Interaction of Brain Cancer Stem Cells and the Tumour Microenvironment: A Computational Study

Glioblastoma multiforme (GBM) is one of the most common and aggressive primary brain tumours, with a median patient survival time of 6-12 months in adults. It has been recently suggested that a typically small sub-population of brain tumour cells, in possession of certain defining properties of stem cells, is responsible for initiating and maintaining the tumour. More recent experiments have studied the interactions between this subpopulation of brain cancer cells and tumour microenvironmental factors such as hypoxia and high acidity. In this thesis a computational approach (based on Gillespie’s algorithm and cellular automata) is proposed to investigate the tumour heterogeneities that develop when exposed to various microenvironmental conditions of the cancerous tissue. The results suggest that microenvironmental conditions highly affect the characterization of cancer cells, including the self-renewal, differentiation and dedifferentiation properties of cancer cells

Lattice-gas cellular automata for the analysis of cancer invasion

Cancer cells display characteristic traits acquired in a step-wise manner during carcinogenesis. Some of these traits are autonomous growth, induction of angiogenesis, invasion and metastasis. In this thesis, the focus is on one of the latest stages of tumor progression, tumor invasion. Tumor invasion emerges from the combined effect of tumor cell-cell and cell-microenvironment interactions, which can be studied with the help of mathematical analysis. Cellular automata (CA) can be viewed as simple models of self-organizing complex systems in which collective behavior can emerge out of an ensemble of many interacting "simple" components. In particular, we focus on an important class of CA, the so-called lattice-gas cellular automata (LGCA). In contrast to traditional CA, LGCA provide a straightforward and intuitive implementation of particle transport and interactions. Additionally, the structure of LGCA facilitates the mathematical analysis of their behavior. Here, the principal tools of mathematical analysis of LGCA are the mean-field approximation and the corresponding Lattice Boltzmann equation. The main objective of this thesis is to investigate important aspects of tumor invasion, under the microscope of mathematical modeling and analysis: Impact of the tumor environment: We introduce a LGCA as a microscopic model of tumor cell migration together with a mathematical description of different tumor environments. We study the impact of the various tumor environments (such as extracellular matrix) on tumor cell migration by estimating the tumor cell dispersion speed for a given environment. Effect of tumor cell proliferation and migration: We study the effect of tumor cell proliferation and migration on the tumor’s invasive behavior by developing a simplified LGCA model of tumor growth. In particular, we derive the corresponding macroscopic dynamics and we calculate the tumor’s invasion speed in terms of tumor cell proliferation and migration rates. Moreover, we calculate the width of the invasive zone, where the majority of mitotic activity is concentrated, and it is found to be proportional to the invasion speed. Mechanisms of tumor invasion emergence: We investigate the mechanisms for the emergence of tumor invasion in the course of cancer progression. We conclude that the response of a microscopic intracellular mechanism (migration/proliferation dichotomy) to oxygen shortage, i.e. hypoxia, maybe responsible for the transition from a benign (proliferative) to a malignant (invasive) tumor. Computing in vivo tumor invasion: Finally, we propose an evolutionary algorithm that estimates the parameters of a tumor growth LGCA model based on time-series of patient medical data (in particular Magnetic Resonance and Diffusion Tensor Imaging data). These parameters may allow to reproduce clinically relevant tumor growth scenarios for a specific patient, providing a prediction of the tumor growth at a later time stage.Krebszellen zeigen charakteristische Merkmale, die sie in einem schrittweisen Vorgang während der Karzinogenese erworben haben. Einige dieser Merkmale sind autonomes Wachstum, die Induktion von Angiogenese, Invasion und Metastasis. Der Schwerpunkt dieser Arbeit liegt auf der Tumorinvasion, einer der letzten Phasen der Tumorprogression. Die Tumorinvasion ensteht aus der kombinierten Wirkung von den Wechselwirkungen Tumorzelle-Zelle und Zelle-Mikroumgebung, die mit die Hilfe von mathematischer Analyse untersucht werden können. Zelluläre Automaten (CA) können als einfache Modelle von selbst-organisierenden komplexen Systemen betrachtet werden, in denen kollektives Verhalten aus einer Kombination von vielen interagierenden "einfachen" Komponenten entstehen kann. Insbesondere konzentrieren wir uns auf eine wichtige CA-Klasse, die sogenannten Zelluläre Gitter-Gas Automaten (LGCA). Im Gegensatz zu traditionellen CA bieten LGCA eine einfache und intuitive Umsetzung der Teilchen und Wechselwirkungen. Zusätzlich erleichtert die Struktur der LGCA die mathematische Analyse ihres Verhaltens. Die wichtigsten Werkzeuge der mathematischen Analyse der LGCA sind hier die Mean-field Approximation und die entsprechende Lattice - Boltzmann - Gleichung. Das wichtigste Ziel dieser Arbeit ist es, wichtige Aspekte der Tumorinvasion unter dem Mikroskop der mathematischen Modellierung und Analyse zu erforschen: Auswirkungen der Tumorumgebung: Wir stellen einen LGCA als mikroskopisches Modell der Tumorzellen-Migration in Verbindung mit einer mathematischen Beschreibung der verschiedenen Tumorumgebungen vor. Wir untersuchen die Auswirkungen der verschiedenen Tumorumgebungen (z. B. extrazellulären Matrix) auf die Migration von Tumorzellen dürch Schätzung der Tumorzellen-Dispersionsgeschwindigkeit in einem gegebenen Umfeld. Wirkung von Tumor-Zellenproliferation und Migration: Wir untersuchen die Wirkung von Tumorzellenproliferation und Migration auf das invasive Verhalten der Tumorzellen durch die Entwicklung eines vereinfachten LGCA Tumorwachstumsmodells. Wir leiten die entsprechende makroskopische Dynamik und berechnen die Tumorinvasionsgeschwindigkeit im Hinblick auf die Tumorzellenproliferation- und Migrationswerte. Darüber hinaus berechnen wir die Breite der invasiven Zone, wo die Mehrheit der mitotischer Aktivität konzentriert ist, und es wird festgestellt, dass diese proportional zu den Invasionsgeschwindigkeit ist. Mechanismen der Tumorinvasion Entstehung: Wir untersuchen Mechanismen, die für die Entstehung von Tumorinvasion im Verlauf des Krebs zuständig sind. Wir kommen zu dem Schluss, dass die Reaktion eines mikroskopischen intrazellulären Mechanismus (Migration/Proliferation Dichotomie) zu Sauerstoffmangel, d.h. Hypoxie, möglicheweise für den Übergang von einem gutartigen (proliferative) zu einer bösartigen (invasive) Tumor verantwortlich ist. Berechnung der in-vivo Tumorinvasion: Schließlich schlagen wir einen evolutionären Algorithmus vor, der die Parameter eines LGCA Modells von Tumorwachstum auf der Grundlage von medizinischen Daten des Patienten für mehrere Zeitpunkte (insbesondere die Magnet-Resonanz-und Diffusion Tensor Imaging Daten) ermöglicht. Diese Parameter erlauben Szenarien für einen klinisch relevanten Tumorwachstum für einen bestimmten Patienten zu reproduzieren, die eine Vorhersage des Tumorwachstums zu einem späteren Zeitpunkt möglich machen

Implementing a New Data Model for Simulating Process

The paper describes the development of a new methodological approach for simulating geographic processes through the development of a data model that represents a process. This methodology complements existing approaches to dynamic modelling, which focus on the states of the system at each time step, by storing and representing the processes that are implicit in the model. The data model, called nen, focuses existing modelling approaches on representing and storing process information, which provides advantages for querying and analysing processes. The flux simulation framework was created utilizing the nen data model to represent processes. This simulator includes basic classes for developing a domain specific simulation and a set of query tools for inquiring after the results of a simulation. The methodology is prototyped with a watershed runoff simulation

Investigating the performance of transport infrastructure using real-time data and a scalable multi-modal agent based model

The idea that including more information in more dynamic and iterative ways is central to the promise of the big data paradigm. The hope is that via new data sources, such as remote sensors and mobile phones, the reliance on heavily simplified generalised functions for model inputs will be erased. This trade between idealised and actual empirical data will be matched with dynamic models which consider complexity at a fundamental level, inherently mirroring the systems they are attempting to replicate. Cloud computing brings the possibility of doing all of this, in less time than the simplified macro models of the past, thus enabling better answers and at the time of critical decision making junctures. This research was task driven - the question of high speed rail versus aviation led to an investigation into the simplifications and assumptions that back up many of the commonly held beliefs on the sustainability of different modes of transport. The literature ultimately highlighted the need for context specific information; actual load factors, actual journey times considering traffic/engineering works and so on. Thus, rather than being explicitly an exercise in answering a specific question, a specific question was used to drive the development of a tool which may hold promise for answering a range of transportation related questions. The original contributions of this work are, firstly the use of real-time data sources to quantify temporally and spatially dynamic network performance metrics (eg. journey times on different transport models) and secondly to organise these data sources in a framework which can handle the volume and type of the data and organise the data in a way so that it is useful for the dynamic agent based modelling of future scenarios.EPSRC I Case Studentship with Ove Arup & Partner