Parameters in mathematical models for glioblastoma multiforme (GBM) tumour growth are highly patient specific. Here, we aim to estimate parameters in a Cahn–Hilliard type diffuse interface model in an optimised way using model order reduction (MOR) based on proper orthogonal decomposition (POD). Based on snapshots derived from finite element simulations for the full‐order model (FOM), we use POD for dimension reduction and solve the parameter estimation for the reduced‐order model (ROM). Neuroimaging data are used to define the highly inhomogeneous diffusion tensors as well as to define a target functional in a patient‐specific manner. The ROM heavily relies on the discrete empirical interpolation method, which has to be appropriately adapted in order to deal with the highly nonlinear and degenerate parabolic partial differential equations. A feature of the approach is that we iterate between full order solvers with new parameters to compute a POD basis function and sensitivity‐based parameter estimation for the ROM problems. The algorithm is applied using neuroimaging data for two clinical test cases, and we can demonstrate that the reduced‐order approach drastically decreases the computational effort.

中文翻译：

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从神经影像数据中学习弥散性胶质母细胞瘤模型的患者特定参数

多形性胶质母细胞瘤（GBM）肿瘤生长的数学模型中的参数是高度针对患者的。在这里，我们的目的是使用基于适当正交分解（POD）的模型降阶（MOR），以优化的方式估算Cahn-Hilliard型扩散界面模型中的参数。基于从全阶模型（FOM）的有限元模拟中获得的快照，我们使用POD进行维降，并求解降阶模型（ROM）的参数估计。神经影像数据可用于定义高度不均匀的扩散张量以及以患者特定的方式定义目标功能。ROM严重依赖于离散经验插值方法，该方法必须进行适当调整才能处理高度非线性和退化的抛物线偏微分方程。该方法的一个特点是，我们在具有新参数的全阶求解器之间进行迭代，以计算POD基函数和针对ROM问题的基于灵敏度的参数估计。该算法在两个临床测试案例中使用了神经影像数据，并且可以证明降阶方法极大地减少了计算量。