Question 19

College Answer

The equations for nett fluid flux and for nett filtration pressure were incorrect in many answers. 
Better answers presented the equations and discussed each of the elements as relevant to the 
pulmonary capillary bed, including difference from systemic capillary beds. 
Mention of the role of lymphatics and of the effect of surfactant, left atrial pressure, gravity and 
posture gained marks, also.

Discussion

The equation for "nett fluid flux" is usually this:

Qf = k × A_m × ΔP  / (η × Δx)

Where

• Qf  is the net movement of fluid,
• k is the filtration constant of the capillary membrane,
• A_m 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
• Δx is the thickness of the capillary wall.

However, there is no mention of capillary wall thickness or fluid viscosity in the college answer, and - judging by the rest of their comments, a better choice would probably have been the Starling equation, which looks like this:

Jv = L_p S [ (P_c - P_i) - σ(Π_c - Π_i) ];

It is easier to break down its components into something relevant and specific to the pulmonary circulation:

• L_p 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 surface area, i.e.  approximately 140m². In contrast, the total surface area of systemic capillaries is around 4000-7000m². 
• P_c, 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
• P_i,  the interstitial hydrostatic pressure, which is essentially alveolar pressure:
  • In the capillaries, essentially equal to atmospheric pressure
  • Changes from slightly negative to slightly 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
• Π_c - Capillary oncotic pressure =  25mmHg throughout the circulation
  • affected by blood protein content (esp. albumin)
• Π_i is the interstitial oncotic pressure 
  • Due to the presence of protein in interstitial (or alveolar) fluid
  • In the alveoli, about 3mmHg, as opposed to 5mm Hg in solid tissue (Levine et al, 1967, and Mellins et al, 1969). Elsewhere in lung interstitium, eg. lung lymphatic fluid, the interstitial oncotic pressure is apparently 17 mmHg according to Kerry Brandis, although it is not clear where he got it from.
• 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)

Starling, Ernest Henry. "On the absorption of fluids from the connective tissue spaces." Classic Papers in Critical Care 19 (1896): 303.

Woodcock, T. E., and Thomas M. Woodcock. "Revised Starling equation and the glycocalyx model of transvascular fluid exchange: an improved paradigm for prescribing intravenous fluid therapy." British journal of anaesthesia 108.3 (2012): 384-394.

Erstad, Brian L. "The Revised Starling Equation: The Debate of Albumin Versus Crystalloids Continues." Annals of Pharmacotherapy (2020): 1060028020907084.

Krogh, August, E. M. Landis, and A. H. Turner. "The movement of fluid through the human capillary wall in relation to venous pressure and to the colloid osmotic pressure of the blood." The Journal of clinical investigation 11.1 (1932): 63-95.

Levine, O. Robert, et al. "The application of Starling's law of capillary exchange to the lungs." The Journal of clinical investigation 46.6 (1967): 934-944.

Mellins, Robert B., et al. "Interstitial pressure of the lung." Circulation research 24.2 (1969): 197-212.

Staub, Norman C. "Pulmonary edema." Physiological Reviews 54.3 (1974): 678-811.