用于脑肿瘤模型快速贝叶斯校准的几何感知神经求解器
Geometry-aware neural solver for fast Bayesian calibration of brain tumor models
摘要：
脑肿瘤动力学建模有可能推进治疗计划。目前的建模方法诉诸于根据给定的微分方程模拟肿瘤进展的数值求解器。使用高效的数值求解器，一个单一的正演模拟需要几分钟的计算时间。同时，肿瘤建模的临床应用通常意味着解决逆问题，当用于通过采样的贝叶斯模型个性化时，需要多达数万个正向模型评估。这导致总推理时间对于临床翻译来说过于昂贵。虽然最近的数据驱动的方法变得能够仿真物理模拟，但它们往往无法概括由患者特定解剖结构施加的边界条件的可变性。在本文中，我们提出了一个可学习的替代模拟肿瘤生长的生物物理模型参数直接映射到模拟输出，即局部肿瘤细胞密度，同时尊重病人的几何形状。我们测试神经求解器对神经胶质瘤患者的贝叶斯肿瘤模型个性化。贝叶斯推断使用建议的替代产量估计类似于通过求解正演模型与常规数值求解器。近实时的计算成本使得所提出的方法适用于临床环境。该代码可在https://github.com/IvanEz/tumor-surrogate上获得。
英文摘要：
Modeling of brain tumor dynamics has the potential to advance therapeutic planning. Current modeling approaches resort to numerical solvers that simulate the tumor progression according to a given differential equation. Using highly-efficient numerical solvers, a single forward simulation takes up to a few minutes of compute. At the same time, clinical applications of tumor modeling often imply solving an inverse problem, requiring up to tens of thousands forward model evaluations when used for a Bayesian model personalization via sampling. This results in a total inference time prohibitively expensive for clinical translation. While recent data-driven approaches become capable of emulating physics simulation, they tend to fail in generalizing over the variability of the boundary conditions imposed by the patient-specific anatomy. In this paper, we propose a learnable surrogate for simulating tumor growth which maps the biophysical model parameters directly to simulation outputs, i.e. the local tumor cell densities, whilst respecting patient geometry. We test the neural solver on Bayesian tumor model personalization for a cohort of glioma patients. Bayesian inference using the proposed surrogate yields estimates analogous to those obtained by solving the forward model with a regular numerical solver. The near-real-time computation cost renders the proposed method suitable for clinical settings. The code is available at https://github.com/IvanEz/tumor-surrogate.
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