Biomathematische Modellierung von Chemo- und Immuntherapie bei aggressiven Non-Hodgkin-Lymphomen

Dosis- und Zeitintensivierungen von Chemotherapie verbesserten das ereignisfreie Überleben bei Patienten mit aggressiven Non-Hodgkin-Lymphomen. Klinische Studien zeigten jedoch, dass zu starke Therapien in schlechteren Überlebensraten resultieren können. Rituximab ist ein monoklonaler Antikörper, der zu einem Durchbruch der Immuntherapie bei CD20-positiven B-Zell-Lymphomen geführt hat. Unterschiede bei den Überlebensraten zwischen einzelnen Therapievarianten werden durch Rituximab allerdings abgeschwächt. In dieser Promotionsarbeit wurde ein Modell entwickelt, welches diese Phänomene aus klinischen Studien durch die Annahme eines Anti-Tumor-Effekts des Immunsystems erklärt. Ein Differentialgleichungsmodell beschreibt die Dynamiken und Interaktionen zwischen Tumor- und Immunzellen unter Immunchemotherapie. Spezielle Parameter des Modells wurden durch Überlebenskurven aus klinischen Studien geschätzt. Dazu wurde ein Algorithmus entwickelt, der die Heterogenität der Überlebens- und Rezidivraten innerhalb eines Patientenkollektivs auf die Variabilität einiger weniger Parameter zurückführt. Das Modell wurde so an verschiedene Patientenkollektive angepasst. Schlechtere Ergebnisse bei zu intensiven Therapien werden im Modell durch eine zu starke Schädigung des Immunsystems erklärt, welches nicht mehr in der Lage ist, den residualen Tumor nach Therapieende zu bekämpfen. Ein weiterer Bestandteil des Modells ist die Vorhersage neuer Chemo- sowie Immuntherapievarianten, um vielversprechende Therapieszenarien zu ermitteln, die in die Konzeption neuer klinischen Studien einfließen können. Prognosen in Abhängigkeit von bestimmten Risikogruppen der Patienten können gestellt werden, indem Modellparameter mit messbaren Risikofaktoren assoziiert werden. Die wesentlichen Ergebnisse dieser Arbeit werden in zwei Publikationen vorgestellt

Cost Utility Analysis in Health Policy

The problem of valuing the benefits of health care programmes is a ubiquitous one in health economics. since most health care systems in OECD countries have a large element of public provision, many of the goods and services they provide do not have market prices. Where markets in health care do exist, the prices generated are unlikely to provide reliable signals of the relative value of these goods and services to society, due to numerous market imperfections. Over the last fifteen years, the technique of cost-utility analysis has been developed as a new approach to the problem of valuing health care benefits. A distinctive feature of cost-utility analysis (CUA) lies in the fact that the outcomes of health care programmes are valued not in monetary terms but in terms of a new unit, the quality-adjusted-life-year (QALY), which embodies both the life-saving and the quality-of-life-improving dimensions of health care. The method of cost-utility analysis has two main elements: an analysis of the additional utilities (or quality-adjusted-life-years) generated by health care interventions, and an analysis of the costs entailed

The role of Walsh structure and ordinal linkage in the optimisation of pseudo-Boolean functions under monotonicity invariance.

Optimisation heuristics rely on implicit or explicit assumptions about the structure of the black-box fitness function they optimise. A review of the literature shows that understanding of structure and linkage is helpful to the design and analysis of heuristics. The aim of this thesis is to investigate the role that problem structure plays in heuristic optimisation. Many heuristics use ordinal operators; which are those that are invariant under monotonic transformations of the fitness function. In this thesis we develop a classification of pseudo-Boolean functions based on rank-invariance. This approach classifies functions which are monotonic transformations of one another as equivalent, and so partitions an infinite set of functions into a finite set of classes. Reasoning about heuristics composed of ordinal operators is, by construction, invariant over these classes. We perform a complete analysis of 2-bit and 3-bit pseudo-Boolean functions. We use Walsh analysis to define concepts of necessary, unnecessary, and conditionally necessary interactions, and of Walsh families. This helps to make precise some existing ideas in the literature such as benign interactions. Many algorithms are invariant under the classes we define, which allows us to examine the difficulty of pseudo-Boolean functions in terms of function classes. We analyse a range of ordinal selection operators for an EDA. Using a concept of directed ordinal linkage, we define precedence networks and precedence profiles to represent key algorithmic steps and their interdependency in terms of problem structure. The precedence profiles provide a measure of problem difficulty. This corresponds to problem difficulty and algorithmic steps for optimisation. This work develops insight into the relationship between function structure and problem difficulty for optimisation, which may be used to direct the development of novel algorithms. Concepts of structure are also used to construct easy and hard problems for a hill-climber

Mathematical methods for magnetic resonance based electric properties tomography

Magnetic resonance-based electric properties tomography (MREPT) is a recent quantitative imaging technique that could provide useful additional information to the results of magnetic resonance imaging (MRI) examinations. Precisely, MREPT is a collective name that gathers all the techniques that elaborate the radiofrequency (RF) magnetic field B1 generated and measured by a MRI scanner in order to map the electric properties inside a human body. The range of uses of MREPT in clinical oncology, patient-specific treatment planning and MRI safety motivates the increasing scientific interest in its development. The main advantage of MREPT with respect to other techniques for electric properties imaging is the knowledge of the input field inside the examined body, which guarantees the possibility of achieving high-resolution. On the other hand, MREPT techniques rely on just the incomplete information that MRI scanners can measure of the RF magnetic field, typically limited to the transmit sensitivity B1+. In this thesis, the state of art is described in detail by analysing the whole bibliography of MREPT, started few years ago but already rich of contents. With reference to the advantages and drawbacks of each technique proposed for MREPT, the particular implementation based on the contrast source inversion method is selected as the most promising approach for MRI safety applications and is denoted by the symbol csiEPT. Motivated by this observation, a substantial part of the thesis is devoted to a thoroughly study of csiEPT. Precisely, a generalised framework based on a functional point of view is proposed for its implementation. In this way, it is possible to adapt csiEPT to various physical situations. In particular, an original formulation, specifically developed to take into account the effects of the conductive shield always employed in RF coils, shows how an accurate modelling of the measurement system leads to more precise estimations of the electric properties. In addition, a preliminary study for the uncertainty assessment of csiEPT, an imperative requirement in order to make the method reliable for in vivo applications, is performed. The uncertainty propagation through csiEPT is studied using the Monte Carlo method as prescribed by the Supplement 1 to GUM (Guide to the expression of Uncertainty in Measurement). The robustness of the method when measurements are performed by multi-channel TEM coils for parallel transmission confirms the eligibility of csiEPT for MRI safety applications

Gene Regulatory Networks: Modeling, Intervention and Context

abstract: Biological systems are complex in many dimensions as endless transportation and communication networks all function simultaneously. Our ability to intervene within both healthy and diseased systems is tied directly to our ability to understand and model core functionality. The progress in increasingly accurate and thorough high-throughput measurement technologies has provided a deluge of data from which we may attempt to infer a representation of the true genetic regulatory system. A gene regulatory network model, if accurate enough, may allow us to perform hypothesis testing in the form of computational experiments. Of great importance to modeling accuracy is the acknowledgment of biological contexts within the models -- i.e. recognizing the heterogeneous nature of the true biological system and the data it generates. This marriage of engineering, mathematics and computer science with systems biology creates a cycle of progress between computer simulation and lab experimentation, rapidly translating interventions and treatments for patients from the bench to the bedside. This dissertation will first discuss the landscape for modeling the biological system, explore the identification of targets for intervention in Boolean network models of biological interactions, and explore context specificity both in new graphical depictions of models embodying context-specific genomic regulation and in novel analysis approaches designed to reveal embedded contextual information. Overall, the dissertation will explore a spectrum of biological modeling with a goal towards therapeutic intervention, with both formal and informal notions of biological context, in such a way that will enable future work to have an even greater impact in terms of direct patient benefit on an individualized level.Dissertation/ThesisPh.D. Computer Science 201

Mathematical Models of Tumor Heterogeneity and Drug Resistance

In this dissertation we develop mathematical models of tumor heterogeneity and drug resistance in cancer chemotherapy. Resistance to chemotherapy is one of the major causes of the failure of cancer treatment. Furthermore, recent experimental evidence suggests that drug resistance is a complex biological phenomena, with many influences that interact nonlinearly. Here we study the influence of such heterogeneity on treatment outcomes, both in general frameworks and under specific mechanisms. We begin by developing a mathematical framework for describing multi-drug resistance to cancer. Heterogeneity is reflected by a continuous parameter, which can either describe a single resistance mechanism (such as the expression of P-gp in the cellular membrane) or can account for the cumulative effect of several mechanisms and factors. The model is written as a system of integro-differential equations, structured by the continuous ``trait," and includes density effects as well as mutations. We study the limiting behavior of the model, both analytically and numerically, and apply it to study treatment protocols. We next study a specific mechanism of tumor heterogeneity and its influence on cell growth: the cell-cycle. We derive two novel mathematical models, a stochastic agent-based model and an integro-differential equation model, each of which describes the growth of cancer cells as a dynamic transition between proliferative and quiescent states. By examining the role all parameters play in the evolution of intrinsic tumor heterogeneity, and the sensitivity of the population growth to parameter values, we show that the cell-cycle length has the most significant effect on the growth dynamics. In addition, we demonstrate that the agent-based model can be approximated well by the more computationally efficient integro-differential equations, when the number of cells is large. The model is closely tied to experimental data of cell growth, and includes a novel implementation of transition rates as a function of global density. Finally, we extend the model of cell-cycle heterogeneity to include spatial variables. Cells are modeled as soft spheres and exhibit attraction/repulsion/random forces. A fundamental hypothesis is that cell-cycle length increases with local density, thus producing a distribution of observed division lengths. Apoptosis occurs primarily through an extended period of unsuccessful proliferation, and the explicit mechanism of the drug (Paclitaxel) is modeled as an increase in cell-cycle duration. We show that the distribution of cell-cycle lengths is highly time-dependent, with close time-averaged agreement with the distribution used in the previous work. Furthermore, survival curves are calculated and shown to qualitatively agree with experimental data in different densities and geometries, thus relating the cellular microenvironment to drug resistance

Estimating the effects on the dose distribution through the Bragg Peak degradation of lung tissue in proton therapy of thoracic tumors

Particle therapy offers to be a promising therapeutic option for tumors in the lung like Non-small cell lung cancer (NSCLC). However, the irradiation of NSCLCs with protons or carbon ions poses different challenges. The movement of the tumor, the heart and the entire thorax through breathing and the heartbeat requires a motion mitigated radiation application. In addition, the microscopic structure of the lung tissue holds further uncertainties of the calculation of the optimized dose distribution. In clinical CTs, on which treatment planning and dose calculation is based, the micrometer-sized air-filled alveoli of the lungs are not fully resolved, but are mapped through a medium density. As each particle of the beam passes a slightly different composition of air and tissue which leads to a slightly different range of the particles, the Bragg peak is degraded when irradiating such a heterogeneous tissue as lung. If this degradation of the Bragg peak is not taken into account into treatment planning, it can potentially lead to an underdose in the target volume and thus to a loss in tumor control. Additionally, the degradation can also lead to a higher dose in the organs at risk and normal tissue, endangering the success of the therapy by a higher toxicity of the treatment. In this dissertation, the effects of the Bragg Peak degradation on the dose distribution are calculated and analyzed so that an assessment of the effects for the clinical routine is available. For this purpose, CT images are manipulated with the help of a density modulation function, which modulates the density of the macroscopic lung voxel to reproduce the microscopic effect. Thus, a direct comparison between the dose distributions with and without the degrading effect is possible. Various dependencies like the tumor size, position and shape are systematically examined and the results of the degradation on clinical plans are presented for five patients. Hence, the clinical relevance can be estimated and assessed. In addition, measurements are presented which show the introduced material property of the "modulation power" of lung tissue. On the basis of this data, the uncertainties of the presented calculation and analysis can be reduced and estimated better. In addition, a mathematical model is presented which allows to estimate the modulation power on the basis of a clinical CT histogram analysis. Together, the works presented offer a basis for the patient-specific translation of the Bragg peak degradation of lung tissue into the clinical treatment planning procedure

Etude quantitative des aspects dynamiques et spatiaux du développement métastatique à l'aide de modèles mathématiques

In this thesis, a quantitative study of the metastatic process in the mouse has been performed thanks to mathematical modeling. Precisely, longitudinal data of the total metastatic burden and MRI data on the macrometastatic size distribution are confronted to a mathematical model describing the metastatic process by the independent growths of metastatic foci starting from one or few cells. This \standard" theory, able to describe the dynamics of the total metastatic burden, is on the other hand unable to describe the observed metastatic size distributions. Indeed, this model predicts many small metastases, whereas the observed metastases are much larger and fewer. In order to explain these differences, we proposed two hypotheses that were not taken into account in the initial theory. In the first one, metastases that are growing in close vicinity could merge, resulting in one larger metastasis. In the second one, metastatic foci could attract arriving circulating tumor cells, resulting also in fewer foci but much larger ones. These hypotheses have been tested experimentally by our biologists collaborators, and in silico thanks to a spatial model of tumor growth. The results of this study show that the previously suggested phenomena could have a substantial impact on the number and the sizes of the metastatic foci during metastatic development. Another part of this thesis is devoted to the numerical and mathematical analysis of the previous spatial model. This model takes into account the effect of the pressure on the proliferation of tumor cells. Numerical convergence of the numerical method that has been used and data assimilation on imaging data of pulmonary metastases are presented. Finally, a last part deals with the interactions between metastasis and its supportive stroma. Recent studies shed light on the implication of hematopoietic progenitors in the formation of a permissive soil in the future metastatic site, a phenomenon so-called premetastatic niche. In this thesis, a mathematical model describing the premetastatic and metastatic dynamics is proposed to study quantitative aspects of this phenomenon.L'objet de cette thèse est l'étude du processus métastatique par la confrontation de données in vivo chez la souris avec des modèles mathématiques. Plus précisément, des données longitudinales sur la masse métastatique totale combinées à des données IRM fournissant des informations sur le nombre et la taille des macrométastases ont été confrontées à un modèle décrivant l'évolution de la distribution en tailles des métastases par une équation aux dérivées partielles de populations structurées. La théorie sous-jacente au modèle, décrivant le processus métastatique par des métastases initiées par quelques cellules et croissant indépendamment les unes des autres, s'est révélée incapable de décrire les distributions de tailles métastatiques observées à l'IRM, suggérant la présence de phénomènes non pris en compte dans la théorie \standard" du développement métastatique. Ces résultats nous ont conduit à proposer des hypothèses expliquant les différences de distributions métastatiques entre le modèle et les données. Ces hypothèses ont été étudiées expérimentalement par nos collaborateurs biologistes mais également in silico à l'aide de modèles d'équations aux dérivées partielles décrivant la croissance de plusieurs métastases pouvant interagir spatialement. Les résultats obtenus à l'aide de notre approche de modélisation suggèrent des interactions jouant un rôle important dans la dynamique métastatique, comme l'agrégation de germes métastatiques ou l'attraction de cellules métastatiques par des foyers métastatiques déja existants. Une partie de cette thèse est également dédiée à l'analyse mathématique et numérique du nouveau modèle spatial introduit pour l'étude quantitative précédemment évoquée. Ce modèle mécanique décrit notamment l'effet de la pression sur la prolifération des cellules tumorales. Des résultats de convergence de la méthode numérique utilisée sont présentés, ainsi qu'une confrontation du modèle à des données de croissance de métastases pulmonaires. Enfin, une partie traitant des interactions métastases-microenvironnement est également présentée. Des études récentes ont en effet montré que certaines cellules progénitrices de la lignée hématopoïétique ou encore certaines cellules immunitaires pourraient jouer un r^ole important dans le développement métastatique. Au cours de cette thèse, ce phénomène appelé niche prémétastatique a été étudié dans la littérature biologique puis modélisé mathématiquement afin de mieux comprendre le rôle de cette niche dans la dynamique métastatique