Convection as a mechanism of solute removal

This chapter is related to the aims of Section H3(i) from the 2017 CICM Primary Syllabus, which expects the exam candidate to "describe the principles of dialysis and renal replacement fluid". Convection certainly fits into this category, as it is one of the main mechanisms of middle molecule clearance and could be the sole mechanism of small solute clearance during CVVH. 

In brief summary:

• Convection is bulk-flow of solute across a semi-permeable membrane together with a solvent in a manner that is dependent on transmembrane pressure and sieving coefficient for that membrane 
• The sieving coefficient (SC) is the ratio of a specific solute concentration in the ultrafiltrate (removed only by a convective mechanism), divided by the mean plasma concentration in the filter.
• The rate of convection is relatively independent of solute size, in contrast to the rate of diffusion
• When the dose of dialysis is the same, the clearance of small solutes is going to be approximately the same for dialysis and haemofiltration, but when larger molecules convection has a significant advantage. 
• Membrane characteristics which make a membrane suitable for high solute clearance by ultrafiltration are similar to the performance characteristics of the glomerular basement membrane, with the pore size cut-off excluding most molecules resembling albumin in size.

There are multiple references one could quote, but specific outstanding examples include the article by Ronco (2000) who discusses the characteristics of dialysis filter membranes, and the article by Ledebo et al (2009) which puts these principles in context of practical applications.

Convection:

The ADQI definition of convection is:

In different words, convection is the transport of a solute across a membrane along with solvent (by "solvent drag"). The physicist/chemist definition is "Convection is the collective movement of molecules within fluids." This is how middle molecules are cleared during haemofiltration.

The diagram above reiterates the same point graphically. As solvent is sucked across the membrane of the haemofilter, so the little molecules dissolved in it are pulled along. It would therefore make sense that this process would be at least in some way related to the rate of solvent movement, i.e ultrafiltration rate. Indeed, it turns out that the movement of the solute along with the solvent (decribed as convective flux, J_c )  is proportional to ultrafiltration rate, as well as solute concentration and sieving coefficient.

What is the Sieving Coefficient

One might wax literal, and assume that its some sort of measure of the degree to which something is sieved, depending on what does the sieving. Indeed a sieving coefficient is the measure of how easily a substance passes from the blood compartment to the dialysate compartment in a haemofilter. A more formal definition from Neri et al (2016) is:

The sieving coefficient (SC) is the ratio of a specific solute concentration in the ultrafiltrate (removed only by a convective mechanism), divided by the mean plasma concentration in the filter.

This is obviously going to depend on membrane properties, and any given filter will have a different sieving coefficient for any given substance (and it will change over the course of a dialysis session because the tiny pores get clogged).

Using Neri's text, the equation can be expanded to account for the fact that the concentration in the donating stream changes along the length of the filter, and therefore some sort of average value should be used:

where

• C_UF is the solute concentration in the ultrafiltrate
•  C_Pi is the plasma solute concentrations at the filter inlet 
• C_Po is the the plasma solute concentrations at the filter outlet

Thus, a sieving coefficient of 1.0 means the solute is 100% filterable,  i.e. in a haemofilter, the solute will equilibrate on both sides of the membrane. The returning blood and the effluent both have the same concentration (50:50). An example of a solute with a sieving coefficient of 1.0 is potassium. Similarly, the sieving coefficients for urea, creatinine, urate and phosphate are all around 0.96 for most commercially available membranes. Conversely, a sieving coefficient of 0 means the solute does not cross the membrane, eg. albumin.

Having a sieving coefficient of 1.0 does not mean that the solute will have excellent clearance by convection. Ricci et al (2006) compared the clearance of solutes by both dialysis and convection and found that clearance of urea was no better with CVVH than dialysis, as is well demonstrated by this graph of their data:

The situation is clearer for larger molecules solutes which diffuse poorly. In this context, the advantage of convective clearance is more obvious. For example, the same paper presents data on the clearance of β-2 microglobulin, an 11-kDa protein. CVVH was the clear winner:

In summary, when the dose of dialysis is the same, the clearance of small solutes is going to be approximately the same for dialysis and haemofiltration, but when larger molecules convection has a significant advantage. This is a good segue into the discussion of the relationship of solute characteristics to convective clearance.

Solute characteristics which promote convective clearance

Diffusion is famously dependent on the radius of the particles, such that molecular mass plays a major role in the diffusional clearance of solutes in the dialyser. Not so for convective clearance. There is a size barrier to the haemofiltration membrane, but convection is less dependent on molecule size than diffusion. Yes, large proteins (eg. albumin and globulins) as well as blood cells are still all concentrated on one side of the membrane. But: small and middle molecules are equally likely to get convected across the membrane by solvent drag, because as you can see the molecule size does not play any role in determining the convective flux (i.e. there is just no place to plug it in to the equation). Below, a modified graph from Ronco's chapter in the 1998 edition of Critical Care Nephrology (p.1213-1223 ) demonstrates the relationship of solute molecule size and convective clearance (the molecules in question were dextrans of various molecular weight).

Membrane characteristics which promote convective clearance

One might recall that the ultrafiltration rate is strongly related to the ultrafiltration coefficient (KUF) of the membrane. This coefficient is in turn related to the porosity of the membrane, such that more porous membranes have a higher KUF. More porous membranes will also have a higher sieving coefficient for larger molecules.

Given that the "definitive" gold standard of a sieving membrane for this purpose is the glomerular basement membrane, it would make sense to compare all other membranes against it, and indeed somebody has. The following diagram is adopted from Ledebo et al (2009). 

Therefore, the ideal properties of a haemofilter membrane, from the viewpoint of optimising convection, are:

• High cut-off, just below  albumin
• High sieving coefficient for all molecules smaller than albumin
• Steep sigmoid curve, i.e. high rejection coefficient rapidly develops around the molecular weight of plasma proteins