用于模拟不同血管结构缺氧肿瘤中氧气分布的模型。

A model to simulate the oxygen distribution in hypoxic tumors for different vascular architectures.

机构信息

Department of Medical Physics in Radiation Oncology, German Cancer Research Center (DKFZ), Heidelberg 69120, Germany.

出版信息

Med Phys. 2013 Aug;40(8):081703. doi: 10.1118/1.4812431.

DOI:10.1118/1.4812431

PMID:23927300

Abstract

PURPOSE

As hypoxic cells are more resistant to photon radiation, it is desirable to obtain information about the oxygen distribution in tumors prior to the radiation treatment. Noninvasive techniques are currently not able to provide reliable oxygenation maps with sufficient spatial resolution; therefore mathematical models may help to simulate microvascular architectures and the resulting oxygen distributions in the surrounding tissue. Here, the authors present a new computer model, which uses the vascular fraction of tumor voxels, in principle measurable noninvasively in vivo, as input parameter for simulating realistic PO2 histograms in tumors, assuming certain 3D vascular architectures.

METHODS

Oxygen distributions were calculated by solving a reaction-diffusion equation in a reference volume using the particle strength exchange method. Different types of vessel architectures as well as different degrees of vascular heterogeneities are considered. Two types of acute hypoxia (ischemic and hypoxemic) occurring additionally to diffusion-limited (chronic) hypoxia were implemented as well.

RESULTS

No statistically significant differences were observed when comparing 2D- and 3D-vessel architectures (p>0.79 in all cases) and highly heterogeneously distributed linear vessels show good agreement, when comparing with published experimental intervessel distance distributions and PO2 histograms. It could be shown that, if information about additional acute hypoxia is available, its contribution to the hypoxic fraction (HF) can be simulated as well. Increases of 128% and 168% in the HF were obtained when representative cases of ischemic and hypoxemic acute hypoxia, respectively, were considered in the simulations.

CONCLUSIONS

The presented model is able to simulate realistic microscopic oxygen distributions in tumors assuming reasonable vessel architectures and using the vascular fraction as macroscopic input parameter. The model may be used to generate PO2 histograms, which are needed as input in models predicting the radiation response of hypoxic tumors.

摘要

目的

由于缺氧细胞对光子辐射更具抵抗力，因此在放射治疗前，需要获得肿瘤内氧气分布的信息。目前，非侵入性技术无法提供具有足够空间分辨率的可靠氧合图；因此，数学模型可能有助于模拟微血管结构和周围组织中的氧气分布。在这里，作者提出了一种新的计算机模型，该模型使用肿瘤体素的血管分数作为输入参数，假设特定的 3D 血管结构，模拟肿瘤中真实的 PO2 直方图。

方法

通过使用粒子强度交换方法在参考体积中求解反应-扩散方程来计算氧气分布。考虑了不同类型的血管结构和不同程度的血管异质性。还实现了除扩散限制（慢性）缺氧之外的两种类型的急性缺氧（缺血性和低氧性）。

结果

当比较 2D 和 3D 血管结构时，没有观察到统计学上的显著差异（在所有情况下 p>0.79），并且高度异质分布的线性血管与公布的实验血管间距离分布和 PO2 直方图具有良好的一致性。结果表明，如果有关于额外急性缺氧的信息，则可以模拟其对缺氧分数（HF）的贡献。当在模拟中考虑代表性的缺血性和低氧性急性缺氧病例时，HF 增加了 128%和 168%。