"What makes killing wrong?" ask Sinnott-Armstrong and Miller. Not the loss of life or consciousness, but the loss of all remaining abilities. It's an interesting proposition, whose practical consequences they outline with regards to organ donation. I'm somewhat envious of this work, because it deals with fundamental concepts we're all familiar with and situations whose complexities we can all appreciate. Almost anyone could read this paper and appreciate the arguments and conclusions.

Meanwhile, other fields of science continue to pursue knowledge on smaller and smaller scales, at higher and higher levels of precision. As per the oft-used quote (un-attributed, to the best of my knowledge): "you learn more and more about less and less, until you know everything about nothing."

Juxta-medullary nephrons are consistently found to have higher filtration rates than superficial nephrons. Is this due to the underlying anatomy of the cortical radial artery, from which the juxta-medullary afferent arterioles branch before the superficial arterioles? Is it due to anatomical differences in the glomeruli, such as length, surface area or permeability? Or is it perhaps a matter of differences in the regulation of glomerular blood flow?

Due in part to the physical difficulty of observing juxta-medullary glomeruli without damaging the kidney, this is not an easy question to answer. And indeed, I have been unable to find any experimental results that directly address this issue. The most relevant papers that I have been able to find detail studies of the filtration rates in superficial and juxta-medullary nephrons, without investigation of the underlying cause(s).

• Glomerular filtration in single nephrons (Wright and Giebisch, 1972) is a great review article with a wealth of references to experimental data. Perhaps the most pertinent sentence is: "At this time, therefore, a role for redistribution of SNGFR within the kidney during natriuretic states is not established. Natriuresis can occur without redistribution; however, the disproportionate increases in superficial SNGFR seen in some rat experiments seem to be real changes."
• Heterogeneity of Nephron Function (1977) is another great review article with a lot of useful data and critical evaluations of a wide range of experimental studies. They make a key observation: "In addition, all direct measurements of juxta-medullary nephron SNGFR have been obtained from young rats or desert rodents since the extrarenal part of the papilla is more readily accessi­ble to micropuncture in the immature animal than in the adult. Whether these values are similar in adult rats has been evaluated with more indirect estimates of SNGFR."
• Glomerular blood flow (1990) is another great source of experimental references and data (such as Table 3B).
• Functional Heterogeneity of Nephrons II. Filtration Rates, Intraluminal Flow Velocities and Fractional Water Reabsorption (1969) provides mean SNGFRs for superficial, mid- cortical and juxta-medullary nephrons.
• The companion article, Functional Heterogeneity of Nephrons I. Intraluminal Flow Velocities (1969) is also interesting, and points to yet another interesting study: Renal hemodynamic factors in congestive heart failure (1966).

The (non-definitive) answer seems to be that redistribution of SNGFR is rarely and inconsistently observed in adult models, and so the safest modelling assumption is to assume a constant (or near-constant) ratio of juxta-medullary to superficial SNGFR in the range 1.5–2.0.

Other papers that consider the distribution of SNGFR between the superficial and deep cortex include:

• Micropuncture studies on the filtration rate of single superficial and juxtamedullary glomeruli in the rat kidney (1968), which describes the bewildering observation that in response to a high-sodium diet, the rats under observation showed almost a two-fold increase in superficial SNGFR and almost a four-fold decrease in juxta-medullary SNGFR.
• Function of juxtamedullary nephrons in normotensive and chronically hypertensive rats (1969) observes that unilateral Goldblatt hypertension produced a slight increase in total kidney GFR, but without a change in superficial SNGFR.
• Sodium Metabolism and Intrarenal Distribution of Nephron Glomerular Filtration Rates in the Unanesthetized Rat (1974) addresses an earlier study where "anesthesia may have blunted a physiological response" and concludes that "this study supports the view that dietary sodium does not affect the intrarenal distribution of nephron filtration rates."
• A micropuncture study of renal salt and water retention in chronic bile duct obstruction (1975), in contrast, states "single nephron filtration fraction, calculated from measurements of efferent arteriolar and arterial hematocrits, was significantly elevated in the cortical nephrons, even though whole kidney filtration fraction was the same as in normal rats."
• Renal handling of sodium and water in the hypothyroid rat: Clearance and micropuncture studies (1972) showed that "superficial single nephron filtration rate was reduced proportionately to the decrease in total filtration rate in the hypothyroid rats. The data also suggest that the observed decrease in glomerular filtration rate in the hypothyroid animals is not caused by a decrease in the number of functioning nephrons and that the observed increase in sodium and water excretion is not caused by a redistribution of filtrate from juxtamedullary to superficial nephrons."
• Effect of Dietary Sodium Intake on the Intrarenal Distribution of Nephron Glomerular Filtration Rates in the Rat (1973) comes to the same conclusion: "These variations in dietary sodium intake appeared to have no detectable effect on the intrarenal SNGFR distribution."
• Abnormal relationship between sodium excretion and hypertension in spontaneously hypertensive rats (1975) likewise agrees: "... indicating that no significant intrarenal GFR redistribution occurs in SH [spontaneous hypertension] following an acute hypertonic saline load."
• The influence of tubulo-glomerular feedback on the autoregulation of filtration rate in superficial and deep glomeruli (1984) has great data and figures, except that the results were obtained from young Sprague Dawley rats, and as noted in several review articles, it appears likely that structural changes with age modify the response of SNGFR distribution.
• Redistribution of glomerular filtration and renal plasma flow in CNS-induced natriuresis (1986) shows an increase in the ratio between inner-cortical and outer- cortical SNGFR with the infusion of hypertonic sodium chloride solution into the third cerebral ventricle (Table 2 and Figure 2). I could not determine if these results were obtained from young or adult rats.
• Nephron functional heterogeneity in the postobstructive kidney (1975) showed evidence of "redistribution of nephron function after relief of chronic, rather than acute, obstruction", which may be due to severe structural damage in the chronic condition.
• Isotonic saline loading and intrarenal distribution of glomerular filtration in dogs (1972) indicates "that a redistribution of glomerular filtration towards SUP [superficial] nephrons is not responsible for the natriuresis observed in these conditions. This finding is also in agreement with the data which demonstrate that the vasodilatation occurring in the kidney following isotonic saline loading is observed throughout the whole cortex."
• Evidence for redistribution of filtrate among nephrons after beta-adrenergic stimulation and blockade (1974) is a study that does show evidence of SNGFR redistribution: "Total kidney GFR did not change after both substances, whereas superficial nephron GFR increased after propranolol by 35% and decreased after isoprenaline by 35%. A redistribution of glomerular filtration rates among nephrons therefore must have occured with a shift of the GFR to deep nephrons after isoprenaline and to superficial nephrons after propranolol."
• Détermination du taux individuel de filtration glomérulaire des néphrons accessibles et inaccessibles à la microponction (1970) demonstrates a careful refinement to Hanssen's technique of estimating SNGFRs in nephrons that are inaccessible to micropuncture. Superficial and juxta-medullary SNGFRs were measured in non- diuretic rats (29.1 and 40.1 nL/min, respectively).
• Étude chez le rat des variations du débit individuel de filtration glomérulaire des néphrons superficiels et profonds en fonction de l'apport sodé (1970) is another study by the same authors, who determined that "the increase of the GFR of the whole kidney during salt loading was due to an increase of SGFR of all the nephrons. However, the increase of SGFR was more important for the superficial ones and the ratio SGFR superficial nephrons/SGFR juxtamedullary nephrons which was 0.7 in the normal rats reached 1.0 in the salt-loaded rats, indicating that there was no more functional heterogeneity of nephrons during our salt loadings." This variation is compared to the sodium-dependent intra-renal distribution of renin that has been observed in other studies.
• Micropuncture study of superficial and juxtamedullary nephrons in the rat (1970) found juxta- medullary SNGFRs to be about double the superficial SNGFRs (60.2 and 25.6 nL/min, respectively).
• Effect of saline infusion on superficial and juxtamedullary nephrons in the rat (1971) observes that superficial nephrons appeared to participate to a greater degree than juxtamedullary nephrons in the response to acute volume expansion.
• Effect of sodium balance on intrarenal distribution of blood flow in normal man (1970) is a rare study of the intra-renal distribution of blood flow in humans, but I cannot say for sure whether it is directly relevant, since I do not know what the "most rapid and second most rapid flow compartments" are.

On a side note, I'm happy to finally cite two papers by Christian de Rouffignac, which were published in French.

It's funny how the mind works. The placebo effect remains an unknowable mystery, where the body somehow compensates for an expected effect even in cases where the subject is aware that they are receiving a placebo. On an equally mysterious topic, I was deeply surprised when I first discovered the serious consideration with which some bizarre superstitions were treated in the healthcare field.

• A controlled trial of arthroscopic surgery for osteoarthritis of the knee (2002) shows that a placebo effect exists for osteoarthritic patients who undergo (or don't) arthroscopic surgery of the knee to relieve pain and improve knee function.
• The moon and the stones. Can the moon’s attractive forces cause renal colic? (2002) The answer is cautious: "The forces are negligible and not strong enough to be a physiological stimulus and cause renal colic. We are aware that our study at this point, because it was performed with a limited number of patients, can not be significant."
• Lunar phases and zodiac signs do not influence quality of radical cystectomy—a statistical analysis of 452 patients with invasive bladder cancer (2007) presents a much larger study and state: "Although this was not a prospective randomized trial, the statistical magnitude of the results do not support any recommendations for scheduling patients for radical cystectomy at any particular day of the lunar phase."
• Popular belief meets surgical reality: impact of lunar phases, Friday the 13th and zodiac signs on emergency operations and intraoperative blood loss (2011) couches the conclusion more emphatically: "Scientific analysis of our data does not support the belief that moon phases, zodiac signs, or Friday 13th influence surgical blood loss and emergency frequency. Our data indicate that such beliefs are myths far beyond reality." But in a move that cynical observers might suggest stems from a desire for continued funding, they end with: "So far, however, studies with adequate power and sample size calculation rejecting any association between superstition and medicine are under-represented in the medical literature."

A mixture of papers concerning renal function and chronic kidney disease (CKD), IgA nephropathy, and modelling tumour vascularisation and growth.

• Biomarkers in chronic kidney disease: a review (2011)
• Is There Something Better than the Best Marker of Kidney Function? (2011)
• Current Therapy for IgA Nephropathy (2011)
• The Pathophysiology of IgA Nephropathy (2011)
• A Quantitative Theory of Solid Tumor Growth, Metabolic Rate and Vascularization (2011)

For me, the choice of platform came down to R or SciPy. I am aware of Sage, but it seemed like such a huge and sprawling collection that I found it a little off-putting (and I suspect it greatly exceeds my needs). In the end, I chose R because I had (very limited) experience with it, and I figured I'd enjoy using a statistical language more than a general-purpose language for this kind of work. That's not to say I didn't get thoroughly confused at times, of course. I found the following R packages and documentation very useful:

• The R manuals and FAQs are a good place to start.
• ggplot2 is a very flexible (and pretty!) graphing package.
• ROCR is a visualisation package for evaluating classifiers (e.g., GLMs).
• Writing R Extensions (in html and pdf) describes how to write your own packages (such as my clumsy attempt as part of a sensitivity analysis of the Guyton model).
• If you're having difficulties, the R Inferno may be useful (from the preface: "If you are using R and you think you're in hell, this is a map for you").
• The R community has recently started a wiki book, whose sections are currently in varying stages of completeness.

In addition, there are several other tools that can be very handy at certain times:

• g3data is an excellent tool for extracting data points from published graphs.
• GGobi is a visualisation tool for exploring high-dimensional data.
• Mondrian is an interactive data visualisation tool.

But despite all the time I've spent with R and other statistical tools, I'm still very much aware that I am a complete novice when it comes to statistics. I really need to start reading some good foundational texts, although I always ended up digging through the proofs and derivations because I'm rarely comfortable unless I'm convinced I understand the how and the why.

This paper caught my eye a while back: "Positive" Results Increase Down the Hierarchy of the Sciences (2010). To quote the abstract:

If the hierarchy hypothesis is correct, then researchers in "softer" sciences should have fewer constraints to their conscious and unconscious biases, and therefore report more positive outcomes. Results confirmed the predictions at all levels considered: discipline, domain and methodology broadly defined.

I wonder where the authors would classify this work on the soft/hard scale?

Bearing the plain title of Renal Circulation (2011), this review article provides great detail about renal microcirculation and autoregulation. It's probably just as useful for the references as for the actual content.

Update: I didn't realise that this is a chapter from Handbook of Physiology that is now available as part of Comprehensive Physiology, and that this body of work is being regularly updated.

Several papers that discuss the complexities of kidney oxygenation and the utility of mathematical models.

• Intrarenal oxygenation: unique challenges and the biophysical basis of homeostasis (2008);
• Methods for studying the physiology of kidney oxygenation (2008); and
• A mathematical model of diffusional shunting of oxygen from arteries to veins in the kidney (2011).

Some existing whole-kidney models, which also include other portions the cardio-vascular system.

• Mathematical model of the human renal system (1985);
• Systems model of renal dialysis: Formulation, validation identification (1982);
• A System of Models for Fluid-Electrolyte Dynamics (1985);
• A computer model of the kidney (1992); and
• Long-term mathematical model involving renal sympathetic nerve activity, arterial pressure, and sodium excretion (2005).