Department of Mechanical Engineering, K. N. Toosi University of Technology, Tehran, Iran.
Department of Electrical and Computer Engineering, University of Waterloo, Waterloo, ON, Canada.
Sci Rep. 2022 Aug 26;12(1):14582. doi: 10.1038/s41598-022-18723-6.
We present comprehensive mathematical modeling of radiopharmaceutical spatiotemporal distributions within vascularized solid tumors. The novelty of the presented model is at mathematical level. From the mathematical viewpoint, we provide a general modeling framework for the process of radiopharmaceutical distribution in the tumor microenvironment to enable an analysis of the effect of various tumor-related parameters on the distribution of different radiopharmaceuticals. We argue that partial differential equations (PDEs), beyond conventional methods, including ODE-based kinetic compartment modeling, can be used to evaluate radiopharmaceutical distribution in both time and space. In addition, we consider the spatially-variable dynamic structure of tumor microvascular networks to simulate blood flow distribution. To examine the robustness of the model, the effects of microvessel density (MVD) and tumor size, as two important factors in tumor prognosis, on the radiopharmaceutical distribution within the tumor are investigated over time (in the present work, we focus on the radiopharmaceutical [F]FDG, yet the framework is broadly applicable to radiopharmaceuticals). Results demonstrate that the maximum total uptake of [F]FDG at all time frames occurs in the tumor area due to the high capillary permeability and lack of a functional lymphatic system. As the MVD of networks increases, the mean total uptake in the tumor is also enhanced, where the rate of diffusion from vessel to tissue has the highest contribution and the rate of convection transport has the lowest contribution. The results of this study can be used to better investigate various phenomena and bridge a gap among cancer biology, mathematical oncology, medical physics, and radiology.
我们提出了一种综合的数学模型，用于描述血管化实体肿瘤内放射性药物的时空分布。所提出模型的新颖之处在于数学层面。从数学角度来看，我们提供了一个放射性药物在肿瘤微环境中分布过程的通用建模框架，以分析各种与肿瘤相关的参数对不同放射性药物分布的影响。我们认为，偏微分方程（PDE）可以超越传统方法，包括基于 ODE 的动力学室模型，用于评估放射性药物在时间和空间中的分布。此外，我们还考虑了肿瘤微血管网络的空间变化动态结构，以模拟血流分布。为了检验模型的稳健性，我们研究了微血管密度（MVD）和肿瘤大小这两个对肿瘤预后至关重要的因素对肿瘤内放射性药物分布的随时间的影响（在本工作中，我们专注于放射性药物[F]FDG，但该框架广泛适用于放射性药物）。结果表明，由于高毛细血管通透性和缺乏功能性淋巴管系统，[F]FDG 的最大总摄取量始终发生在肿瘤区域。随着网络 MVD 的增加，肿瘤内的平均总摄取量也会增强，其中从血管到组织的扩散速率的贡献最大，而对流传输速率的贡献最小。这项研究的结果可用于更好地研究各种现象，并弥合癌症生物学、数学肿瘤学、医学物理学和放射学之间的差距。
