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An “age”-structured model of hematopoietic stem cell organization with application to chronic myeloid leukemia. (English) Zbl 1182.92043

Summary: Previously, we have modeled hematopoietic stem cell organization by a stochastic, single cell-based approach [M. Loeffler and I. Roeder, Cells, Tissues, Organs 171, No. 1, 8–26 (2002); I. Glauche et al., Stem Cells 25, No. 7, 1791–1799 (2007)]. Applications to different experimental systems demonstrated that this model consistently explains a broad variety of in vivo and in vitro data. A major advantage of the agent-based model (ABM) is the representation of heterogeneity within the hematopoietic stem cell population. However, this advantage comes at the price of time-consuming simulations if the systems become large.

One example in this respect is the modeling of disease and treatment dynamics in patients with chronic myeloid leukemia (CML), where the realistic number of individual cells to be considered exceeds 10 6 . To overcome this deficiency, without losing the representation of the inherent heterogeneity of the stem cell population, we propose to approximate the ABM by a system of partial differential equations (PDEs). The major benefit of such an approach is its independence from the size of the system. Although this mean field approach includes a number of simplifying assumptions compared to the ABM, it retains the key structure of the model including the “age”-structure of stem cells. We show that the PDE model qualitatively and quantitatively reproduces the results of the agent-based approach.

92C50Medical applications of mathematical biology
92C37Cell biology
35Q92PDEs in connection with biology and other natural sciences
65C20Models (numerical methods)
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