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首页> 外文期刊>Journal of Mathematical Biology >A mixture theory model of fluid and solute transport in the microvasculature of normal and malignant tissues. II: Factor sensitivity analysis, calibration, and validation
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A mixture theory model of fluid and solute transport in the microvasculature of normal and malignant tissues. II: Factor sensitivity analysis, calibration, and validation

机译：正常和恶性组织微血管中流体和溶质传输的混合理论模型。 II：因子敏感性分析，校准和验证

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The treatment of cancerous tumors is dependent upon the delivery of therapeutics through the blood by means of the microcirculation. Differences in the vasculature of normal and malignant tissues have been recognized, but it is not fully understood how these differences affect transport and the applicability of existing mathematical models has been questioned at the microscale due to the complex rheology of blood and fluid exchange with the tissue. In addition to determining an appropriate set of governing equations it is necessary to specify appropriate model parameters based on physiological data. To this end, a two stage sensitivity analysis is described which makes it possible to determine the set of parameters most important to the model's calibration. In the first stage, the fluid flow equations are examined and a sensitivity analysis is used to evaluate the importance of 11 different model parameters. Of these, only four substantially influence the intravascular axial flow providing a tractable set that could be calibrated using red blood cell velocity data from the literature. The second stage also utilizes a sensitivity analysis to evaluate the importance of 14 model parameters on extravascular flux. Of these, six exhibit high sensitivity and are integrated into the model calibration using a response surface methodology and experimental intra- and extravascular accumulation data from the literature (Dreher et al. in J Natl Cancer Inst 98(5):335-344, 2006). The model exhibits good agreement with the experimental results for both the mean extravascular concentration and the penetration depth as a function of time for inert dextran over a wide range of molecular weights.
机译：癌性肿瘤的治疗取决于通过微循环将治疗剂通过血液输送。正常和恶性组织的脉管系统差异已经被认识到，但由于血液和与组织的流体交换的复杂流变学特性，目前还没有完全了解这些差异如何影响运输，并且在微观上质疑现有数学模型的适用性。除了确定适当的控制方程组之外，还必须根据生理数据指定适当的模型参数。为此，介绍了两阶段灵敏度分析，该分析可以确定对模型校准最重要的参数集。在第一阶段，检查流体流动方程，并使用敏感性分析来评估11个不同模型参数的重要性。在这些中，只有四个实质上影响血管内轴向流动，从而提供可以使用文献中的红细胞速度数据进行校准的易处理组。第二阶段还利用敏感性分析来评估14个模型参数对血管外通量的重要性。其中六个具有高灵敏度，并使用响应面方法和来自文献的实验性血管内和血管外蓄积数据整合到模型校准中（Dreher等人在J Natl Cancer Inst 98（5）：335-344，2006 ）。对于大分子分子量范围内的惰性右旋糖酐，平均血管外浓度和渗透深度随时间的变化，该模型与实验结果具有很好的一致性。

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