Mollee T R, Bracken A J
Department of Mathematics, University of Queensland, Brisbane, 4072, Queensland, Australia.
Bull Math Biol. 2007 Aug;69(6):1887-907. doi: 10.1007/s11538-007-9197-x. Epub 2007 Apr 25.
A one-dimensional model of solute transport through the stratum corneum is presented. Solute is assumed to diffuse through lipid bi-layers surrounding impermeable corneocytes. Transverse diffusion (perpendicular to the skin surface) through lipids separating adjacent corneocytes, is modeled in the usual way. Longitudinal diffusion (parallel to the skin surface) through lipids between corneocyte layers, is modeled as temporary trapping of solute, with subsequent release in the transverse direction. This leads to a linear equation for one-dimensional transport in the transverse direction. The model involves an arbitrary function whose precise form is uncertain. For a specific choice of this function, closed form expressions for the Laplace transform of solute out-flux at the inner boundary, and for the time lag are obtained in the case that a constant solute concentration is maintained at the outer skin surface, with the inner boundary of the stratum corneum kept at zero concentration, and with the stratum corneum initially free of solute.
本文提出了一种溶质通过角质层的一维传输模型。假设溶质通过围绕不可渗透角质形成细胞的脂质双分子层扩散。通过分隔相邻角质形成细胞的脂质进行的横向扩散（垂直于皮肤表面），采用常规方式建模。通过角质形成细胞层之间的脂质进行的纵向扩散（平行于皮肤表面），被建模为溶质的暂时捕获，随后在横向方向释放。这导致了横向一维传输的线性方程。该模型涉及一个精确形式不确定的任意函数。对于该函数的特定选择，在皮肤外表面保持恒定溶质浓度、角质层内边界保持零浓度且角质层初始无溶质的情况下，获得了内边界处溶质流出通量的拉普拉斯变换以及时间滞后的封闭形式表达式。
