We present an efficient numerical method to quantify the spatial variation of glioma growth based on subject-specific medical images using a mechanically-coupled tumor model. The method is illustrated in a murine model of glioma in which we consider the tumor as a growing elastic mass that continuously deforms the surrounding healthy-appearing brain tissue. As an inverse parameter identification problem, we quantify the volumetric growth of glioma and the growth component of deformation by fitting the model predicted cell density to the cell density estimated using the diffusion-weighted magnetic resonance imaging data. Numerically, we developed an adjoint-based approach to solve the optimization problem. Results on a set of experimentally measured, in vivo rat glioma data indicate good agreement between the fitted and measured tumor area and suggest a wide variation of in-plane glioma growth with the growth-induced Jacobian ranging from 1.0 to 6.0.

中文翻译：

---

线性机械耦合肿瘤模型的伴随方法：基于扩散加权磁共振成像估计小鼠神经胶质瘤生长的空间变化的应用

我们提出了一种有效的数值方法，使用机械耦合肿瘤模型根据特定主题的医学图像来量化神经胶质瘤生长的空间变化。该方法在神经胶质瘤的小鼠模型中进行了说明，在该模型中，我们将肿瘤视为不断生长的弹性物质，不断使周围看似健康的脑组织变形。作为逆参数识别问题，我们通过将模型预测的细胞密度拟合到使用扩散加权磁共振成像数据估计的细胞密度来量化神经胶质瘤的体积生长和变形的生长分量。在数值上，我们开发了一种基于伴随的方法来解决优化问题。一组实验测量的体内大鼠神经胶质瘤数据的结果表明，拟合和测量的肿瘤区域之间具有良好的一致性，并表明平面内神经胶质瘤生长的变化很大，生长诱导的雅可比行列式的范围为 1.0 至 6.0。