Cyclin and DNA distributed cell cycle model for GS-NS0 cells.

Mammalian cell cultures are intrinsically heterogeneous at different scales (molecular to bioreactor). The cell cycle is at the centre of capturing heterogeneity since it plays a critical role in the growth, death, and productivity of mammalian cell cultures. Current cell cycle models use biological variables (mass/volume/age) that are non-mechanistic, and difficult to experimentally determine, to describe cell cycle transition and capture culture heterogeneity. To address this problem, cyclins-key molecules that regulate cell cycle transition-have been utilized. Herein, a novel integrated experimental-modelling platform is presented whereby experimental quantification of key cell cycle metrics (cell cycle timings, cell cycle fractions, and cyclin expression determined by flow cytometry) is used to develop a cyclin and DNA distributed model for the industrially relevant cell line, GS-NS0. Cyclins/DNA synthesis rates were linked to stimulatory/inhibitory factors in the culture medium, which ultimately affect cell growth. Cell antibody productivity was characterized using cell cycle-specific production rates. The solution method delivered fast computational time that renders the model's use suitable for model-based applications. Model structure was studied by global sensitivity analysis (GSA), which identified parameters with a significant effect on the model output, followed by re-estimation of its significant parameters from a control set of batch experiments. A good model fit to the experimental data, both at the cell cycle and viable cell density levels, was observed. The cell population heterogeneity of disturbed (after cell arrest) and undisturbed cell growth was captured proving the versatility of the modelling approach. Cell cycle models able to capture population heterogeneity facilitate in depth understanding of these complex systems and enable systematic formulation of culture strategies to improve growth and productivity. It is envisaged that this modelling approach will pave the model-based development of industrial cell lines and clinical studies.

Optimal planning of the COVID-19 vaccine supply chain.

This work presents a novel framework to simultaneously address the optimal planning of COVID-19 vaccine supply chains and the optimal planning of daily vaccinations in the available vaccination centres. A new mixed integer linear programming (MILP) model is developed to generate optimal decisions regarding the transferred quantities between locations, the inventory profiles of central hubs and vaccination centres and the daily vaccination plans in the vaccination centres of the supply chain network. Specific COVID-19 characteristics, such as special cold storage technologies, limited shelf-life of mRNA vaccines in refrigerated conditions and demanding vaccination targets under extreme time pressure, are aptly modelled. The goal of the model is the minimization of total costs, including storage and transportation costs, costs related to fleet and staff requirements, as well as, indirect costs imposed by wasted doses. A two-step decomposition strategy based on a divide-and-conquer and an aggregation approach is proposed for the solution of large-scale problems. The applicability and efficiency of the proposed optimization-based framework is illustrated on a study case that simulates the Greek nationwide vaccination program. Finally, a rolling horizon technique is employed to reactively deal with possible disturbances in the vaccination plans. The proposed mathematical framework facilitates the decision-making process in COVID-19 vaccine supply chains into minimizing the underlying costs and the number of doses lost. As a result, the efficiency of the distribution network is improved, thus assisting the mass vaccination campaigns against COVID-19.

In Silico Closed-Loop Control Validation Studies for Optimal Insulin Delivery in Type 1 Diabetes.

This study presents a general closed-loop control strategy for optimal insulin delivery in type 1 Diabetes Mellitus (T1DM). The proposed control strategy aims toward an individualized optimal insulin delivery that consists of a patient-specific model predictive controller, a state estimator, a personalized scheduling level, and an open-loop optimization problem subjected to patient-specific process model and constraints. This control strategy can be also modified to address the case of limited patient data availability resulting in an "approximation" control strategy. Both strategies are validated in silico in the presence of predefined and unknown meal disturbances using both a novel mathematical model of glucose-insulin interactions and the UVa/Padova Simulator model as a virtual patient. The robustness of the control performance is evaluated under several conditions such as skipped meals, variability in the meal time, and metabolic uncertainty. The simulation results of the closed-loop validation studies indicate that the proposed control strategies can potentially achieve improved glycaemic control.

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.

Modeling and analysis of individualized pharmacokinetics and pharmacodynamics for volatile anesthesia.

The presented procedure aims to establish an in-depth understanding of a derived mathematical model for drug distribution, pharmacokinetics, and drug effect, pharmacodynamics, during volatile anesthesia. A physiologically based, patient-specific model is derived, where the pharmacokinetic (PK) part consists of multiple blood and tissue compartmental models, each adjusted to the weight, height, gender, and age of the patient. The pharmacodynamic (PD) part is described by an effect site compartment and the Hill equation both linking the hypnotic effect measured by the Bispectral Index (BIS) to the arterial anesthetic concentration. Via a global sensitivity analysis the patient-specific PK and PD variables and parameters are analyzed regarding their influence on the measurable outputs, which are the end-tidal concentration of the volatile anesthetic and the BIS. Via this analysis, the uncertainty introduced by PD variability is identified to be more significant than the uncertainty introduced by PK variability. A case study of isoflurane-based anesthesia shows that the simulation results of the individualized PK variables are in good accordance with the measured end-tidal concentration. However, the PD parameters need to be estimated online to predict the hypnotic depth, measured by the BIS, correctly. As a result of this study, the aim should be to focus on the individual identification of the PD parameters before and during anesthesia with future application in safe and robust model predictive control.