Mathematical analysis of the Cancitis model and the role of inflammation in blood cancer progression

Mathematical modelling of clonal reduction therapeutic strategies in acute myeloid leukemia

Over the years, the overall survival of older patients diagnosed with acute myeloid leukemia (AML) has not significantly increased. Although standard cytotoxic therapies that rapidly eliminate dividing myeloblasts are used to induce remission, relapse can occur due to surviving therapy-resistant leukemic stem cells (LSCs). Hence, anti-LSC strategies have become a key target to cure AML. We have recently shown that previously approved cardiac glycosides and glucocorticoids target LSC-enriched CD34+ cells in the primary human AML 8227 model with more efficacy than normal hematopoietic stem cells (HSCs). To translate these in vitro findings into humans, we developed a mathematical model of stem cell dynamics that describes the stochastic evolution of LSCs in AML post-standard-of-care. To this, we integrated population pharmacokinetic-pharmacodynamic (PKPD) models to investigate the clonal reduction potential of several promising candidate drugs in comparison to cytarabine, which is commonly used in high doses for consolidation therapy in AML patients. Our results suggest that cardiac glycosides (proscillaridin A, digoxin and ouabain) and glucocorticoids (budesonide and mometasone) reduce the expansion of LSCs through a decrease in their viability. While our model predicts that effective doses of cardiac glycosides are potentially too toxic to use in patients, simulations show the possibility of mometasone to prevent relapse through the glucocorticoid's ability to drastically reduce LSC population size. This work therefore highlights the prospect of these treatments for anti-LSC strategies and underlines the use of quantitative approaches to preclinical drug translation in AML.

Mathematical Modeling of MPNs Offers Understanding and Decision Support for Personalized Treatment

(1) Background: myeloproliferative neoplasms (MPNs) are slowly developing hematological cancers characterized by few driver mutations, with JAK2V617F being the most prevalent. (2) Methods: using mechanism-based mathematical modeling (MM) of hematopoietic stem cells, mutated hematopoietic stem cells, differentiated blood cells, and immune response along with longitudinal data from the randomized Danish DALIAH trial, we investigate the effect of the treatment of MPNs with interferon-α2 on disease progression. (3) Results: At the population level, the JAK2V617F allele burden is halved every 25 months. At the individual level, MM describes and predicts the JAK2V617F kinetics and leukocyte- and thrombocyte counts over time. The model estimates the patient-specific treatment duration, relapse time, and threshold dose for achieving a good response to treatment. (4) Conclusions: MM in concert with clinical data is an important supplement to understand and predict the disease progression and impact of interventions at the individual level.

Global dynamics of healthy and cancer cells competing in the hematopoietic system

Stem cells in the bone marrow differentiate to ultimately become mature, functioning blood cells through a tightly regulated process (hematopoiesis) including a stem cell niche interaction and feedback through the immune system. Mutations in a hematopoietic stem cell can create a cancer stem cell leading to a less controlled production of malfunctioning cells in the hematopoietic system. This was mathematically modelled by Andersen et al. (2017) including the dynamic variables: healthy and cancer stem cells and mature cells, dead cells and an immune system response. Here, we apply a quasi steady state approximation to this model to construct a two dimensional model with four algebraic equations denoted the simple cancitis model. The two dynamic variables are the clinically available quantities JAK2V617F allele burden and the number of white blood cells. The simple cancitis model represents the original model very well. Complete phase space analysis of the simple cancitis model is performed, including proving the existence and location of globally attracting steady states. Hence, parameter values from compartments of stem cells, mature cells and immune cells are directly linked to disease and treatment prognosis, showing the crucial importance of early intervention. The simple cancitis model allows for a complete analysis of the long term evolution of trajectories. In particular, the value of the self renewal of the hematopoietic stem cells divided by the self renewal of the cancer stem cells is found to be an important diagnostic marker and perturbing this parameter value at intervention allows the model to reproduce clinical data. Treatment at low cancer cell numbers allows returning to healthy blood production while the same intervention at a later disease stage can lead to eradication of healthy blood producing cells. Assuming the total number of white blood cells is constant in the early cancer phase while the allele burden increases, a one dimensional model is suggested and explicitly solved, including parameters from all original compartments. The solution explicitly shows that exogenous inflammation promotes blood cancer when cancer stem cells reproduce more efficiently than hematopoietic stem cells.