A model framework for computer simulation of overall renal function

Numerical simulation of the vascular structure dependence of blood flow in the kidney

A numerical simulation was performed to clarify renal blood flow determination by the vascular structures. Large and small vessels were modeled as symmetric and asymmetric branching vessels, respectively, with simple geometries to parameterize the vascular structures. Modeling individual vessels as straight pipes, Murray's law was used to determine the vessel diameters. Blood flow in the vascular structure was calculated by network analysis based on Hagen-Poiseuille's law. Blood flow simulations for a vascular network segment demonstrated that blood flow rate and pressure vary within the same-generation vessels because of an asymmetric vessel branch while they generally tend to decrease with vessel diameter; thus, the standard deviation of flow rate relative to the mean (relative standard deviation [RSD]) increased from 0.4 to 1.0 when the number of the daughter vessels increased from 3 to 10. Blood flow simulations for an entire vascular network of a kidney showed that the vessel number and branching style, rather than Strahler order, are major parameters in successfully reproducing renal blood flow measured in published experiments. The entire vascular network could generate variation in the physiological flow rate in afferent arterioles at 0.2-0.38 in RSD, which is at least compatible with 0.16 by diameter variation within the same-generation vessels.

Hormonal regulation of salt and water excretion: a mathematical model of whole kidney function and pressure natriuresis

We present a lumped-nephron model that explicitly represents the main features of the underlying physiology, incorporating the major hormonal regulatory effects on both tubular and vascular function, and that accurately simulates hormonal regulation of renal salt and water excretion. This is the first model to explicitly couple glomerulovascular and medullary dynamics, and it is much more detailed in structure than existing whole organ models and renal portions of multiorgan models. In contrast to previous medullary models, which have only considered the antidiuretic state, our model is able to regulate water and sodium excretion over a variety of experimental conditions in good agreement with data from experimental studies of the rat. Since the properties of the vasculature and epithelia are explicitly represented, they can be altered to simulate pathophysiological conditions and pharmacological interventions. The model serves as an appropriate starting point for simulations of physiological, pathophysiological, and pharmacological renal conditions and for exploring the relationship between the extrarenal environment and renal excretory function in physiological and pathophysiological contexts.

Long-term mathematical model involving renal sympathetic nerve activity, arterial pressure, and sodium excretion

This paper presents a physiological long-term model of the cardiovascular system. It integrates the previous models developed by Guyton, Uttamsingh and Coleman. Additionally it introduces mechanisms of direct effects of the renal sympathetic nerve activity (rsna) on tubular sodium reabsorption and renin secretion in accordance with experimental data from literature. The resulting mathematical model constitutes the first long-term model of the cardiovascular system accounting for the effects of rsna on kidney functions in such detail. The objective of developing such a model is to observe the consequences of long-term rsna increase and impairment of rsna inhibition under volume loading. This model provides an understanding of the rsna-related mechanisms, which cause mean arterial pressure increase in hypertension and total sodium amount increase (sodium retention) in congestive heart failure, nephrotic syndrome and cirrhosis.

On the viability of a physiological system. Regulation of potassium by aldosterone

Physiological systems maintain their variables within limits through regulatory processes. We have studied potassium regulation on the basis of the viability theory. The viability kernel is determined by taking into account the constraints of the variables of the dynamical system, i.e. the set of initial states for which there exists at least one viable trajectory. The set of regulations which maintain the viability of the physiological system is also determined. Finally, we investigate the influence of various strategies that allow the choice of one control among the viable regulations.

The effect of cancer on the spin-lattice relaxation time of mouse blood and tissue

Spin-lattice relaxation time measurements were made on the muscle, heart, kidneys, spleen, liver, brain and blood of both normal mice and those injected with Sarcoma-180. As well as a marked increase in the relaxation time of the tumour itself, mice injected with Sarcoma-180 showed a rise in the kidney relaxation time, along with blood relaxation times which were often either above or below the range found in normal mice. Correlation coefficients for the relaxation times of the various organs were calculated and found to be very sensitive to the physiological state of the animal. For healthy mice, the correlations were reasonably high, but even mild stress decreased the correlations, whilst the presence of cancer almost completely destroyed the correlations. These findings are all consistent with the hypothesis that cancer affects the water regulatory system of the animal as a whole.