  Haematopoiesis is the process of generation of blood cells. Lymphopoiesis
generates lymphocytes, the cells in charge of the adaptive immune response.
Disruptions of this process are associated with diseases like leukaemia, which
is especially incident in children. The characteristics of self-regulation of
this process make them suitable for a mathematical study.
  In this paper we develop mathematical models of lymphopoiesis using currently
available data. We do this by drawing inspiration from existing structured
models of cell lineage development and integrating them with paediatric bone
marrow data, with special focus on regulatory mechanisms. A formal analysis of
the models is carried out, giving steady states and their stability conditions.
We use this analysis to obtain biologically relevant regions of the parameter
space and to understand the dynamical behaviour of B-cell renovation. Finally,
we use numerical simulations to obtain further insight into the influence of
proliferation and maturation rates on the reconstitution of the cells in the B
line. We conclude that a model including feedback regulation of cell
proliferation represents a biologically plausible depiction for B-cell
reconstitution in bone marrow. Research into haematological disorders could
benefit from a precise dynamical description of B lymphopoiesis.
