抑制剂作用下肿瘤生长模型的参数识别

Abstract

Abstract:

In this paper, the authors consider a model of tumor growth in the presence of inhibitors. The tumor is assumed to be spherically symmetric and its surface is a moving boundary denoted by a function r=R(t). Since multicellular tumor spheroids (MTS) are routinely used as in vitro models of cancer growth and they can be observed and controlled in the laboratory, the authors study the following inverse problem: Given
observed dynamics of MTS growth (i.e., given R(t)), the authors determine the inhibitor's parameter. The authors first prove the uniqueness of
solution to the inverse parabolic problem by the maximum principle. Then the authors develop an optimal control framework for studying the reconstruction of the inhibitor's parameter. The authors prove the existence of solution to the optimal control problem, and the authors derive the necessary optimality conditions which have to be satisfied by each optimal control.

Key words: Tumors, inhibitors, Free boundary problem, Inverse problem, Optimal control

CLC Number:

35K35

TAO You-Shan, BIAN Bao-Jun. Parameter Identification for a Model of Tumor Growth in the Presence of Inhibitors[J].Acta mathematica scientia,Series A, 2009, 29(5): 1175-1186.

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Parameter Identification for a Model of Tumor Growth in the Presence of Inhibitors

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