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A novel method for the solution of convection-diffusion problems with applications to nitric oxide production and transport in vitro.

机译：一种解决对流扩散问题的新方法，并应用于一氧化氮的体外生产和运输。

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摘要

Nitric Oxide (NO) has been widely studied as the endothelial derived factor responsible for acute vasomotor responses to flow and vessel remodeling in response to chronic changes in flow. In this study we developed a steady state analytical solution to the problem of mass transport under forced convection and a dynamic/steady numerical model to investigate the production and transport of NO generated by a monolayer of cultured endothelial cells exposed to flow in a parallel plate flow chamber. The analytical solution was obtained by generalizing the method of substitution of variables in order to include any type of boundary condition. At first, an approximated velocity profile was employed to reduce the governing Partial Differential Equation (PDE) to an Ordinary Differential Equation (ODE). Subsequently, the governing PDE was reduced to a set of recursive ODEs for a generic fully developed velocity profile. The approximated ODE was reduced to a known quantum mechanical ODE and solved by hypergeometric functions. The analytical solution indicates that it may not be possible, at steady-state, to determine a priori the existence of a diffusion boundary layer. A critical ratio between length and height of the conduit for which the analytical solution applies has been developed. Numerical results are in excellent agreement with the approximated solution of the governing PDE. Numerical modeling was also used to suggest a quantitative relationship between shear stress and NO production rate. NO production was described as a combination of a basal production rate term and a shear-dependent term, which is shown to influence the nature of mass transport in proximity of the boundary. The steady state NO concentration near the endothelial surface exhibits a biphasic dependence on shear stress, in which at low flow, NO concentration decreases owing to the enhanced removal by convective transport while only at higher shear stresses does the increased production cause an increase in NO concentration. The unsteady response to step changes in flow exhibits transient fluctuations in NO that can be explained by time-dependent changes in the diffusive and convective mass transport as the concentration profile evolves.
机译：一氧化氮（NO）已被广泛研究为内皮衍生因子，负责对血管的急性血管舒缩反应和对血管的慢性变化的血管重塑。在这项研究中，我们开发了一种稳态分析解决方案，以解决强迫对流条件下的传质问题，并建立了动态​​/稳态数值模型，以研究由单层培养的内皮细胞在平行板流中暴露而产生的NO的产生和传递。室。通过概括变量的替换方法以包括任何类型的边界条件，可以得到解析解。首先，采用近似速度曲线将控制性偏微分方程（PDE）简化为常微分方程（ODE）。随后，将控制PDE简化为一组递归ODE，以生成通用的完全展开的速度曲线。近似的ODE简化为已知的量子力学ODE，并通过超几何函数求解。分析解决方案表明，在稳态下，不可能先验确定扩散边界层的存在。已经开发出适用分析溶液的导管的长度和高度之间的临界比。数值结果与控制PDE的近似解非常吻合。数值模型也被用来暗示剪切应力和NO产生速率之间的定量关系。 NO生产被描述为基础生产速率项和剪切相关项的组合，这表明会影响边界附近质量传输的性质。内皮表面附近的稳态NO浓度表现出对剪切应力的两相依赖性，其中在低流量下，由于对流传输的去除作用增强，NO浓度降低，而只有在较高的剪切应力下，产量的增加才引起NO浓度的增加。对流量阶跃变化的非稳态响应表现出NO的瞬时波动，这可以通过随着浓度分布的变化随时间变化的扩散和对流传质来解释。

著录项

  • 作者

    Fadel, Aiman Amir.;

  • 作者单位

    Drexel University.;

  • 授予单位 Drexel University.;
  • 学科 Engineering Biomedical.
  • 学位 Ph.D.
  • 年度 2009
  • 页码 134 p.
  • 总页数 134
  • 原文格式 PDF
  • 正文语种 eng
  • 中图分类
  • 关键词

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