# Starling forces and fluid exchange in the microcirculation

This chapter is relevant to Section G4(i) of the 2023 CICM Primary Syllabus, which expects the exam candidate to "describe the essential features of the micro-circulationincluding fluid exchange and its control mechanisms". Multiple past paper questions have explored this topic:

In summary:

• Starling's principle: Transvascular fluid exchange depends on a balance between hydrostatic and oncotic pressure gradients in the capillary lumen and the interstitial fluid.
• This balance can be expressed as the Starling equation:
J
v = Lp S [ (Pc - Pi) - σ(Πc - Πi) ]; where
• Pc - Pi is the capillary-interstitial hydrostatic pressure gradient
• Capillary hydrostatic pressure is usually:
• 32 mmHg at the arteriolar end of the cpaillary
• 15 mm Hg at the venular end
• Affected by gravity (eg. posture) and blood pressure
• Interstitial hydrostatic pressure is usually:
• negative (-5-0 mmHg) in most tissues (except for encapsulated organs)
• Affected by anything that modifies lymphatic drainage, eg. tourniquet or immobility
• Πc - Πis the capillary-interstitial oncotic pressure gradient
• Capillary oncotic pressure =  25mmHg
• Interstitial oncotic pressure = 5 mmHg
• Lp S is the permeability coefficient of the capillary surface, and is affected by shear stress and endothelial dysfunction
• σ is the reflection coefficient for protein permeability and is a dimensionless number which is specific for each membrane and protein
• σ = 0 means the membrane is maximally permeable
• σ = 1 means the membrane is totally impermeable
• In the muscles, σ for total body protein is high (0.9)
• In the intestine and lung, σ is low (0.5-0.7)

There is, fortunately, no shortage of good literature on this topic. What needs to be said about these concepts is already said there with a maximum economy of words and greatest clarity, and so this chapter mainly acts as something of an ornamental border, framing the works of  Erstad (2020)Woodcock (2017)Michel et al (2019), and so forth. Every which way you turn, there is also a high quality FOAM resource, among which Part One,  fluidphysiology.org and PulmCCM shine the brightest.

## Starling forces and the classical Starling Equation

"A clear explanation of Starling’s forces" was called for in the examiner comments to Question 16 from the second paper of 2018. Surely, nothing can be clearer than a mathematical formula, and the Starling equation seems like a suitable one to start with.

As is often the case, Ernest Starling never called it "my equation", and in fact there was no equation described in the original 1896 paper.  The basis of his work was the observation that haemorrhage causes the blood to become more dilute. From this, Starling concluded that there must be some mechanism to allow fluid to move into and out of blood vessels. He made the hind leg of a dog oedematous by the subcutaneous injection of isotonic saline, and then perfused it with some blood of a known haematocrit. The blood, as it emerged from the veins of the dog's leg, had "in all cases absorbed fluid: the whole blood and the serum were more dilute and the haemoglobin percentage was diminished."  From his findings, Starling deduced that the capillaries and post-capillary venules behave as semi-permeable membranes absorbing fluid from the interstitial space.

Starling attributed the uptake of water by venules to "molecular imbibition, e.g. the process by which gelatin will take up water and salts from proteid solutions", as the term oncotic pressure had not yet come to common parlance. Unfortunately, he did not have any way to support his idea by measuring it, and the concept itself (at this stage called "high endosmotic equivalent of albumen") was not completely accepted at that stage, or rather blown off as irrelevant by the prevailing winds of physiology literature. As osmometers became more common and reliable, other investigators were able to demonstrate that all aspects of it were experimentally supportable. For example, Eugene Landis in 1926 was able to show that when oncotic pressure and capillary hydrostatic pressure were equal, there was no net fluid movement across the capillary wall.  Starling's principle was further developed after his death in 1927 by Krogh, Landis and Turner (1931), who called it "Starling's conception" and by the time Keys et al wrote about "famine edema" in 1946, the equation had become a part of the laboratory furniture.

Thus, finally, Starling's principle can be expressed as

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,
• Pcand Piare the capillary hydrostatic pressure and interstitial hydrostatic pressure
• σ is the reflection coefficient for protein, which is discussed below,
• Πc is the oncotic pressure in the capillary blood,
• Πi is the oncotic pressure of the interstitial fluid, and

There are several variants of this equation, which mainly differ in their notation. Ganong (23rd ed) use k to denote the hydraulic permeability coefficient, where it presumably stands for Koefficient. Pappano & Weir use Qf  to describe the net fluid transport as flow (Q) of fluid (f). All textbook versions of this formula are otherwise identical, and the trainee would be expected to reproduce this version in their exam answers, even though it might be technically inaccurate (as is discussed at the very end of this chapter). It goes without saying that the technical accuracy of one's answer will be poor comfort to the candidate who failed by that exact number of marks.

The basis of this classical model is expressed in the statement,

Transvascular fluid exchange depends on a balance between hydrostatic and oncotic pressure gradients in the capillary lumen and the interstitial fluid.

If one had some sort of preoccupation with creating confusing elaborate diagrams, one would be tempted to represent these relationships like so:

To say the same thing except twenty times longer,

• At the arteriolar end of the capillary, fluid is filtered through the semipermeable endothelium into the interstitial space. The driving pressure gradient here is the difference between the hydrostatic pressure of the interstitial fluid (Pi) and the much higher capillary hydrostatic pressure (Pc); this gradient favours the movement of fluid out of the capillaries and into the interstitium.
• This (Pc- Pi) gradient is opposed by the oncotic pressure gradient (oncotic pressure being the carefully scrutinised subject of another chapter). The capillary oncotic pressure (Πc) is higher than the interstitial oncotic pressure (Πi) owing to the abundance of protein in the capillary blood. This gradient favours the movement of fluid out of the interstitium, and into the capillary.
• At the arteriolar end of the capillary, the hydrostatic pressure gradient is a more powerful force than the oncotic pressure gradient. Oncotic pressure is defeated, and fluid is ultrafiltered into the interstitial space. In the postcapillary venules, the hydrostatic pressure is very low, and the oncotic forces become dominant, attracting some (but not all) of the ultrafiltered fluid back into the intravascular compartment. The remaining fluid relies on lymphatic drainage to mediate its return into the circulation.

Hopefully, this is what the examiners meant by their cryptic statement, "the importance of the relative difference along the length of the capillary" (Question 16 from the second paper of 2018). As one will see later, the last component of this relative difference is somewhat controversial, as modern investigators have not always been able to demonstrate the sort of back-filtration that the Starling equation describes.

## How large are these pressures and gradients?

Is a question which the college examiners are clearly anxious for you to know the answer to. The examiners insisted on "approximate values and examples of factors that influence them" in their comments for Question 16 from the second paper of 2018, and "numerical values pertaining to hydrostatic and oncotic pressure gradients" in  Question 18 from the first paper of 2011. These weirdly specific demands seem to suggest that they were writing the question while looking at a specific page in some textbook where all these numbers are clearly laid out in some sort of figure or table. Fortunately, the abovementioned SAQ comes from a distant long-gone time when time and effort were invested in writing the examiner's comments, and a vague reference to Ganong was left as a breadcrumb for the readers. It leads to the 23rd edition, where on page 548 all of the coveted values are listed:

• Capillary hydrostatic pressure (Pc) = 37 mmHg
• Interstitial hydrostatic pressure (Pi) = 1 mmHg
• Hydrostatic pressure gradient is therefore 36 mmHg
• Capillary oncotic pressure (Πc) = 25 mmHg
• Interstitial oncotic pressure (Πi) = 1 mmHg
• Oncotic pressure gradient is therefore 24 mmHg

Where did these come from? The textbook, as is usually the case, does not offer any references. Measurements of these variables pressure along the capillary are obviously going to be different from measurement to measurement, even within the same organism. In short, the trainee is advised to randomly pick a set of values and commit them to memory with the somber knowledge that they are probably wrong.

Capillary hydrostatic pressure is basically the blood pressure, which at the level of the capillaries should be quite low, mainly due to the drop in pressure which is observed at the arterioles. Lots of authors give numbers here, and none are more trustworthy than the others. For instance,  Pappano & Weir report a starting capillary pressure of 32 mmHg which drops to 15 mmH in the post-capillary venule. This somewhat differs from Davis et al (1986), who recorded a pressure difference from 25 mmHg to 17 mmHg in their hamsters, and Gore (1974), who got 32-28 mmHg in his cats. Brandis quotes Landis (1930), whose human values were 32 and 12mmHg.  This pressure is still sort-of pulsatile, but the pulse pressure is only 1-2mmHg.

Obviously, gravity will play a role here, and hydrostatic pressure will increase in dependent regions, eg. the legs stuffed under economy class seats for many hours.  Logically, the effect of gravity is more profound the taller you are, to the point where Hargens et al (2007) report on multiple unique permeability-controlling mechanisms in the lower limbs of the giraffe, designed to prevent them from uncontrollably leaking their whole body fluid volume out into the soft tissues of their legs. For the record, the capillary hydrostatic pressure in the feet of the upright giraffe is probably between 260 and 150 mmHg, compared to something like 90 mmHg in the feet of an upright zookeeper.

Interstitial hydrostatic pressure is the pressure of the interstitial fluid compartment, which is not a discrete anatomical destination but rather a messy tangle of intercellular spaces which are filled with a fluid we call lymph for lack of a better term. One might develop the impression that this stuff just sloshes around haphazardly in the spaces between cells, but this is probably unfair. Guyton & Barber (1980) report that most of the time the vast majority of this fluid exists in the form of a hydrated gel, and free mobile fluid is in a minority. Measurement of an interstitial fluid pressure is accomplished by artificially creating a fluid-filled space inside the tissue which communicates with the interstitium (eg. by using a porous capsule), and then measuring the pressure of the fluid inside that space.

As one might imagine, this is something that is going to differ considerably between tissues. A fairly large range of pressures is reported among authors who bravely stuck probes into them, ranging from extremely positive to extremely negative. For example:

In general, solid organs with a capsule tend to have positive interstitial fluid pressure, and organs and tissues which are not confined tend to have negative interstitial fluid pressure. That negative pressure has been attributed to the suction generated by the lymphatic system, which has valves of various sorts and which only permits a unidirectional flof of fluid. Then, anything that might obstruct lymphatic flow (or anything that might increase intracapsular organ pressure, such as hydronephrosis) will give rise to an increase in the interstitial fluid pressure.

Oncotic pressure is discussed in detail elsewhere. Otherwise known as colloid osmotic pressure, it is defined formally as "the osmotic pressure exerted by colloids in solution" (Bevan, 1980). This pressure is exerted by the large volume of high-molecular-weight molecules in the blood stream, which might only contribute obut 0.5% to the total osmolality of plasma. However, because of their vast bulk, these large molecules are unable to cross into the interstitial space, in contrast to basically all the other molecules contributing to the osmolality of blood. Thus, though their total contribution to osmolality is minimal, they still contribute to the -osmotic pressure difference.   In the normal human, this oncotic pressure is usually fairly stable, as blood protein content is a carefully regulated property. This is probably one of the numbers which does not seem to vary erratically from textbook to textbook, as they all quote the values reported by Lundsgaard-Hansen (1986), 25-27 mmHg. As protein in ICU patients tends to be anything but normal, here is a graphical relationship from Bevan (1980). It also demonstrates the non-ideality of these solutions; as more protein particles are packed into the fluid volume, they begin to intract with one another, and this means that the relationship of oncotic pressure and protein content is non-linear at the higher range of concentrations.

The interstitial fluid is of course not without its own oncotic pressure, albeit lower than the plasma. Selen & Persson (1983) measured some rat values which ranged from  7.5 mmHg in the dehydrated animals to 2.8 mmHg in controls, giveing the average value of 5mm Hg which is usually quoted in textbooks.

Hydraulic permeability coefficient is the product of the hydraulic conductivity of the membrane (Lp) and its surface area (S) In some books, such as Pappano & Weir, it is represented purely by an all-encompassing k, the filtration constant for that specific capillary membrane, which wraps the entire equation, like so:

Qf = [(Pc − Pi) − σ ( ΠpΠi)]

Though it might look different, it is essentially the same thing, and this abbreviation should be viewed as a refreshing move towards simplicity in a complex field. When Lp is measured (eg. in  Williams, 1999) it is usually reported in cm·s−1·mmHg−1. It increases with shear stress on the capillary wall, which makes the wall more permeable to fluid by distressing the endothelium. It would be highly surprising if anybody ever was expected to randomly quote this completely irrelevant value in an exam. In case that happens, you will not remember the normal value for an unstressed capillary, which is probably about 20×107 cm·s−1·mmHg−1

Reflection coefficient, or Staverman's reflection coefficient, or sigma (σ),  is a coefficient which describes the leakiness of the capillary membrane to protein. This value ranges from 0 (completely permeable) to 1 (totally impermeable). Staverman's original 1951 paper was actually completely unrelated to haemodynamics and was mainly about the measurement of oncotic pressure using an osmometer, the membranes of which were hoped to be impermeable to colloids. "It is the intention of this paper to show that this hope is vain", cackled Staverman. But at least his coefficient could be used to describe the amount of leakage and to correct for it. It has no units and is just a dimensionless coefficient, which is different for all membranes and all species of solute. Some examples of values for undifferentiated blood proteins, from Taylor et al (1977):

• Limb (dog hind paw) = 0.7-0.99
• Intestine = 0.3-0.7
• Lung = 0.7 (though most textbooks report it as 0.5)

## Net filtration of fluid in the capillaries

Question 18 from the first paper of 2011 asked for some specific numbers to describe "net filtration in a 24 hour period". Additionally, in Question 19 from the second paper of 2016 they insisted on "equations for nett fluid flux and for nett filtration pressure". The net fluid flux equation looks like this:

Qf = k × Am × ΔP  / (η × Δx)

Where

• Qf  is the net movement of fluid,
• is the filtration constant of the capillary membrane,
• Am is the area of the capillary walls (all of them),
• ΔP is the net pressure balance between the hydrostatic and oncotic pressures,
• η is the viscosity of the fluid, and
• Δis the thickness of the capillary wall.

Using this, "net filtration in a 24 hour period" can be either measured or estimated. According to Ganong (23rd ed., p. 548) the total daily ultrafiltration volume is  24L of fluid, of which the authors claim 85% is reabsorbed into the capillaries. It is not clear where they got this from. Pappano & Weir give a more believable figure for the total filtration coefficient for the whole human body (0.0061 mL/min/100 g of tissue/mm Hg), which is not referenced but which seems to originate from Mellander & ÖBerg (1967)

## Application of the Starling principle to the pulmonary circulation

"Describe how Starling forces determine fluid flux within the pulmonary capillary bed", asked Question 19 from the second paper of 2016. Let us look again at the Starling equation and discuss how its elements change in the pulmonary ciculation:

Jv = Lp S [ (Pc - Pi) - σ(Πc - Πi) ];

• Lp S,  the permeability coefficient of the capillary surface:
• In the pulmonary capillaries, permeability is at least as high, or higher than systemic (as the capillary wall is often thinner)
• Surface area is similar to the total alveolar suface area, i.e.  approximately 140m2. In contrast, the total surface area of systemic capillaries is around 4000-7000m2
• Pc, capillary hydrostatic pressure:
• Low in the pulmonary capillaries: 4-12 mmHg (similar to LA pressure)
• Affected by:
• Gravity: lower in the apices and  higher in the bases of the upright lung
•  LA pressure: eg. in heart failure, where LA pressure increases
• Pi,  the interstitial hydrostatic pressure, which is essentially alveolar pressure:
• In the capillaries, essentially equal to atmospheric pressure
• Changes from slightly negative to slighly positive with resp. cycle
• Affected by positive pressure ventilation (increases) and during obstructed breathing (decreases; hence negative pressure pulmonary oedema)
• Pulmonary surfactant, by decreasing surface tension, decreases alveolar hydrostatic pressure
• Πc - Capillary oncotic pressure =  25mmHg throughout the circulation
• affected by blood protein content (esp. albumin)
• Πis the interstitial oncotic pressure
• σ is the reflection coefficient for protein permeability and is a dimensionless number which is specific for each membrane and protein
• σ = 1 means the membrane is totally impermeable
• σ = 0 means the membrane is maximally permeable
• In the lung, σ is low (0.5-0.7) because the capillaries are more permeable to protein
• In the muscles, σ for total body protein is high (0.9)

## Modern apostasy of the classical Starling principle

Even though the classical version of this equation is easier to teach, it had to be revised for the 21st century, because it does not accurately predict the behaviour of fluid.  Specifically, in 2004, Adamson and colleagues revealed that the effect of Πi on the transvascular fluid exchange is substantially less than what one might predict from the classical Starling model. This discovery had prompted a 2010 revision of the Staring model by Levick and Michel, which is the carefully considered subject of an excellent review article in the BJA.  Here is a version of the revised equation from  Erstad (2020):

Jv = Lp S [ (Pc - Pi) - σ(ΠeslΠb) ]

where

• Jis the net fluid transport,
• Lp  is the hydraulic permeability coefficient,
• S is the surface area,
• Pcand Piare the capillary hydrostatic pressure and interstitial hydrostatic pressure
• σ is the reflection coefficient for protein,
• Πeslis the oncotic pressure in the endothelial glycocalyx layer, and
• Πb is the oncotic pressure of the subglycocalyx.

This equation is slightly different to the original interpretation of Starling's hypothesis, and the basic principle is also slightly different. In short:

• The expected reabsorption of interstitial fluid via venules probably does not occur in most soft tissue vascular beds; rather, the ultrafiltered fluid returns into the circulation as lymph.
• Some capillaries can vigorously ultrafilter fluid along their entire length; one such example is the renal glomerulus.
• Some capillaries can absorb fluid along their entire length, such as the capillaries of the intestinal mucosa.
• The endothelial glycocalyx, rather than the interstitium, is probably the space which should be considered in the equation, instead of the interstitial space. There could have been no mention of the glycocalyx in the original Starling equation, as it was not really discovered until  J.R Luft visualised it under an electron microscope in 1966.

The endothelial glycocalyx is thought to play the role of the semipermeable membrane in this new revised model. Stated simply, it is a 500-2000nm thick hydrogel-like layer of membrane-bound proteoglycans and glycoproteins, which lines the entire several-thousand-square-meter surface area of the human vascular tree. The gradients involved are not between the interstitial oncotic pressure (Πi) and intravascular oncotic pressure (Πc). Instead, the place of Πi is taken by Πesl, the oncotic pressure within a carefully protected sub-glycocalyceal space - a potential space between the glycocalyx and the vascular endothelium, which is completely free from protein, much of the time.

The subglycocalyx may not remain completely protein-free over the entire length of the vessel. Indeed protein diffusion into this space underlies some of the mechanisms which maintain the net movement of fluid into the interstitial space. Increased "proteination" of this layer may diminish the oncotic pressure gradient, which decreases the opposition to hydrostatic filtration. In other words, if the subglycocalyx is "dehydrated" by some sort of transient phenomenon (eg. if the capillary pressure suddenly drops, resulting in the hydrostatic "autotransfusion" of water out of the interstitial space and glycocalyx) the drop in the oncotic pressure gradient maintains the net hydrostatic movement of water out of the capillaries.

Thus, the oncotic pressure gradient between Πc and Πesl seems to oppose but not reverse the movement of fluid out of the capillaries. This is interesting. For one, it means that the old technique of "attracting" oedema fluid out of the interstitial compartment by intravenous albumin should not work.

This is consistent with the current data:

This modification of the original Starling principle is included here mainly for completeness, as well as to develop in the author the impression that he has done his due diligence and remained honest with the reader. It is with the same spirit that some caveats must be introduced. One should be reasonably confident in the expectation that CICM primary examiners will be reusing questions written a decade ago, or longer. Those questions, in turn, would have been written on the basis of textbooks which were published a decade before that, on the basis of studies published another decade earlier. A couple more years here or there and we suddenly find ourselves in the eighties. In short, CICM trainees are advised to reproduce the classical Starling equation, and to omit all mention of the endothelial glycocalyx from their answer, in case it deviates heretically from the marking rubric written by L.I.G Worthley in 1992.

## Localised regional variations in Starling forces

The Starling equation describes the movement of fluid between compartments and is therefore an explanation of interstitial fluid content anywhere, which means it could theoretically be relied on to give an account of why some body parts are more oedematous than others. In general clinicians will agree that patients usually develop oedema in specific areas, with the excess interstitial water distributing itself unevenly around their body. Several factors govern this distribution:

• Gravity is perhaps the most important, as it influences the hydrostatic capillary pressure and therefore increases the transcapillary fluid movement. Gravity is responsible for the distribution of oedema into the legs of ambulatory CCF patients, and for the collection of presacral oedema in recumbent ICU patients.
• Localised changes in hydrostatic capillary pressure can occur due to changes in venous drainage, eg. where the venous circulation is obstructed. The swelling of the leg that contains the DVT is one example.
• Localised variation in hydrostatic interstitial pressure can restrict or encourage the accumulation of interstitial fluid by opposing hydrostatic capillary pressure (or not opposing it enough). Tissues are obviously not infinitely capacious, and there are limits to how much fluid can accumulate in an interstitial compartment before the boundaries of the compartment are stretched and begin to exert a back-pressure, opposing further fluid movement. Moerover, various connective tissue structures (skin, fascia) act as barriers to the movement of interstitial fluid. This is illustrated by the example of periorbital oedema. The malar septum is a fascial boundary that originates at the orbital rim and extends down through the suborbital fat to join the skin of the face; the cheek tissues below it are therefore separated from the tissues of the orbit, and fluid can accumulate in the orbit without draining into the rest of the face, giving rise to localised periorbital oedema.
• Localised capillary permeability can vary regionally, and this alters the Lp  (hydraulic permeability coefficient). The most familiar version of this would obviously be the oedema that develops locally at the site of inflammation or trauma.
• Localised changes in interstitial oncotic pressure produce regional oedema where the normal mechanisms that deproteinate the interstitial space are impaired  (for example due to the failure of lymphatic drainage, as in lymphedema)

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