A new semiempirical mathematical model for prediction of internal filtration in hollow fiber hemodialyzers

Gianfranco B. Fiore, Gualtiero Guadagni, Andrea Lupi, Zaccaria Ricci, Claudio Ronco

Research output: Contribution to journalArticlepeer-review


The potential of convective solute transport for blood purification has been widely explored. New techniques (such as hemodiafiltration), based on a combination of diffusion and convection techniques, have been developed. Owing to the internal filtration/backfiltration (IF/BF) phenomenon, high-flux dialysis also relies on a convective component, which, however, is hard to quantify and thus optimize. In this work, we developed a mathematical model designed to supply the clinician with a quantification of the IF/BF fluxes taking place during high-flux dialysis. IF fluxes are predicted based on the machine settings and blood hematocrit/protein concentration. The hydraulic characteristics of commercial dialyzers were derived from bloodless bench tests. Moreover, an in vitro blood test was conducted on a 1.8 m2 polysulfone dialyzer using an established scintigraphic analysis, for verification of model prediction accuracy. Results of simulations show that the IF/BF rate is sensitive to the blood flow rate and (to a lesser extent) to the dialysate flow rate. Increasing net ultrafiltration rates resulted in parallel increases of direct filtration and simultaneous decreases of BF. IF/BF is rather influenced by blood composition, due to the complex dependence of oncotic pressure and blood viscosity upon hematocrit and plasma protein concentration. Simulation results showed an excellent agreement with the experimental results obtained with scintigraphy, with only a 3% prediction error. With respect to some previous works, this model is simpler in its theoretical approach. It allows implementation into a user-friendly software tool and might be used to predict the convective component in high-flux dialysis and possibly to optimize it.

Original languageEnglish
Pages (from-to)555-568
Number of pages14
JournalBlood Purification
Issue number5-6
Publication statusPublished - Dec 2006


  • Backfiltration
  • Filtration, internal
  • High-flux hemodialyzer
  • Mathematical model
  • Ultrafiltration

ASJC Scopus subject areas

  • Nephrology
  • Hematology


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