Accelerating Parameter Inference in Diffusion-Reaction Models of Glioblastoma Using Physics-Informed Neural Networks
Accelerating Parameter Inference in Diffusion-Reaction Models of Glioblastoma Using Physics-Informed Neural Networks
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DOI：
10.1137/22s1472814
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发表时间：
2022
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通讯作者：
Andy Zhu
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作者：
Andy Zhu
胶质母细胞瘤是一种侵袭性脑肿瘤，其细胞迅速浸润并增殖到周围的脑组织中。当前胶质母细胞瘤生长的数学模型使用通过数值求解器模拟的偏微分方程 (PDE) 来捕捉这种行为，高效的实现可能需要大约 80 秒才能完成一次前向评估。然而，肿瘤建模的临床应用通常被视为需要复杂的数值方法的逆问题，如果简单地实施，可能会导致运行时间过长，使其不适合临床环境。最近，物理信息神经网络（PINN）已成为科学机器学习中解决非线性偏微分方程的一种新方法。与传统求解器相比，PINN 利用无监督深度学习方法来最小化无网格域中的残差，从而实现更大的灵活性，同时避免复杂的网格构造。在这里，我们描述并实现了一种通用方法，用于求解胶质母细胞瘤的时间依赖性扩散反应 PDE 模型，并通过 PINN 从数值数据推断生物物理参数。我们根据患者特定的几何形状评估 PINN，并考虑术前 MRI 扫描得出的扩散迁移率的个体差异。使用合成数据，我们展示了我们的算法在患者特定几何形状中的性能。我们证明，由于机器学习算法具有强大的插值能力，PINN 能够在大约一小时内解决参数推断逆问题，将之前的方法加快了 20-40 倍。我们预计这种方法对于临床使用来说可能足够准确和有效，有可能使个性化治疗在标准护理医疗方案中更容易实现。
Glioblastoma is an aggressive brain tumor with cells that infiltrate and proliferate rapidly into surrounding brain tissue. Current mathematical models of glioblastoma growth capture this behavior using partial differential equations (PDEs) that are simulated via numerical solvers—a highly-efficient implementation can take about 80 seconds to complete a single forward evaluation. However, clinical applications of tumor modeling are often framed as inverse problems that require sophisticated numerical methods and, if implemented naively, can lead to prohibitively long runtimes that render them inadequate for clinical settings. Recently, physics-informed neural networks (PINNs) have emerged as a novel method in scientific machine learning for solving nonlinear PDEs. Compared to traditional solvers, PINNs leverage unsupervised deep learning methods to minimize residuals across mesh-free domains, enabling greater flexibility while avoiding the need for complex grid constructions. Here, we describe and implement a general method for solving time-dependent diffusion-reaction PDE models of glioblastoma and inferring biophysical parameters from numerical data via PINNs. We evaluate the PINNs over patient-specific geometries, accounting for individual variations with diffusion mobilities derived from pre-operative MRI scans. Using synthetic data, we demonstrate the performance of our algorithm in patient-specific geometries. We show that PINNs are capable of solving parameter inference inverse problems in approximately one hour, expediting previous approaches by 20–40 times owing to the robust interpolation capabilities of machine learning algorithms. We anticipate this method may be sufficiently accurate and efficient for clinical usage, potentially rendering personalized treatments more accessible in standard-of-care medical protocols.