Physical mechanisms of haemodialysis

Dialysis

Blood and dialysate flow in countercurrent, separated by a solute-permeable membrane.

Small molecules are cleared by diffusion. $$\text{Solute flux} = k \Delta C \frac{SA \cdot \text{solubility}}{\text{membrane thickness} \cdot \sqrt{MW}}$$

Therefore, flux is increased by

1. Higher concentration gradient (most important, \(\uparrow\) by \(\uparrow\)blood and dialysate flow, and by countercurrent arrangement \(\to\) maintains gradient along tube)
2. Higher surface area and porosity
3. Smaller particle size

Diafiltration

Blood in the circuit is placed under pressure. Water is ultrafiltered from blood\(\to\)dialysate; small and middle molecules follow by convection / solvent drag. $$H_2O\text{ flux} = Q_{UF} = SA \cdot K_{UF} \cdot (TMP - \Delta P_{\pi})$$ where \(TMP = \text{Transmembrane pressure} = \frac{1}{2}(P_{filter} + P_{return}) - P_{effluent}\). Then, $$\text{Solute flux} = S \cdot Q_{UF} [\text{solute}]_{plasma}$$ where S is the sieving coefficient for the (solute,membrane) pair. NB that convection rate is largely independent of solute size.

Factors affecting both modalities

1. Adsorption of protein to membrane \(\to\) worse performance
2. Protein bound fraction of solute cannot be dialysed
3. Distribution; only drug in central compartment can be dialysed
4. Gibbs-Donnan; impermeable anionic protein resists dialysis of cations