Mathematical Modelling of the Dynamics of Pathological Hematopoiesis during Treatments

Zamra Sajid

Research output: Book/ReportPh.D. thesis


The Philadelphia-negative myeloproliferative neoplasms (MPNs) are a group of hematopoietic stem-cell disorders, including essential thrombocythemia (ET), polycythemia vera (PV) and primary myelofibrosis (PMF). The excessive production in myeloid, erythroid or megakaryocytic cell lines characterizes the three classical MPNs. Furthermore, inflammation is thought to be a driver of MPNs and becomes a reason for developing other cancers in MPN patients. However, MPN patients may become alive for several years with a high risk of thrombosis, cardiovascular complications and chronic inflammatory diseases. Although many pathogenetic working mechanisms of MPNs are discovered, many of the therapeutic tools are still unexplored.

In this thesis, a series of mechanism-based mathematical models contribute to building further knowledge about the pathogenesis of MPNs. Inspired by the bio-medical literature, we address various research questions related to MPNs. In addition to the pathogenesis of MPNs, we propose a novel mathematical model describing the coupled mechanisms of thrombopoiesis and erythropoiesis.

The first mechanism-based Cancitis model describes the coupling between chronic inflammation and the development of MPNs. We perform a thorough mathematical investigation of the model and find the crucial parameters for the progression of the disease. Thereby we identify that the inflammatory stimuli and a few grouped parameters involved in the hematopoietic stem cell (HSC) dynamics are mainly responsible for governing the behavior of the model. Based on the Cancitis model, we further develop a range of mathematical models in the presented work.

A second model is a novel mathematical model proposed for PV dynamics. We zoom in on the excessive production of red blood cells and erythropoietin (EPO) feedbacks on healthy and malignant cells. A mathematical analysis of the model highlights HSC fitness and suggests that HSC dynamics govern disease progression. The model is capable of reproducing clinically observed dynamics before and during treatment.

A third novel mathematical model is proposed for ET dynamics where the excessive production of platelets is addressed. In addition, thrombopoietin (TPO) feedbacks mediates healthy and malignant cell lineage. The overall analysis reflects that targeted HSC therapy can control disease progression.

Finally, we develop a mathematical model combining the dynamics of erythrocytes and platelets. In contrast to previous models, this model does not contain malignant cells. It is known that erythrocytes and platelets share the same precursor megakaryocyte-erythroid progenitor (MEP). The purpose of the model is the investigation of the coupled mechanisms between erythrocytes and platelets. The model is validated and calibrated for various clinical experiments such as phlebotomy, body's reaction to EPO and TPO regimens.
Original languageEnglish
Place of PublicationRoskilde
PublisherRoskilde Universitet
Number of pages251
Publication statusPublished - 13 Apr 2021
SeriesIMFUFA-tekst : i, om og med matematik og fysik

Cite this