Many recent studies have shown that the initiation of human cancer is due to the malfunction of some genes at the R-checkpoint during the G1-to-S transition of the cell cycle. Identifying and modeling the dynamics of these genes has a paramount advantage in controlling and, possibly, treating human cancer. In this study, a new mathematical model for the dynamics of a cancer sub-network concentration is developed. Positive equilibrium points are determined and rigorously analyzed. We have found a condition for the existence of the positive equilibrium points from the activation, inhibition and degradation parameter values of the dynamical system. Numerical simulations have also been carried out. These results confirm analyses in the literature. / Thesis (M.Sc.)-University of KwaZulu-Natal, Westville, 2011.

Made available in DSpace on 2015-03-04T18:57:59Z (GMT). No. of bitstreams: 1 thesis.pdf: 5073087 bytes, checksum: f23ad1a1747577782cd9c9eab7574795 (MD5) Previous issue date: 2014-04-29 / Conselho Nacional de Desenvolvimento Cientifico e Tecnologico / The development of predictive computational models of tumor initiation, growth, and decline is faced with many formidable challenges. Phenomenological models which attempt to capture the complex interactions of multiple tissue and cellular species must cope with moving interfaces of heterogeneous media and the huge uncertainties of the parameters and their evolution. They must be able to deliver predictions consistent with events that take place at cellular scales, and they must faithfully depict biological mechanisms and events that are known to be associated with various forms of cancer. In the present work, some models for the tumor behavior are presented which fall within the framework of phase-field (or diffuse-interface) models suggested by continuum mixture theory. This framework provides for the simultaneous treatment of interactions of multiple evolving species, such as tumor cells, necrotic cell cores, nutrients, and other cellular and tissue types that exist and interact in living tissue. In the present work, a hybrid phase field ten-species vascular model for the tumor growth is developed, which couples the tumor growth with sprouting through angiogenesis. The model is able to represent the branching of new vessels through coupling a discrete model for which the angiogenesis is started upon pre-defined conditions on the nutrient deprivation in the continuum model. Such conditions are represented by hypoxic cells that release tumor growth factors that ultimately trigger vascular growth. We discuss the numerical approximation of the model using mixed finite elements. We also consider an avascular stochastic six-species tumor growth model derived directly from the hybrid ten-species model. The stochasticity comes from modeling uncertainties in the parameters of the model. We perform a sensitivity analysis to identify the more relevant parameters on the tumor mass growth. The stochastic model is then developed taking into account the uncertainty of the most influential parameter. The numerical approximation of the model using Stochastic Collocation method to treat uncertainties in the nonlinear system is presented. The results of numerous numerical experiments are also presented and discussed. / Modelos matematicos e computacionais sao utilizados na compreensao de fenomenos complexos, sendo aplicados em diversas areas como engenharia, fisica e biologia. Na Medicina tem um importante papel na simulacao do tratamento e evolucao de algumas doencas, entre elas o cancer. O desenvolvimento de modelos computacionais para o crescimento tumoral se depara com desafios formidaveis. Modelos fenomenologicos que tentam capturar as complexas interacoes de multiplos tecidos e especies celulares devem lidar com interfaces em meios heterogeneos e as enormes incertezas dos parametros e suas evolucoes. Eles devem ser capazes de proporcionar predicoes consistentes com eventos que ocorrem em escalas celulares, e devem representar fielmente os mecanismos biologicos associados ao cancer. No presente trabalho, sao apresentados alguns modelos para o crescimento tumoral. Esses modelos inserem-se no ambito de modelos de campo de fase (ou interface difusiva) sugeridos pela teoria mistura. Esta metodologia preve o tratamento simultaneo de interacoes entre multiplos constituintes, como as celulas tumorais, celulas necroticas, nutrientes e outros tipos celulares e teciduais que existem e interagem em tecidos vivos. Neste trabalho, um modelo hibrido de campo de fases, de dez constituintes e desenvolvido para o crescimento tumoral vascular, que acopla o crescimento de tumores com crescimento de novos vasos sanguineos atraves da angiogenese. O modelo é capaz de representar a ramificacao de novos vasos atraves do acoplamento de um modelo discreto, no qual a angiogenese é iniciada mediante condicoes pre-definidas, relacionadas a privacao de nutrientes no modelo macroscopico. Tais condicoes sao representadas por celulas hipoxicas que liberam quimicos reponsaveis por induzir a angiogenese tumoral. A aproximacao numerica do modelo usando elementos finitos mistos é discutida. Considera-se tambem um modelo estocastico avascular de seis constituintes para o crescimento tumoral, derivado diretamente do modelo hibrido de dez constituintes. A estocasticidade vem de incertezas na modelagem dos parametros do modelo. Realiza-se uma analise de sensibilidade para identificar os parametros mais relevantes sobre o crescimento da massa tumoral. O modelo estocastico é entao desenvolvido tendo em conta a incerteza no parametro mais influente. A aproximacao numerica do modelo usando o metodo estocastico de Colocacao para tratar incertezas no sistema nao-linear é apresentada. Os resultados de varios experimentos numericos tambem sao apresentados e discutidos.

We present mathematical models to study the mechanism of interaction of tumour infiltrating cytotoxic lymphocytes (TICLs) with tumour cells. We focus on the phase spaces of the systems and the nature of the solutions for the cell densities in the short and long term. The first model describes the production of offspring through cell proliferation, death and local kinetic interactions. The second model characterises the spatial distribution dynamics of the cell densities through reaction diffusion, which describes the random movement of the cells, and chemotaxis, which describes the immune cell movements towards the tumour cells. We then extend these models further to incorporate the effects of immunotherapy by developing two new models. In both situations, we analyse the phase spaces of the homogeneous models, investigate the presence of travelling wave solutions in our systems, and provide numerical simulations. Our analysis shows that cancer dormancy can be attributed to TICLs. Our study also shows that TICLs reduce the tumour cell density to a cancer dormant state but even with immunotherapy do not completely eliminate tumour cells from body tissue. Travelling wave solutions were confirmed to exist in the heterogeneous model, a linear stability analysis of the homogeneous models and numerical simulations show the existence of a stable tumour dormant state and a phase space analysis confirms that there are no limit cycles. / Thesis (M.Sc.)-University of KwaZulu-Natal, Pietermaritzburg, 2013.

Orientadores: Laercio Luis Vendite, Wagner Eduardo Matheus / Dissertação (mestrado) - Universidade Estadual de Campinas, Instituto de Matematica, Estatistica e Computação Cientifica / Made available in DSpace on 2018-08-13T05:08:40Z (GMT). No. of bitstreams: 1 Savergnini_KeniaDutra_M.pdf: 1467980 bytes, checksum: 83b757a2cd7718c6df26353b748ab05a (MD5) Previous issue date: 2009 / Resumo: O câncer de bexiga é, atualmente, a quarta neoplasia mais frequente em adultos e o segundo tumor urogenital mais frequente. Estimar os riscos de recidiva e progressão de tumores superficiais de bexiga, com as informações clínicas disponíveis para decidir a terapia a ser aplicada, é uma tarefa árdua. Neste trabalho, dois modelos matemáticos são elaborados para auxiliar especialista na tomada de decisão. A ferramenta utilizada para desenvolver estes modelos foi a Teoria dos Conjuntos Fuzzy, por sua capacidade em lidar com incertezas inerentes aos conceitos médicos. No primeiro modelo, o Estádio, o Grau e o Tamanho do tumor foram considerados como variáveis de entrada e o Risco de Recidiva de um tumor superficial de bexiga como variável de saída do primeiro sistema baseado em regras fuzzy (SBRF). Já no segundo modelo, além do Estádio, do Grau e do Tamanho do tumor, também foi considerado como variável de entrada de um segundo SBRF o Carcinoma in situ e como variável de saída, o Risco de Progressão de tumores superficiais Para cada modelo, foram feitas simulações com dados de pacientes do Hospital das Clínicas/UNICAMP e do Hospital A. C. Camargo de São Paulo, com o objetivo de verificar a contabilidade dos resultados gerados pelos dois sistemas. A partir do banco de dados e das possibilidades encontradas pelos SBRF, após a transformação possibilidade-probabilidade, pudemos gerar a probabilidade do caso real de cada conjunto fuzzy de saída. / Abstract: Nowadays, the bladder cancer is the fourth most common cancer in adults and the second most frequent urogenital tumor. Predicting recurrence and progression of superficial bladder tumors, with available clinical information to decide the therapy to be used is hard work. In this work, two mathematical models were developed to help specialist on the decision process. The tool used to developed these models was the fuzzy sets theory, by it capacity in dealing with uncertainties inherent in medical concepts. In the first model, Stage, Grade and Size of tumor had been considered input variables and Risk of Recurrence of a superficial bladder tumor as output variable of the first Fuzzy Rule-Based Systems (FRBS). In the second model, in addition to the Stage, Grade and Size of the tumor, also was considered as input variable of a second FRBS Carcinoma in situ and as a output variable, the Risk of Progression of superficial tumors. For each model, simulations were made with data of patients of the Clinics Hospital/UNICAMP and A. C. Camargo Hospital of São Paulo, with the aim to verify the reliability of results generated by the two systems. From a database and possibility found by FRBS, after the possibility-probability transformation, we can generate the real case probability of each fuzzy output set. / Mestrado / Mestre em Matemática Aplicada

Orientador: Laercio Luis Vendite / Dissertação (mestrado) - Universidade Estadual de Campinas, Instituto de Matemática, Estatística e Computação Científica / Made available in DSpace on 2018-08-08T14:27:24Z (GMT). No. of bitstreams: 1 Silveira_GracieleParaguaia_M.pdf: 1619969 bytes, checksum: 570ad2c7d6e368e955ded50b3177ab52 (MD5) Previous issue date: 2007 / Resumo: O aumento da incidência de casos de câncer de próstata, nos últimos anos, é um importante problema de saúde pública e um desafio para a ciência médica. Nesta dissertação estudamos a construção de um modelo matemático, que foi desenvolvido para predizer o estadiamento patológico do câncer de próstata. A intenção é auxiliar o especialista no processo de tomada de decisão, com relação ao estágio da doença. O modelo consiste num sistema baseado em regras fuzzy, que combina os dados pré-cirúrgicos - estado clínico, nível de PSA e grau de Gleason - valendo-se de um conjunto de regras, de natureza lingüística, elaborado a partir das informações presentes nos nomogramas já existentes. Com isso esperava-se obter, na saída do sistema, a chance de o indivíduo, com determinado quadro clínico, estar em cada estágio de extensão do tumor: localizado, localmente avançado e metastático. Foram feitas simulações, com dados de pacientes do Hospital das Clínicas/UNICAMP. Os resultados obtidos foram comparados com as probabilidades de Kattan et al, que embora sejam utilizadas nas decisões médicas, são consideradas pessimistas, em relação ao estágio da doença. Com o objetivo de aproximar os resultados, da realidade vivida pelos pacientes, efetuamos algumas modificações na modelagem. Tais mudanças foram suficientes para deixar os resultados mais otimistas e, portanto, mais realísticos / Abstract: The increase of the incidence of prostate cancer is a important problem of public health and a challenge to medical science. In this dissertation, we studied the construction of a mathematical model wich it was developed to predict the pathologic stage of prostate cancer. The intention is to help specialist on the decision process about stage of the disease. The model consists on a system founded in fuzzy laws that it combine the pre-surgicals dates - clinic state, PSA levels and Gleason score - availing of a linguistic laws set made with base on informations of the existents nomograms. Herewith we were hoping to ger person's chance, with clinics characteristics determinates, is in each stage of tumor extension: localized, advanced locally and metastatic. Simulations were made with patient's dates of the Clinics Hospital / UNICAMP. The results were compared with Kattan's probabilities that are used on the medicals decisions. However this probabilities to the disease are considered pessimists. With the aim of approach the results and the reality lived by patients, we did some modifications on the model. This changes were enough to became the results more otimists and therefore more realistics / Mestrado / Biomatematica / Mestre em Matemática Aplicada

We attempted a mathematical model for expected prognosis of lung cancer patients based on a multivariate analysis of the values of ER-interacting proteins (ERbeta) and a membrane bound, glycosylated phosphoprotein MUC1), and patients clinical data recorded at the time of initial surgery. We demonstrate that, even with the limited sample size available to use, combination of clinical and biochemical data (in particular, associated with ERbeta and MUC1) allows to predict survival of lung cancer patients with about 80% accuracy while prediction on the basis of clinical data only gives about 70% accuracy. The present work can be viewed as a pilot study on the subject: since results confirm that ER-interacting proteins indeed influence lung cancer patients’ survival, more data is currently being collected.

Thesis (MSc)--Stellenbosch University, 2014. / ENGLISH ABSTRACT: In recent years, HIV-associated cancers have proven to be the bane of our time, since HIV is decimating humanity across the globe, even in the twilight of the last century. Cancer rates continue to rise in developing countries, where 95% of the world’s HIV-infected population lives, yet less than 1% have access to antiretroviral therapy. HIV-infected individuals have a higher proclivity to develop cancers, mainly from immunosuppression. An understanding of the immunopathogenesis of HIV-related cancers (HRC) is therefore a major prerequisite for rationally developing and/or improving therapeutic strategies, developing immunotherapeutics and proplylatic vaccines. In this study, we explore the pathology of HIV-related cancer malignancies, taking into account the pathogenic mechanisms and their potential for improving the treatment of management of these malignancies especially in developing countries. We mathematically model the dynamics of malignant tumors in an HIV-free environment, investigate the impact of cancer malignancies on HIV-positive patients and explore the benefits of various therapeutic intervention strategies in the management of HIV-related cancers. We present two deterministic models of infectious diseases to implement these, and they were analysed. We use HIV-related lymphomas in the Western Cape of South Africa as a case study. We validated the proposed models using lymphoma incidence data from the Tygerberg Lymphoma Study Group (TLSG), Tygerberg Hospital, Western Cape, South Africa. We show that the increasing prevalence of HIV increases lymphoma cases, and thus, other HIV-related cancers. Our models also suggests that an increase in the roll-out of the HAART program can reduce the number of lymphoma cases in the nearest future, while it averts many deaths. Furthermore, the results indicate that a highly crucial factor to consider in the prognosis of the incidence of lymphoma (and other cancer types) in HIV-infected patients is their CD4 cell count, irrespective of whether the patient has developed an HRC or not.