Mathematical modeling in cancer addressing the early stage and treatment of avascular tumors

Orientador: Hyun Mo YangTese (doutorado) - Universidade Estadual de Campinas, Instituto de Matemática Estatística e Computação CientíficaResumo: Esta tese trata de modelos matemáticos para descrever o surgimento e tratamento de tumores avasculares. Os modelos são baseados em sistemas de equações diferenciais ordinárias. Primeiramente, propomos um modelo para descrever o surgimento do câncer como um processo multi-passo, envolvendo transições entre células normais, células pré-malignas, e células tumorais, e considerando instabilidade genética como um fator que aumenta a taxa de mutações. O modelo prevê que a agressividade das células tumorais abre espaço para a sobrevivência das células menos adaptadas. Simulações numéricas mostram que o tempo para o tumor alcançar um tamanho detectável varia de cinco a oitenta anos, em razão de alterações mínimas nos parâmetros. Em seguida, estudamos um caso particular do primeiro modelo de um ponto de vista da teoria da Resiliência Ecológica. Os resultados ilustram como o surgimento e o tratamento efetivo do câncer podem ser vistos como a alternância entre dois estados de equilíbrio estáveis antagônicos. Neste contexto, alterações genéticas em uma escala de tempo lenta podem levar à destruição ou perda de estabilidade de um destes estados, tornando impossível tanto a cura ou o surgimento da doença. Na etapa seguinte, estudamos um modelo para quimioterapia metronômica em tumores avasculares, e mostramos como este tipo de tratamento pode levar à cura do paciente. Uma condição relacionando a toxicidade do tratamento aos parâmetros do modelo surge naturalmente e sua interpretação indica que a terapia metronômica tem baixa toxicidade quando administrada em tumores de crescimento lento, tumores com alta agressividade e competitividade por recursos, ou tumores com alta capacidade de suporte. Na última etapa, consideramos tratamentos não-autônomos visando comparar diversos regimes de dosagem em busca de protocolos ótimos. Mostramos como a utilização de uma abordagem simples para parametrizar a função que descreve o tratamento implica em facilidades tanto para a aplicação de métodos de otimização, quanto para a elaboração de critérios de otimalidade que englobem diversas características, como toxicidade, risco de recidiva, tempo de recuperação, e limitações na dosagem de drogaAbstract: This thesis studies mathematical models describing the onset and treatment of avascular tumors. The models are based on systems of ordinary differential equations. Initially, we propose a model to the onset of cancer as a multi-step process, involving transitions among normal cells, pre-malignant cells and tumor cells. The model considers genetic instability as a factor that enhances the mutation rates. Results predict that aggressiveness of tumor cells opens space to survival of less adapted cells. Numerical simulations show that the time for the tumor attains a detectable size ranges from five to eighty years, depending on minimal changes in parameters. Next, we study a particular case of the first model, from the point of view of Ecological Resilience. Results illustrate how the onset and the effective treatment of cancer may be seen as the switching between two alternative stable states. In this context, genetic alterations in a slow time-scale may cause the destruction or the loss of stability of one of these states, what makes impossible either the cure or the beginning of the disease. In the next stage, we study a model for metronomic chemotherapy in an avascular tumor, and we show how this treatment may lead to cure. A condition regarding toxicity and related to parameters arises naturally. Its interpretation indicates that metronomic chemotherapy has lower toxicity when administered in slow-growing tumors, tumors with high aggressiveness or competitiveness, and tumors with a high support capacity. In last, we consider non-autonomous treatments in order to compare different dosage regimes seeking for an optimal protocol. We show how the use of a simple approach for parameterizing the function which describes the treatment implies in advantages both for applying optimization methods as well as for formulating optimality criteria encompassing diverse features such as toxicity, relapse risk, recovery time and drug dosageDoutoradoMatematica AplicadaDoutor em Matemática AplicadaCAPE

Security Analysis of System Behaviour - From "Security by Design" to "Security at Runtime" -

The Internet today provides the environment for novel applications and processes which may evolve way beyond pre-planned scope and purpose. Security analysis is growing in complexity with the increase in functionality, connectivity, and dynamics of current electronic business processes. Technical processes within critical infrastructures also have to cope with these developments. To tackle the complexity of the security analysis, the application of models is becoming standard practice. However, model-based support for security analysis is not only needed in pre-operational phases but also during process execution, in order to provide situational security awareness at runtime. This cumulative thesis provides three major contributions to modelling methodology. Firstly, this thesis provides an approach for model-based analysis and verification of security and safety properties in order to support fault prevention and fault removal in system design or redesign. Furthermore, some construction principles for the design of well-behaved scalable systems are given. The second topic is the analysis of the exposition of vulnerabilities in the software components of networked systems to exploitation by internal or external threats. This kind of fault forecasting allows the security assessment of alternative system configurations and security policies. Validation and deployment of security policies that minimise the attack surface can now improve fault tolerance and mitigate the impact of successful attacks. Thirdly, the approach is extended to runtime applicability. An observing system monitors an event stream from the observed system with the aim to detect faults - deviations from the specified behaviour or security compliance violations - at runtime. Furthermore, knowledge about the expected behaviour given by an operational model is used to predict faults in the near future. Building on this, a holistic security management strategy is proposed. The architecture of the observing system is described and the applicability of model-based security analysis at runtime is demonstrated utilising processes from several industrial scenarios. The results of this cumulative thesis are provided by 19 selected peer-reviewed papers