research partners    
Ph.D. students    
consortium members    

Piotr Gwiazda
Institute of Applied Mathematics and Mechanics
University of Warsaw
Banacha 2,
02-097 Warsaw
phone: +48 22 5544551
fax: +48 22 5544700

Structured population models of cell aging and differentiation
Piotr Gwiazda (MIM, University of Warsaw) and Anna Marciniak-Czochra (IWR, University of Heidelberg)
in collaboration with Benoît Perthame (Pierre & Marie Curie University, Paris)
The project is carried out by Grzegorz Jamróz at University of Warsaw
This project is devoted to mathematical modelling, analysis and simulation of stem cells renewal and differentiation, in particular the role of replicative senescence in hematopoiesis.

Hematopoiesis is a multi-step process, in which relatively small population of hematopoietic stem cells (HSC) gives rise to all types of blood cells. Understanding of the mechanisms governing this process is of central interest in stem cell biology, especially because of its clinical impact. High regenerative properties of HSC are used to reconstitute blood structure of patients after treatment with high-dose chemotherapy.

One established method of modelling of such hierarchical cell systems is to use a discrete collection of ordinary differential equations, each of which describes a well-defined differentiation stage (e.g.,[2]). However, there are indications that the differentiation process is less rigid and that it involves transitions which are continuous, along with discrete ones.

The aim of this interdisciplinary project is to develop and analyse new structured population models of hematopoiesis in the form of coupled systems of transport equation and ordinary differential equations. In particular, the models will account for the phenomenon of replicative senescence of adult stem cells. The aim is to explore if replicative senescence is important for human hematopoiesis and how the cells at different differentiation stages are affected by the process of aging.

This aim will be achieved through a close collaboration with the experimental group of Prof. Anthony Ho and Dr. Wolfgang Wagner (Heidelberg Medical Clinic), and comprehensive analytical investigations of the model equations. The method of relative entropy has proven to be a very useful tool to investigate the convergence of solutions to steady states in growth and cell division models [1,3, 4].

Analytical work will be handled in collaboration with Prof. Benoît Perthame. Advanced numerical methods developed in the group of Prof. Rolf Rannacher (University of Heidelberg) will be applied to simulate the models.

[1] P. Gwiazda and B. Perthame, (2006) Markov Proc. Related Fields, 12: 413-425.
[2] A. Marciniak-Czochra, T. Stiehl, A.D. Ho, W. Jäger and W. Wagner, (2008) Stem Cells Dev., 17: 1-10.
[3] P. Michel, S. Mischler and B. Perthame, (2005) J. Math. Pures Appl., 84: 1235-1260.
[4] B. Perthame, (2007) Transport equations in biology, Frontiers in Mathematics. Birkhäauser Verlag, Basel.