Ledzewicz Urszula, Schättler Heinz
Department of Mathematics and Statistics, Southern Illinois University at Edwardsville, Edwardsville, IL 62026-1653, USA.
J Theor Biol. 2008 May 21;252(2):295-312. doi: 10.1016/j.jtbi.2008.02.014. Epub 2008 Feb 16.
Tumor anti-angiogenesis is a cancer treatment approach that aims at preventing the primary tumor from developing its own vascular network needed for further growth. In this paper the problem of how to schedule an a priori given amount of angiogenic inhibitors in order to minimize the tumor volume is considered for three related mathematical formulations of a biologically validated model developed by Hahnfeldt et al. [1999. Tumor development under angiogenic signalling: a dynamical theory of tumor growth, treatment response, and postvascular dormancy. Cancer Res. 59, 4770-4775]. Easily implementable piecewise constant protocols are compared with the mathematically optimal solutions. It is shown that a constant dosage protocol with rate given by the averaged optimal control is an excellent suboptimal protocol for the original model that achieves tumor values that lie within 1% of the theoretically optimal values. It is also observed that the averaged optimal dose is decreasing as a function of the initial tumor volume.
肿瘤抗血管生成是一种癌症治疗方法，旨在阻止原发性肿瘤形成其进一步生长所需的自身血管网络。本文针对Hahnfeldt等人[1999年。血管生成信号下的肿瘤发展：肿瘤生长、治疗反应和血管生成后休眠的动力学理论。癌症研究。59, 4770 - 4775]开发的生物验证模型的三种相关数学公式，考虑了如何安排先验给定数量的血管生成抑制剂以最小化肿瘤体积的问题。将易于实施的分段常数方案与数学上的最优解进行了比较。结果表明，对于原始模型，由平均最优控制给出速率的恒定剂量方案是一种出色的次优方案，其实现的肿瘤值在理论最优值的1%以内。还观察到平均最优剂量作为初始肿瘤体积的函数在减小。
