Tumor growth analysis using cellular automata based on the cancer hallmarks

Programa Oficial de Doutoramento en Computación . 5009V01[Resumen]En esta tesis se ha realizado un modelado del crecimiento tumoral, considerando éste consecuencia emergente de las interacciones entre las células y su entorno. El modelado se ha considerado en el nivel de comportamiento celular, modelando los procesos de mitosis y muerte celular en función de la adquisición de una serie de rasgos característicos del cáncer (hallmarks) y del entorno inmediato de cada célula. Para el modelado hemos considerado la herramienta de Autómata Celular (AC). En la tesis se ha analizado la relevancia de los diferentes hallmarks en diferentes escenarios, las transiciones de comportamientos al aplicar un tratamiento, además de introducir la modelización de células madre de cáncer (CSCs). Al incorporar CSCs en el modelado se analizan además diferentes estrategias de tratamientos en el contexto de CSC, teniendo en cuenta la capacidad de recrecimiento del tumor debido a la presencia de CSCs. Finalmente, hemos aplicado optimización evolutiva para la obtención automática de los tratamientos que minimicen el efecto de la recidiva.[Abstract] In this thesis we used computational models based on cellular automata and the abstract model of cancer hallmarks to analyze the emergent behavior of tumor growth at cellular level. Tumor growth is modeled with a cellular automaton which determines cell mitotic and apoptotic behaviors. These behaviors depend on the cancer hallmarks acquired in each cell as consequence of mutations. The presence of the cancer hallmarks defines cell states and cell mitotic behaviors. Additionally, these hallmarks are associated with a series of parameters, and depending on their values and the activation of the hallmarks in each of the cells, the system can evolve to different dynamics. With the simulation tool we performed an analysis of the first phases of cancer growth. Firstly, we studied the evolution of cancer cells and hallmarks in different representative situations regarding initial conditions and parameters, analyzing the relative importance of the hallmarks for tumor progression; Secondly, we focused on the analysis of the effect of killing cancer cells, inspecting the time evolution of the multicellular system under such conditions and the possible behavioral transitions between the predominance of cancer and healthy cells. Later, we analyzed the effect of treatment applications on cancer growth taking into account the presence of Cancer Stem Cells (CSCs) and their regrowth capacity. Finally, we used evolutionary computing to analyze the implications of treatment strategies in a CSC context. In this way, we determined the best strategies of treatment applications in terms of intensity, duration and periodicity considering the regrowth capacity of CSCs

Using Cellular Automata and Lattice Boltzmann Methods to Model Cancer Growth: Analysis of Combination Treatment Outcomes

In Canada it is estimated that 76,600 people will die of cancer in 2014. Cancer, a collection of over 200 diseases, has differences existing between globally, between individuals and overtime in one individual. Treatment options are similarly varied. These differences make selecting the best possible treatment for every type of cancer very challenging. In addition, with no single cure for cancer, treatments are often combined in different ways to form the best overall option. In an attempt to synthesize the properties of these diseases into a collection of common cellular changes, Hanahan and Weinberg proposed ``the hallmarks of cancer -- 10 differences between healthy cells and cancer cells, present in almost every cancer. There exists the potential for treatments that are broadly applicable if they reverse these general properties. This work seeks to simulate early cancer growth, specifically looking at these hallmarks, and detect the best combinations of hallmarks to remove in order to stop cancer growth. This hybrid simulation combines a discrete model of cancer cells using cellular automata, with a continuous model of blood flow using lattice Boltzmann methods. Hallmarks relevant during the early growth stages of solid tumour development are simulated using rules in the cellular automata. Hallmarks were removed in pairs, triplets and quadruplets in order to model combination therapy, abstracting drugs that target these properties as the removal of the hallmark from the system. Overall growth of the tumours with ``treatments applied were compared to tumours where all hallmarks were present. It was found that many combinations had no effect on tumour growth. In some cases combinations even increased growth, selecting for the most aggressive hallmarks since weaker hallmarks were unavailable. However, in general, as more treatments were applied, cancer growth decreased. This work is the first to simulate removing hallmarks in pairs, triplets and quadruplets from a model with biologically relevant oxygen flow. It provides a proof of concept that not all combinations are equally effective, even if the individual treatments are effective. This work suggests some combinations should be avoided while others could potentially be beneficial in a variety of diseases

A Lock Free Approach To Parallelize The Cellular Potts Model: Application To Ductal Carcinoma In Situ

In the field of computational biology, in order to simulate multiscale biological systems, the Cellular Potts Model (CPM) has been used, which determines the actions that simulated cells can perform by determining a hamiltonian of energy that takes into account the influence that neighboring cells exert, under a wide range of parameters. There are some proposals in the literature that parallelize the CPM; in all cases, either lockbased techniques or other techniques that require large amounts of information to be disseminated among parallel tasks are used to preserve data coherence. In both cases, computational performance is limited. This work proposes an alternative approach for the parallelization of the model that uses transactional memory to maintain the coherence of the information. A Java implementation has been applied to the simulation of the ductal adenocarcinoma of breast in situ (DCIS). Times and speedups of the simulated execution of the model on the cluster of our university are analyzed. The results show a good speedup

Modelling Chromosome Missegregation in Tumour Evolution

Cancer is a disease in which the controls that usually ensure the coordinated behaviour of individual cells break down. This rarely happens all at once. Instead, the clone of cells that grows into a developing tumour is under high selection pressure, leading to the evolution of a complex and diverse population of related cells that have accumulated a wide range of genetic defects. One of the most evident but poorly characterized of these genetic abnormalities is a disorder in the number of chromosomes, or aneuploidy. Aneuploidy can arise though several different mechanisms. The project explores one such mechanism - chromosome missegregation during cell division- and its role in oncogenesis. To address the role that chromosome missegregation may have in the development of cancer a computational model was devised. We then defined the behaviour of individual cells, their genomes and a tissue niche, which could be used in simulations to explore the different types of cell behaviour likely to arise as the result of chromosome missegregation. This model was then used to better understand how defects in chromosome segregation affect cancer development and tumour evolution during cancer therapy. In stochastic simulations, chromosome missegregation events at cell division lead to the generation of a diverse population of aneuploid clones that over time exhibit hyperplastic growth. Significantly, the course of cancer evolution depends on genetic linkage, as the structure of chromosomes lost or gained through missegregation events and the level of genetic instability function in tandem to determine whether tumour growth is driven primarily by the loss of tumour suppressors or by the overexpression of oncogenes. As a result, simulated cancers diff er in their level of genetic stability and in their growth rates. We then used this system to investigate the consequences of these differences in tumour heterogeneity for anti¬cancer therapies based on surgery and anti-mitotic drugs that selectively target proliferating cells. Results show that simulated treatments induce a transient delay in tumour growth, and reveal a significant difference in the efficacy of different therapy regimes in treating genetically stable and unstable tumours. These data support clinical observations in which a poor prognosis is correlated with a high level of chromosome missegregation. However, simulations run in parallel also exhibit a wide range of behaviours, and the response of individual simulations (equivalent to single tumours) to anti-cancer therapy prove extremely variable. The model therefore highlights the difficulties of predicting the outcome of a given anti-cancer treatment, even in cases in which it is possible to determine the genotype of the entire set of cells within the developing tumour

Mathematical approaches for the clinical translation of hyperpolarised 13C imaging in oncology

Dissolution dynamic nuclear polarisation is an emerging clinical technique which enables the metabolism of hyperpolarised 13C-labelled molecules to be dynamically and non- invasively imaged in tissue. The first molecule to gain clinical approval is [1-13C]pyruvate, the conversion of which to [1-13C]lactate has been shown to detect early treatment re- sponse in cancers and correlate with tumour grade. As the technique has recently been translated into humans, accurate and reliable quantitative methods are required in order to detect, analyse and compare regions of altered metabolism in patients. Furthermore, there is a requirement to understand the biological processes which govern lactate pro- duction in tumours in order to draw reliable conclusions from this data. This work begins with a comprehensive analysis of the quantitative methods which have previously been applied to hyperpolarised 13C data and compares these to some novel approaches. The most appropriate kinetic model to apply to hyperpolarised data is determined and some simple, robust quantitative metrics are identified which are suitable for clinical use. A means of automatically segmenting 5D hyperpolarised imaging data using a fuzzy Markov random field approach is presented in order to reliably identify regions of abnormal metabolic activity. The utility of the algorithm is demonstrated on both in silico and animal data. To gain insight into the processes driving lactate metabolism, a mathematical model is developed which is capable of simulating tumour growth and treatment response under a range of metabolic and tissue conditions, focusing on the interaction between tumour and stroma. Finally, hyperpolarised 13C-pyruvate imaging data from the first human subjects to be imaged in Cambridge is analysed. The ability to detect and quantify lactate production in patients is demonstrated through application of the methods derived in earlier chapters. The mathematical approaches presented in this work have the potential to inform both the analysis and interpretation of clinical hyperpolarised 13C imaging data and to aid in the clinical translation of this technique.Joint funded by GlaxoSmithKline and the Cambridge Biomedical Research Centre

Contributions of cluster shape and intercellular adhesion to epithelial discohesion and emergent dynamics in collective migration

As a physical system, a cell interacts with its environment through physical and chemical processes. The cell can change these interactions through modification of its environment or its own composition. This dissertation presents the overarching hypothesis that both biochemical regulation of intercellular adhesion and physical interaction between cells are required to account for the emergence of cluster migration and collective dynamics observed in epithelial cells. Collective migration is defined as the displacement of a group of cells with transient or permanent cell-cell contacts. One mode, cluster migration, plays an important role during embryonic development and in cancer metastasis. Despite its importance, collective migration is a slow process and hard to visualize, and therefore it has not been thoroughly studied in three dimensions (3D). Based on known information about cluster migration from 2D studies of epithelial sheets and 3D single cell migration, this dissertation presents theoretical and experimental techniques to assess the independent contribution of physical and biochemical factors to 3D cluster migration. It first develops two computational models that explore the interaction between cells and the ECM and epithelial discohesion. These discrete mechanistic models reveal the need to account for intracellular regulation of adherens junctions in space and time within a cluster. Consequently, a differential algebraic model is developed that accounts for cross-reactivity of three pathways in a regulatory biochemical network: Wnt/β-catenin signaling, protein N-glycosylation, and E-cadherin adhesion. The model is tested by matching predictions to Wnt/β-catenin inhibition in MDCK cells. The model is then incorporated into a self-propelled particle (SPP) model, creating the first SPP model for study of adhesive mammalian cellular systems. MDCK cell clusters with fluorescent nuclei are grown, seeded, and tracked in 3D collagen gels using confocal microscopy. They provide data on individual cell dynamics within clusters. Borrowed from the field of complex systems, normalized velocity is used to quantify the order of both in vitro and simulated clusters. An analysis of sensitivity of cluster dynamics on factors describing physical and biochemical processes provides new quantitative insights into mechanisms underlying collective cell migration and explains temporal and spatial heterogeneity of cluster behavior

Cell migration and capillary plexus formation in wounds and retinae

Cell migration is a fundamental biological phenomenon that is critical to the development and maintenance of tissues in multi-cellular organisms. This thesis presents a series of discrete mathematical models designed to study the migratory response of such cells when exposed to a variety of environmental stimuli. By applying these models to pertinent biological scenarios and benchmarking results against experimental data, novel insights are gained into the underlying cell behaviour. The process of angiogenesis is investigated first and models are developed for simulating capillary plexus expansion during both wound healing and retinal vascular development. The simulated cell migration is coupled to a detailed model of blood perfusion that allows prediction of dynamic flow-induced evolution of the nascent vascular architectures – the network topologies generated in each case are found to successfully reproduce a number of longitudinal experimental metrics. Moreover, in the case of retinal development, the resultant distributions of haematocrit and oxygen are found to be essential in generating vasculatures that resemble those observed in vivo. An alternative cell migration model is then derived that is capable of more accurately describing both individual and collective cell movement. The general model framework, which allows for biophysical cell-cell interactions and adaptive cell morphologies, is seen to have the potential for a range of applications. The value of the modelling approach is well demonstrated by benchmarking in silico cell movement against experimental data from an in vitro fibroblast scrape wound assay. The results subsequently reveal an unexplained discrepancy that provides an intriguing challenge for future studies