A number of renal physiology presentations dealt with modeling of kidney functions. They featured Departments of Mathematics, something which I find a bit intimidating:
Brendan Fry, Anita Layton
Duke University, Durham, NC
The first thing that caught my attention with this abstract was its medullary focus. Nephrologists and physiologists often give the medulla little love. It's not the part of the kidney that we biopsy (at least not what we want to get), and while it does a bunch of stuff for water and volume control, most folks only pay attention to their little piece of it.
So what does it take to model the structure of a kidney? Let's look at an example of a medullary reconstruction in the figure on the right. In this study by Pannabecker and Dantzler, segment-specific markers were used to reconstruct the medullary architecture on sections through the kidney. Cross-sectional photos were "assembled" into these tubular models going from corticomedullary junction (a) through the papilla (e). Red structures are descending thin limbs of the loop of Henle, while blue tubes represent collecting ducts.
And these are only two of the tubular structures that course through the medulla and give it a striped appearance.
So these sorts of studies give us a picture of the anatomic relationships within the medulla. Now we need to start adding what we know about functional relationships. For that, we will see the next figure from Lemley and Kriz.
In this cartoon (not as pithy as the XKCD one, huh?), some known transport properties of various segments gets thrown into the mix. This is, of course, one of the simplest diagrams from this paper.
So people have been doing this stuff for many years (that last paper is 26, the same age as my daughter). As time has passed, our understanding of both the structure and function of these areas of the medulla has improved, allowing a mathematical model to be created. The original model by Anita Layton is illustrated in the next figure. I will let you pull the paper if you want the key to the abbreviations.
In this version, certain assumptions were made about the regions in which these segments lie.
The new model adds to this 2011 version, with further refinements about the spatial relationships and how oxygen would traverse the interstitial goo at various levels. They hope to work further functions into their models in the near future, things like the nitric oxide system and acid-base handling.
I have not done this paper justice; I am merely an MD, at best a humble biologist. I can appreciate how an elegant model can direct new hypotheses and future experiments. I'm afraid, though, that when I model a kidney it will be something like my final figure...