c o m p u t e r m e t h o d s a n d p r o g r a m s i n b i o m e d i c i n e 1 0 8 ( 2 0 1 2 ) 68–79 j o ur nal homep age : w ww.intl.elsevierhealth.com/journals/cmpb Mathematical analysis for internal ﬁltration of convection-enhanced high-ﬂux hemodialyzer Jung Chan Lee a , Kyungsoo Lee b , Hee Chan Kim a,c,d,* a Institute of Medical and Biological Engineering, Medical Research Center, Seoul National University, Seoul, Republic of Korea b Department of Internal Medicine, University of Michigan School of Medicine, Ann Arbor, MI, USA c Department of Biomedical Engineering, Seoul National University College of Medicine, Seoul, Republic of Korea d Department of Biomedical Engineering, Seoul National University Hospital, Seoul, Republic of Korea a r t i c l e i n f o Article history: Received 1 March 2011 Received in revised form 3 January 2012 Accepted 9 January 2012 Keywords: Hemodialysis High-ﬂux Hemodialyzer Convection Internal ﬁltration Backﬁltration Ultraﬁltration a b s t r a c t Structural modiﬁcations using a conventional hemodialyzer improved the internal ﬁltra- tion and clearance of middle molecular weight wastes by enhanced convection effect. In this study, we employed a mathematical model describing the internal ﬁltration rate as well as the hemodynamic and hematologic parameters in highﬂux dialyzer to inter- pret the previous reported experimental results. Conventional high-ﬂux hemodialysis and convection-enhanced high-ﬂux hemodialysis were conﬁgured in the mathematical forms and integrated into the iterative numerical method to predict the internal ﬁltration phe- nomena inside the dialyzers during dialysis. The distributions of blood pressure, dialysate pressure, oncotic pressure, blood ﬂow rates, dialysate ﬂow rates, local ultraﬁltration, hema- tocrit, protein concentration and blood viscosity along the axial length of dialyzer were calculated in order to estimate the internal ﬁltration volume. The results show that the ﬁl- tration volumes by internal ﬁltration is two times higher in a convection-enhanced high-ﬂux hemodialyzer than in a conventional high-ﬂux hemodialzer and explains the experimen- tal result of improved clearance of middle molecular size waste in convection-enhanced high-ﬂux hemodialyzer. © 2012 Elsevier Ireland Ltd. All rights reserved. 1. Introduction Although various renal replacement therapies are available to treat kidney disease, it is important to achieve the balance of convective and diffusive therapies when treating patients with chronic renal failure. Some convection-enhanced treat- ments have been developed and applied clinically to achieve sufﬁcient clearance of not only small molecular waste but also intermediate molecular weight toxins [1,2]. For the purpose of the effective clearance of middle molecular weight uremic ∗ Corresponding author at: Department of Biomedical Engineering, Seoul National University College of Medicine, 28 Yongon-dong, Jongro- gu, Seoul 110-744, Republic of Korea. Tel.: +82 2 2072 2931; fax: +82 2 741 8597. E-mail address: hckim@snu.ac.kr (H.C. Kim). toxins, high-ﬂux dialysis and hemodiaﬁltration are used widely to treat patients instead of conventional hemodial- ysis [3,4]. Additionally, protein-bound uremic toxins such as p-cresol, hippuric acid, indole acetic acid and indoxyl sulfates which are poorly cleared by diffusive effect in con- ventional low-ﬂux dialysis can be effectively cleared by the convective effect in high-ﬂux dialysis and hemodiaﬁltra- tion [5–7]. However, an enormous volume of substitution ﬂuid is needed to achieve sufﬁcient efﬁcacy using the hemodiaﬁltration treatment [8]. High-ﬂux hemodialysis is a convection-enhanced renal replacement treatment that does 0169-2607/$ – see front matter © 2012 Elsevier Ireland Ltd. All rights reserved. doi:10.1016/j.cmpb.2012.01.001