Roeder, Ingo; Herberg, Maria; Horn, Matthias An “age”-structured model of hematopoietic stem cell organization with application to chronic myeloid leukemia. (English) Zbl 1182.92043 Bull. Math. Biol. 71, No. 3, 602-626 (2009). 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. Cited in 17 Documents MSC: 92C50 Medical applications (general) 92C37 Cell biology 35Q92 PDEs in connection with biology, chemistry and other natural sciences 65C20 Probabilistic models, generic numerical methods in probability and statistics Keywords:chronic myeloid leukemia; imatinib; hematopoietic stem cell; mathematical model; partial differential equation; computer simulation PDFBibTeX XMLCite \textit{I. Roeder} et al., Bull. Math. Biol. 71, No. 3, 602--626 (2009; Zbl 1182.92043) Full Text: DOI References: [1] Atkinson, K.A., 1989. An Introduction to Numerical Analysis, 2nd edn. Wiley, New York. · Zbl 0718.65001 [2] Branford, S., Hughes, T.P., Rudzki, Z., 1999. Monitoring chronic myeloid leukaemia therapy by real-time quantitative PCR in blood is a reliable alternative to bone marrow cytogenetics. Br. J. Haematol. 107(3), 587–99. [3] Buchdunger, E., Zimmermann, J., Mett, H., Meyer, T., Müller, M., Druker, B.J., Lydon, N.B., 1996. 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