Background:
Blood leukocytes constitute two interchangeable sub-populations, the marginated and circulating pools. these two sub-compartments are found in normal conditions and are potentially affected by non-normal situations, either pathological or physiological. the dynamics between the compartments is governed by rate constants of margination (m) and return to circulation (r). therefore, estimates of m and r may prove of great importance to a deeper understanding of many conditions. however, there has been a lack of formalism in order to approach such estimates. the few attempts to furnish an estimation of m and r neither rely on clearly stated models that precisely say which rate constant is under estimation nor recognize which factors may influence the estimation.
Results:
The returning of the blood pools to a steady-state value after a perturbation (e.g., epinephrine injection) was modeled by a second-order differential equation. this equation has two eigenvalues, related to a fast- and to a slow-component of the dynamics. the model makes it possible to identify that these components are partitioned into three constants: r, m and sb; where sb is a time-invariant exit to tissues rate constant. three examples of the computations are worked and a tentative estimation of r for mouse monocytes is presented.
Conclusions:
This study establishes a firm theoretical basis for the estimation of the rate constants of the dynamics between the blood sub-compartments of white cells. it shows, for the first time, that the estimation must also take into account the exit to tissues rate constant, sb.