Måseide K, Rofstad E K
Institute for Cancer Research and The Norwegian Cancer Society, The Norwegian Radium Hospital, Montebello, 0310, Oslo, Norway.
Radiother Oncol. 2000 Feb;54(2):171-7. doi: 10.1016/s0167-8140(99)00154-1.
To model mathematically how potential doubling time and hypoxic cell lifetime affect the extent of chronical hypoxia in tumor tissue segments. Three capillary geometries were modeled under idealized steady state conditions.
The capillary geometries are: tissue surrounding an axial capillary, tissue enclosed by a cylindrical capillary network, and tissue enclosed by a spherical capillary network. The tissue segments are modeled as three-compartment systems, where well nourished cells proliferate near the vasculature and, in so doing, displace 'older' cells into a quiescent compartment and, ultimately into a hypoxic region. The extent of the hypoxic zone is the distance traversed by cells during their hypoxic lifetime before becoming necrotic. The steady state situation, where the necrotic cell loss equals the cell gain caused by cell proliferation was investigated.
The hypoxic fraction, HF, was found to be inversely proportional to the potential doubling time of the tumor segment, T(pot), and proportional to the hypoxic cell lifetime, T(hypox). The extent of the oxygenated zone depends only on the capillary geometry, the capillary radius, the intracapillary oxygen tension, and the tissue respiration rate. The extent of the hypoxic zone in addition depends on T(pot) and T(hypox).
Mathematical modeling of idealized steady state conditions shows that the ratio of hypoxic cell lifetime and potential doubling time, T(hypox)/T(pot), determines the hypoxic fraction, HF, in tumor segments. The extents of the oxygenated and the hypoxic zones can be predicted from the models.
通过数学建模研究潜在倍增时间和乏氧细胞寿命如何影响肿瘤组织切片中慢性乏氧的程度。在理想稳态条件下对三种毛细血管几何结构进行建模。
毛细血管几何结构包括：围绕轴向毛细血管的组织、被圆柱形毛细血管网络包围的组织以及被球形毛细血管网络包围的组织。将组织切片建模为三室系统，其中营养良好的细胞在血管附近增殖，在此过程中，将“较老”的细胞置换到静止区，并最终进入乏氧区。乏氧区的范围是细胞在其乏氧寿命期间直至坏死所经过的距离。研究了坏死细胞损失等于细胞增殖引起的细胞增加的稳态情况。
发现乏氧分数（HF）与肿瘤切片的潜在倍增时间T(pot)成反比，与乏氧细胞寿命T(hypox)成正比。富氧区的范围仅取决于毛细血管几何结构、毛细血管半径、毛细血管内氧张力和组织呼吸速率。乏氧区的范围还取决于T(pot)和T(hypox)。
理想稳态条件下的数学建模表明，乏氧细胞寿命与潜在倍增时间之比T(hypox)/T(pot)决定了肿瘤切片中的乏氧分数HF。可以从模型预测富氧区和乏氧区的范围。
