Klank Rebecca L, Rosenfeld Steven S, Odde David J
Department of Biomedical Engineering, University of Minnesota, Minneapolis, MN, United States of America.
Burkhardt Brain Tumor Center, Department of Cancer Biology, Cleveland Clinic, Cleveland, OH, United States of America.
Converg Sci Phys Oncol. 2018 Mar;4(1). doi: 10.1088/2057-1739/aa9e6e. Epub 2018 Jan 3.
Tumor progression modeling offers the potential to predict tumor-spreading behavior to improve prognostic accuracy and guide therapy development. Common simulation methods include continuous reaction-diffusion (RD) approaches that capture mean spatio-temporal tumor spreading behavior and discrete agent-based (AB) approaches which capture individual cell events such as proliferation or migration. The brain cancer glioblastoma (GBM) is especially appropriate for such proliferation-migration modeling approaches because tumor cells seldom metastasize outside of the central nervous system and cells are both highly proliferative and migratory. In glioblastoma research, current RD estimates of proliferation and migration parameters are derived from computed tomography or magnetic resonance images. However, these estimates of glioblastoma cell migration rates, modeled as a diffusion coefficient, are approximately 1-2 orders of magnitude larger than single-cell measurements in animal models of this disease. To identify possible sources for this discrepancy, we evaluated the fundamental RD simulation assumptions that cells are point-like structures that can overlap. To give cells physical size (~10 m), we used a Brownian dynamics approach that simulates individual single-cell diffusive migration, growth, and proliferation activity via a gridless, off-lattice, AB method where cells can be prohibited from overlapping each other. We found that for realistic single-cell parameter growth and migration rates, a non-overlapping model gives rise to a jammed configuration in the center of the tumor and a biased outward diffusion of cells in the tumor periphery, creating a quasi-ballistic advancing tumor front. The simulations demonstrate that a fast-progressing tumor can result from minimally diffusive cells, but at a rate that is still dependent on single-cell diffusive migration rates. Thus, modeling with the assumption of physically-grounded volume conservation can account for the apparent discrepancy between estimated and measured diffusion of GBM cells and provide a new theoretical framework that naturally links single-cell growth and migration dynamics to tumor-level progression.
肿瘤进展建模为预测肿瘤扩散行为提供了可能，有助于提高预后准确性并指导治疗方案的制定。常见的模拟方法包括连续反应扩散（RD）方法，该方法可捕捉肿瘤在时空上的平均扩散行为；以及离散的基于主体（AB）的方法，该方法可捕捉单个细胞事件，如增殖或迁移。脑癌胶质母细胞瘤（GBM）特别适合这种增殖-迁移建模方法，因为肿瘤细胞很少转移到中枢神经系统之外，而且细胞具有高度增殖性和迁移性。在胶质母细胞瘤研究中，目前对增殖和迁移参数的RD估计是从计算机断层扫描或磁共振图像中得出的。然而，这些对胶质母细胞瘤细胞迁移率的估计（建模为扩散系数）比该疾病动物模型中的单细胞测量值大约大1-2个数量级。为了找出这种差异的可能来源，我们评估了RD模拟的基本假设，即细胞是可以重叠的点状结构。为了赋予细胞物理尺寸（约10微米），我们使用了一种布朗动力学方法，该方法通过一种无网格、非晶格的AB方法模拟单个单细胞的扩散迁移、生长和增殖活动，在这种方法中细胞可以被禁止相互重叠。我们发现，对于实际的单细胞参数生长和迁移率，非重叠模型会在肿瘤中心产生堵塞构型，并在肿瘤周边导致细胞向外扩散偏向，从而形成准弹道式推进的肿瘤前沿。模拟结果表明，进展迅速的肿瘤可能由扩散极小的细胞导致，但速率仍取决于单细胞扩散迁移率。因此，基于物理的体积守恒假设进行建模可以解释GBM细胞估计扩散率与测量扩散率之间的明显差异，并提供一个新的理论框架，自然地将单细胞生长和迁移动力学与肿瘤水平的进展联系起来。
