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首页> 外文会议>Proceedings of the 2014 6th International Advanced Research Workshop on In Silico Oncology and Cancer Investigation - The TUMOR Project Workshop >Modeling glioblastoma growth and inhomogeneous tumor invasion with explicitly numerically treated neumann boundary conditions
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Modeling glioblastoma growth and inhomogeneous tumor invasion with explicitly numerically treated neumann boundary conditions

机译：使用明确数值处理的Neumann边界条件对胶质母细胞瘤生长和不均匀肿瘤浸润进行建模

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A couple of multiscale spatiotemporal simulation models of glioblastoma multiforme (GBM) growth and invasion into the surrounding normal brain tissue is presented. Both models are based on a continuous and subsequently finite mathematical approach centered around the non-linear partial differential equation of diffusion-reaction referring to glioma tumour cells. A novel explicit, strict and thorough numerical treatment of the three dimensional adiabatic Neumann boundary conditions imposed by the skull is also included in both models. The first model assumes a homogeneous representation of normal brain tissue whereas the second one, assuming an inhomogeneous representation of normal brain tissue, distinguishes between white matter, grey matter and cerebrospinal fluid. The predictions of the tumour doubling time by both models are compared for specific data sets. Clinical observational data regarding the range of the GBM doubling time values are utilized in order to ensure the realism of both models and their predictions. We assume that the inhomogeneous normal brain tissue representation is a virtual rendering of reality more credible than its homogeneous counterpart. The simulation results for the cases considered show that using the homogeneous normal brain based model may lead to an error of up to 10% for the first 25 simulated days in relation to the predictions of the inhomogeneous model. However, the error drops to less than 7% afterwards. This observation suggests that even by using a homogeneous brain based model and a realistic weighted average value of its diffusion coefficient, a rough but still informative estimate of the expected tumour doubling time can be achieved. Additional in silico experimentation aiming at statistically testing and eventually further supporting the validity of this hypothesis is in progress. It is noted that the values of the diffusion coefficients and the cell birth and death rates of the model are amenable to refinement and per- onalization by exploiting the histological and molecular profile of the patient. Work on this aspect is in progress.
机译：提出了几种胶质母细胞瘤（GBM）生长和侵袭周围正常脑组织的多尺度时空模拟模型。两种模型均基于连续且随后的有限数学方法，该方法以围绕神经胶质瘤肿瘤细胞的扩散反应的非线性偏微分方程为中心。两种模型还包括对头骨施加的三维绝热诺伊曼边界条件的新颖的显式，严格和彻底的数值处理。第一个模型假定正常脑组织的同质表示，而第二个模型假定正常脑组织的不均质表示，可以区分白质，灰质和脑脊液。对于特定数据集，比较了两个模型对肿瘤倍增时间的预测。利用有关GBM倍增时间值范围的临床观察数据，以确保两个模型及其预测的真实性。我们假设不均匀的正常脑组织表示是一种现实的虚拟渲染，比其同质的对应更为可信。所考虑案例的模拟结果表明，相对于非均匀模型的预测，使用基于同类正常大脑的模型可能会导致前25个模拟日的误差高达10％。但是，此后误差降至不到7％。该观察结果表明，即使使用基于均质脑的模型及其扩散系数的实际加权平均值，也可以实现对预期肿瘤加倍时间的粗略但仍能提供有用信息的估计。正在进行其他旨在进行统计检验并最终进一步支持该假设有效性的计算机模拟实验。需要注意的是，通过利用患者的组织学和分子特征，模型的扩散系数值以及细胞的出生和死亡率都可以改善和精确化。这方面的工作正在进行中。

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