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arXiv 1801.05136physics.med-phcond-mat.soft
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浸没在半无限介质中的多层球体的质量扩散模型:在药物输送中的应用

Modelling mass diffusion for a multi-layer sphere immersed in a semi-infinite medium: application to drug delivery

Elliot J. Carr, Giuseppe Pontrelli

摘要:

我们提出了一个一般的机械模型的质量扩散的复合球放置在一个大的环境介质。多层问题是由一个系统的扩散方程耦合通过层间边界条件,如施加有限的质量电阻在球体的外表面。虽然这项工作是适用于在一个多层球的传热或传质的一般问题,分析和结果的背景下,解吸和吸收球形微胶囊的药物动力学。我们推导出一个解析解的浓度在球体和周围介质中,避免任何人为截断在有限的距离。在每个同心层的封闭形式的解决方案表示在一个适当定义的逆拉普拉斯变换,可以进行数值计算。的浓度分布和药物质量曲线在球形层和外部环境中,并在球体的表面上的传质系数的解决方案的依赖性进行了分析。

英文摘要:

We present a general mechanistic model of mass diffusion for a composite sphere placed in a large ambient medium. The multi-layer problem is described by a system of diffusion equations coupled via interlayer boundary conditions such as those imposing a finite mass resistance at the external surface of the sphere. While the work is applicable to the generic problem of heat or mass transfer in a multi-layer sphere, the analysis and results are presented in the context of drug kinetics for desorbing and absorbing spherical microcapsules. We derive an analytical solution for the concentration in the sphere and in the surrounding medium that avoids any artificial truncation at a finite distance. The closed-form solution in each concentric layer is expressed in terms of a suitably-defined inverse Laplace transform that can be evaluated numerically. Concentration profiles and drug mass curves in the spherical layers and in the external environment are presented and the dependency of the solution on the mass transfer coefficient at the surface of the sphere analyzed.

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