基于扩散方程的非均匀介质中肿瘤生长的模拟
Simulation tumor growth in heterogeneous medium based on diffusion equation
摘要：
在本文中，扩散方程被用来模拟肿瘤的时空动力学，考虑到介质的异质性。这种方法使得在建模中考虑肿瘤的复杂几何形状成为可能。工作的主要目的是通过将所获得的结果与临床观察数据进行比较来证明这种方法的适用性。我们使用了一种基于微分算子的显式有限差分近似的算法来求解扩散方程。获得了模型输入参数与临床观察结果相匹配的可能值的范围。它的结论是，模型的物理参数的异质性，特别是扩散系数，对肿瘤的形状有显着的影响。
英文摘要：
In the present article the diffusion equation is used to model the spatio-temporal dynamics of a tumor, taking into account the heterogeneous of the medium. This approach makes it possible to take into account the complex geometric shape of the tumor in modeling. The main purpose of the work is demonstration the applicability of this approach by comparing the obtained results with the data of clinical observations. We used an algorithm based on an explicit finite-difference approximation of differential operators for solve the diffusion equation. The ranges of possible values that the input parameters of the model can take to match the results of clinical observations are obtained. It is concluded that the heterogeneity of the physical parameters of the model, in particular the diffusion coefficient, has a significant effect on shape of tumor.
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