Università Campus Bio-Medico di Roma, via Álvaro del Portillo, 21, 00128 Roma, Italy.
Math Biosci. 2011 Dec;234(2):147-53. doi: 10.1016/j.mbs.2011.10.002. Epub 2011 Oct 15.
Cancer represents one of the most challenging issues for the biomedical research, due its large impact on the public health state. For this reason, many mathematical methods have been proposed to forecast the time evolution of cancer size and invasion. In this paper, we study how to apply the Gompertz's model to describe the growth of an avascular tumor in a realistic setting. To this aim, we introduce mathematical techniques to discretize the model, an important requirement when discrete-time measurements are available. Additionally, we describe observed-based techniques, borrowed from the field of automation theory, as a tool to estimate the model unknown parameters. This identification approach is a promising alternative to traditional statistical methods, and it can be easily extended to other models of cancer growth as well as to the evaluation of not measurable variables, on the basis of the available measurements. We show an application of this method to the analysis of solid tumor growth and parameters estimation in presence of a chemotherapy agent.
癌症是生物医学研究中最具挑战性的问题之一，因为它对公众健康状况有很大的影响。出于这个原因，已经提出了许多数学方法来预测癌症大小和侵袭的时间演变。在本文中，我们研究如何应用 Gompertz 模型来描述在现实环境中无血管肿瘤的生长。为此，我们引入了数学技术来对模型进行离散化，这是在存在离散时间测量时的一个重要要求。此外，我们还描述了从自动化理论领域借用的基于观测的技术，作为估计模型未知参数的工具。这种识别方法是对传统统计方法的一种有前途的替代方法，并且可以很容易地扩展到其他癌症生长模型以及基于可用测量值评估不可测量变量。我们展示了这种方法在分析实体瘤生长和存在化疗药物时参数估计中的应用。
