Publications:

Models of discrete and continuous cell differentiation in the framework of transport equation, SIAM Journal on Mathematical Analysis. Accepted. Preprint available at http://mmns.mimuw.edu.pl/preprints/2011-007.pdf (with P. Gwiazda and G. Jamróz)

Effective pressure interface law for transport phenomena between an unconfined fluid and a porous medium using homogenization, SIAM Multiscale Meth. Sim. Accepted. Preprint available at http://arxiv.org (with A. Mikelic)

Mathematical modelling of leukemogenesis and cancer stem cell dynamics. Math. Mod. Natural Phenomena. Accepted.

Structured population model of stem cell differentiation. SIAM J. Appl. Math. 71: 1918-1940 Published online: http://link.aip.org/link/?SMM/71/1918 doi:10.1137/100816584; 2011 (with M. Doumic, B. Perthame and J. Zubelli)

Strong two-scale convergence and corrector result for the receptorbased model of the intercellular communication. IMA J. Appl. Math. Accepted, 2011;

Stability of nonconstant stationary solutions in a reaction-diffusion equation coupled to the system of ordinary differential equations. Comm. Pure Appl. Anal. 11: 229-241 Accepted, 2011 (with Y. Golovaty and M. Ptashnyk)

A model for stem cell population dynamics with regulated maturation delay", Discrete Cont. Dyn. Systems, B. Suppl.: 32-43, Accepted, 2011 (with T. Alarcon, P. Getto and M. Vivanco)

Stability analysis of multi-compartment models for cell production systems. J. Biol. Dynamics. Published online: http://dx.doi.org/10.1080/17513758.2011.558214, 2011 (with Y. Nakata, P. Getto and T. Alarcon)

Three-Scale Convergence for Processes in Complex Heterogeneous Media. J. Appl. Anal. Published online: 10.1080/00036811.2011.569498 (with D. Trucu and M. Chaplain)

Characterization of stem cells using mathematical models of multiscale cell lineages. Math. Comp. Models. 53: 1505-1517, 2011 (with T. Stiehl)

Expansion of Mesenchymal Stromal Cells is affected by Serum Supplements and Passaging: Comprehensive Insights from a Cell Automaton Model. Cell Transplantation. Published online: doi:10.3727/096368910X557218, 2011 (with D. Cholewa, T. Stiehl, G. Bokermann, S. Joussen, C. Koch, T. Walenda, N. Pallua, C. V. Suschek and W. Wagner)

Boundedness of solutions of a haptotaxis model. Math. Mod. Meth. Appl. 20: 449 - 476, 2010 (with M. Ptashnyk)

Structured population models in metric spaces. J. Hyp. Diff. Eq. 7: 733-773, 2010 (with P.Gwiazda)

A nonlinear structured population model: Global existence and structural stability of measure-valued solutions. J. Diff. Eq. 11: 2703-2735, 2010 (with T. Lorenz and P. Gwiazda)

Modeling of Replicative Senescence in Hematopoietic Development. Aging 1: 723-732, 2009 (with T. Stiehl and W. Wagner)

Modeling asymmetric cell division in hematopietic stem cells - regulation of self-renewal is essential for efficient repopulation. Stem Cells Dev. 17: 1-10, 2009 (with T. Stiehl, A. D. Ho., W. Jäger and W. Wagner)

Mathematical modelling of the influence of heat shockproteins on cancer invasion of tissue. J. Math. Biol. 58: 819-840, 2009 (with Z. Szymańska, J. Urbański)

Derivation of a macroscopic receptor-based model using homogenisation techniques. SIAM J. Mat. Anal. 40: 215-237, 2008 (with M. Ptashnyk)

Reaction-difusion model of early carcinogenesis: The effects of influx of mutated cells. Math. Mod. Natural Phenomena 7: 90-114, 2008 (with M. Kimmel)

Modelling and analysis of dynamics of viral infection of cells and of interferon resistance. J. Math. Anal. Appl. 344: 821--850, 2008 (with P. Getto and M. Kimmel)

Modelling of early lung cancer progression: Influence of growth factor production and cooperation between partially transformed cells. Math. Mod. Meth. Appl. Sci. 17: 1693-1719, 2007 (with M. Kimmel)

Perspectives of mathematical modelling for understanding of macrophage function. Immunobiology, 2007 (with J. Kzhyshkowska and A. Gratchev)

Receptor-based models with hysteresis for pattern formation in hydra. Math. Biosci. 199: 97-119, 2006

Stochastic regulation in eukaryotic gene expression. J. Theor. Biol. 238: 348-367, 2006 (with T. Lipniacki, P. Paszek, A. R. Brasier and M. Kimmel)

Dynamics of growth and signalling along linear and surface structures in very early tumours. Comp. Math. Meth. Med. 7: 189-213, 2006 (with M. Kimmel)

Reaction-diffusion approach to modeling of the spread of early tumors along linear or tubular structures. J. Theor. Biol. 244: 375-387, 2006 (with M. Kimmel)

Mathematical model of tumour invasion along linear or tubular structures. Math. Comp. Modelling. 41: 1097-1108, 2005 (with M. Kimmel)

Receptor-based models with diffusion-driven instability for pattern formation in hydra. J. Biol. Sys. 11: 293-324, 2003

Logistic equation in tumor growth modelling. Internat. J. Appl. Math. Comput. Sci. 13: 317-325, 2003 (with U. Forys).

Diffusion limit for the phenomenon of random genetic drift. Appl. Math. 27: 81-101, 2000.

Manuscripts conditionally accepted for publication and under revision:

A continuous mechanobiological model of lateral inhomogeneous biological surfaces. J. Math. Biol. Conditionally accepted. Revised version submitted. Preprint available at http://www.ub.uni-heidelberg.de/archiv/11591 (with M. Mercker and D. Hartmann)

Modeling the reconstitution time after bone marrow transplant: Impact of transplant size and composition. Blood. Under revision (with T. Stiehl, A. D. Ho and W. Wagner)

Submitted papers:

Unstable patterns in reaction-diffusion model of early carcinogenesis, Submitted. Preprint available at http://arxiv.org/abs/1104.3592 (with G. Karch and K. Suzuki)

A reaction-diffusion model for viral infection and immune response. Submitted in 10/2010 (with M. Labadie)

Global dynamics of two compartment models for cell production systems with regulatory mechanisms, Submitted (with P. Getto, A. Nakata and M Vivanco)

Proceedings:

Multistability and hysteresis-based mechanism of pattern formation in biology. In "Pattern Formation in Morphogenesis-problems and their Mathematical Formalization", Capasso, V., Gromov, M., Morozova, N., (Eds.) Springer Verlag. To appear (with A. Köthe)

Mathematical Models of Hematopoietic Reconstitution after Stem Cell Transplantation. In "Model Based Parameter Estimation: Theory and Applications" Bock, H.G., Carraro, T., Jäger, W., Körkel, S., Rannacher, R., Schlöder, J.P., (Eds.) Contributions in Mathematical and Computational Sciences, Vol. 3, Springer Verlag. To appear (with T. Stiehl)

Mathematical models of stem cells renewal and differentiation. Oberwolfach Reports, 2, 2009;

Effects of logistic proliferation in the model of cancer invasion, Proceedings of the XIII National Conference Application of Mathematics in Biology and Medicine, Leszno, September 17-19, 2008 (with M. Ptashnyk)