从神经影像数据学习患者特异性的弥漫界面胶质母细胞瘤模型参数
Learning patient-specific parameters for a diffuse interface glioblastoma model from neuroimaging data
AI总结：
本文提出基于POD和DEIM的模型降阶方法，结合神经影像数据对GBM弥漫界面模型进行患者特异性参数估计，并在两个临床病例上验证其显著降低计算成本。
摘要：
多形性胶质母细胞瘤（GBM）肿瘤生长的数学模型中的参数具有高度的患者特异性。本文旨在利用基于本征正交分解（POD）的模型降阶（MOR），以优化方式估计 Cahn-Hilliard 型弥漫界面模型中的参数。基于由全阶模型（FOM）的有限元模拟得到的快照，我们使用 POD 进行降维，并针对降阶模型（ROM）求解参数估计问题。神经影像数据被用于定义高度非均匀的扩散张量，并以患者特异性的方式定义目标泛函。降阶模型在很大程度上依赖于离散经验插值方法（DEIM），必须对其进行适当改造，以处理高度非线性和退化抛物型偏微分方程。该方法的一个特点是：我们在使用新参数进行全阶求解以计算 POD 基函数与针对 ROM 问题基于灵敏度的参数估计之间进行迭代。该算法被应用于两个临床测试病例的神经影像数据，我们能够证明降阶方法大幅降低了计算开销。
英文摘要：
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 reduced order model heavily relies on the discrete empirical interpolation method (DEIM) which has to be appropriately adapted in order to deal with the highly nonlinear and degenerate parabolic PDEs. A feature of the approach is that we iterate between full order solves 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.
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