IJPAM: Volume 79, No. 3 (2012)

MATHEMATICAL MODELING FOR HOLLOW FIBER
DIALYZER: BLOOD AND $HCO_{3}^{-} $-DIALYSATE
FLOW CHARACTERISTICS

Kodwo Annan
Department of Mathematics and Computer Science
Minot State University
Minot, North Dakota, 58707, USA


Abstract. In an attempt to improve the quality and efficacy of Hemodialysis (HD) therapy, dialyzers headers have been redesigned to improve uniform blood and dialysate flows. Any mismatch caused by non-uniform flow distributions in either blood or dialysate compartment would result in inefficiency of a dialyzer. Mathematical modeling technique was used to investigate and provide insights into the flow distributions during dialysis session. A suite of convection-diffusion models for blood and dialysate counter-current flows were deployed. The model coupled blood and dialysate side geometries through a Trans-membrane layer using Kedem-Katchalsky equations. The blood flow distributions were observed to be uniform across each cross-section while a non-uniform dialysate flow distributions were observed near the hollow-fiber packing area at the dialysate-side. The uniform blood-side flow distribution suggested that the new blood header design used in modern hollow-fiber dialyzers was an efficient flow distributor. The non-uniform dialysate flow profile indicated that the collars used in existing hollow-fiber dialyzers to help dialysate uniform flow failed to promote uniform flow. Consequently, the flow distributions mismatch in the dialyzer affected the boundary and bulk solute concentrations exchange across the membrane. The flow distribution analysis may have practical significances for the design of high efficient hollow-fiber dialyzers.

Received: April 26, 2012

AMS Subject Classification:

Key Words and Phrases: mathematical modeling, hollow fiber, dialyzer, blood flow

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Source: International Journal of Pure and Applied Mathematics
ISSN printed version: 1311-8080
ISSN on-line version: 1314-3395
Year: 2012
Volume: 79
Issue: 3