Department of Mathematics, University of Akron, Akron, OH 44325-4002, USA.
Ann Biomed Eng. 2013 Jan;41(1):53-67. doi: 10.1007/s10439-012-0626-0. Epub 2012 Aug 10.
We develop a mathematical model of nanoparticles depositing onto and penetrating into a biofilm grown in a parallel-plate flow cell. We carry out deposition experiments in a flow cell to support the modeling. The modeling and the experiments are motivated by the potential use of polymer nanoparticles as part of a treatment strategy for killing biofilms infecting the deep passages in the lungs. In the experiments and model, a fluid carrying polymer nanoparticles is injected into a parallel-plate flow cell in which a biofilm has grown over the bottom plate. The model consists of a system of transport equations describing the deposition and diffusion of nanoparticles. Standard asymptotic techniques that exploit the aspect ratio of the flow cell are applied to reduce the model to two coupled partial differential equations. We perform numerical simulations using the reduced model. We compare the experimental observations with the simulation results to estimate the nanoparticle sticking coefficient and the diffusion coefficient of the nanoparticles in the biofilm. The distributions of nanoparticles through the thickness of the biofilm are consistent with diffusive transport, and uniform distributions through the thickness are achieved in about four hours. Nanoparticle deposition does not appear to be strongly influenced by the flow rate in the cell for the low flow rates considered.
我们开发了一个数学模型，用于描述纳米颗粒在平行板流动池中生长的生物膜上的沉积和穿透过程。我们在流动池中进行沉积实验，以支持模型的建立。该模型和实验的动机是将聚合物纳米颗粒用作治疗策略的一部分，以杀死感染肺部深部通道的生物膜。在实验和模型中，携带聚合物纳米颗粒的流体被注入到一个平行板流动池中，生物膜已经在底部板上生长。模型由一组描述纳米颗粒沉积和扩散的传输方程组成。利用流动池的纵横比的标准渐近技术被应用于将模型简化为两个耦合的偏微分方程。我们使用简化模型进行数值模拟。我们将实验观察结果与模拟结果进行比较，以估计纳米颗粒在生物膜中的附着系数和扩散系数。纳米颗粒在生物膜厚度方向上的分布与扩散传输一致，并且在大约四个小时内实现了厚度方向上的均匀分布。对于所考虑的低流速，纳米颗粒的沉积似乎不受细胞中流速的强烈影响。
