Detecting autocatalytic dynamics in data modeled by a compartmental model

Modeling growth or reaction dynamics within a compartment in a compartmental model is often based on theoretical or first principle considerations. This approach is frequently applied due to the inability to observe or collect data directly from the compartment. When the internal dynamics are difficult to surmise, it is often the case that several competing models are constructed and compared in some way. In this paper, the dynamics which characterize the data of an autocatalytic process are used to describe a quantitative data analysis strategy to both recognize the presence of the autocatalytic process and to obtain some estimates of important parameters in the process. The compartmental model structure serves to communicate this dynamical information to the downstream compartments. This method has been applied to examine the dynamics of the engraftment of blood cells following hematopoietic stem cell transplantation in a clinical setting [Modeling the time to engraftment of white blood cells and platelets following autologous peripheral blood stem cell transplantation (2001)].