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.

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.

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.

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.

Chemotherapy drug scheduling for the induction treatment of patients with acute myeloid leukemia

Leukemia is an immediately life-threatening cancer wherein immature blood cells are overproduced, accumulate in the bone marrow (BM) and blood and causes immune and blood system failure. Treatment with chemotherapy can be intensive or nonintensive and can also be life-threatening since only relatively few patient-specific and leukemia-specific factors are considered in current protocols. We have already presented a mathematical model for one intensive chemotherapy cycle with intravenous (i.v.) daunorubicin (DNR), and cytarabine (Ara-C). This model is now extended to nonintensive subcutaneous (SC) Ara-C and for a standard intensive chemotherapy course (four cycles), consistent with clinical practice. Model parameters mainly consist of physiological patient data, indicators of tumor burden and characteristics of cell cycle kinetics. A sensitivity analysis problem is solved and cell cycle parameters are identified to control treatment outcome. Simulation results using published cell cycle data from two acute myeloid leukemia patients are presented for a course of standard treatment using intensive and nonintensive protocols. The aim of remission-induction therapy is to debulk the tumor and achieve normal BM function; by treatment completion, the total leukemic population should be reduced to at most 10(9) cells, at which point BM hypoplasia is achieved. The normal cell number should be higher than that of the leukemic, and a 3-log reduction is the maximum permissible level of population reduction. This optimization problem is formulated and solved for the two patient case studies. The results clearly present the benefits from the use of optimization as an advisory tool for treatment design.