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.

Bayesian parameter estimation for phosphate dynamics during hemodialysis.

Hyperphosphatemia in patients with renal failure is associated with increased vascular calcification and mortality. Hemodialysis is a conventional treatment for patients with hyperphosphatemia. Phosphate kinetics during hemodialysis may be described by a diffusion process and modeled by ordinary differential equations. We propose a Bayesian model approach for estimating patient-specific parameters for phosphate kinetics during hemodialysis. The Bayesian approach allows us to both analyze the full parameter space using uncertainty quantification and to compare two types of hemodialysis treatments, the conventional single-pass and the novel multiple-pass treatment. We validate and test our models on synthetic and real data. The results show limited identifiability of the model parameters when only single-pass data are available, and that the Bayesian model greatly reduces the relative standard deviation compared to existing estimates. Moreover, the analysis of the Bayesian models reveal improved estimates with reduced uncertainty when considering consecutive sessions and multiple-pass treatment compared to single-pass treatment.

Dynamics of competing heterogeneous clones in blood cancers explains multiple observations - a mathematical modeling approach.

Heterogeneity of stem cell clones provide a key ingredient in altered hematopoiesis and is of main interest in the study of predisease states as well as in the development of blood cancers such as chronic myeloid leukemia (CML) and the Philadelphia-negative myeloprofilerative neoplasms (MPNs). A mathematical model based on biological mechanisms and basic cell descriptors such as proliferation rates and apoptosis rates is suggested, connecting stem cell dynamics with mature blood cells and immune mediated feedback. The flexible approach allows for arbitrary numbers of mutated stem cell clones with perturbed properties. In particular, the stem cell niche provides a competition between wild type and mutated stem cells. Hence, the stem cell niche can mediate suppression of the wild type clones and up-regulation of one or more malignant clones. The model is parameterized using clinical data to show typical disease progression in several blood cancers and the hematological and molecular response to treatment. Intriguingly, occasional oscillatory cell counts observed during treatment of CML and MPNs can be explained by heterogeneous stem cell clone dynamics. Thus, the vital heterogeneous stem cell dynamics may be inferred from mathematical modeling in synergy with clinical data to elucidate hematopoiesis, blood cancers and the outcome of interventions.