关于描述肿瘤细胞化疗治疗的数学模型
On a Mathematical Model Describing Chemotherapeutic Drug Treatment for Tumor Cells
AI总结：
本文提出一个包含强阿莱效应的肿瘤化疗数学模型，通过CNBE方案模拟显示，集中脉冲治疗可更有效抑制肿瘤，同时保护正常组织。
摘要：
在本文中，我们研究了一个半线性抛物型偏微分方程组，该模型描述了正常细胞、肿瘤细胞和免疫细胞与化疗药物之间的相互作用。该模型扩展了之前的模型，加入了强阿莱效应在正常组织和肿瘤动力学中的影响。在较弱的假设下，我们建立了全局时间内的非负弱解的存在性和唯一性，并推导了所有时间的L无穷界。然后，我们利用隐式Crank Nicolson Backward Euler（CNBE）方案研究了该模型的空间时间动态和治疗调度。在异质的二维空间组织区域中进行的模拟显示，没有治疗的情况下肿瘤快速入侵，而在脉冲化疗治疗下肿瘤显著受到抑制。此外，在固定总剂量内，当保持每次注射时间固定时，集中脉冲会产生更强的早期肿瘤密度下降，而更频繁但更温和的脉冲则在四周内实现了对肿瘤侵袭前沿的可控，同时更好地保护了正常组织。
英文摘要：
In this paper, we study a semilinear parabolic PDE system which describes the interaction of normal cells, tumor cells, immune cells, with a chemotherapeutic drug. The model extends the previous model with incorporating strong Allee affects in the normal-tissue and tumor dynamics. Under mild assumptions, we establish global-in-time existence and uniqueness of nonnegative weak solutions and derive L-infinity bounds for all time. We then investigate spatiotemporal dynamics of the model and therapy scheduling using an implicit Crank Nicolson Backward Euler (CNBE) scheme. Simulations in a heterogeneous two-dimensional space-dimensional tissue region with three tumor peaks indicate rapid tumor invasion without treatment and significant tumor suppression under pulsed chemotherapeutic treatment. Moreover, in a fixed total dose delivered within the treatment cycle, while keeping each injection duration fixed, concentrated pulses produce stronger early knock-down of tumor density, while more frequent but gentler pulses achieve comparable control of the tumor invasive front while better preserving normal tissue over a four-week period.
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