Evaluation of the Toxin-to-Protein Binding Rates during Hemodialysis Using Sorbent-Loaded Mixed-Matrix Membranes  
[PERSON]  
1 Institute of Chemical Engineering Sciences (ICE-HT), Foundation for Research and Technology, Hellas (FORTH), Stadiou, Platani, GR-26504 Patras, Greece; [EMAIL_ADDRESS] (C.S.S. ); [PERSON]] (E.D.S.) 2 Department of Chemical Engineering, University of Patras, GR-26504 Patras, Greece  
3 Department of Mechanical Engineering TE, TEI of Western Greece, GR-26334 Patras, Greece  
4(Bio)artificial Organs group, Department of Biomaterials Science and Technology, TechMed Institute for Biomedical Technology and Technical Medicine, University of Twente, 7522 NB Enschede, The Netherlands; [EMAIL_ADDRESS] (D.P. ); [EMAIL_ADDRESS] (D.S.) 5 Correspondence: [EMAIL_ADDRESS]; Tel. : +30-261-096-5215  
called the \"free fraction\", while the majority of the PBTs are attached to albumin, forming a complex called the \"bound fraction\". The protein-binding of the uremic toxins is considered reversible, because it is mainly driven by van der Waals forces [PERSON] (1936). As free toxins are removed, for instance through a hemodialysis membrane, the toxin concentration in the blood is gradually diminished. According to [PERSON]'s principle, the partial subtraction of the free form will shift the equilibrium towards the enhancement of dissociation of the complex [PERSON] (1936). This argument is further supported by the fact that, due to the membrane cut-off function, the protein-bound toxins are removed almost exclusively as free fractions, thus the dissociation of a protein-bound toxin to its dissolved free form is the only possible way of removal [PERSON] (1936). Moreover, the presence of the activated carbon as a sorbent in the membrane matrix increases the concentration gradient and, thus, helps deplete the region around the albumin from the free fraction of the toxin, favoring in this way the detachment of the bound fraction from the protein. Despite the experimental evidence of this removal enhancement, it is necessary to develop a detailed macroscopic model that will encompass the mechanisms behind the toxin removal, quantify their effects, and assist the experimental, as well as the operational, aspects of the membrane development. Most of the models in the literature describe the mass transfer of a toxin through the membrane with an overall mass transfer coefficient, \(K_{o}\), that accounts for the mass transfer resistances in the blood side, the membrane, and the dialysate [PERSON] (1936). However, these models fail to provide accurate predictions under variable operating conditions, because all the reaction and transport mechanisms are encompassed in an overall mass transfer coefficient. In other studies, separate treatment of mass transfer through convection and diffusion is performed [PERSON] (1936), assuming constant volumetric flux through the membrane. There are also studies where phenomenological description of the carrier fluid and the transport of the toxins on linear non-equilibrium thermodynamics is applied [PERSON] (1936). The toxin concentrations on the membrane surfaces in contact with blood and dialysate are assumed constant and are related to the bulk toxin concentrations through a linear equilibrium relationship. This assumption is not valid, however, in the case of membrane fibers of sufficient length to allow variation of the toxin concentration in the blood along the fiber length. Moreover, most of the models in the literature appear to neglect the complex interactions of proteins, such as albumin and fibrinogen, with the blood and the toxins. Recently, an indirect calculation of toxin interaction constants was suggested using experimental data [PERSON] (1936). In this work, a detailed flow and mass transport model is developed that considers the characteristics and the operational conditions of the whole hemodialysis module, as it includes terms like flowrates, packing density of the fibers in the module, as well as blood and dialysate compositions.