Mathematical modelling of human hematopoiesis

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Human hematopoiesis is a beautiful full organ system for studying cellular proliferation, differentiation and maturation. A small number of long term hematopoietic stem cells (HSCs) which reside in the bone marrow and may divide as rarely as once every 10 months, sit at the heart of a vast web of production which produces more than 1011 blood cells per day. This process requires many cellular divisions and takes several weeks from the initial differentiation of a long term HSC until resulting mature cells appear in circulation. Remarkably, all the different blood cell types including neutrophils, monocytes, erythrocytes and platelets among others are created from a small pool of apparently homogeneous HSCs in this way. Despite the tremendous production rate, significant maturation delays in the system, and need to produce different quantities of various daughter cells, for nearly all individuals hematopoiesis proceeds flawlessly over many decades, implying the existence of finely tuned control mechanisms and feedback loops. Most of the production process occurs in the bone marrow where direct observation is markedly more difficult than in the circulation. Consequently, we mathematically model the dynamics and processes occurring in the bone marrow, using observations of the changing circulating concentrations of mature cells to validate the models. Using such models we will elucidate the processes taking place in the bone marrow in a non-invasive manner. Our main objective is to understand the regulation of normal hematopoiesis, and to do this we will study the principal cytokines and the control loops formed by their kinetics and dynamics. We already modelled in detail the kinetics and dynamics of G-CSF, the main cytokine acting in granulopoiesis, and demonstrated how it regulates the production of neutrophils. We will extend our modelling to include monocytes and erythrocytes and their associated cytokines. Recent insights into human HSC physiology will be translated into a mathematical model for HSC regulation that distinguishes between long, intermediate and short term HSCs, and includes both symmetric and asymmetric cell division. Our mathematical models are mechanistic with each variable, coefficient and function representing a specific cell type or process. They are typically stated as systems of delay-differential equations, where delays arise due to the time to complete the cell cycle or due to maturation times. Because hematopoiesis is usually so well regulated, to gain insight into its control mechanisms it is necessary to consider the system when not at homeostasis. Data from various sources, including administering synthetic forms of cytokines to healthy subjects, or to patients undergoing chemotherapy or autologous peripheral blood stem cell transplantation, will be used to guide our modelling and reveal the details of the feedback loops that control hematopoiesis.