Department of Mathematics, Duke University, Box 90320, Durham, NC, 27708-0320, USA,
Bull Math Biol. 2013 Dec;75(12):2551-74. doi: 10.1007/s11538-013-9907-5. Epub 2013 Oct 9.
We have developed a mathematical model of the rat's renal hemodynamics in the nephron level, and used that model to study flow control and signal transduction in the rat kidney. The model represents an afferent arteriole, glomerular filtration, and a segment of a short-loop nephron. The model afferent arteriole is myogenically active and represents smooth muscle membrane potential and electrical coupling. The myogenic mechanism is based on the assumption that the activity of nonselective cation channels is shifted by changes in transmural pressure, such that elevation in pressure induces vasoconstriction, which increases resistance to blood flow. From the afferent arteriole's fluid delivery output, glomerular filtration rate is computed, based on conservation of plasma and plasma protein. Chloride concentration is then computed along the renal tubule based on solute conservation that represents water reabsorption along the proximal tubule and the water-permeable segment of the descending limb, and chloride fluxes driven by passive diffusion and active transport. The model's autoregulatory response is predicted to maintain stable renal blood flow within a physiologic range of blood pressure values. Power spectra associated with time series predicted by the model reveal a prominent fundamental peak at ∼165 mHz arising from the afferent arteriole's spontaneous vasomotion. Periodic external forcings interact with vasomotion to introduce heterodynes into the power spectra, significantly increasing their complexity.
我们开发了一个在肾小管水平上大鼠肾脏血液动力学的数学模型,并利用该模型研究了大鼠肾脏中的流量控制和信号转导。该模型代表了入球小动脉、肾小球滤过和短环肾小管的一段。模型的入球小动脉具有肌源性活性,代表平滑肌膜电位和电耦合。肌源性机制基于这样一种假设,即非选择性阳离子通道的活性通过跨壁压力的变化而移位,使得压力升高引起血管收缩,从而增加对血流的阻力。根据血浆和血浆蛋白的守恒,从入球小动脉的液体输送输出计算肾小球滤过率。然后根据溶质守恒计算沿肾小管的氯离子浓度,溶质守恒代表沿近端小管和下降支的水通透段的水重吸收,以及被动扩散和主动转运驱动的氯离子通量。该模型的自动调节反应预计将在血压值的生理范围内维持稳定的肾血流量。模型预测的时间序列的功率谱揭示了一个显著的基本峰,约 165 mHz,源于入球小动脉的自发性血管运动。周期性的外部强迫与血管运动相互作用,将差频引入功率谱中,显著增加了其复杂性。