Home Research CV Publications Teaching Links  


Publications:

2017
Steady states of FitzHugh-Nagumo system with non-diffusive activator and diffusive inhibitor. Tohoku J. Math. Accepted, 2017 (with Y. Li, I. Takagi, B. Wu)
Measures under the flat norm as ordered normed vector space, Positivity, Accepted, doi:10.1007/s11117-017-0503-z, 2017 (with P. Gwiazda, H.R. Thieme)
Reduced Hematopoietic Stem Cells Frequency Predicts Outcome In Acute Myeloid Leukemia, Haematologica, doi:10.3324/haematol.2016.163584, 2017 (with W. Wang, T. Stiehl, S. Raffel, VT. Hoang, I. Hoffmann, L. Poisa-Beiro,BR. Saeed, R. Blume, L. Manta, V. Eckstein, T. Bochtler, P. Wuchter, M. Essers, A. Jauch, A. Trumpp, AD. Ho, C. Lutz)
The escalator boxcar train method for a system of aged-structured equations in the space of measures: The convergence, 2017 (with J. A. Carrillo, P. Gwiazda, K. Kropielnicka)
Revealing age-related changes of adult hippocampal neurogenesis, bioRxiv 112128; doi: https://doi.org/10.1101/112128, 2017 (with F. Ziebell, S. Dehler, A. Martin-Villalba)
Instability of Turing patterns in reaction-diffusion-ODE systems, J. Math. Biol. 74: 583-618, 2017 (with G. Karch, K. Suzuki)
Stable patterns with jump discontinuity in systems with Turing instability and hysteresis, Disc. Cont. Dyn. Sys. A. 37: 757 - 800, 2017 (with S. Härting, I. Takagi)
2016
The escalator boxcar train method for a system of age-structured equations, Networks and Heterogeneous Media 11(1), 123-143, 2016 (with P. Gwiazda, K. Kropielnicka)
Diffusion-driven blowup of nonnegative solutions to reaction-diffusion-ODE systems, Differential Integral Equations 29, 715-730, 2016 (with G. Karch, K. Suzuki, J. Zienkiewicz)
Emergence of heterogeneity in acute leukemias, Biology Direct 11(51), doi: 10.1186/s13062-016-0154-1, 2016 (with T. Stiehl, C. Lutz)
Shadow limits via the renormalization group method and the center manifold method, Vietnam Journal of Mathematics. A special issue in honour of Prof. Willi Jäger 1-23, doi: 10.1007/s10013-016-0199-6, 2016 (with A. Mikelić)
Single cell analysis uncovers clonal acinar cell heterogeneity in the adult pancreas, Dev. Cell 39: 289-301, 2016 (with D. Wollny, S. Zhao, I. Everlien, X. Lun, J. Brunken, D. Brüne, F. Ziebell, I. Tabansky, W. Weichert, A.Martin-Villalba)
Bifurcation analysis of a Diffusion-ODE Model with Turing instability and hysteresis", Hiroshima Mathematical Journal, 2016, accepted (with Y. Li, I. Takagi, B. Wu)
Beyond Turing: Mechanochemical pattern formation in biological tissues, Biol. Direct., 11:22, doi: 10.1186/s13062-016-0124-7, 2016 (with M. Mercker, F. Brinkmann, T. Richter)
Mass concentration in a nonlocal model of clonal selection, J. Math. Biol., 73(4):1001-1033, doi: 10.1007/s00285-016-0979-3, 2016 (with J.- E. Busse, P.Gwiazda)
2015
Pattern formation in a diffusion-ODE model with hysteresis, Differential and Integral Equations, 28: 655-694, 2015 (with M. Nakayama, I. Takagi)
A rigorous derivation of the equation for the clampled Biot-Kirchhoff-Love poroelastic plate, Arch. Rat. Mech. Anal. 215: 1035-1062, doi: 10.1007/s00205-014-0805-2, 2015 (with A. Mikelić)
Effective interface conditions for the forced infiltration of a viscous fluid into a porous medium using homogenization, Computer Meth. Appl. Mech. Eng. 292: 195-220, doi: 10.1016/j.cma.2014.10.050, 2015 (with T. Carraro, C. Goll, A. Mikielić)
Mathematical modelling as a tool to understand cell self-renewal and differentiation, Methods Mol Biol., 1293:247-66, doi: 10.1007/978-1-4939-2519-3_15, 2015 (with P. Getto)
Mechanochemical symmetry breaking in Hydra aggregates, Biophys J., 108(9): 2396-2407, doi: 10.1016/j.bpj.2015.02.033, 2015 (with M. Mercker, A. Köthe)
Bud-neck scaffolding as a possible driving force in ESCRT-induced membrane budding, Biophys J., 17;108(4):833-43, doi: 10.1016/j.bpj.2014.12.040, 2015 (with M. Mercker)
Cell division patterns in acute myeloid leukemia stem-like cells determine clinical course: a model to predict patient survival, Cancer Res. 75 (6): 940-9. doi: 10.1158/0008-5472.CAN-14-2508., 2015 (with T. Stiehl, N. Baran and A.D. Ho)
2014
Clonal selection and therapy resistance in acute leukemias: Mathematical modelling explains different proliferation patterns at diagnosis and relapse, J. Royal Society Interface 11: 20140079, doi: http://dx.doi.org/10.1098/rsif.2014.0079, 2014 (with T. Stiehl, N. Baran and A.D. Ho)
Feedback Signals in Myelodysplastic Syndromes: Increased Self-Renewal of the Malignant Clone Suppresses Normal Hematopoiesis, PLOS Comp Biol., Accepted, 2014 (with T. Walenda, T. Stiehl, H. Braun, J. Fröbel, A.D. Ho, T. Schroeder, T. Goecke, U.U. Germing and W. Wagner)
Mathematical modelling of adult hippocampal neurogenesis: effect of altered stem cell dynamics on cell counts and BrdU-labelled cells, J. Royal Society Interface 11: 20140144, doi: http://dx.doi.org/10.1098/rsif.2014.0144, 2014 (with F. Ziebell and A. Martin-Villaba)
Revealing the role of SGK1 in the dynamics of medulloblastoma using mathematical models, J Theor Biol. doi: 10.1016/j.jtbi.2014.03.028, 2014 (with J. Kawka, S. Pfister, S. Pleier and D. Sturm)
The Role of Multiscale Modelling in Systems Medicine, Genome Medicine 6:21, doi: 10.1186/gm538, 2014 (with O. Wolkenhauer, C. Auffray, O. Brass, J. Clairambault, A. Deutsch, D. Drasdo, F. Gervasio, L. Preziosi, P. Maini, C. Kossow, L. Kuepfer, K. Rateitschak, I. Ramisole, B. Ribba, A, Schuppert, R. Smallwood, G. Stamatakos, F. Winter and H. Byrne)
The impact of CD34+ cell dose on engraftment after Stem Cell Transplantations: personalized estimates based on mathematical modeling, Bone Marrow Transp. 49, 30-37, doi: 10.1038/bmt.2013.138, 2014 (with T. Stiehl and A.D. Ho)
Analysis of particle methods for structured population models with nonlocal boundary term in the framework of bounded Lipschitz distance, Numer. Methods Partial Differential Eq.,30: 1797-1820.doi:10.1002/num.21879, 2014 (with P. Gwiazda, J. Jabłoński and A. Ulikowska)
2013
Modelling the experimental impossible: Dance of the molecules, Ruperto Carola, Forschungsmagazin 3, 132-139, 2013 (with M. Mercker)
A mechanochemical model for embryonic pattern formation: Coupling tissue mechanics and morphogen expression, PLOS ONE doi: 10.1371/journal.pone.0082617, 2013 (with M. Mercker and D. Hartmann)
Modeling and computing of the deformation dynamics of inhomogeneous biological surface, SIAM J. Appl. Math. 73(5), 1768-1792, 2013 (with M. Mercker, T. Richter and D. Hartmann)
Global dynamics of two-compartment models for cell production systems with regulatory mechanisms, Math. Biosci. 245: 258-268, 2013 (with P. Getto, Y. Nakata and M. Vivanco)
Unstable patterns in autocatalytic reaction-diffusion-ODE systems, Submitted. Preprint available at http://arxiv.org/abs/1301.2002, 2013 (with G. Karch, K. Suzuki)
Spike patterns in a reaction-diffusion-ode model with Turing instability, Math. Meth. Appl. Sci. Accepted. Preprint available at http://arxiv.org/abs/1303.5362, 2013 (with S. Härting)
A nonlinear effective slip interface law for transport phenomena between a fracture flow and a porous medium, Submitted. Preprint available at http://arxiv.org/abs/1303.3496, 2013 (with A. Mikelic)
Efficient algorithms computing distances between Radon measures on R, Submitted. Preprint available at http://arxiv.org/abs/1304.3501, 2013 (with J. Jabłoński)
Dynamical spike solutions in a nonlocal model of pattern formation, Submitted. Preprint available at http://arxiv.org/abs/1307.6236, 2013 (with A. Härting, S. Karch and K. Suzuki)
Pressure jump interface law for the Stokes-Darcy coupling: Confirmation by direct numerical simulations, J. Fluid Mechanics 732: 510-536, 2013 (with T. Carraro, C. Goll and A. Mikelic)
A reaction-diffusion model for viral infection and immune response, Submitted. Preprint available at http://hal.archives-ouvertes.fr/, 2013 (with M. Labadie)
Assessing Hematopoietic (Stem-) Cell Behavior during Regenerative Pressure. In: "Systems Biology of Blood" Corey, S., Kimmel, M., Leonard, J., Springer, New York, to appear, 2013 (with T. Stiehl and A.D. Ho)
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 Proceedings in Mathematics 15: 153-173, 2013 (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, 2013 (with T. Stiehl)
2012
Unstable patterns in reaction-diffusion model of early carcinogenesis, J. Math. Pures et Appliques, Published online: http://dx.doi.org/10.1016/j.matpur.2012.09.011, 2012 (with G. Karch and K. Suzuki)
Models of discrete and continuous cell differentiation in the framework of transport equation, SIAM Journal on Mathematical Analysis 44:1103-1133, 2012 (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. 10:285-305, 2012 (with A. Mikelic)
Mathematical modelling of leukemogenesis and cancer stem cell dynamics. Math. Mod. Natural Phenomena 7:166-202; 2012 (with T. Stiehl)
2011
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. Published online: doi:10.1093/imamat/hxs052, 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)
2010
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)
2009
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)
2008
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)
2007
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)
2006
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)
2005
Mathematical model of tumour invasion along linear or tubular structures. Math. Comp. Modelling. 41: 1097-1108, 2005 (with M. Kimmel)
2003
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).
2000
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)

Back to top: Back to Top