Centre for Mathematical Medicine and Biology, School of Mathematical Sciences, University of Nottingham, University Park, Nottingham NG7 2RD, UK.
Placenta. 2010 Jan;31(1):44-52. doi: 10.1016/j.placenta.2009.11.003. Epub 2009 Nov 27.
We present a mathematical model for maternal blood flow in a placental circulatory unit (a placentone), describing flow of maternal blood via Darcy's law and steady advective transport of a dissolved nutrient. The method of images and computational integration along streamlines are employed to find flow and solute concentration distributions, which are illustrated for a range of governing system parameters. The model shows how the calibre of the basal vessels can be a dominant determinant of the maternal blood flow rate through the placentone, given a driving pressure difference between the spiral arteries and decidual veins. The model supports the hypothesis that basal veins are located on the periphery of the placentone in order to optimise delivery of nutrients and suggests the existence of an optimal volume fraction of villous tissue.
我们提出了一个胎盘循环单位（胎盘单位）中母体血液流动的数学模型，描述了母体血液通过达西定律的流动和溶解营养物质的稳定对流输送。采用镜像法和流线计算积分来寻找流动和溶质浓度分布，并针对一系列控制体系参数进行了说明。该模型表明，在螺旋动脉和蜕膜静脉之间存在压力差的情况下，基底血管的口径可以成为决定胎盘单位中母体血流速率的主要因素。该模型支持这样一种假设，即基底静脉位于胎盘单位的外围，以优化营养物质的输送，并表明绒毛组织的最佳体积分数的存在。
