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Mathematical Medicine and Biology 1987 4(1):59-68; doi:10.1093/imammb/4.1.59
© 1987 by Institute of Mathematics and its Applications
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One-Dimensional Theory of Haemofilters

N. F. BRITTON and J. WANIEWSKI

School of Mathematics, University of Bath Bath, BA2 7AY, U.K.
Institute of Biocybernetics and Biomedical Engineering PAS, Warsaw, Poland

Equations describing mass transfer in haemodialysers are discussed and applied to the haemofiltration process. Solutions are obtained in quadratures. In one case, the integral may be performed explicity to give a regular solutions, in spite of the singularity in the equations. A comparison with an approximate description of a haemofilter obtained by neglecting the filtrate flow along the membrane is given, and analytical expressions are derived in the case of low ultrafiltration flows. It is shown that a simple one-dimensional theroy is often sufficient in a determination of the parameters important in clinical applications of haemofilters.


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