The goal of this paper is to investigate the validity of a hybrid embedded/homogenized in-silico approach for modeling perfusion through solid tumors. The rationale behind this novel idea is that only the larger blood vessels have to be explicitly resolved while the smaller scales of the vasculature are homogenized. As opposed to typical discrete or fully-resolved 1D-3D models, the required data can be obtained with in-vivo imaging techniques since the morphology of the smaller vessels is not necessary. By contrast, the larger vessels, whose topology and structure is attainable non-invasively, are resolved and embedded as one-dimensional inclusions into the three-dimensional tissue domain which is modeled as a porous medium. A sound mortar-type formulation is employed to couple the two representations of the vasculature. We validate the hybrid model and optimize its parameters by comparing its results to a corresponding fully-resolved model based on several well-defined metrics. These tests are performed on a complex data set of three different tumor types with heterogeneous vascular architectures. The correspondence of the hybrid model in terms of mean representative elementary volume blood and interstitial fluid pressures is excellent with relative errors of less than 4%. Larger, but less important and explicable errors are present in terms of blood flow in the smaller, homogenized vessels. We finally discuss and demonstrate how the hybrid model can be further improved to apply it for studies on tumor perfusion and the efficacy of drug delivery.

中文翻译：

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混合嵌入式/均质实体瘤灌注模型的验证和参数优化

本文的目的是研究混合嵌入式/均质计算机模拟方法对实体瘤灌注建模的有效性。这个新颖想法的基本原理是，只有较大的血管必须明确分辨，而较小的脉管系统才是均质的。与典型的离散或完全解析的1D-3D模型相反，可以使用体内成像技术获得所需的数据，因为不需要较小血管的形态。相比之下，较大的血管（其拓扑结构和结构可通过非侵入性方式获得）被解析并作为一维包含物嵌入到以多孔介质为模型的三维组织域中。健全的砂浆型配方用于耦合脉管系统的两种表示。我们验证混合模型并通过将其结果与基于几个明确定义的指标的相应完全解析模型进行比较来优化其参数。这些测试是在具有不同血管结构的三种不同肿瘤类型的复杂数据集上执行的。混合模型在平均代表基本血容量和组织液压力方面的对应性极佳，相对误差小于4％。就较小，均质的血管中的血流而言，存在较大但较不重要的可解释错误。我们最终讨论并演示了如何进一步改进混合模型，以将其应用于肿瘤灌注和药物递送功效的研究。