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This paper introduces a new concept to solve car sequencing problem called the Car Sequencing Problem 4.0, focuses the paint shop. The problem of effective car sequencing in the paint shop is caused by the specifics of the production process itself and the structure of the production line. Sequencing of cars as required by the painting process is justified economically. The main goal is to minimize the number of costly changeovers of the painting guns because of color changes and to synchronize those with periodic cleanings, forced by technological requirements. For this purpose, a buffer located in the paint shop is applied. In this paper a game theoretic framework is presented to analyze the problem. Three games are introduced: Buffer Slot Assignment Game–Buffer-OutShuttle Game called the BSAG-BOSG, In–Out Shuttle Game and its modification called modified In–Out Shuttle Game. Based on the simulations performed the efficiency of the algorithms is verified using several datasets.

Lung cancer is the most common type of cancer across the world. There are known two main types of lung cancer non-small cell lung (NSCLC) and small cell one (SCLC). Here, we focus on NSCLC that is known to disseminate to distant organs such as the brain or bones. What is more, the death of a patient with this type of cancer is caused usually by metastases. It justifies tackling the problem of the emergence of metastases in NSLC in this paper. Here, we investigated which mathematical parameters affect the emergence of metastases using the mathematical oncology approach. We developed a mathematical model of lung cancer growth and metastasis dissemination by taking into account stochasticity in the process. We incorporated into the model two paths of metastasis dissemination through lymphatic and blood vessels. We performed a global sensitivity analysis to identify parameters that affect the model output (metastasis-free survival) the most. We discover that four model parameters have dominating effect on the output and two of them are controllable - the growth rate of primary tumor cells (through the administration of chemotherapeutic agents) and carrying capacity (through the administration of angio-therapy). In conclusion, a mathematical oncology approach could be applied to investigate which treatment modalities in cancer could delay the emergence of metastases.

We developed a computational platform including machine learning and a mechanistic mathematical model to find the optimal protocol for administration of platinum-doublet chemotherapy in a palliative setting. The platform has been applied to advanced metastatic non-small cell lung cancer (NSCLC). The 42 NSCLC patients treated with palliative intent at Maria Sklodowska-Curie National Research Institute of Oncology, Gliwice Branch, were collected from a retrospective cohort of patients diagnosed in 2004–2014. Patients were followed-up, for three years. Clinical data collected include complete information about the clinical course of the patients including treatment schedule, response according to RECIST classification, and survival. The core of the platform is the mathematical model, in the form of a system of ordinary differential equations, describing dynamics of platinum-sensitive and platinum-resistant cancer cells and interactions reflecting competition for space and resources. The model is simulated stochastically by sampling the parameter values from a joint probability distribution function. The machine learning model is applied to calibrate the mathematical model and to fit it to the overall survival curve. The model simulations faithfully reproduce the clinical cohort at three levels long-term response (OS), the initial response (according to RECIST criteria), and the relationship between the number of chemotherapy cycles and time between two consecutive chemotherapy cycles. In addition, we investigated the relationship between initial and long-term response. We showed that those two variables do not correlate which means that we cannot predict patient survival solely based on the initial response. We also tested several chemotherapy schedules to find the best one for patients treated with palliative intent. We found that the optimal treatment schedule depends, among others, on the strength of competition among various subclones in a tumor. The computational platform developed allows optimizing chemotherapy protocols, within admissible limits of toxicity, for palliative treatment of metastatic NSCLC. The simplicity of the method allows its application to chemotherapy optimization in different cancers., Author summary Lung cancer is usually diagnosed at an advanced stage because of non-specific symptoms. The most common subtype of lung cancer is non-small cell lung cancer, which constitutes 80% of lung cancer cases. Here, we developed the methodology for finding the optimal treatment schedule for patients treated with palliative intent. The goal is not to cure the patients who are at an advanced stage but to prolong their survival by the administration of platinum-based chemotherapy. The method is based on the mathematical model describing the growth of tumors and its response to chemotherapy which is calibrated using real clinical data.

We summarize results of our research studies on models of combined anticancer radio- and chemotherapy and their comparison with real clinical data. We use two mathematical techniques, which, to our knowledge, have not been applied simultaneously: optimal control theory and survival analysis. We recall results of analytical optimization of combined chemo-radio-therapy for a simple model of tumor growth with respect to the order, in which these two modes of treatment should be applied. Then we study both structural and parametric sensitivity of this model and related optimal control problem. Afterwards, we present results of survival analysis based on the Kaplan-Meier curves for different protocols of chemo-radio-therapy and compare them with real clinical data and results of optimal treatment protocols.

The paper presents a novel approach to the prediction of the combined therapy outcome for non-small lung cancer patients. A hybrid model is proposed, consisting of two parts. The first one is a mathematical model of tumor response to therapy, whose parameters are expressed as linear function of data from massspectrometry of patient blood plasma samples. These linear functions constitute thesecond component of the hybrid model. A comparison of clinical and simulation-based survival curves is used to evaluate the quality of the model.

In this work, we consider a simple mathematical model of radiochemotherapy which includes a term responsible for radiosensitization. We focus on finding theoretically optimal controls which maximise tumour cure probability for a finite, fixed therapeutic horizon. We prove that the optimal controls for both therapies are of 0-bang type, a result which is not altered by the inclusion of the radiosensilization term. By means of numerical simulations, we show that optimal control offers a moderate increase in survival time over a sequential treatment. We then revisit in more detail a question of measuring the synergy between the therapies by means of isobolograms, a common experimental technique for measuring the additivity of two treatments.

The main goal of this paper is to study properties of a classical hawk-dove model using Mixed Spatial Evolutionary Games (MSEG). These games are played on a multiple lattices corresponding to the possible phenotypes and give possibility to simulate and investigate heterogeneity on the player-level in addition to the population-level. Furthermore, diverse polymorphic equilibrium points dependent on individuals reproduction, model parameters and their simulation are discussed. The analysis demonstrates the sensitivity properties of MSEGs and the possibility for further development of spatial games.

We present sufficient conditions of local controllability for a class of models of treatment response to combined anticancer therapies which include delays in control strategies. The combined therapy is understood as combination of direct anticancer strategy e.g. chemotherapy and indirect modality (in this case antiangiogenic therapy). Controllability of the models in the form of semilinear second order dynamic systems with delays in control enables to answer the questions of realizability of different objectives of multimodal therapy in the presence of PK/PD effects. We compare results for the models without delays and conditions for relative local controllability of models with delays.

We compare sufficient conditions for local controllability for a class of models of treatment response to antiangiogenic and combined anticancer therapies. The combined therapy is understood as combination of direct anticancer strategy e.g. chemotherapy and indirect modality (in this case antiangiogenic therapy). We discuss different control objectives related to multimodal therapies in the light of present knowledge of self-organization of tumor cell populations treated by anticancer drugs. Controllability of the models in the form of semilinear second order dynamic systems enables to expect that the objectives could be reached.

In the paper we study some control properties of a two compartmental model of response to anticancer treatment which combines antiangiogenic and cytotoxic drugs and takes into account multiple delays in control. Mode precisely we formulate sufficient local controllability conditions for semilinear systems which result from the use of Hakufeldt et al. model, endowed with two control variables representing antiangiogenic modality, combined with chemotherapy which contain delays related to PK/PD effects and some clinical recommendations e.g. normalization of vascular network. Then the optimized protocols of the combined therapy for the model, considered as solutions of an optimal control problem for dynamical systems with delays in control, are found using necessary conditions of optimality and numerical calculations . Structural sensitivity of considered control properties and optimal solutions are also discussed.

In this work we present SPICY (SPecialized Classification sYstem) application for a supervised data analysis (feature selection, classification, model validation and model selection) with the structure preventing the data processing work-flow from so called information leak. The information leak may result in optimistically biased classification quality assessment, especially for large-scale, small-sample data sets. The application uses the Galaxy Server environment that originally allows the user to manual data processing and is not prevented from the information leak. The way how the classification model is built by the user and the specific structure of all implemented methods makes the information leak impossible. The lack of information leak in the presented supervised data analysis tool is demonstrated on numerical examples, where synthetic and real data sets are used.

Ionizing radiation activates a large variety of intracellular mechanisms responsible for maintaining appropriate cell functionality or activation of apoptosis which eliminates damaged cells from the population. The mechanism of such induced cellular death is widely used in radiotherapy in order to eliminate cancer cells, although in some cases it is highly limited by increased cellular radio-resistance due to aberrations in molecular regulation mechanisms of malignant cells. Despite the positive correlation between the radiation dose and the number of apoptotic cancer cells, radiation has to be limited because of extensive side effects. Therefore, additional control signals whose role will be to maximize the cancer cells death-ratio while minimizing the radiation dose and by that the potential side effects are worth considering. In this work we present the results of simulation studies showing possibilities of single gene regulation by small interfering RNA (siRNA) that can increase radio-sensitivity of malignant cells showing aberrations in the p53 signaling pathway, responsible for DNA damage-dependant apoptosis. By blocking the production of the p53 inhibitor Mdm2, radiation treated cancer cells are pushed into the apoptotic state on a level normally achievable only with high radiation doses. The presented approach, based on a simulation study originating from experimentally validated regulatory events, concerns one of the basic problems of radiotherapy dosage limitations, which, as will be shown, can be partially avoided by using the appropriate siRNA based control mechanism.

Analysis of the models presented in the preceding chapters may be focused on drawing conclusions of either qualitative or quantitative nature. In the first case, parameter values are not needed, as the goal is to determine, for example, stability properties or the form of the optimal control. Such conclusions subsequently provide the basis for quantitative analysis that concerns a particular cancer type and attempts to determine the outcome of a therapy, or, in more advanced studies, the optimal therapy protocol. The latter is of more value from the clinical point of view. However, applicability of modeling results depends on the ability to estimate correct parameter values for the models under consideration. In subsequent sections, estimation of the model parameters is discussed in the context of experimental and numerical procedures, relevant for the models described in previous chapters.

Tumorigenesis is a very complex pathological process, evolving through different parallel pathways. The list of hallmark capabilities which cancer has to acquire was presented in two famous review papers by Hanahan and Weinberg (Cell 100:57–70, 2000; Cell 144:646–674, 2011). Following recent biological discoveries, especially those in molecular biology, mathematicians try to create models adequate to knowledge in the biomedical field, oriented on specific aspects of tumor development. They apply various modeling techniques in order to perform this task. Among these techniques one can distinguish models based on partial differential equations, single-cell-based models, cellular automata, and others. This chapter is devoted to models with structure. Structure may have different meanings, it may refer to the space where cells develop, cellular level of differentiation, or some other physiological feature of the cell, it may also refer to mutual relations among the elements forming the whole system, as it is in agent-based models.

The rapid development of the biological research techniques in recent years provides more and more high quality data. Current technology allows to observe not only the whole body, tissue, or cell but also what happens inside the single cell, for example the time change (dynamics) of the number and location of biomolecules such as proteins, and their properties such as phosphorylation. With this knowledge it becomes obvious that the intracellular interactions between various molecules are not straightforward but complex with many mutual dependencies and feedback loops. It becomes clear that for a better understanding of the networks and their dynamics a complex approach is required. This approach can be based on the methodology of system engineering. It involves construction of mathematical models of observed phenomena and then their analysis. Mathematical models may be deterministic, based on ordinary differential equations (ODEs) or stochastic based on reaction propensities. They cover the network of interactions of intracellular species called the signaling pathways. In this chapter we define signaling pathways, describe main reaction types and corresponding equations, describe the main numerical methods for simulation of deterministic and stochastic models, and discuss the basics of the signaling pathways model analysis including stability, sensitivity, and bifurcation analysis. At the end we present an example of the p53 signaling pathway model and discuss possible anticancer therapies using available control signals.

This chapter is devoted to models of cancer growth and anticancer therapies that put special emphasis on the dependence of therapy efficiency on cell cycle. First, biological background is introduced and detailed description of a cell cycle is given, based on the review of biological literature. It is supplemented with information about chosen chemotherapeutic drugs and their efficacy with respect to the cell cycle. Next, pharmacokinetic and pharmacodynamics aspects of chemotherapeutics are briefly described. They along with cell cycle specificity of drugs may lead to various phenomena of resonances and aftereffects that need to be taken into account in therapy and synchronization of treatment protocols. These issues are mentioned in a separate section of this chapter. Finally, models that incorporate evolution of drug resistance are presented. For all models, the problem of finding a suitable treatment protocol is formulated as a problem of control optimization and some results of application of optimization theory to solve these problems are presented.

Cell subpopulations dealt with in the preceding chapter were the result of compartmentalizing the model. In this chapter we focus on growth of cancer cells and the associated vascular system and interactions with the immune system. Therefore, though the variables will still describe the amount of cells of different type, there will be no flux from one type to another. We start with introduction of standard models of population dynamics, with exponential, Gompertzian, and logistic growth. The difference between stochastic and deterministic approach to model population size is explained, a point often misinterpreted in various sources. Then, the angiogenic aspects of cancer growth are discussed, followed by several models of cancer growth including vascularization. Consequently, the problem of optimization of antiangiogenic and combined therapies is analyzed. Finally, models of gene and immunotherapy in cancer treatments are briefly reviewed. In addition to discussion of optimal treatment protocols, the focus of this chapter is on the formal, system engineering-based analysis of dynamical properties of systems under investigation, such as stability and controllability.

Testing biomedical hypotheses is performed based on advanced and usually many-step analysis of biomedical data. This requires sophisticated analytical methods and data structures that allow to store intermediate results, which are needed in the subsequent steps. However, biomedical data, especially reference data, often change in time and new analytical methods are created every year. This causes the necessity to repeat the iterative analyses with new methods and new reference data sets, which in turn causes frequent changes of the underlying data structures. Such instability of data structures can be mitigated by the use of the idea of data lake, instead of traditional database systems.

Living cells, like whole living organisms during evolution, communicate with their neighbors, interact with the environment, divide, change their phenotypes, and eventually die. The development of specific ways of communication (through signaling molecules and receptors) allows some cellular subpopulations to survive better, to coordinate their physiological status, and during embryonal development to create tissues and organs or in some conditions to become tumors. Populations of cells cultured in vitro interact similarly, also competing for space and nutrients and stimulating each other to better survive or to die. The results of these intercellular interactions of different types seem to be good examples of biological evolutionary games, and have been the subjects of simulations by the methods of evolutionary game theory where individual cells are treated as players. Here we present examples of intercellular contacts in a population of living human cancer HeLa cells cultured in vitro and propose an evolutionary game theory approach to model the development of such populations. We propose a new technique termed Mixed Spatial Evolutionary Games (MSEG) which are played on multiple lattices corresponding to the possible cellular phenotypes which gives the possibility of simulating and investigating the effects of heterogeneity at the cellular level in addition to the population level. Analyses performed with MSEG suggested different ways in which cellular populations develop in the case of cells communicating directly and through factors released to the environment.

In this paper we consider a problem of controllability of discrete time linear system with randomly jumping parameters which can be described by finite state Markov chain. Necessary and sufficient conditions for existence of control which governs the system from any initial conditions to zero, from zero initial condition to any final value and from any initial condition to any final value in given time and with probability one are given. The relations between such kinds of controllability and stochastic stabilizability are discussed.

In this paper, the optimal control law for the continuous infinite time-varying stochastic control system with jumps and quadratic cost is found under the assumption that the coefficient have limits as time tends to infinity and the boundary system is absolutely observable and stabilizable. In addition, the asymptotic properties of the solution of the differential Riccati equations for continuous time Markovian jump linear quadratic control problem with time-varying coefficient are established.

DNA microarray technology is the latest and the most advanced tool for parallel measuring of the activity and interactions of thousands of genes. This modern technology promises new insight into mechanisms of living systems, for example only two high-density oligonucleotide microarrays are sufficient to inspect the whole human genome. However, it provides unprecedented amount of data that require application of advanced computational methods. The appropriate choice of data analysis technique depends both on data and on goals of an experiment. In this paper we focus on two promising methods: singular value decomposition and support vector machines. We discuss the possibility of application of these methods for different purposes; particularly for clustering, classification, feature selection and modeling of dynamics of gene expression. We use for testing presented approaches existing data sets, which are widely available via Internet, and one new tumor/normal thyroid microarray data set.

This paper is concerned with the optimal control of time-varying, continuous-time linear systems both with parameters depending on time and the process being a finite-state Markovian one. The performance index to be minimized is the infinite-time quadratic cost functional. The solution of this time-varying jump linear quadratic control problem consists of the study of nonnegative definite global and bounded solution of coupled differential Riccati equation. Necessary and sufficient conditions for existence of such a solution are obtained in terms of optimizability and detectability. Moreover, the conditions for stability of the optimal closed-loop system are established.

Purpose/Objective : Our goal was to analyze the repopulation of surviving tumor cells during a treatment gap in radiotherapy for head-and-neck cancer. Methods and Materials : Clinical material is based on the records of 1502 patients treated by radiotherapy alone in Maria Sklodowska-Curie Memorial Institute in Gliwice during the period between1980 and 1989. All patients had histologically confirmed squamous cell carcinoma of the larynx or pharynx. The mean gap duration was 9 days. Only 10% of patients were treated without gaps. The dose per fraction was in the range of 1.5 to 2.5 Gy. Patient data were fitted directly to the mixed linear-quadratic model using maximum-likelihood estimation. Tumor stage or tumor localization was introduced into the equation as a categorical variable. Tumor proliferation was estimated by dividing the treatment gaps into three groups: the first 2 weeks, second 2 weeks, and the period after 4 weeks of irradiation. Results : Tumor control probability was significantly correlated with radiation dose, tumor progression (according to TNM), overall treatment time, and gap duration. Laryngeal cancers had a better prognosis than cancers of the oro- and nasopharynx. Significant tumor repopulation was found after the first 2 weeks of radiotherapy. During the treatment gap, the proliferation rate was equal to 0.75 Gy/day. During the days with irradiation, repopulation was slower and equal to 0.2 Gy/day. Conclusion : The repopulation of tumor cells is faster during a gap than during the normal days of irradiation. Accelerated repopulation probably starts soon after 2 weeks of irradiation.

The goal of this paper is to study the classical hawk-dove model using mixed spatial evolutionary games (MSEG). In these games, played on a lattice, an additional spatial layer is introduced for dependence on more complex parameters and simulation of changes in the environment. Furthermore, diverse polymorphic equilibrium points dependent on cell reproduction, model parameters, and their simulation are discussed. Our analysis demonstrates the sensitivity properties of MSEGs and possibilities for further development. We discuss applications of MSEGs, particularly algorithms for modelling cell interactions during the development of tumours. Display Omitted Introducing time-varying payoff matrices in mean-field games.New possibilities for more accurate and complex game theoretic simulation.Spatial lattice with simulation of interaction between cells and environment.Heterogeneity of individuals (poly-phenotypic players) in spatial games (MSEG).More precisely biological phenomena, especially for cancer cell populations.

We compare results of different reproduction schemes used in modelling of radiation induced bystander effect in normal cells. The model is based on the theory of spatial evolutionary games on a lattice and pay-offs are defined by changes in fitness measure resulting from intersections between cells representing different phenotypes. We discuss also qualitative differences between results of simulations of spatial evolutionary games and steady state solutions of replicator dynamics equations for relevant mean field games.

MicroRNAs (miRNAs) are small RNA molecules that posttranscriptionally regulate gene expression. The aim of this paper is to present a survey on published application of these molecules in cancer diagnosis including our own results in this area. As an illustrative example of the use of miRNA in cancer diagnosis we present some main points from our study related to thyroid carcinoma.

The main interest of the authors was to develop vascular solid tumour growth model, implement efficient numerical methods for simulations towards finding a solution of the model and trying to optimise influence of different types of therapies. A system of partial differential equations was introduced in order to simulate growth of tumour and normal cells as well as the dynamics of the diffusing nutrient and anti-angiogenic or chemotherapeutic factors within the tissue. Numerical simulations of our model were executed toward finding a suboptimal therapy protocol using stable FDTD (finite difference time-domain) method implementation. Combined therapy protocols has been selected by means of meta-heuristic algorithms. In this work we have selected genetics algorithms, ant colony algorithms and simulated annealing method. For those algorithms convergence to suboptimal solution was examined and compared, as well as average tumour size, average iteration count and average execution time.

The main goal of the study is modelling of radiation induced bystander effect using evolutionary game theory. A payoff table for three different phenotypes (game-theoretic strategies) contains: costs/profits of bystander effect, choice of apoptotic pathway, producing growth factors and resistance against bystander effect. Games are played on a lattice and for that purpose two kinds of spatial evolutionary games are presented and compared. Moreover different polymorphic equilibrium points dependent on model parameters and cells reproductions are discussed.

In this paper, we present our recent results which may play a role in improving the situation in the practical implications of mathematical modeling of cancer chemotherapy. We are concerned with control problems for a model of the dynamics of emergence of resistance of cancer cells to chemotherapy, as understood based on recent progress in molecular biology. In some special cases of this model, their asymptotic behavior and the stability problem for the infinite dimensional case were studied. In the case of finite initial condition the stability conditions were derived by asymptotical analysis of the analytical solution to the system of equations. In the case of initial condition with infinite number of elements the stability verification was based on the spectral properties of the infinitesimal generator of the system.

This paper is a review of mathematical models of control of cell cycle dynamics using external agents which take into account cell-cycle-phase specificity of the drugs. Although still far from being ready for clinical usage the results of these investigations give a new insight into difficulties in introduction of effective strategies in the war against cancer.

The study looked for an optimal set of genes differentiating between papillary thyroid cancer (PTC) and normal thyroid tissue and assessed the sources of variability in gene expression profiles. The analysis was done by oligonucleotide microarrays (GeneChip HG-U133A) in 50 tissue samples taken intraoperatively from 33 patients (23 PTC patients and 10 patients with other thyroid disease). In the initial group of 16 PTC and 16 normal samples, we assessed the sources of variability in the gene expression profile by singular value decomposition which specified three major patterns of variability. The first and the most distinct mode grouped transcripts differentiating between tumor and normal tissues. Two consecutive modes contained a large proportion of immunity-related genes. To generate a multigene classifier for tumor-normal difference, we used support vector machines-based technique (recursive feature replacement). It included the following 19 genes: DPP4, GJB3, ST14, SERPINA1, LRP4, MET, EVA1, SPUVE, LGALS3, HBB, MKRN2, MRC2, IGSF1, KIAA0830, RXRG, P4HA2, CDH3, IL13RA1, and MTMR4, and correctly discriminated 17 of 18 additional PTC/normal thyroid samples and all 16 samples published in a previous microarray study. Selected novel genes (LRP4, EVA1, TMPRSS4, QPCT, and SLC34A2) were confirmed by Q-PCR.Our results prove that the gene expression signal of PTC is easily detectable even when cancer cells do not prevail over tumor stroma. We indicate and separate the confounding variability related to the immune response. Finally, we propose a potent molecular classifier able to discriminate between PTC and nonmalignant thyroid in more than 90% of investigated samples.

Upper bounds for eigenvalues of a solution to continuous time coupled algebraic Riccati equation (CCARE) and discrete time coupled algebraic Riccati equation (DCARE) are developed as special cases of bounds for the uni...ed coupled algebraic Riccati equation (UCARE). They include bounds of the maximal eigenvalues, the sums of the eigenvalues and the trace.

Background Evolutionary game theory (EGT) has been widely used to simulate tumour processes. In almost all studies on EGT models analysis is limited to two or three phenotypes. Our model contains four main phenotypes. Moreover, in a standard approach only heterogeneity of populations is studied, while cancer cells remain homogeneous. A multilayer approach proposed in this paper enables to study heterogeneity of single cells. Method In the extended model presented in this paper we consider four strategies (phenotypes) that can arise by mutations. We propose multilayer spatial evolutionary games (MSEG) played on multiple 2D lattices corresponding to the possible phenotypes. It enables simulation and investigation of heterogeneity on the player-level in addition to the population-level. Moreover, it allows to model interactions between arbitrary many phenotypes resulting from the mixture of basic traits. Results Different equilibrium points and scenarios (monomorphic and polymorphic populations) have been achieved depending on model parameters and the type of played game. However, there is a possibility of stable quadromorphic population in MSEG games for the same set of parameters like for the mean-field game. Conclusion The model assumes an existence of four possible phenotypes (strategies) in the population of cells that make up tumour. Various parameters and relations between cells lead to complex analysis of this model and give diverse results. One of them is a possibility of stable coexistence of different tumour cells within the population, representing almost arbitrary mixture of the basic phenotypes. Reviewers This article was reviewed by Tomasz Lipniacki, Urszula Ledzewicz and Jacek Banasiak.