Abstract
Hemodialysis (HD) is one type of procedure for eliminating toxic chemicals and infusing bicarbonate in patients with end-stage renal disease (ESRD). Research and development in the hemodialyzer industry have, hitherto, depended mostly on empirical evidence to optimize HD therapy. This is often costly and involves numerous clinical trials. Developing a comprehensive time-dependent mathematical model to examine the dynamic exchange of solutes (HCO-3 and pCO2), blood pH and H+ ions in a prototype hollow-fiber hemodialyzer is essential in optimizing future design and improvement. A comprehensive mathematical model which is represented by a coupled set of transport equations and delineates the blood and dialyzate compartments of the hemodialyzer, and includes bicarbonate-buffering reaction in the blood channel and bicarbonate replenishment mechanism in the dialysate, is used to describe the time-dependent bulk concentration and exit concentration of solutes, blood pH and H+ ions in the hollow-fiber prototype hemodialyzer. A numerical simulation of the model is used to test several time-dependent bulks and exit concentration profiles of solutes in the blood and dialyzate. Results obtained from the numerical solution of the model show the bulk and exit concentrations of solute at various distances along the blood and dialyzate channels at different times. This modeling exercise will also allow us in our next study to examine some physical mechanisms of the hemodialyzer.
Highlights
A comprehensive mathematical model which is represented by a coupled set of transport equations and delineates the blood and dialyzate compartments of the hemodialyzer, and includes bicarbonate-buffering reaction in the blood channel and bicarbonate replenishment mechanism in the dialysate, is used to describe the time-dependent bulk concentration and exit concentration of solutes, blood pH and H+ ions in the hollow-fiber prototype hemodialyzer
In a similar experiment performed over 12 weeks, Ward et al [5] were faced with the problem of how to control bicarbonate during HD therapy and that resulted in abnormally high pH value which puts the patient at risk of post-dialytic alkalosis
In order to go beyond black-box input-output ordinary differential equation models, and efficiently address the dynamic exchange of solutes in the prototype hemodialyzer, a comprehensive partial differential equation model incorporating internal properties, the dimensions and the surface area of the hollow fibers used during hemodialysis, the nature of solute transfer across the hemodialyzer semi permeable membrane, the hemodialysis flow rates and the duration of the administration of hemodialysis were taken into account
Summary
Monti et al [7] used a black box input-output ordinary differential equation model to describe the dynamic exchange process of bicarbonate during and after HD This black-box model was oversimplified because the internal structure and variables of the prototype hemodialyzer unit were not taken into account. In order to go beyond black-box input-output ordinary differential equation models, and efficiently address the dynamic exchange of solutes in the prototype hemodialyzer, a comprehensive partial differential equation model incorporating internal properties, the dimensions and the surface area of the hollow fibers used during hemodialysis, the nature of solute transfer across the hemodialyzer semi permeable membrane, the hemodialysis flow rates and the duration of the administration of hemodialysis were taken into account. The knowledge gained from this study will eventually lead to a means of predicting the underlying mechanisms of solute transfer in a prototype hemodialyzer, thereby minimizing the need to perform costly and time-consuming clinical trials
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