I. Lecture notes on principles of fluid and solute exchange.
II. Quantitative aspects of fluid and solute exchange. Questions and answers.
III. Clinical Situations. Discussion in small groups.

Objectives.

By the end of the session you will be expected to be able to

1. Understand the basic principles of fluid and solute exchange
2. Describe the quantitative effects of alteration in fluid flow across capillary wall resulting from changes in driving pressures.
3. Understand and describe the microvascular response to tissue damage and a variety of pathologies.
4. Describe the basic design and physiological function of the lymphatic system.

Part I.

I. Diffusive Flux.

Diffusion is the principal mechanism for exchange of oxygen, nutrients and metabolic waste (small solutes). It is the net effect of random movement of small ions and molecules due to their thermodynamic energy. Two or more substances can move in opposite directions without affecting each other (e.g. O2 and CO2).

The relationship between concentration and rate of flux is described by Fick's Law

Js(diff)=PA(Cp-Ct)

Solute flux = Permeability x Surface Area x plasma to tissue concentration difference.

Lipid soluble solutes. e.g. O2, anaesthetic gases

Lipid soluble solutes can diffuse across the entire capillary surface. The permeability depends on their oil:water partition coefficient.

Lipid insoluble, small solutes.

Small lipid insoluble solutes, such as sodium ions and glucose, cannot cross the plasma membrane by diffusion, and move across the capillary wall primarily through small pores, probably existing as junctions between endothelial cells. The size and shape of these pores relative to the size of the solute, determine the permeability of the wall to that solute. The pores are modelled to be about 8-10nm in diameter in continuous capillaries, and occupy less than 0.1% of the capillary surface area.

Solute permeability - P.
The permeability of a membrane to a particular solute depends upon the size of the pores in the membrane (radius r), relative to size of the molecule (radius a), the length of the pores (dx, related, but not equal to the thickness of the membrane), the restricted diffusion coefficient of the solute (D') and the area of the pores relative to the total surface area (Ap/A).

P=(D'Ap) Ø



   (dxA)

Where Ø is (r-a)2/r2 - the equilibrium partition coefficient. This is a measure of the size of the molecule relative to that of the pore. A high Ø means that the molecule is much smaller than the pore and the area available for diffusion within the pore is almost equal to the area of the pore. If Ø is low then the molecule is similar in size to the pore, and therefore the effective size of the pore is smaller than the actual size. The permeability of a membrane to a solute therefore decreases with solute size.
 

Flow limited solute flux.
If the permeability is high, and flow is slow, as the blood passes from the arterial to the venous end of a capillary the concentration difference decreases, so reducing solute flux. In this case solute flux is flow limited. An decrease in flow through an individual capillary will limit solute delivery.

Large lipid insoluble molecules.

The permeability of molecules larger than small proteins (10,000MW) have a much lower permeability than smaller molecular weight solutes. Albumin, for example has a diameter of 7nm, and is therefore almost the same size as the small pores. However, larger molecules, greater than 10nm diameter do cross the capillary wall, and have a low, but measurable permeability. There appears to be a much rarer population of large pores of diameter 60-80nm, although the actual identification of these pores is not yet complete. There appear to be approximately 12,000 small pores to each large pore, so the large pore contribution to small solutes and water flux is negligible. However they are the principal route of transport for large molecular weight solutes.

Diffusion limited solute flux.
If the permeability is low, there is no great change in Cp-Ct as the blood passes through an individual capillary. So solute flux is limited by the diffusive capacity of the molecule through the membrane. In this case solute flux is diffusion limited.

II. Convective Flux.

Water flows across the capillary wall. The rate of flow of water depends on the balance of pressures inside and outside the capillaries, and their permeability to water. There is a hydrostatic pressure inside the capillaries (Pc - generated by the action of the heart) which must be counteracted by another pressure holding fluid in the blood vessels. This is the osmotic pressure exerted by the plasma proteins (to which the capillaries are not highly permeable) &frac14 c. Remembering that there is also an interstitial colloid osmotic (or oncotic) pressure (&frac14 i), and a interstitial tissue pressure (Pi) we can describe filtration rate (Jv) in the following terms.

Jv = Lp A [(Pc-Pi)- Ó (¼c- ¼i)] The Starling Equation

Where Lp is the hydraulic conductivity (or permeability to water), A is the surface area, and Ó is the oncotic reflection coefficient. This relationship was first pointed out by Ernest Starling in 1896, at University College London.

Oncotic reflection coefficient.
The oncotic reflection coefficient (Ó ) is the probability that a particular molecule will bounce off the sides of a pore rather than go through it. If the molecule is close to the same size as the pore (e.g. albumin) then it will have a high reflection coefficient (0.95-0.98 usually). If the molecule is larger than the pore then it will have a reflection coefficient of 1.0. If the molecule was very much smaller than the pore (e.g. Na+) then it will have a reflection coefficient close to zero (0.05-0.1).

Solvent drag
As water moves through the pores it will drag solutes with it. It will in effect increase the velocity of the solute in one direction. For small solutes this will have a negligible effect on solute flux because the additional flux is so small compared to the diffusive flux. For large molecules however, solvent drag may be a very significant contribution to solute flux. Solvent drag (also referred to as convective flux can be calculated as:
Js(conv)= Jv(1- Ó )Cp.

If we include both diffusive and convective fluxes, we can estimate total solute flux.

Js=PA(Cp-Ct)+Jv(1- Ó )Cp

It can be seen from this that for molecules to which P is very low, solute flux is heavily dependent on filtration rate.

Interstitial Protein concentration.
The interstitial protein concentration sets the interstitial colloid osmotic pressure, and therefore influences filtration rate. But interstitial protein concentration is itself set by capillary pressure. Interstitial protein concentration (in mg/ml) depends on the mass of protein crossing the capillary wall (mg/min, solute flux) divided by the volume of fluid crossing the capillary wall (ml/min, filtration rate). If filtration rate increases, the volume of fluid will go up, and so protein concentration will go down (solute flux will also go up, but not by as much due to reflection of protein molecules at the wall). Conversely, if filtration rate decreases, then interstitial protein concentration will go up. If filtration rate falls to zero, then the interstitial protein concentration will rise to equal the plasma protein concentration.

Lymph, interstitial pressure and oedema.

Throughout most capillary beds there is a continuous overproduction of interstitial fluid, i.e. a net filtration rate into the tissue. This is because the capillary pressure is usually higher than the oncotic pressure difference through most, or all of the capillary bed. It can be seen from the previous paragraph, that if filtration rate falls to zero, or starts to absorb fluid, then the interstitial protein concentration will rise and reduce the oncotic pressure difference.

The extra fluid that is formed during filtration is removed by the lymphatic system. The lymph system consists of blind ending sacs connected together that forms a network throughout most of the body. The tubes join up to form major (afferent) lymph vessels which pump lymph, by active contraction towards the lymph nodes. Here some of the fluid is absorbed into the blood stream, and some passes to the efferent lymphatics and eventually to either the thoracic duct - which empties into the left subclavian vein at its junction with the jugular vein, or to a much lesser extent to the right or cervical lymphatic ducts, which again empties into the venous system. The rate of lymph flow (JL) appears to be controlled by the interstitial fluid pressure - the higher the pressure the higher the lymph flow, although the mechanism is not known.

Interstitial pressure.
Interstitial pressure in most tissues is usually close to zero, and often slightly below zero. However, as net filtration rate increases, lymph flow increases in concert. Eventually maximal lymph flow is reached, the lymphatics cannot pump any more fluid, and the tissue swells, and tissue pressure increases. This is oedema.

Part II

1. a) Calculate Jv (in ml/min/100g tissue) for typical values given. Does fluid flow into or out of the vasculature?
b) Extrapolate this to the whole body of a 70kg person. What proportion of plasma volume turns over each day?
c) Calculate lymph flow for the tissue and for the whole body, assuming a steady state (no swelling).
Lp=0.16x10-7 cm/sec/mmHg, surface area is 100cm2 /g. Capillary pressure=20mmHg, Interstitial hydrostatic pressure=0, plasma colloid osmotic pressure=25mmHg, interstitial oncotic pressure=5mmHg, oncotic reflection coefficient=0.95.
Answers
2. What factors determine whether a solute is flow limited or diffusion limited. Give examples of flow limited and diffusion limited solutes. Which parameters of the Fick equation will change under flow limiting conditions?
Answers
3. Calculate the diffusive and convective fluxes of glucose and albumin. Which flux is more important for delivery of each solute to the tissue? Would you expect P, A, Cp or Ct to vary between tissues?
PAglucose=0.08ml/sec/100g, PAalbumin=1.2x10-4ml/min/100g, Cp=60g/l for albumin, 0.9mg/ml for glucose, Ct=4.7mM for glucose, and 10mg/ml for albumin, sigma=0.95 for albumin and 0.1 for glucose and MW= 180 for glucose
Answers

Part III.

4. During heavy exercise, glucose consumption may increase 43 fold. Which of the following parameters do you think would be the most important ways that the cardiovascular system could supply this increased glucose?
a) Increased arterial glucose concentration
b) Decreased interstitial glucose concentration
c) Increased blood flow
d) Increased filtration rate
e) Increased permeability to glucose
f) Decreased lymph flow
Answers
5. How would you expect glucose permeability, albumin permeability, hydraulic conductivity and oncotic reflection coefficient to albumin and glucose to be affected by?
a) An increase in pore density (number of pores per square cm of capillary).
b) An increase in pore path length.
c) An increase in pore radius.
d) A doubling in the ratio of large to small pores.
e) An increase in blood flow.
Answers
6. What happens (up, down or no change) to the following parameters for albumin and water during the following states? Please state whether you mean acutely (within a few minutes) or chronically (over five minutes to an hour). Which parameters change due directly to the primary challenge to the body, and which ones change as a response to the primary challenge?

                                        Jv      Js      Pc      Pi      ¼c       ¼i       Cp      Ct      P       Lp      s       S       JL



Heavy exercise



Hot weather



Severe haemorrhage



Sprained ankle



Burned Finger



Renal Failure



Filariasis*



Right Ventricular Failure



Deep venous thrombosis



Severe malnutrition

*Filariasis is a parasitic infection of the lymph nodes which results in lymphatic insufficiency. Answers

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