A Continuous Integral Model for White Blood Cell Production

SIAM Journal on Applied Mathematics, vol. 82, pp. 2111–2130

Abstract

Abstract. Production of blood cells is a complex and tightly regulated process. Its quantitative understanding is highly relevant for the treatment of various diseases, including blood cancers. White blood cells (WBCs) originate from the so-called hematopoietic stem cell (HSC) population. HSCs give rise to immature WBCs that divide and further differentiate into mature cells. It is still a matter of debate whether cell differentiation resembles a discrete or a continuous process. We propose a novel continuous integral model (CIM) to describe WBC production. In agreement with recent experimental results, the maturity level of cells is described by a one-dimensional continuous variable. The process of maturation is modeled by an integral term that accounts for the influx of cells of maturity level [Formula: see text] from the differentiation of cells with lower maturity levels. In the model, cell proliferation and differentiation are controlled by a feedback signal which is a function of the mature cell population. We investigate the relationships between the proposed CIM, the multicompartment ordinary differential equations model introduced in [A. Marciniak-Czochra et al., Stem Cells Dev., 18 (2009), pp. 377–385] which treats differentiation as a discrete process, and the partial differential equations model of transport type studied by Doumic et al. [ SIAM J. Appl. Math., 71 (2011), pp. 1918–1940] which describes differentiation as a continuous process. We show that both models can be derived from the CIM and we perform numerical simulations to compare them qualitatively.

Authors 3

1. Yaming Zhang

   Shanghai Jiao Tong University

   Affiliation as printed

   School of Mathematics and Institute of Natural Sciences, Shanghai Jiao Tong University, Shanghai, People’s Republic of China

   School of Mathematics and Institute of Natural Sciences, Shanghai Jiao Tong University, Shanghai, People's Republic of China

2. Thomas Stiehl Aachen Institute for Computational Biomedicine-Disease Modeling

   RWTH Aachen University

   Affiliation as printed

   Institute for Computational Biomedicine - Disease Modeling, RWTH Aachen Medical School, Aachen, Germany

3. Min Ming Tang

   Shanghai Jiao Tong University

   Affiliation as printed

   School of Mathematics and Institute of Natural Sciences, MOE-LSC, and Qing Yuan Research Institute, Shanghai Jiao Tong University, Shanghai, People’s Republic of China

   School of Mathematics and Institute of Natural Sciences, MOE-LSC, and Qing Yuan Research Institute, Shanghai Jiao Tong University, Shanghai, People's Republic of China