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 𝑟𝑟 approaches the semi-permeable membrane 𝑅𝑅𝐵𝐵, that is, 𝑟𝑟→𝑅𝑅𝐵𝐵. 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 𝑣𝑣𝑧𝑧(𝑟𝑟)=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.
