Subramanian Shashank, Gholami Amir, Biros George
Institute for Computational Engineering and Sciences, University of Texas at Austin, Austin, TX, 78712, USA.
Department of Electrical Engineering and Computer Sciences, UC Berkeley, Berkeley, CA, 94720, USA.
J Math Biol. 2019 Aug;79(3):941-967. doi: 10.1007/s00285-019-01383-y. Epub 2019 May 24.
In this article, we present a multispecies reaction-advection-diffusion partial differential equation coupled with linear elasticity for modeling tumor growth. The model aims to capture the phenomenological features of glioblastoma multiforme observed in magnetic resonance imaging (MRI) scans. These include enhancing and necrotic tumor structures, brain edema and the so-called "mass effect", a term-of-art that refers to the deformation of brain tissue due to the presence of the tumor. The multispecies model accounts for proliferating, invasive and necrotic tumor cells as well as a simple model for nutrition consumption and tumor-induced brain edema. The coupling of the model with linear elasticity equations with variable coefficients allows us to capture the mechanical deformations due to the tumor growth on surrounding tissues. We present the overall formulation along with a novel operator-splitting scheme with components that include linearly-implicit preconditioned elliptic solvers, and a semi-Lagrangian method for advection. We also present results showing simulated MRI images which highlight the capability of our method to capture the overall structure of glioblastomas in MRIs.
在本文中，我们提出了一个多物种反应-平流-扩散偏微分方程，并结合线性弹性来模拟肿瘤生长。该模型旨在捕捉在磁共振成像（MRI）扫描中观察到的多形性胶质母细胞瘤的现象学特征。这些特征包括强化和坏死的肿瘤结构、脑水肿以及所谓的“占位效应”，这是一个专业术语，指的是由于肿瘤的存在导致脑组织变形。多物种模型考虑了增殖、侵袭和坏死的肿瘤细胞，以及一个简单的营养消耗和肿瘤诱导脑水肿模型。该模型与变系数线性弹性方程的耦合使我们能够捕捉肿瘤生长对周围组织造成的机械变形。我们给出了整体公式以及一种新颖的算子分裂格式，其组成部分包括线性隐式预处理椭圆求解器和一种用于平流的半拉格朗日方法。我们还展示了模拟MRI图像的结果，突出了我们的方法捕捉MRI中胶质母细胞瘤整体结构的能力。
