Mathematical study on kinetics of hematopoietic stem cells--theoretical conditions for successful transplantation

Numerous haematological diseases occur due to dysfunctions during homeostasis processes of blood cell production. Haematopoietic stem cell transplantation (HSCT) is a therapeutic option for the treatment of haematological malignancy and congenital immunodeficiency. Today, HSCT is widely applied as an alternative method to bone marrow transplantation; however, HSCT can be a risky procedure because of potential side effects and complications after transplantations. Although an optimal regimen to achieve successful HSCT while maintaining quality of life is to be developed, even theoretical considerations such as the evaluations of successful engraftments and proposals of clinical management strategies have not been fully discussed yet. In this paper, we construct and investigate mathematical models that describe the kinetics of hematopoietic stem cell self-renewal and granulopoiesis under the influence of growth factors. Moreover, we derive theoretical conditions for successful HSCT, primarily on the basis of the idea that the basic reproduction number R (0) represents a threshold condition for a population to successfully grow in a given steady-state environment. Successful engraftment of transplanted haematopoietic stem cells (HSCs) is subsequently ensured by employing a concept of dynamical systems theory known as 'persistence'. On the basis of the implications from the modelling study, we discuss how the conditions derived for a successful HSCT are used to link to experimental studies.