In a recent modelling study we extended an existing model of afferent arteriole autoregulation (originally presented by Feldberg et al.) by adding an explicit glomerulus and calculating model SNGFR in addition to afferent blood and plasma flows.
See this description of our extensions, the updated model equations, and a number of plots. The source code is available under the BSD 3-Clause license.
"Dominant factors that govern pressure natriuresis in diuresis and antidiuresis: a mathematical model" (a collaboration with Anita T. Layton) has been accepted by AJP Renal and is now available online in advance of final publication.
Building on observations in my previous modelling study, we investigated how pressure natriuresis—in both diuresis and antidiuresis—can be influenced by changes in medullary blood flow autoregulation and by inhibition of transport in the proximal convoluted tubule (PCT). We found that inhibited reabsorption in the model PCT (to degrees consistent with experimental measurements) is sufficient to stimulate a pressure natriuresis.
The challenge here is that there is insufficient experimental data to quantify the pressure-dependent reabsorption inhibition in the PCT, but it is precisely this response that appears to play the single largest role in driving pressure natriuresis. Our modelling study establishes a reasonable benchmark for this quantitative relationship, which can be applied to future whole-kidney models.
My article "Hormonal regulation of salt and water excretion: a mathematical model of whole-kidney function and pressure-natriuresis" (a collaboration with S. Randall Thomas), has been published in AJP Renal. It was also selected as the subject for an Editorial Focus essay, "Advancement in integrated models of renal function: closing the gap between simulation and real life", written by Branko Braam.
We present a whole-kidney model that incorporates glomerular and tubular function, differentiates cortical and medullary function, and describes vascular and reabsorptive characteristics of the kidney. Model simulations explore the regulation of renal function by aldosterone, angiotensin II, and antidiuretic hormone (ADH), and also the inhibition of sodium reabsorption in response to the administration of a thiazide and of amiloride. This model of integrated renal function is quite successful in simulating renal function, although there are of course several caveats. The article also provides a broad survey of both renal modelling and the experimental literature.
In addition to the manuscript itself, interactive versions of a key figure—a comparison of model excretion rates against data from a number of experimental studies of acute pressure natriuresis in the rat—allow the viewer to examine each data series in isolation and refer back to the original articles.