We discuss solution algorithms for calibrating a tumor growth model using imaging data posed as a deterministic inverse problem. The forward model consists of a nonlinear and time-dependent reaction-diffusion partial differential equation (PDE) with unknown parameters (diffusivity and proliferation rate) being spatial fields. We use a dimension-independent globalized, inexact Newton Conjugate Gradient algorithm to solve the PDE-constrained optimization. The required gradient and Hessian actions are also presented using the adjoint method and Lagrangian formalism.

翻译：本文讨论了将医学影像数据用于肿瘤生长模型校准的求解算法，该问题被表述为确定性逆问题。前向模型包含具有未知空间场参数（扩散系数与增殖速率）的非线性时变反应-扩散偏微分方程（PDE）。我们采用一种维度无关的全局化非精确牛顿共轭梯度算法求解该PDE约束优化问题，并通过伴随法和拉格朗日形式体系给出了所需的梯度与海森矩阵作用计算方法。