It is argued that the realism of computer simulations of network models of the immune system depends basically on the coherence of these models with the essentials of the known physiology of the cells and molecules selected to be modelled and on the incorporation in them of the different compartments of activated B cells. Focusing on these two aspects, here we analyse the simplifications and assumptions that go implicit in the formulation of a recently developed new class of network models that distinguish between immunoglobulins and B cells. This is approached by first building a general model which incorporates explicitly the kinetics of different B-cell compartments as well as a splenic compartment and a peripheric one for immunoglobulins, and then formally studying the simplifications on this model that are necessary to recover the initial simpler models. Following this procedure, it is shown that the effective coefficients of the different rate terms in the simpler models are particular combinations of the elementary rates obtained empirically. These relations reflect the particular assumptions associated with each simplification step. Also, it is shown that the usual biological interpretation of some of the coefficients in the ordinary differential equations of the simpler models is inconsistent with the more exact general model, unless one makes certain unreasonable assumptions about B-cell physiology. The relevance of this approach in providing variables with a biologically identifiable reality and for realistic, testable, computer simulations is discussed.