Using Mathematical Models to Study the Decrease and Multiplication Processes of Hepatitis C Virus Antigen During the Course of Clinical Dialysis Therapy

Hirohisa KOTERA, Masatomo YASHIRO, Atsushi OHASHI, Toshiro KATAYAMA
Vol. 1 (2012) p. 60-67

Hepatitis C virus (HCV) viral loads are reported to be lower in HCV-positive dialysis patients than in HCV-positive non-dialysis patients. Previously, we conducted in vitro experiments of HCV reperfusion using different dialysis membranes and performed curve fitting. We revealed that adsorption of HCV antigen onto the surface of dialysis membranes could be explained by the mathematical model of Langmuir’s adsorption isotherm. In the present study, we aimed at verifying the applicability of this mathematical model in clinical dialysis, by investigating the elimination dynamics of HCV antigen using the same dialysis membranes, comprising regenerated cellulose membrane (CU), cellulose triacetate membrane (CTA), polymethylmethacrylate membrane (PMMA), and polysulfone membrane (PS), in the clinical experiment. We estimated post-dialysis HCV antigen levels from measured pre-dialysis HCV antigen levels, using the mathematical model of Langmuir’s adsorption isotherm. Our results confirmed high adsorption of HCV antigen with the PS membrane, and demonstrated that the correlation coefficients between measured and estimated HCV antigen levels were over 0.97 with the PS, CTA, CU membranes. These results indicated the usefulness of Langmuir’s adsorption isotherm in clinical dialysis. However, HCV antigen increased again after a dialysis session until the next dialysis. Therefore, we applied the mathematical model of logistic growth to the multiplication process of HCV antigen during the inter-dialysis interval. Our results confirmed the usefulness of the logistic growth curve in describing the multiplication process of HCV antigen, and suggested that the increase in HCV antigen level during the dialysis interval was proportional to the decrease in HCV antigen level by hemodialysis therapy. In conclusion, we confirmed the usefulness of these mathematical models, and demonstrated that for each dialysis session, HCV antigen decreases and multiplies within a uniform range, which is characteristic of each dialysis membrane. The continuous multiplication of HCV antigen could be controlled, and we propose that the equilibrium of HCV antigen levels might be maintained by dialysis.