A Personalized Framework for Dynamic Modeling of Disease Trajectories in Chronic Lymphocytic Leukemia

Chronic Lymphocytic Leukemia (CLL) is the most common peripheral blood and bone marrow cancer in the developed world. This manuscript proposes mathematical model equations representing the disease dynamics of B-cell CLL. We interconnect delay differential cell cycle models in each of the tumor-involved disease centers using physiologically-relevant cell migration. We further introduce 5 hypothetical case studies representing CLL heterogeneity commonly seen in clinical practice and demonstrate how the proposed CLL model framework may capture disease pathophysiology across patient types. We conclude by exploring the capacity of the proposed temporally- and spatially-distributed model to capture the heterogeneity of CLL disease progression. By using Global Sensitivity Analysis, the critical parameters influencing disease trajectory over space and time are: (i) the initial number of CLL cells in peripheral blood, the number of involved lymph nodes, the presence and degree of splenomegaly; (ii) the migratory fraction of nonproliferating as well as proliferating CLL cells from bone marrow into blood and of proliferating CLL cells from blood into lymph nodes; (iii) the parameters inducing nonproliferative cells to proliferate. The proposed model offers a practical platform which may be explored in future personalized patient protocols once validated

Framework and Tools A Framework for Modelling, Optimization and Control of Biomedical Systems

Drug delivery can be defined as the process of administering a pharmaceutical agent in the human body, including the consequent effects of this agent on the tissues and organs. Mathematical modelling of drug delivery can be divided into two different yet complementary approaches, the pharmacokinetic and pharmacodynamic approaches. Pharmacokinetics describes the effect of the drug in the body, by capturing absorption, distribution, diffusion and elimination of the drug. Pharmacodynamics describes the effects of a drug in the body, which are expressed mathematically by relations of drug dose-body responses. Usually, modelling of the drug delivery system requires a pharmacokinetic part, a pharmacodynamics part and a link between the two. Mathematical optimization and control of biomedical systems could lead to a better prediction of the optimal drug and/or therapy treatment for a specific disease

A mathematical model of subpopulation kinetics for the deconvolution of leukaemia heterogeneity.

Acute myeloid leukaemia is characterized by marked inter- and intra-patient heterogeneity, the identification of which is critical for the design of personalized treatments. Heterogeneity of leukaemic cells is determined by mutations which ultimately affect the cell cycle. We have developed and validated a biologically relevant, mathematical model of the cell cycle based on unique cell-cycle signatures, defined by duration of cell-cycle phases and cyclin profiles as determined by flow cytometry, for three leukaemia cell lines. The model was discretized for the different phases in their respective progress variables (cyclins and DNA), resulting in a set of time-dependent ordinary differential equations. Cell-cycle phase distribution and cyclin concentration profiles were validated against population chase experiments. Heterogeneity was simulated in culture by combining the three cell lines in a blinded experimental set-up. Based on individual kinetics, the model was capable of identifying and quantifying cellular heterogeneity. When supplying the initial conditions only, the model predicted future cell population dynamics and estimated the previous heterogeneous composition of cells. Identification of heterogeneous leukaemia clones at diagnosis and post-treatment using such a mathematical platform has the potential to predict multiple future outcomes in response to induction and consolidation chemotherapy as well as relapse kinetics

Robust multi-parametric control of continuous-time linear dynamic systems

We extend a recent methodology called multi-parametric NCO-tracking for the design of parametric controllers for continuous-time linear dynamic systems in the presence of uncertainty The approach involves backing-off the path and terminal state constraints based on a worst-case uncertainty propagation determined using either interval analysis or ellipsoidal calculus. We address the case of additive uncertainty and we discuss approaches to handling multiplicative uncertainty that retain tractability of the mp-NCO-tracking design problem, subject to extra conservatism. These developments are illustrated with the case study of a fluidized catalytic cracking (FCC) unit operated in partial combustion mode

Selecting a differential equation cell cycle model for simulating leukemia treatment

This work studies three differential equation models of the leukemia cell cycle: a population balance model (PBM) using intracellular protein expression levels as state variables representing phase progress; a delay differential equation model (DDE) with temporal phase durations as delays; and an ordinary differential equation model (ODE) of phase-to-phase progression. In each type of model, global sensitivity analysis determines the most significant parameters while parameter estimation fits experimental data. To compare models based on the output of their structural properties, an expected behavior was defined, and each model was coupled to a pharmacokinetic/pharmacodynamic model of chemotherapy delivery. Results suggest that the particular cell cycle model chosen highly affects the simulated treatment outcome, given the same steady state kinetic parameters and drug dosage/scheduling. The manuscript shows how cell cycle models should be selected according to the complexity, sensitivity, and parameter availability of the application envisioned