María Fuentes-Garí

A framework for the design, modeling and optimization of biomedical systems

Abstract We present an overview of the key building blocks of a design framework for modeling and optimization of biomedical systems with main focus on leukemia, that we have been developing in the Biological Systems Engineering Laboratory and the Centre for Process Systems Engineering at Imperial College. The framework features the following areas: (i) a three-dimensional, biomimetic, in vitro platform for culturing both healthy and diseased blood; (ii) a novel, hollow fiber bioreactor that upgrades this in vitro platform to enable expansion and continuous harvesting of healthy and diseased blood; (iii) a global optimization-based approach for the design and operation of the aforementioned bioreactor; (iv) a pharmacokinetic / pharmacodynamic model representing patient response to Acute Myeloid Leukemia treatment; (v) an experimental framework for cell cycle modeling and quantitative analysis of environmental stress. This manuscript recapitulates the progress made in the different areas as well as the way in which these areas are connected, finally leading to a hybrid in vitro/in silico platform which allows the optimization of the ex vivo expansion of healthy and diseased blood.

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.

Stem cell biomanufacturing under uncertainty: A case study in optimizing red blood cell production

As breakthrough cellular therapy discoveries are translated into reliable, commercializable applications, effective stem cell biomanufacturing requires systematically developing and optimizing bioprocess design and operation. This article proposes a rigorous computational framework for stem cell biomanufacturing under uncertainty. Our mathematical tool kit incorporates: high‐fidelity modeling, single variate and multivariate sensitivity analysis, global topological superstructure optimization, and robust optimization. The advantages of the proposed bioprocess optimization framework using, as a case study, a dual hollow fiber bioreactor producing red blood cells from progenitor cells were quantitatively demonstrated. The optimization phase reduces the cost by a factor of 4, and the price of insuring process performance against uncertainty is approximately 15% over the nominal optimal solution. Mathematical modeling and optimization can guide decision making; the possible commercial impact of this cellular therapy using the disruptive technology paradigm was quantitatively evaluated.

Cell cycle model selection for leukemia and its impact in chemotherapy outcomes

Abstract The cell cycle is the biological process used by cells to replicate their genetic material and give birth to new cells that are in turn eligible to proliferate. It is highly regulated by the timed expression of proteins which trigger cell cycle events such as the start of DNA replication or the commencement of mitosis (when the cell physically divides into two daughter cells). Mathematical models of the cell cycle have been widely developed both at the intracellular (protein kinetics) and macroscopic (cell duplication) levels. Due to the cell cycle specificity of most chemother-apeutic drugs, these models are increasingly being used for the study and simulation of cellular kinetics in the area of cancer treatment. In this work, we present a population balance model (PBM) of the cell cycle in leukemia that uses intracellular protein expression as state variable to represent phase progress. Global sensitivity analysis highlighted cell cycle phase durations as the most significant parameters; experiments were performed to extract them and the model was validated. Our model was then tested against other differential cell cycle models (ODEs, delay differential equations (DDEs)) in their ability to fit experimental data and oscillatory behavior. We subsequently coupled each of them with a pharmacokinetic/pharmacodynamic model of chemotherapy delivery that was previously developed by our group. Our results suggest that the particular cell cycle model chosen highly affects the outcome of the simulated treatment, given the same steady-state kinetic parameters and drug dosage/scheduling, with our PBM appearing to be the most sensitive under the same dose.

Key environmental stress biomarker candidates for the optimisation of chemotherapy treatment of leukaemia

The impact of fluctuations of environmental parameters such as oxygen and starvation on the evolution of leukaemia is analysed in the current review. These fluctuations may occur within a specific patient (in different organs) or across patients (individual cases of hypoglycaemia and hyperglycaemia). They can be experienced as stress stimuli by the cancerous population, leading to an alteration of cellular growth kinetics, metabolism and further resistance to chemotherapy. Therefore, it is of high importance to elucidate key mechanisms that affect the evolution of leukaemia under stress. Potential stress response mechanisms are discussed in this review. Moreover, appropriate cell biomarker candidates related to the environmental stress response and/or further resistance to chemotherapy are proposed. Quantification of these biomarkers can enable the combination of macroscopic kinetics with microscopic information, which is specific to individual patients and leads to the construction of detailed mathematical models for the optimisation of chemotherapy. Due to their nature, these models will be more accurate and precise (in comparison to available macroscopic/black box models) in the prediction of responses of individual patients to treatment, as they will incorporate microscopic genetic and/or metabolic information which is patient-specific.

A comprehensive mathematical analysis of a novel multistage population balance model for cell proliferation

Abstract Multistage population balances provide a more detailed mathematical description of cellular growth than lumped growth models, and can therefore describe better the physics of cell evolution through cycles. These balances can be formulated in terms of cell age, mass, size or cell protein content and they can be univariate or multivariate. A specific three stage population balance model based on cell protein content has been derived and used recently to simulate evolution of cell cultures for several applications. The behavior of the particular mathematical model is studied in detail here. A one equation analog of the multistage model is formulated and it is solved analytically in the self-similarity domain. The effect of the initial condition on the approach to self-similarity is studied numerically. The three equations model is examined then by using asymptotic and numerical techniques. It is shown that in the case of sharp interstage transition the discontinuities of the initial condition are preserved during cell growth leading to oscillating solutions whereas for distributed transition, the cell distribution converges to a self-similar (long time asymptote) shape. The closer is the initial condition to the self similar distribution the faster is the convergence to the self-similarity and the smaller the amplitude of oscillations of the total cell number. The findings of the present work lead to a better understanding of the multistage population balance model and to its more efficient use for description of experimental data by employing the expected solution behavior.

Mathematical analysis of multistage population balances for cell growth and death

Abstract The cell cycle is a biologically timed process by which cells duplicate. It consists of 4 phases, during which cells undergo different mandatory transformations. Modelling the cell cycle therefore requires capturing the evolution of those processes inside of each phase. A specific three stage biologically supported population balance model employed to simulate evolution of several cell cultures is studied here in detail. The three governing equations of this model are composed by growth and transition terms. A one equation analogue of the multistage model is formulated and it is solved analytically in the self-similarity domain. The effect of initial conditions at the system evolution is studied numerically. The three model equations are then considered by using asymptotic and numerical techniques. It is shown that in the case of sharp interstage transition the discontinuities of the initial conditions are preserved during cell growth leading to eternal oscillations whereas for distributed transition the cell distribution converges to a self-similar (long time asymptote) shape. It is also illustrated that the closer the initial condition to the self similar distribution the faster the convergence to self-similarity and the smaller the oscillations of the total cell number. Exact results are given for the growth parameters of the population balance and lumped models.