Sohrabi Salman, Saidi Mohammad Said, Saadatmand Maryam, Banazadeh Mohamad Hossein, Firoozabadi Bahar
Department of Mechanical Engineering, Sharif University of Technology, Tehran, Iran.
Department of Mechanical Engineering, Sharif University of Technology, Tehran, Iran.
Math Biosci. 2014 Dec;258:44-56. doi: 10.1016/j.mbs.2014.08.010. Epub 2014 Sep 16.
The urine formation and excretion system have long been of interest for mathematicians and physiologists to elucidate the obscurities within the process happens in renal tissue. In this study, a novel three-dimensional approach is utilized for modeling the urine concentrating mechanism in rat renal outer medulla which is essentially focused on demonstrating the significance of tubule's architecture revealed in anatomic studies and physiological literature. Since nephrons and vasculatures work interdependently through a highly structured arrangement in outer medulla which is dominated by vascular bundles, a detailed functional unit is proposed based on this specific configuration. Furthermore, due to relatively lesser influence of vasa recta on interstitial medullary osmolality and osmotic gradients as well as model structure simplicity, central core assumption is employed. The model equations are based on three spatial dimensional mass, momentum and species transport equations as well as standard expressions for solutes and water transmural transport. Our model can simulate preferential interactions between different tubules and it is shown that such interactions promote solute cycling and subsequently, enhance urine-concentrating capability. The numerical results are well consistent with tissue slice experiments and moreover, our model predicts more corticomedullary osmolality gradient in outer medulla than previous influential 1-D simulations.
长期以来，尿液生成和排泄系统一直吸引着数学家和生理学家，以阐明肾组织中发生的过程中的模糊之处。在本研究中，一种新颖的三维方法被用于模拟大鼠肾外髓质中的尿液浓缩机制，其主要侧重于证明解剖学研究和生理学文献中揭示的肾小管结构的重要性。由于肾单位和脉管系统通过外髓质中由血管束主导的高度结构化排列相互依存地工作，基于这种特定构型提出了一个详细的功能单元。此外，由于直小血管对髓质间质渗透压和渗透梯度的影响相对较小，以及模型结构简单，采用了中心核假设。模型方程基于三维空间的质量、动量和物质传输方程以及溶质和水跨膜传输的标准表达式。我们的模型可以模拟不同肾小管之间的优先相互作用，结果表明这种相互作用促进溶质循环，进而增强尿液浓缩能力。数值结果与组织切片实验非常一致，而且，我们的模型预测外髓质中的皮质髓质渗透压梯度比以前有影响力的一维模拟结果更大。
