School of Mathematical Sciences, Queensland University of Technology (QUT), Brisbane, Australia.
Istituto per le Applicazioni del Calcolo - CNR Via dei Taurini 19, Rome 00185, Italy.
Math Biosci. 2018 Sep;303:1-9. doi: 10.1016/j.mbs.2018.04.004. Epub 2018 Apr 12.
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.
我们提出了一种复合球体在大环境介质中扩散的通用力学模型。多层问题通过扩散方程系统描述，通过层间边界条件耦合，例如在球体外部表面施加有限质量阻力。虽然该工作适用于多层球中热或质量传递的一般问题，但分析和结果是在脱附和吸收球形微胶囊的药物动力学背景下提出的。我们推导出了球体和周围介质中浓度的解析解，避免了在有限距离处的任何人为截断。每个同心层中的封闭形式解表示为适定的逆拉普拉斯变换，可以数值评估。给出了球形层和外部环境中浓度分布和药物质量曲线，并分析了表面质量转移系数对解的依赖性。
