# Glomerular filtration

This chapter is vaguely relevant to the aims of Section H1(iii) from the 2023 CICM Primary Syllabus, which expects the exam candidate to "describe glomerular filtration and tubular function". The topic of glomerular filtration has come up multiple times in the CICM exam papers, and almost always in the form of a "what factors affect" SAQ. This is not surprising, because this is a topic which lends itself very well to diagrams and graphs, and one can see how that would be very attractive to the CICM examiners. Those questions on the factors affecting glomerular filtration are included here:

Realistically, it would have been ideal to discuss the filtration functions of the glomerulus alongside with its structure, as the two are closely associated, but in attempting to do so the author produced a completely unworkable Voynich manuscript overgrown with profane apocrypha. Some uncomfortable self-examination followed, and most of these digressions were expelled into a separate chapter on glomerular structure, prefaced with a stern warning against anyone ever trying to read it.

So, in summary:

Glomerular filtration rate (GFR) is the sum of the ultrafiltrate produced by all nephrons

• This is about 20% of renal blood flow, which itself is 20% of cardiac output
• This proportion of filtered blood volume is the filtration fraction (20%)
• Therefore normal GFR = about 90-120 ml/min/1.73m2

Glomerular ultrafiltration is influenced by the Starling equation:

GFR = Kf [ (Pgc - PBC) - σ(Πgc - Πi) ]

where

• GFR is the glomerular filtration rate,
• K is the filtration coefficient of the glomerular filtration surface,
which is itself a product of:
• k, the hydrostatic permeability constant of the membrane, and
• S, the surface area of the glomerular filtration surface, which can be affected by the contraction of glomerular mesangial cells
• Pgc  is the glomerular capillary hydrostatic pressure
• PBC  is the hydrostatic pressure of fluid in Bowman's capsule
• σ is the reflection coefficient for blood protein
• Πgc is the oncotic pressure in the glomerular capillary blood,
• ΠBC is the oncotic pressure of the fluid in Bowman's capsule (usually zero)

Glomerular filtration of solutes is affected by:

• Molecule size: glomerular size barrier resists the passage of large molecules (>7000 Da)
• Molecule charge:​ anionic charge of the glomerular filtration surface may resist the passage of anioninc molecules​​​​​​

Regulation of glomerular ultrafiltration is achieved by controlling the vascular resistance of the afferent and efferent arterioles, via these factors:

• Myogenic autoregulation
• Tubuloglomerular feedback
• Sympathetic stimulation
• Angiotensin II
• Endothelin
• Prostaglandin (PGE2)
• Protein ingestion and amino acid infusion
• Glucose (hyperlglycaemia)

In terms of legitimate peer-reviewed resources, there are several one could immediately recommend.  Renkin & Robinson (1974) is good, but old, and paywalled. On the other hand, Pollak (2014) is good, recent, and free. It also has a pun in the title, which instantly elevates it above the rest of nephrology literature. Another excellent (and incredibly detailed) entry is Deen et al (2001), not the least of its merits being that it was co-authored by William Deen who is responsible for some of the seminal research in glomerular function during the seventies.

## Origins of the glomerular ultrafiltrate

Glomerular ultrafiltration, which is the extrusion of blood water into Bowman's space, happens only because of an imbalance of Starling forces in the glomerulus. If one had to explain this to somebody who has never heard of the Starling equation, in the shortest possible form:

• Blood is pushed into the glomerulus under a certain hydrostatic pressure.
• That pressure is greater than the pressure in Bowman's space
• Thus, water would naturally move into Bowman's space along this pressure gradient
• The oncotic pressure inside the glomerular capillary is higher than the oncotic pressure in Bowman's space (because there is more protein in the capillary)
• Thus, oncotic forces also attract the water in Bowman's space back into the glomerular capillary
• Thus, glomerular filtration is determined by the balance between the hydrostatic pressure gradient and the oncotic pressure gradient

For exam purposes, mention of the Starling equation is probably essential. As this is a highly glomerulocentric chapter, the equation would have to have some modification to its terms so that it is clear to the examiner that one is specifically discussing the glomerulus.

Thus, the original formula

Jv = Lp S [ (Pc - Pi) - σ(Πc - Πi) ]

where

• Jis the net fluid transport,
• Lp  is the hydraulic permeability coefficient,
• S is the surface area of the membrane,
• Pc and Pi are the capillary hydrostatic pressure and interstitial hydrostatic pressure
• σ is the reflection coefficient for protein, which is discussed elsewhere
• Πc is the oncotic pressure in the capillary blood,
• Πi is the oncotic pressure of the interstitial fluid

...is transformed into this:

GFR = Kf [ (Pgc - PBC) - σ(Πgc - Πi) ]

where

• GFR is the glomerular filtration ratet,
• K is the filtration coefficient of the glomerular filtration surface,
which is itself a product of:
• k, the hydrostatic permeability constant of the membrane, and
• S, the surface area of the glomerular filtration surface
• Pgc  is the glomerular capillary hydrostatic pressure
• PBC  is the hydrostatic pressure of fluid in Bowman's capsule
• σ is the reflection coefficient for blood protein
• Πgc is the oncotic pressure in the glomerular capillary blood,
• ΠBC is the oncotic pressure of the fluid in Bowman's capsule (usually zero)

The symbols used in the literature vary erratically in terms of the Greek letters used, capitals versus lower-case, the use of subscript etc., and so trainees answering written questions are advised to define the variables in their answers, as the examiners may not immediately recognise their semiotic choices. It would be unfair and unexpected to be asked to discuss these factors individually in any great detail, but in case you have to, that's exactly what happens below.

### Kf  - the ultrafiltration coefficient of the glomerulus

K is an empirical constant value that describes the ease (or difficulty) with which water migrates across the filtration membrane. It is a fairly fixed property of the glomerulus, or rather it is not something that is expected to vary over a short timeframe, and it is certainly not something susceptible to regulation or manipulation. Obviously with renal disease (eg. diabetic nephropathy, which thickens the glomerular basement membrane) this variable will change, but this occurs over the timeframe of years.

What is the normal value for Kf? And how would you even express it? It is a measure of how fast a volume of fluid migrates across a membrane under a given pressure, which means you would probably want to express it in terms of volume per unit pressure per second, which is indeed what seems to happen in the literature. For example, Deen and colleagues measured the Kf of individual rat glomeruli in 1973 and reported an average value of 0.08 nl/(s × mm Hg). Obviously individual nephron values are pretty meaningless, but you can scale Deen's formula to report a total Kfor both kidneys. For young human subjects, Hoang et al (2003) reported an average value of 11.3 ± 4.9 mL/(min × mm Hg).

### k - the permeability of the glomerular filtration surface

Kf  is itself a composite of two influence, one the permeability of the glomerular filtration surface to water, and the other its surface area. Both of these are difficult to measure or estimate, and are themselves composites of other variables (for example the permeability to water consists of separate permeability coefficients for the basement membrane, endothelial pores, glycocalyx and podocyte slits). For a truly granular mathematical description of these, one can refer to Deen et al (2001).

### S - the surface area of the glomerular capillaries

The surface area is somewhat easier to discuss than membrane permeability. For the reader with an unhealthy fixation on measurements and numbers, Bohle et al (1998) give the total glomerular surface area as around 500 cm2.  Interestingly, this property does seem to be under some degree of regulatory control. Mesangial cells are apparently capable of managing this aspect of glomerular filtration by contracting and relaxing.   They are, after all, just severely mutated versions of vascular smooth muscle cells. That they contract in vitro is certain, and old light microscopy studies recorded cinematic loops of glomeruli pulsating weirdly under the influence of vasoactive mediators (i.e. they surely do change their size). However, whether this really makes any difference to the overall rate of glomerular filtration is uncertain, and articles about it have titles with words like "lingering doubts" in their titles (Ghayur et al, 2008). The consensus of experts seems to be that, if this contractile function is indeed a part of the glomerular regulatory toolkit, then it is surely the tiniest screwdriver at the very bottom.

### Pgc - the glomerular capillary hydrostatic pressure

This is the pressure of the blood coming out of the afferent arteriole as it flows through the glomerular capillaries. Next to the permeability of the actual membrane, this is probably the most important factor which determines the product of the glomerular Starling equation, and is definitely the most important pressure variable. It is also markedly higher than the pressure in normal capillaries, where it is roughly 32 mmHg at the arteriolar end of the capillary and 15 mm Hg at the venular end. Brenner et al (1971) performed the first measurements of this in rats, and found that glomerular capillary pressure was around 50% of the systemic value, close to 50 mmHg.

Another reason for the importance of this variable is its susceptibility to manipulation. Afferent arterioles supply the glomerular capillaries with blood, and efferent arterioles drain it, which means varying the resistance in either will give rise to changes in capillary hydrostatic pressure. By changing this variable, one is able to adjust the net ultrafiltration pressure at the glomerulus (or, keep it stable in the face of other changing variables). Observe:

• The afferent arteriole is the resistance vessel that receives blood at close to systemic arterial pressure and - by acting as a resistor - decreases that pressure down to the 50 mmHg we have come to expect. Thus, in scenarios where capillary hydrostatic pressure is falling, the afferent arteriole can dilate to increase it.
• The efferent arteriole is a resistance vessel into which glomerular blood is flowing. Thus, by constricting, it can increase the resistance to that flow, and increase the glomerular capillary pressure.

By pulling on these levers, in the following ways, these regulatory factors can adjust glomerular filtration:

• Myogenic autoregulation: where the afferent arteriole automatically vasoconstricts in response to increased systemic blood pressure, by sensing itself being stretched.
• Tubuloglomerular feedback: delivery of salt to the macula densa produces an ATP-mediated vasoconstriction of the afferent arteriole, mediated by juxtaglomerular cells
• Sympathetic stimulation: by vasoconstricting the efferent arteriole by a greater degree than the afferent, catecholamines and the SNS can maintain glomerular filtration rate even when systemic blood flow is poor or redistributed away from the kidneys.
• Angiotensin II: also vasoconstricts both arterioles, but the efferent more so, thereby preserving the glomerular filtration rate.
• Endothelin decreases renal blood flow and glomerular filtration mainly by acting on afferent arterioles
• Prostaglandin (PGE2) vasodilates the afferent arteriole directly
• Protein ingestion and amino acid infusion vasodilates the afferent arteriole by stimulating NO production
• Glucose, particularly in hyperglycaemia, acts as an afferent arteriolar vasodilator.

The reader's surprise at the unexpected brevity of these explanations will be relieved by knowing that the mechanisms which influence renal blood flow are discussed in excessive detail elsewhere.

### PBC - the hydrostatic pressure of fluid in Bowman's capsule

This is the pressure which the ultrafiltrate is draining into. As the pressure gradient between this pressure and the capillary hydrostatic pressure is an important determinant of the total ultrafiltrate flow rate, you would want this pressure to be as low as possible, and usually it is. According to Wirz (1956), it is around 7mmHg. Practically, it is rather difficult to measure this directly without brutally destroying the renal corpuscle, but people have successfully shoved pressure probes up into the proximal tubule which (everybody agrees) is close enough.

### (Πgc- ΠBC), the oncotic pressure gradient

We shan't digress overmuch on ΠBC, the oncotic pressure in Bowman's capsule, as under normal circumstances it should be zero, and it is therefore boring. The osmotic pressure in the glomerular capillary is much more interesting because it is a) high, and b) gets higher during intraglomerular blood transit. The main reason for this is the filtration of water out of the glomerular capillary, which has the effect of concentrating glomerular blood, increasing the oncotic pressure from 18 to 34 mmHg according to Pollak (2014). As the result of this, Starling forces become less and less favourable to filtration along the length of a glomerular capillary, which gives rise to a potentially examinable graph:

This is theoretically sound, the CICM examiners certainly seem to believe it, and it is mentioned in official textbook canon. Most of the measurements which are often quoted seem to be coming from Ott et al (1976), where "systemic protein concentration were compared to values determined from micropuncture of efferent arterioles in 14 dogs". The protein concentration in efferent arteriolar plasma was about 84g/L, compared to about 48g/L in the systemic arterial blood.

## Filtration of solutes at the glomerulus

The factors that influence the filtration of solutes at the glomerulus are different to the familiar Starlingy factors that influence the ultrafiltration of water. Some CICM questions ask about both, or one instead of the other, and trainees have been caught out. For example, Question 4 from the first paper of 2016 asked about "the factors that influence filtration across the glomerular basement membrane" and the answer was clearly expected to include a discussion of the molecular size barrier, not just the Starling forces.

The barrier function of the glomerular filtration surface is itself beyond doubt, evidenced by the fact that we don't all leak our blood protein content out through our urine every couple of hours. The exact mechanism by which this gatekeeping is accomplished however remains the topic of debate. Particularly, there is no agreement whether there is just a size barrier or whether molecules are sorted in some other way as well, for example by their charge.

### Glomerular charge barrier

This "charge barrier" is mentioned in textbooks, and is both physiologically plausible (as the glomerular basement membrane is certainly packed full of highly anionic heparan sulfate proteoglycans) and supported by experiments (see below). In spite of this, it remains the subject of debate in the literature. Milner (2008) expanded upon the controversies which surround this concept, and was unable to conclude anything helpful. Trainees are advised to come up with some way of making mention of the charge barrier in their answer without committing to any specific heretical theory, for example stating that "anionic molecules in the glomerular filtration surface may repel anionic blood proteins", which is technically not a lie. Moreover, they could quote the classic charged dextran experiments by Bohrer et al (1978) . The graph of their data displayed below has enjoyed great popularity among textbook authors, and is still quoted wherever the charge barrier is invoked.

### Glomerular size barrier

The size barrier is less controversial. For one, its presense and function have been known for longer, and the experiments which described it have aged better. The college answers to their SAQs seem to indicate that 7000 Daltons is some sort of cut-off, but in fact there is something of a spectrum here, with the filtration fraction gradually decreasing as molecular size increases. This is usually reproduced as a table, as follows:

Everybody who ever reproduces this table of filtration fractions vs. molecular weight tends to reference the 3rd edition of Physiology of the Kidney and Body Fluids, a 1974 textbook by Pitts et al (eds). Even textbooks are doing this, and have been repetitively re-doing it since the 1980s. The original text is not available online, except as a vintage hardcover at extortionist prices, which one should not be paying for a book that was critically panned as "inelegant" and "awkward". Fortunately, memorising such tables is probably not essential for passing exam questions about glomerular filtration. One could simply reproduce this graph from Renkin & Robinson (1974), which plots the molecular weight of some unknowable unlabelled "proteins" against their ultrafiltrate/plasma ratio.

### Sieving coefficient and filtration fraction

These are concepts which one often encounters during their reading about the clearance of solutes in the glomerulus. There are official definitions, which

Sieving coefficient is the ratio of a molecule's concentration in the filtrate to that in plasma

The sieving coefficient is therefore substance-specific, i.e. each molecule gets its own sieving coefficient. This requires a measurement of the molecule in the plasma, and - ideally - in Bowman's space, because the proximal tubule does have a tendency to reabsorb various molecules, changing their concentration in the filtrate. As an example, the sieving coefficient for albumin is said to be about 0.006, i.e. only about 0.6% of the plasma albumin ends up in the ultrafiltrate.

Filtration fraction is the ratio of of the glomerular filtration rate to renal plasma flow

In other words, it is the metric which describes how much of the plasma delivered to the kidney ends up as ultrafiltrate. Under normal circumstances, it is 20%.

## Total glomerular filtration rate (GFR)

The total glomerular ultrafiltration of any given human organism is the sum total of the activity of perhaps two million nephrons, with each nephron pitching in its tiny unequal contribution. Horster & Thurau (1968) measured the GFR of individual rat nephrons and found that they can vary markedly in their performance (eg. 23.5 nl/min in superficial nephrons and  58.2 nl/min in juxtaglomerular nephrons).

Yes, that's nanolitres per minute. So how much does the entire system produce? If you consider that the total renal blood flow is about 1.0L/min  (20% of the total cardiac output), and that the normal filtration fraction is 20%, you'd have to conclude that the total rate of glomerular ultrafiltrate production in the Bowman spaces of a pair of normal kidneys is around 200ml/min. This, in fact, would be close to correct. In order to adjust renal function measurements to human beings who vary in size, the GFR is usually indexed to 1.73 m2 (the BSA of an average 70kg male), where the normal range is 90-120 ml/min/1.73 m2. This is a bit weird (why not report it like the cardiac index, in ml/min/m2?) but it does allow for the comparison of GFR values between individuals. As some authors have pointed out (eg. Delanaye & Krzesinski, 2011), this can lead to wild misestimates for patients with unusual body proportions.  An unadjusted (or "de-indexed") glomerular filtration rate would have to be multiplied by the patient's actual BSA, and then divided by 1.73.

## References

Renkin, Eugene M., and Roscoe R. Robinson. "Glomerular filtration." New England Journal of Medicine 290.14 (1974): 785-792.

Pollak, Martin R., et al. "The glomerulus: the sphere of influence.Clinical journal of the American Society of Nephrology 9.8 (2014): 1461-1469.

Horster, M., and K. Thurau. "Micropuncture studies on the filtration rate of single superficial and juxtamedullary glomeruli in the rat kidney." Pflüger's Archiv für die gesamte Physiologie des Menschen und der Tiere 301.2 (1968): 162-181.

Deen, William M., et al. "Dynamics of glomerular ultrafiltration in the rat. IV. Determination of the ultrafiltration coefficient." The Journal of clinical investigation 52.6 (1973): 1500-1508.

Hoang, Khoi, et al. "Determinants of glomerular hypofiltration in aging humans." Kidney international 64.4 (2003): 1417-1424.

Deen, William M., Matthew J. Lazzara, and Bryan D. Myers. "Structural determinants of glomerular permeability." American Journal of Physiology-Renal Physiology 281.4 (2001): F579-F596.

Squarer, A., et al. "Mechanisms of progressive glomerular injury in membranous nephropathy." Journal of the American Society of Nephrology 9.8 (1998): 1389-1398.

Bohle, Adalbert, et al. "Human glomerular structure under normal conditions and in isolated glomerular disease." Kidney International 54 (1998): S186-S188.

Brenner, Barry M., Julia L. Troy, and Terrance M. Daugharty. "The dynamics of glomerular ultrafiltration in the rat." The Journal of clinical investigation 50.8 (1971): 1776-1780.

Wirz, H. "Die Druckverhältnisse in der normalen Niere." Schweiz. med. Wschr 86 (1956): 377.

Ott, C. E., et al. "Determinants of glomerular filtration rate in the dog.American Journal of Physiology-Legacy Content 231.1 (1976): 235-239.

Ghayur, Muhammad N., Joan C. Krepinsky, and Luke J. Janssen. "Contractility of the renal glomerulus and mesangial cells: lingering doubts and strategies for the future.Medical hypotheses and research: MHR 4.1 (2008): 1.

Miner, Jeffrey H. "Glomerular filtration: the charge debate charges ahead." Kidney international 74.3 (2008): 259-261.

Bohrer, Michael P., et al. "Permselectivity of the glomerular capillary wall: Facilitated filtration of circulating polycations." The Journal of clinical investigation 61.1 (1978): 72-78.

Delanaye, Pierre, and Jean-Marie Krzesinski. "Indexing of renal function parameters by body surface area: intelligence or folly?." Nephron Clinical practice 119.4 (2011): c289-c292.