Glioblastoma is the most common and deadly primary brain tumor in adults. To optimize the treatment strategies, it is essential to understand the tumor growth dynamics in different periods. In this study, we use image processing techniques to combine the available early-stage imaging data and applied a fractional reaction–diffusion equation to predict the human glioblastoma multiforme tumor growth. We consider the heterogeneity of the brain tissue by assigning different diffusion coefficients for the three regions of the human brain. A meshfree method based on the thin plate spline radial basis function is used for the numerical solution of nonlinear time fractional Proliferation-Invasion equation. The results show that the proposed model has a better fit with the experimental data. The prediction of tumor growth at any desired time with no need to repeated imaging is another advantages of the model which could reduce the side effects and cost of diagnostic and therapeutic methods. The model can also incorporate the effects of various treatment modalities such as hyperthermia, radiation, and surgery on tumor growth. Furthermore, it can enable the use of patient-specific characteristics in diagnosis and treatment and facilitate the development of personalized medicine approaches.

中文翻译：

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分数导数在预测人多形性胶质母细胞瘤肿瘤生长中的新应用


胶质母细胞瘤是成人中最常见和致命的原发性脑肿瘤。为了优化治疗策略，了解不同时期肿瘤的生长动态至关重要。在本研究中，我们使用图像处理技术结合可用的早期成像数据，并应用分数反应扩散方程来预测人类多形性胶质母细胞瘤肿瘤的生长。我们通过为人脑的三个区域分配不同的扩散系数来考虑脑组织的异质性。采用基于薄板样条径向基函数的无网格方法对非线性时间分数式增殖入侵方程进行数值求解。结果表明，所提出的模型与实验数据有较好的拟合。该模型的另一个优点是可以在任何所需时间预测肿瘤生长，而无需重复成像，可以减少诊断和治疗方法的副作用和成本。该模型还可以结合各种治疗方式（例如热疗、放射和手术）对肿瘤生长的影响。此外，它可以在诊断和治疗中利用患者的具体特征，并促进个性化医疗方法的发展。