The International Journal of Artificial Organs/ Vol. 14 /no. 3, 1991/pp.186-188 Hemapheresis Mathematical modeling of antigen and immune complex kinetics during extracorporeal removal of autoantibody I J. WANIEWSKI and A. WERYNSKI Institute of Biocybernetics and Biomedical Engineering PAS, Warsaw - Poland ABSTRACT: The extracorporeal removal of circulating auto-antibodies by repeated plasma exchange or continuous lymph drainage is modeled by single-pool kinetics. Total amounts of antigenic determinants, k-valent antibodies and immune complexes are variables of the model. Factors influencing the course of therapy are included: production rate of antigen and antibody and their natural catabolism. This model can give useful formulae for clinical practice. The effect of treatment can be predicted from the relative depletion of antibodY and the actual severity of the disease. Another formula shows how the changed catabolisrn of antigen after antibody binding can influence the amount of immune complexes. As an example, lymph drainage in myasthenia gravis is calculated using averaged data from three patients. (lnt J Artif Organs, 1991: 14: 186-8) KEY WORDS: Extracorporeal antibody removal, Antibody kinetics, Antigen kinetics, Immune complexes kinetics, Myasthenia gravis INTRODUCTION In autoantibody-mediated disorders the extracorpo- real removal of circulating autoantibody (EGAR) has proved useful for therapy, at least in some cases. Good results of plasma exchange or lymph drainage in myasthenia gravis, Gullain-Barre syndrome and Goodpasture's syndrome are well documented (1). The effectiveness of this therapy depends on many factors. Rate of synthesis of autoantibody, cumulative injury and rate of repair of target organs (2), reversi- bility of autoantibody binding to its target, ratio of amount of antibody to amount of antigenic determi- nants (3) all seem relevant. The existing one-com- partment models of extracorporeal removal of auto- antibody do not take into account interactions be- tween antibody and antigen (4, 5). On the other hand, the mathematical model presented in (3) descri- bes the impact of plasma exchange on the level of bound This paper was presented at the International Symposium on Haemo- perfusion, Adsorbents in part Immobilized Reactants, Rostock, 1988 antibody that can dissociate from the target antigen. However it assumes that production of antigen and antibody and their natural catabolism are negligible during treatment. We propose a model including all the above factors influencing the course of therapy. Model arrangement Antigen and immune complexes are assumed not to circulate in plasma or lymph in large amounts; tor example they are "tissue bound" as in "receptor diseases" (6). Thus, only autoantibody can be re- moved. Total amounts of antigenic determinants (Ag). k-valent antibodies (Ab) and immune complexes (IC) are variables of the model. The following parameters are assumed to be constant during the disease and its treatment: WA 9 and TAg• WAb and TAb• Tic - rates of production and life times, y + - association ©by Wichtig Editore, 1991 0391-3988/186-03 $00. 75/0