The effect of ultrafiltration on dialysance. Mathematical theory and experimental verification

It is known that convective transport (ultrafiltration, QF) augments diffusive transport. This augmentation achieves great importance as solute molecular weight increases. Previous mathematical treatments of dialysance (D) have provided the relationship between D and blood flow rate (QB), dialysate flow rate (QD), and dialyzer membrane surface area permeability product (KoA), in the limit of QF = 0. The authors derived the relationship between D (defined as D') and QB, QD, and KoA for the general case of QF greater than or equal to 0: D' = X-Y/In X/Y . [(1-ó) QF + KoA] for X = X(D', QF, QD) = 1 - [D'/QD + QF] Y = Y(D', QF, QB) = D'-QB/QF-QB ó = the Staverman reflection coefficient. This equation demonstrates an approximate linear increase in D' as QF increases. Experimental verification is provided by in vivo studies of dialysis patients in which the dialysance of vancomycin doubles as QF is increased from 0 to 50. Because D' varies linearly with QF, this allows for the determination of KoA and ó. Using the Cobe 500HG Hemophan membrane, KoA for vancomycin was determined to be 6.54 and ó = 0.88.