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On Mathematical Analysis of Active Drug Transport Coupled With Flow-Induced Diffusion in Blood Vessels
IEEE Transactions on NanoBioscience ( IF 3.9 ) Pub Date : 2020-11-17 , DOI: 10.1109/tnb.2020.3038635
Hamidreza Arjmandi , Mohammad Zoofaghari , Seyed Vahid Rouzegar , Mladen Veletic , Ilangko Balasingham

Blood vessels are flow-induced diffusive molecular channels equipped with transport mechanisms across their walls for conveying substances between the organs in the body. Mathematical modeling of the blood vessel as a molecular transport channel can be used for the characterization of the underlying processes and higher-level functions in the circulatory system. Besides, the mathematical model can be utilized for designing and realizing nano-scale molecular communication systems for healthcare applications including drug delivery systems. In this paper, a continuous-time Markov chain framework is proposed to simply model active transport mechanisms e.g. transcytosis, across the single-layered endothelial cells building the inner vessel wall. Correspondingly, a general homogeneous boundary condition over the vessel wall is introduced. Coupled with the derived boundary condition, the flow-induced diffusion problem in an ideal vessel structure with a cylindrical shape is accurately formulated which takes into account variation in all three dimensions. The corresponding concentration Green’s function is analytically derived in terms of a convergent infinite series. Particle-based simulation results confirm the proposed analysis. Also, the effects of system parameters on the concentration Green’s function are examined.

中文翻译:

血管内主动药物转运与流动诱导扩散耦合的数学分析

血管是流动诱导的扩散分子通道,其壁上装有运输机制,用于在体内器官之间输送物质。血管作为分子传输通道的数学模型可用于表征循环系统中的潜在过程和更高级别的功能。此外,该数学模型可用于设计和实现用于医疗保健应用的纳米级分子通信系统,包括药物输送系统。在本文中,提出了一个连续时间马尔可夫链框架来简单地模拟主动运输机制,例如跨构建内血管壁的单层内皮细胞​​的胞吞作用。相应地,引入了血管壁上的一般均匀边界条件。再加上导出的边界条件,在一个理想的圆柱形容器结构中,流动引起的扩散问题被精确地公式化,它考虑了所有三个维度的变化。对应的浓度格林函数是根据收敛无穷级数解析导出的。基于粒子的模拟结果证实了建议的分析。此外,还检查了系统参数对浓度格林函数的影响。基于粒子的模拟结果证实了建议的分析。此外,还检查了系统参数对浓度格林函数的影响。基于粒子的模拟结果证实了建议的分析。此外,还检查了系统参数对浓度格林函数的影响。
更新日期:2021-01-01
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