The goal of this thesis is to analyze and understand the risks of Chronic Obstructive Pulmonary Disease (COPD) and lung cancer with respect to the provinces of Turkey according to the results of spatial analysis. The insurance sector of the country needs that kind of analysis to make more precise pricing in insurance products. Especially in health and life insurance products, morbidities like COPD and lung cancer may aect the life expectancy as much as the premiums. COPD and lung cancer prevalence may exhibit spatial autocorrelation due to spatial similarity of provinces. Hence understanding of spatial pattern of COPD and lung cancer prevalence may provide better actuarial decisions. In this research, common risk factors of COPD and lung cancer are considered to be tobacco sales, air pollution, urbanization, gross schooling rate, life expectancy, median age and GDP per capita of the provinces. The spatial patterns of these factors in Turkey as well as their correlations to COPD and lung cancer prevalence are explored in this study. The raw data of the morbidities (COPD and lung cancer) are collected from the Social Seiv curity Institution (SGK) and the useful data are selected in these raw data. The data of the independent variables are collected and derived from the Turkish Statistical Institute (TUIK) and Tobacco and Alcohol Market Regulatory Authority (TAPDK). First of all, COPD prevalence ratios and lung cancer prevalence ratios are grouped by 81 provinces of Turkey and every morbidity is separated by gender. Then, it needs to be decided the variables which define prevalence of COPD and that of lung cancer. Age, gender, socio-economic status, urbanization, schooling rate, life expectancy, tobacco sales and air quality may be some of the random variables which are categorized by provinces for both morbidities. After data collection spatial analysis is applied with visualization, explanatory analysis and modeling by using Geographic Information Systems (GIS). In visualization, general spatial patterns are identified for morbidities and variables. In explanatory analysis part, proximity matrices are used to evaluate Moran&rsquo / s I values for understanding the spatial autocorrelation. Then, these Moran&rsquo / s I values are used for plotting correlograms in order to follow the spatial dependence better. After identifying spatial dependence of the variables, Ordinary Linear Regression and Spatial Regression models are established and compared. Finally, as a result of those findings in the analysis, actuarial risk assessments are found for both two morbidities with respect to provinces and gender. The risk assessments are mapped and compared with the explanatory variables in the models which are found in the previous part and the relations between risks and variables are observed. As a result, the parameters show spatial autocorrelation which means that / financial risk assessments of COPD and lung cancer should be taken into account when deciding the pricing of some actuarial products such as health insurance. Generally, spatial correlation is ignored in this kind of calculations, but due to the high autocorrelation the results may indicate serious change. From the actuarial perspective, the results of the analysis are suggested to be used in health insurance premium pricing. Since the analysis could not have been made on the basis of individuals, and financial burden of morbidities for insurance companies are not given clearly, it is not possible to calculate any health insurance product premium, but it is more appropriate to consider the importance of these risk results in the calculations of health insurance products.

Philosophiae Doctor - PhD / Cancer is a complex disease that involves a sequence of gene-environment interactions in a progressive process that cannot occur without dysfunction in multiple systems. From a mathematical point of view, the sequence of gene-environment interactions often leads to mathematical models which are hard to solve analytically. Therefore, this thesis focuses on the design and implementation of reliable numerical methods for nonlinear, first order delay differential equations, second order non-linear time-dependent parabolic partial (integro) differential problems and optimal control problems arising in cancer modeling. The development of cancer modeling is necessitated by the lack of reliable numerical methods, to solve the models arising in the dynamics of this dreadful disease. Our focus is on chemotherapy, biological stoichometry, double infections, micro-environment, vascular and angiogenic signalling dynamics. Therefore, because the existing standard numerical methods fail to capture the solution due to the behaviors of the underlying dynamics. Analysis of the qualitative features of the models with mathematical tools gives clear qualitative descriptions of the dynamics of models which gives a deeper insight of the problems. Hence, enabling us to derive robust numerical methods to solve such models. / 2021-04-30

京都大学 / 0048 / 新制・課程博士 / 博士(医学) / 甲第21665号 / 医博第4471号 / 新制||医||1035(附属図書館) / 京都大学大学院医学研究科医学専攻 / (主査)教授 浅野 雅秀, 教授 齊藤 博英, 教授 遊佐 宏介 / 学位規則第4条第1項該当 / Doctor of Medical Science / Kyoto University / DFAM

abstract: Efforts to treat prostate cancer have seen an uptick, as the world’s most commoncancer in men continues to have increasing global incidence. Clinically, metastatic prostate cancer is most commonly treated with hormonal therapy. The idea behind hormonal therapy is to reduce androgen production, which prostate cancer cells require for growth. Recently, the exploration of the synergistic effects of the drugs used in hormonal therapy has begun. The aim was to build off of these recent advancements and further refine the synergistic drug model. The advancements I implement come by addressing biological shortcomings and improving the model’s internal mechanistic structure. The drug families being modeled, anti-androgens, and gonadotropin-releasing hormone analogs, interact with androgen production in a way that is not completely understood in the scientific community. Thus the models representing the drugs show progress through their ability to capture their effect on serum androgen. Prostate-specific antigen is the primary biomarker for prostate cancer and is generally how population models on the subject are validated. Fitting the model to clinical data and comparing it to other clinical models through the ability to fit and forecast prostate-specific antigen and serum androgen is how this improved model achieves validation. The improved model results further suggest that the drugs’ dynamics should be considered in adaptive therapy for prostate cancer. / Dissertation/Thesis / Masters Thesis Mathematics 2020

Nous introduisons un modèle mathématique d'évolution d'une maladie cancéreuse à l'échelle de l'organisme, prenant en compte les métastases ainsi que leur taille et permettant de simuler l'action de plusieurs thérapies telles que la chirurgie, la chimiothérapie ou les traitements anti-angiogéniques. Le problème mathématique est une équation de renouvellement structurée en dimension deux. Son analyse mathématique ainsi que l'analyse fonctionnelle d'un espace de Sobolev sous-jacent sont effectuées. Existence, unicité, régularité et comportement asymptotique des solutions sont établis dans le cas autonome. Un schéma numérique lagrangien est introduit et analysé, permettant de prouver l'existence de solutions dans le cas non-autonome. L'effet de la concentration de la donnée au bord en une masse de Dirac est aussi envisagé.Le potentiel du modèle est ensuite illustré pour des problématiques cliniques telles que l'échec des anti-angiogéniques, les protocoles temporels d'administration pour la combinaison d'une chimiothérapie et d'un anti-angiogénique et les chimiothérapies métronomiques. Pour tenter d'apporter des réponses mathématiques à ces problèmes cliniques, un problème de contrôle optimal est formulé, analysé et simulé. / We introduce a mathematical model for the evolution of a cancer disease at the organism scale, taking into account for the metastases and their sizes as well as action of several therapies such as primary tumor surgery, chemotherapy and anti-angiogenic therapy. The mathematical problem is a renewal equation with bi-dimensional structuring variable. Mathematical analysis and functional analysis of an underlying Sobolev space are performed. Existence, uniqueness, regularity and asymptotic behavior of the solutions are proven in the autonomous case. A lagrangian numerical scheme is introduced and analyzed. Convergence of this scheme proves existence in the non-autonomous case. The effect of concentration of the boundary data into a Dirac mass is also investigated.Possible applications of the model are numerically illustrated for clinical issues such as the failure of anti-angiogenic monotherapies, scheduling of combined cytotoxic and anti-angiogenic therapies and metronomic chemotherapies. In order to give mathematical answers to these clinical problems an optimal control problem is formulated, analyzed and simulated.

Η διατριβή αφορά την ανάπτυξη και υλοποίηση ενός τετραδιάστατου, διακριτού μοντέλου προσομοίωσης της συμπεριφοράς καρκινικών κυτταρικών συστημάτων σε ελεύθερη ανάπτυξη και της απόκρισής τους σε χημειοθεραπευτική ή και ακτινοθεραπευτική αγωγή. Υλοποιήθηκαν δύο εκδοχές του μοντέλου: η χωρική και η μη χωρική προσέγγιση. Η χωρική προσέγγιση αναφέρεται στην τετραδιάστατη προσομοίωση συμπαγών όγκων. Η μη χωρική προσέγγιση βρίσκει εφαρμογή στην περίπτωση μη συμπαγών όγκων, καθώς και συμπαγών όγκων, όταν δεν δίνεται έμφαση στη χωρική εξέλιξή τους. Η ερευνητική εργασία έχει επικεντρωθεί σε τρεις τύπους καρκινικών όγκων: καρκίνος του μαστού, καρκίνος του πνεύμονα και πολύμορφο γλοιοβλάστωμα και σε θεραπευτικά σχήματα χορήγησης των σκευασμάτων: επιρουβικίνη (epirubicin), τεμοζολομίδη (temozolomide), σισπλατίνη (cisplatin), γεμσιταμπίνη (gemcitabine), βινορελμπίνη (vinorelbine) και δοσεταξέλη (docetaxel). Σκοπός της εργασίας είναι η ανάπτυξη ενός εργαλείου για την αξιόπιστη υποστήριξη ιατρών στη λήψη αποφάσεων σχετικά με την επιλογή θεραπευτικών σχημάτων και την εξατομικευμένη βελτιστοποίηση της θεραπευτικής αγωγής. Η αφετηρία είναι η μοντελοποίηση του κυτταρικού κύκλου και των πιθανών μεταβάσεων μεταξύ των καταστάσεων που μπορεί να βρεθεί ένα κύτταρο. Το μοντέλο βασίζεται στην υπόθεση ότι ο καρκινικός όγκος διατηρείται από μια συγκεκριμένη κατηγορία κυττάρων, τα καρκινικά βλαστικά κύτταρα (cancer stem cells), και έχει επεκταθεί ώστε να περιλαμβάνει σε μεγαλύτερη λεπτομέρεια διάφορους βιολογικούς μηχανισμούς σε μοριακό (πχ. εκφράσεις γονιδίων) και κυτταρικό επίπεδο. Ο μηχανισμός δράσης, η φαρμακοκινητική και η φαρμακοδυναμική των θεωρούμενων σκευασμάτων έχουν μελετηθεί βιβλιογραφικά και έχουν ενσωματωθεί στο μοντέλο. Επίσης, το μοντέλο έχει αναπτυχθεί ώστε να λαμβάνει υπόψη του την κλινική εικόνα του ασθενούς με χρήση εξατομικευμένων κλινικών δεδομένων, όπως απεικονιστικά δεδομένα (π.χ. CT, MRI, PET), ιστοπαθολογικά δεδομένα (π.χ. τύπος όγκου, βαθμός διαφοροποίησης) και μοριακά δεδομένα (π.χ. έκφραση γονιδίων). Στα πλαίσια της διατριβής πραγματοποιούνται έλεγχοι αξιοπιστίας και εκτενείς παραμετρικές μελέτες για την αποσαφήνιση της ευαισθησίας του μοντέλου στη διακύμανση των παραμέτρων του τόσο κατά την προσομοίωση της ελεύθερης ανάπτυξης όσο και κατά την εφαρμογή της χημειοθεραπευτικής αγωγής. Η ποσοτική αξιολόγηση, προσαρμογή και βελτιστοποίηση του μοντέλου πραγματοποιείται στα πλαίσια των ευρωπαϊκών ερευνητικών προγραμμάτων ACGT (Advancing Clinicogenomic Trials on Cancer, FP6-2005-IST-026996), ContraCancrum (Clinically Oriented Cancer Multilevel Modelling, FP7-ICT-2007-2-223979) και P-medicine (From data sharing and integration via VPH models to Personalized medicine, FP7-ICT-2009-6-270089) μέσω της αξιοποίησης πραγματικών κλινικών δεδομένων. Στην παρούσα διατριβή παρουσιάζονται τα αποτελέσματα της προσαρμογής του μοντέλου σε κλινικά δεδομένα του καρκίνου του μαστού, του καρκίνου του πνεύμονα και του πολύμορφου γλοιοβλαστώματος. Επιπλέον, διάφορες εκδόσεις του μοντέλου έχουν αξιοποιηθεί για ‘την επάνδρωση’ μιας ευρωπαϊκής βάσης μοντέλων για τον καρκίνο, που υλοποιείται στα πλαίσια του ευρωπαϊκού ερευνητικού προγράμματος TUMOR (Transatlantic Tumour Model Repositories, FP7-ICT-2009-5-247754). Το μοντέλο υλοποιείται σε γλώσσα προγραμματισμού C++. / In the present thesis, a clinically oriented, multiscale, discrete simulation model of cancer free growth and response to chemotherapy and/or radiotherapy is presented and investigated. Two versions of the model have been implemented: the spatial and the non spatial approach. The spatial model concerns the spatiotemporal evolution of solid tumours, whereas the non spatial model can be applied in the case of non solid cancers, as well as solid tumours, when no emphasis is put on the spatial features of a tumour evolution. The research work has been focused on the paradigms of early breast cancer treated with the single agent epirubicin, primary lung cancer treated with various combinations of cisplatin, gemcitabine, vinorelbin and docetaxel and glioblastoma multiforme treated with combined modality treatment using radiation and chemotherapy with temozolomide. The goal is to end up with a reliable simulation system able to assist clinicians in selecting the most appropriate therapeutic pattern, extracted from several candidate therapeutic schemes in the context of patient individualized treatment optimization. The model incorporates the biological mechanisms of cell cycling, quiescence, recruitment (reentry into the cell cycle), differentiation and death. It is based on the well documented assumption that tumour sustenance is due to the existence of cancer stem cells, i.e. cells which have the ability to preserve their own population, as well as give birth to cells that follow the path towards terminal differentiation. Furthermore, the mechanism of action, pharmacokinetics and pharmacodynamics of all considered agents have been bibliographically studied and incorporated into the model. Finally, the model has been developed to support and incorporate individualized clinical data such as imaging data (e.g. CT, MRI, PET slices, possibly fused), including the definition of the tumour contour and internal tumour regions (proliferating, necrotic), histopathologic (e.g., type of tumour) and genetic data (e.g., gene expression). An exhaustive and in-depth examination of the model behaviour with respect to the variation of its input parameters has been performed, in order to determine the impact of its parameters, guarantee a biologically relevant virtual tumour behaviour and enlighten aspects of the interplay and possible interdependencies of the biological mechanisms modeled. Finally, the model has been quantitativily validated and adaptated in the framework of the ACGT (Advancing Clinicogenomic Trials on Cancer, FP6-2005-IST-026996), ContraCancrum (Clinically Oriented Cancer Multilevel Modelling, FP7-ICT-2007-2-223979) and P-medicine (From data sharing and integration via VPH models to Personalized medicine, FP7-ICT-2009-6-270089) European Commission-funded projects by exploiting real clinical data. In the present thesis, the clinical adaptation of the model focuses on breast cancer, lung cancer and glioblastoma multiforme clinical cases. Moreover, various versions of the model have been uploaded to the EU cancer model repository developed by the TUMOR (Transatlantic Tumour Model Repositories, FP7-ICT-2009-5-247754) European Commission-funded project. The model has been developed in the C++ programming language.