We propose and analyze a mathematical model of hematopoietic stem cell dynamics. This model takesinto account a finite number of stages in blood production, characterized by cell maturity levels,which enhance the difference, in the hematopoiesis process, between dividing cells thatdifferentiate (by going to the next stage) and dividing cells that keep the same maturity level (bystaying in the same stage). It is described by a system of n nonlinear differential equationswith n delays. We study some fundamental properties of the solutions, such as boundedness andpositivity, and we investigate the existence of steady states. We determine some conditions for thelocal asymptotic stability of the trivial steady state, and obtain a sufficient condition for itsglobal asymptotic stability by using a Lyapunov functional. Then we prove the instability of axialsteady states. We study the asymptotic behavior of the unique positive steady state and obtain theexistence of a stability area depending on all the time delays. We give a numerical illustration ofthis result for a system of four equations.

We consider a size structured cell population model where a mother cell gives birth totwo daughter cells. We know that the asymptotic behavior of the density of cells is given by thesolution to an eigenproblem. The eigenvector gives the asymptotic shape and the eigenvalue givesthe exponential growth rate and so the Maltusian parameter. The Maltusian parameter depends onthe division rule for the mother cell, i.e., symmetric (the two daughter cells have the same size) orasymmetric. We use a min-max principle and a differentiation principle to find the variation of thefirst eigenvalue with respect to a parameter of asymmetry of the cell division. We prove that thesymmetrical division is not always the best fitted division, i.e., the Maltusian parameter may be notoptimal.

We review the basic pathology of cyclical neutropenia in both humansand the grey collie, and examine the role that mathematical modelingof hematopoietic cell production has played in our understanding ofthe origins of this fascinating dynamical disease.

Neutropenia is a significant dose-limiting toxicity of cancerchemotherapy, especially in dose-intensified regimens. It iswidely treated by injections of Granulocyte Colony-StimulatingFactor (G-CSF). However, optimal schedules of G-CSF administrationare still not determined. In order to aid in identifying moreefficacious and less neutropenic treatment protocols, we studied adetailed physiologically-based computer model of granulopoiesis,as affected by different treatment schedules of doxorubicin and/orGranulocyte Colony-Stimulating Factor (G-CSF). We validated themodel as evident from accurate prediction of clinical data onhuman granulopoiesis in healthy individuals and indoxorubicin-treated cancer patients, with or without G-CSFsupport. Based on our model, we suggest new G-CSF administrationregimens. These regimens include reduced G-CSF doses, optimallytimed post-chemotherapy. Application of these regimens can lead tominimization of G-CSF side effects, as well as more cost-effectiveand less myelotoxic protocols. Currently clinical trials are beingdesigned in order to test these new treatment regimens.

In this work, we introduce a new software created to study hematopoiesis at the cellpopulation level with the individually based approach. It can be used as an interface between theoreticalworks on population dynamics and experimental observations. We show that this softwarecan be useful to study some features of normal hematopoiesis as well as some blood diseases suchas myelogenous leukemia. It is also possible to simulate cell communication and the formation ofcell colonies in the bone marrow.

Patients with acute myeloblastic leukemia (AML) are divided according to the FrenchAmerican British (FAB) classification into eight subgroups (M0 to M7) on the basis of their degreeof maturation/differentiation. However, even if immunophenotypical characterization by flow cytometryis routinely used to distinguish between AML and acute lymphoblastic leukemia (ALL), itis not yet well established for the identification within the AML subgroups. Here we show that certainsubgroups of AML can be identified with a good accuracy (80% of the patients we analyzed)by means of the expression of specific markers.

Spatial dynamics of fibrin clot formation in non-stirred system activated by glasssurface was studied as a function of FIX activity. Haemophilia B plasma was obtained fromuntreated patients with different levels of FIX deficiency and from severe haemophilia B patienttreated with FIX concentrate (Ahemphil B) during its clearance with half-life t1/2=12 hours. Asreported previously (Ataullakhanov et al. Biochim Biophys Acta 1998; 1425: 453-468), clotgrowth in space showed two distinct phases: activation and propagation. The activation phase ischaracterized by the time required to start clot growth from the activator, while the characteristicparameter of the propagation phase is the clot elongation rate. This rate reaches steady state inapproximately ten minutes after the beginning of growth. In haemophilia B plasma, clotformation is substantially impaired: clot starts to grow from the activating surface later than inhealthy donor plasma, and its propagation rate is considerably lower. The most significantabnormalities in clot growth kinetics are observed at FIX activity below 10% of normal.Simulation of these experiments was performed theoretically using a detailed biochemical model(Panteleev et al. Biophys J 2006; 90: 1489-1500) adapted for experimental conditions used.Suitability of the assumptions used to describe triggering contact activation was verified.