We used the thermodynamic principles governing bound solute dialysis, commonly referred to as "albumin dialysis" or "sorbent dialysis" and practiced clinically with the Molecular Adsorbent Recirculating System (MARS) and Biologic-DT approaches, respectively, to develop a comprehensive understanding of the process. Dimensionless parameters emerging from the thermodynamic analysis that govern bound solute dialysis are as follows: (1) lambda, the binding power of the solute binding moiety; (2) kappa, the dialyzer mass transfer/blood flow rate ratio; (3) alpha, the dialysate/blood flow rate ratio; (4) beta, the dialysate/blood binding moiety concentration ratio, and (5) psi, the solute/binding moiety concentration ratio in the blood. Results from a mathematical model of countercurrent bound solute dialysis for phi = 0.9 indicate that for a given binding moiety (fixed lambda), the most important parameter for achieving high removal rates is the dialyzer mass transfer ratio for free (unbound) solute. The results also show solute removal approaching an asymptote with increasing beta that is dependent on kappa and independent of alpha. More importantly, results indicate that once a dialysis membrane is chosen, solute removal is virtually independent of blood flow rate, dialysate flow rate, and amount of binding moiety in the dialysate, provided the amount is greater than approximately 90% of that required to reach the asymptote. Experimental observations over a range of blood flow rates (100-400 ml/ minute), dialysate flow rates (50-400 ml/minute), and dialysate/blood albumin concentration ratios (beta = 0-0.3) corroborate the model predictions and indicate that < 4 g/L albumin in the dialysate solution is required for effective bound solute dialysis. The experimental results also show evidence of enhanced mass transfer once the dialysis membrane pore structure surface saturates with albumin.