疗，可使约40%的患者获得优于未治疗组的肿瘤控制效果；
（2）采用标准剂量两倍的舒尼替尼给药方案，可使约15%的患者群体获得更高的应答率；
（3）患者应答模拟结果显示，当患者的免疫强度缩放系数与免疫系统强度系数参数取值较低时，患者对舒尼替尼治疗的应答效果更佳，此时天然免疫应答可略微增强。

关键词：肾细胞癌、数学建模、舒尼替尼、免疫系统、调节性T细胞。