Mathematical modelling of stem and progenitor cell dynamics during ruxolitinib treatment of patients with myeloproliferative neoplasms.

Introduction: The Philadelphia chromosome-negative myeloproliferative neoplasms are a group of slowly progressing haematological malignancies primarily characterised by an overproduction of myeloid blood cells. Patients are treated with various drugs, including the JAK1/2 inhibitor ruxolitinib. Mathematical modelling can help propose and test hypotheses of how the treatment works. Materials and methods: We present an extension of the Cancitis model, which describes the development of myeloproliferative neoplasms and their interactions with inflammation, that explicitly models progenitor cells and can account for treatment with ruxolitinib through effects on the malignant stem cell response to cytokine signalling and the death rate of malignant progenitor cells. The model has been fitted to individual patients' data for the JAK2 V617F variant allele frequency from the COMFORT-II and RESPONSE studies for patients who had substantial reductions (20 percentage points or 90% of the baseline value) in their JAK2 V617F variant allele frequency (n = 24 in total). Results: The model fits very well to the patient data with an average root mean square error of 0.0249 (2.49%) when allowing ruxolitinib treatment to affect both malignant stem and progenitor cells. This average root mean square error is much lower than if allowing ruxolitinib treatment to affect only malignant stem or only malignant progenitor cells (average root mean square errors of 0.138 (13.8%) and 0.0874 (8.74%), respectively). Discussion: Systematic simulation studies and fitting of the model to the patient data suggest that an initial reduction of the malignant cell burden followed by a monotonic increase can be recapitulated by the model assuming that ruxolitinib affects only the death rate of malignant progenitor cells. For patients exhibiting a long-term reduction of the malignant cells, the model predicts that ruxolitinib also affects stem cell parameters, such as the malignant stem cells' response to cytokine signalling.

Data-driven analysis of JAK2V617F kinetics during interferon-alpha2 treatment of patients with polycythemia vera and related neoplasms.

Treatment with PEGylated interferon-alpha2 (IFN) of patients with essential thrombocythemia and polycythemia vera induces major molecular remissions with a reduction in the JAK2V617F allele burden to undetectable levels in a subset of patients. A favorable response to IFN has been argued to depend upon the tumor burden, implying that institution of treatment with IFN should be as early as possible after the diagnosis. However, evidence for this statement is not available. We present a thorough analysis of unique serial JAK2V617F measurements in 66 IFN-treated patients and in 6 untreated patients. Without IFN treatment, the JAK2V617F allele burden increased exponentially with a period of doubling of 1.4 year. During monotherapy with IFN, the JAK2V617F allele burden decreased mono- or bi-exponentially for 33 responders of which 28 patients satisfied both descriptions. Bi-exponential description improved the fits in 19 cases being associated with late JAK2V617F responses. The decay of the JAK2V617F allele burden during IFN treatment was estimated to have half-lives of 1.6 year for the monoexponential response and 1.0 year in the long term for the bi-exponential response. In conclusion, through data-driven analysis of the JAK2V617F allele burden, we provide novel information regarding the JAK2V617F kinetics during IFN-treatment, arguing for early intervention.

Bridging blood cancers and inflammation: The reduced Cancitis model.

A novel mechanism-based model - the Cancitis model - describing the interaction of blood cancer and the inflammatory system is proposed, analyzed and validated. The immune response is divided into two components, one where the elimination rate of malignant stem cells is independent of the level of the blood cancer and one where the elimination rate depends on the level of the blood cancer. A dimensional analysis shows that the full 6-dimensional system of nonlinear ordinary differential equations may be reduced to a 2-dimensional system - the reduced Cancitis model - using Fenichel theory. The original 18 parameters appear in the reduced model in 8 groups of parameters. The reduced model is analyzed. Especially the steady states and their dependence on the exogenous inflammatory stimuli are analyzed. A semi-analytic investigation reveals the stability properties of the steady states. Finally, positivity of the system and the existence of an attracting trapping region in the positive octahedron guaranteeing global existence and uniqueness of solutions are proved. The possible topologies of the dynamical system are completely determined as having a Janus structure, where two qualitatively different topologies appear for different sets of parameters. To classify this Janus structure we propose a novel concept in blood cancer - a reproduction ratio R. It determines the topological structure depending on whether it is larger or smaller than a threshold value. Furthermore, it follows that inflammation, affected by the exogenous inflammatory stimulation, may determine the onset and development of blood cancers. The body may manage initial blood cancer as long as the self-renewal rate is not too high, but fails to manage it if an inflammation appears. Thus, inflammation may trigger and drive blood cancers. Finally, the mathematical analysis suggests novel treatment strategies and it is used to discuss the in silico effect of existing treatment, e.g. interferon-α or T-cell therapy, and the impact of malignant cells becoming resistant.

Analysis and validation of a new extended method for estimating plasma free cortisol including neutrophil elastase and competition from other steroids.

A non-linear mechanistic model for the distribution of cortisol in plasma on free and bound forms is proposed. The influence of progesterone, testosterone and neutrophil elastase on the cortisol distribution in the blood is investigated. The activity of neutrophil elastase is directly included in the model with the concentration of elastase and the kinetic constants describing the activity of elastase collected in one single input variable. The model is very sensitive towards this input variable and fits data excellently, when it is allowed to be subject specific. The analysis shows that steroids such as testosterone with low affinity for corticosteroid-binding globulin (CBG) do not significantly influence the concentration of free cortisol. Progesterone has a high affinity for CBG, but low plasma concentrations compared to cortisol. Contrary to expectations, progesterone is shown to impact the distribution of cortisol in plasma both under circumstances with high levels as seen in pregnancy and during the normal menstrual cycle of women. Comparing the predictions of our model with predictions made with the equilibrium models by Coolens et al. [1], Dorin et al. [2] and Nguyen et al. [3] shows that the models differ considerably not only in their predictions for free cortisol, but also for cortisol on bound forms; i.e. bound to albumin, intact CBG and elastase-cleaved CBG. Disregarding some of the smallest terms of the model equations a reduced version of the model in form of a fourth order polynomial equation is obtained. The reduced version of the model performs almost identically to the full version and serves as a new formula for calculating the plasma free cortisol concentration.

Mathematical modelling as a proof of concept for MPNs as a human inflammation model for cancer development.

The chronic Philadelphia-negative myeloproliferative neoplasms (MPNs) are acquired stem cell neoplasms which ultimately may transform to acute myelogenous leukemia. Most recently, chronic inflammation has been described as an important factor for the development and progression of MPNs in the biological continuum from early cancer stage to the advanced myelofibrosis stage, the MPNs being described as "A Human Inflammation Model for Cancer Development". This novel concept has been built upon clinical, experimental, genomic, immunological and not least epidemiological studies. Only a few studies have described the development of MPNs by mathematical models, and none have addressed the role of inflammation for clonal evolution and disease progression. Herein, we aim at using mathematical modelling to substantiate the concept of chronic inflammation as an important trigger and driver of MPNs.The basics of the model describe the proliferation from stem cells to mature cells including mutations of healthy stem cells to become malignant stem cells. We include a simple inflammatory coupling coping with cell death and affecting the basic model beneath. First, we describe the system without feedbacks or regulatory interactions. Next, we introduce inflammatory feedback into the system. Finally, we include other feedbacks and regulatory interactions forming the inflammatory-MPN model. Using mathematical modeling, we add further proof to the concept that chronic inflammation may be both a trigger of clonal evolution and an important driving force for MPN disease progression. Our findings support intervention at the earliest stage of cancer development to target the malignant clone and dampen concomitant inflammation.

Patient-specific modeling of the neuroendocrine HPA-axis and its relation to depression: Ultradian and circadian oscillations.

In the Western world approximately 10% of the population experience severe depression at least once in their lifetime and many more experience a mild form of depression. Depression has been associated with malfunctions in the hypothalamus-pituitary-adrenal (HPA) axis. We suggest a novel mechanistic non-linear model capable of showing both circadian as well as ultradian oscillations of the hormone concentrations related to the HPA-axis. The fast ultradian rhythm is assumed to originate from the hippocampus whereas the slower circadian rhythm is assumed to be caused by the circadian clock. The model is able to describe the oscillatory patterns in hormone concentration data from 29 patients and healthy controls. Using non-linear mixed effects modeling with statistical hypothesis testing, three of the model parameters are identified to be related to depression. These parameters represent underlying physiological mechanisms controlling the average levels as well as the ultradian frequencies and amplitudes of the hormones ACTH and cortisol. The results are promising since they point toward an exact etiology for depression. As a consequence new biomarkers and pharmaceutical targets may be identified.