Enderling, Heiko and Mark Chaplain. 2014. Mathematical Modeling of Tumor Growth and Treatment. Current Pharmacological Design. 20(00): 1-7.
Abstract: Using mathematical models to simulate dynamic biological processes has a long history. Over the past couple of decades or so, quantitative approaches have also made their way into cancer research. An increasing number of mathematical, physical, computational and engineering techniques have been applied to various aspects of tumor growth, with the ultimate goal of understanding the response of the cancer population to clinical intervention. So-called in silico trials that predict patient-specific response to various dose schedules or treatment combinations and sequencing are on the way to becoming an invaluable tool to optimize patient care. Herein we describe fundamentals of mathematical modeling of tumor growth and tumor-host interactions, and summarize some of the seminal and most prominent approaches.
This paper offers some very concrete models with illustrations of application in the field and lots of references. Models are compared with attention to parameter values.
Keywords: Ordinary differential equation, partial differential equation, tumor modeling, angiogenesis.
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