Complex Systems and Cybernetic Control Lab., Faculty of Biomedical Engineering, Amirkabir University of Technology (Tehran Polytechnic), Tehran, P.O. Box 1591634311, Iran.
J Theor Biol. 2013 Oct 7;334:130-40. doi: 10.1016/j.jtbi.2013.05.031. Epub 2013 Jun 11.
Clinicians and oncologists believe that tumor growth has unpredictable dynamics. For this reason they encounter many difficulties in the treatment of cancer. Mathematical modeling is a great tool to improve our better understanding of the complicated biological system of tumor growth. Also, it can help to identify states of the disease and as a result help to predict later behaviors of the tumor. Having an insight into the future behaviors of the tumor can be very useful for the oncologists and clinicians to decide on the treatment method and dosage of the administered drug. This paper suggests that a suitable model for the tumor growth system should be a discrete model capable of exhibiting periodic and complex chaotic dynamics. This is the key feature of the proposed model. The model is validated here through experimental data and its potential dynamics are analyzed. The model can explain many biologically observed tumor states and dynamics, such as exponential growth, and periodic and chaotic behaviors in the steady states. The model shows that even an avascular tumor could become invasive under certain conditions.
临床医生和肿瘤学家认为肿瘤的生长具有不可预测的动态。出于这个原因，他们在癌症治疗中遇到了许多困难。数学建模是一种很好的工具，可以帮助我们更好地理解肿瘤生长这一复杂的生物系统。它还有助于识别疾病的状态，并因此帮助预测肿瘤的后期行为。深入了解肿瘤的未来行为对于肿瘤学家和临床医生来说非常有用，他们可以据此决定治疗方法和给予药物的剂量。本文提出，适合肿瘤生长系统的模型应该是一个能够表现出周期性和复杂混沌动力学的离散模型。这是所提出模型的关键特征。本文通过实验数据验证了该模型，并分析了其潜在的动力学。该模型可以解释许多在生物学上观察到的肿瘤状态和动态，如指数增长以及在稳定状态下的周期性和混沌行为。该模型表明，即使是无血管的肿瘤在某些条件下也可能具有侵袭性。
