Abstract
It has been shown that hematopoietic stem cells migrate in vitro and in vivo following the gradient of a chemotactic factor produced by stroma cells. In this paper, a quantitative model for this process is presented. The model consists of chemotaxis equations coupled with an ordinary differential equation on the boundary of the domain and subjected to nonlinear boundary conditions. The existence and uniqueness of a local solution is proved and the model is simulated numerically. It turns out that for adequate parameter ranges, the qualitative behavior of the stem cells observed in the experiment is in good agreement with the numerical results. Our investigations represent a first step in the process of elucidating the mechanism underlying the homing of hematopoietic stem cells quantitatively.
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References
Aiuti A., Webb I.J., Bleul C., Springer T. and Gutierrez-Ramos J.C. (1997). The Chemokine SDF-1 Is a Chemoattractant for Human CD34+ Hematopoietic Progenitor Cells and Provides a New Mechanism to Explain the Mobilization of CD34+ Progenitors to Peripheral Blood. J. Exp. Med. 185: 111–120
Evans L. (1999). Partial Differential Equations. AMS, Providence
Gajewski H., Gröger K. and Zacharias K. (1974). Nichtlineare Operatorgleichungen und Operatordifferentialgleichungen. Akademie-Verlag, Berlin
Grisvard, P.: Elliptic Problems in Nonsmooth Domains. Monographs and Studies in Mathematics, 24, Pitman (1985)
Horstmann D. (2004). From 1970 until present: The Keller–Segel model in chemotaxis and its consequences. Jahresbericht der DMV 105: 103–165
Jäger W. and Luckhaus S. (1992). On explosions of solutions to a system of partial differential equations. Trans. AMS 329: 819–824
Kettemann A. (2006). Die lokale Existenz und Eindeutigkeit der Lösung eines Chemotaxis-Modells für hämatopoietische Stammzellen. Universität Stuttgart, Diplomarbeit
Ladyženskaya, O., Solonnikov, V., Ural’ceva, N.: Linear and Quasilinear Equations of Parabolic Type. AMS, Translations of Mathematical Monographs, 23 (1968)
Lions J. (1969). Quelque méthodes de résolution des problèmes aux limites non linéaires. Dunod, Paris
Lions, J., Magenes, E.: Non-Homogeneous Boundary Value Problems and Applications. 1, Springer, Heidelberg (1972)
Nagai T. (1995). Blow-up of radially symmetric solutions to a chemotaxis system. Adv. Math. Sci. Appl. 5: 581–601
Neuss-Radu M. and Kettemann A. (2006). A mathematical model for stroma controlled chemotaxis of hematopoietic stem cells. Oberwolfach Rep. 24: 59–62
Post, K.: A system of non-linear partial differential equations modeling chemotaxis with sensitivity functions. Humboldt Universität zu Berlin, Mathematisch-Naturwissenschaftliche Fakultät II, electronic (1999)
Wagner W., Saffrich R., Wrikner U., Eckstein V., Blake J., Ansorge A., Schwager C., Wein F., Miesala K., Ansorge W. and Ho A.D. (2005). Hematopoietic progenitor cells and cellular microenvironment: behavioral and molecular changes upon interaction. Stem Cells 23: 1180–1191
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Kettemann, A., Neuss-Radu, M. Derivation and analysis of a system modeling the chemotactic movement of hematopoietic stem cells. J. Math. Biol. 56, 579–610 (2008). https://doi.org/10.1007/s00285-007-0132-4
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DOI: https://doi.org/10.1007/s00285-007-0132-4