Mathematical Modeling of Cell Growth via Inverse Problem and Computational Approach

被引:1
|
作者
Andrusyak, Ivanna [1 ]
Brodyak, Oksana [1 ]
Pukach, Petro [2 ]
Vovk, Myroslava [1 ]
机构
[1] Lviv Polytech Natl Univ, Dept Math, UA-79013 Lvov, Ukraine
[2] Lviv Polytech Natl Univ, Dept Computat Math & Programming, UA-79013 Lvov, Ukraine
关键词
cell population model; physiological structure; conservation law; the characteristics method; POPULATION; SYSTEMS;
D O I
10.3390/computation12020026
中图分类号
O1 [数学];
学科分类号
0701 ; 070101 ;
摘要
A simple cell population growth model is proposed, where cells are assumed to have a physiological structure (e.g., a model describing cancer cell maturation, where cells are structured by maturation stage, size, or mass). The main question is whether we can guarantee, using the death rate as a control mechanism, that the total number of cells or the total cell biomass has prescribed dynamics, which may be applied to modeling the effect of chemotherapeutic agents on malignant cells. Such types of models are usually described by partial differential equations (PDE). The population dynamics are modeled by an inverse problem for PDE in our paper. The main idea is to reduce this model to a simplified integral equation that can be more easily studied by various analytical and numerical methods. Our results were obtained using the characteristics method.
引用
收藏
页数:13
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