Research
Shock Propagation in a Hollow-Fiber Hemodialyzer
Hemodialysis (HD) is one type of procedure for eliminating toxic chemicals and infusing bicarbonate in patients with end-stage renal disease (ESRD). We have developed a comprehensive mathematical model to describe the dynamic exchange process of solutes in a prototype hemodialyzer. The model, which is represented by a coupled set of transport equations, delineates the blood and dialyzate compartments of the hemodialyzer, and includes bicarbonate-buffering reaction in the blood channel and bicarbonate replenishment mechanism in the dialyzate. In a paper submitted by the author, we ignored the inherent velocity discontinuity in the blood channel as the radius of the blood channel ð‘Ÿð‘Ÿ approaches the semi-permeable membrane ð‘…ð‘…ðµðµ, that is, ð‘Ÿð‘Ÿâ†’ð‘…ð‘…ðµðµ. In this paper, we will investigate the evolution of bicarbonate and carbon dioxide in the blood compartment as the radius of the blood channel approaches the semi-permeable membrane. That is, we will investigate the solutions to the simplified form of the model in the blood compartment near the velocity shock vector, which manifests a discontinuity when ð‘£ð‘£ð‘§ð‘§(ð‘Ÿð‘Ÿ)=0 of the simplified non-steady state model. We will investigate the cases of analytical solutions of the model in the blood channel with negligible diffusion and also shock solutions with diffusion.
