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首页> 外文会议>International Advanced Research Workshop on In Silico Oncology and Cancer Investigation >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：用明确的数值处理的Neumann边界条件建模胶质母细胞瘤生长和不均匀肿瘤侵袭

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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：提出了几个胶质母细胞瘤的多尺度时空模拟模型（GBM）生长和入侵到周围的正常脑组织中。两种型号基于围绕胶质瘤肿瘤细胞的扩散反应的非线性部分微分方程的连续和随后有限的数学方法。两种模型中的三维绝热Neumann边界条件的三维绝热Neumann边界条件的新型明确的，严格和彻底的数值处理。第一模型假设正常脑组织的均匀表示，而第二个模型，则假设正常脑组织的不均匀表示，区分白质，灰质和脑脊液。比较两种模型的肿瘤倍增时间的预测以特定数据集进行了比较。有关GBM倍增时间值范围的临床观测数据，以确保模型及其预测的现实主义。我们假设不均匀的正常脑组织表示是现实的虚拟渲染，而不是其同质对应物更可信。所考虑的案例的模拟结果表明，与非均匀模型的预测相对于预测，使用均匀的正常脑基础的模型可能导致前25个模拟天的误差高达10％。但是，之后，误差下降到小于7％。该观察结果表明，即使使用均匀的基于脑的模型和其扩散系数的逼真的加权平均值，也可以实现对预期肿瘤倍增时间的粗略但仍然提供信息的估计。在统计测试中的含硅实验中的额外旨在进一步支持这一假设的有效性正在进行中。注意，通过利用患者的组织学和分子曲线，可以通过利用患者的组织学和分子曲线来实现模型的扩散系数和细胞出生和死亡率的值。在这方面的工作正在进行中。

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