A Parallel Cellular Automaton Model For Adenocarcinomas in Situ with Java: Study of One Case

Adenocarcinomas are tumors that originate in the lining epithelium of the ducts that form the endocrine glands of the human body. Infiltrating breast and one of the most frequent neoplasms among female population, and the early detection of the disease is then fundamental and, for this reason, a profound knowledge of the biology of tumor at this phase is essential. Among the distinct tools that contribute to this knowledge, computational simulation is more frequently used every day. The availability of fast and efficient computations that allow the simulation of tumor dynamics in situ, under a wide range of different parameters, is an important research topic. Based on cellular automata, this paper proposes a generic simulation model for the Adenocarcinomas In Situ (CIS). We applied it to the breast ductal adenocarcinoma in situ (DCIS), modeling our cells with the genomic load that we currently know that the tumor starts, and proposing a numerical coding method for the genome that allows efficient computational management. We propose a parallelization scheme using data parallelism, and we show the acceleration achieved in multiple nodes of our cluster of processors

Recipes for calibration and validation of agent-based models in cancer biomedicine

Computational models and simulations are not just appealing because of their intrinsic characteristics across spatiotemporal scales, scalability, and predictive power, but also because the set of problems in cancer biomedicine that can be addressed computationally exceeds the set of those amenable to analytical solutions. Agent-based models and simulations are especially interesting candidates among computational modelling strategies in cancer research due to their capabilities to replicate realistic local and global interaction dynamics at a convenient and relevant scale. Yet, the absence of methods to validate the consistency of the results across scales can hinder adoption by turning fine-tuned models into black boxes. This review compiles relevant literature to explore strategies to leverage high-fidelity simulations of multi-scale, or multi-level, cancer models with a focus on validation approached as simulation calibration. We argue that simulation calibration goes beyond parameter optimization by embedding informative priors to generate plausible parameter configurations across multiple dimensions

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

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

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

Single-cell approaches to cell competition: high-throughput imaging, machine learning and simulations

Cell competition is a quality control mechanism in tissues that results in the elimination of less fit cells. Over the past decade, the phenomenon of cell competition has been identified in many physiological and pathological contexts, driven either by biochemical signaling or by mechanical forces within the tissue. In both cases, competition has generally been characterized based on the elimination of loser cells at the population level, but significantly less attention has been focused on determining how single-cell dynamics and interactions regulate population-wide changes. In this review, we describe quantitative strategies and outline the outstanding challenges in understanding the single cell rules governing tissue-scale competition dynamics. We propose quantitative metrics to characterize single cell behaviors in competition and use them to distinguish the types and outcomes of competition. We describe how such metrics can be measured experimentally using a novel combination of high-throughput imaging and machine learning algorithms. We outline the experimental challenges to quantify cell fate dynamics with high-statistical precision, and describe the utility of computational modeling in testing hypotheses not easily accessible in experiments. In particular, cell-based modeling approaches that combine mechanical interaction of cells with decision-making rules for cell fate choices provide a powerful framework to understand and reverse-engineer the diverse rules of cell competition

Translational Oncogenomics and Human Cancer Interactome Networks

An overview of translational, human oncogenomics, transcriptomics and cancer interactomic networks is presented together with basic concepts and potential, new applications to Oncology and Integrative Cancer Biology. Novel translational oncogenomics research is rapidly expanding through the application of advanced technology, research findings and computational tools/models to both pharmaceutical and clinical problems. A self-contained presentation is adopted that covers both fundamental concepts and the most recent biomedical, as well as clinical, applications. Sample analyses in recent clinical studies have shown that gene expression data can be employed to distinguish between tumor types as well as to predict outcomes. Potentially important applications of such results are individualized human cancer therapies or, in general, ‘personalized medicine’. Several cancer detection techniques are currently under development both in the direction of improved detection sensitivity and increased time resolution of cellular events, with the limits of single molecule detection and picosecond time resolution already reached. The urgency for the complete mapping of a human cancer interactome with the help of such novel, high-efficiency / low-cost and ultra-sensitive techniques is also pointed out

The role of space in homeostasis and preneoplasia in stratified squamous epithelia

A major subject of study in biological research is the dynamics of stem cells in squamous epithelia. Given that most common human cancers develop from epithelia, understanding the rules of cell fate decision in these systems is key to explaining not only healthy tissue growth and maintenance but also the processes of mutagenesis and cancer. The aim of my project was to investigate the dynamics in squamous epithelial tissues both in homeostasis and preneoplasia, using cellular automata (CA) models. Stem cell dynamics has been shown to be accurately described by a simple mathematical model, the single progenitor (SP) model. Reliable parameterisation of this model would give access to valuable quantitative information on epithelial tissue maintenance and enable investigating how mutations affect tissue dynamics. I initially identified the most appropriate method for accurately parameterising the homeostatic system. I then sought to account for the spatial patterning of cells by implementing the SP model in two-dimensional space. The spatial model was able to reproduce the key signatures of homeostatic dynamics, thus showing that restrictions imposed by tissue organization do not alter the neutral dynamics. Furthermore, I studied non-homeostatic dynamics in stratified squamous epithelial tissues by spatially modelling the growth and competition of non-neutral mutations as well as the effects of wounding in the tissue. The studied dynamics of Notch and p53 mutant clones in mouse epithelia has been found to be highly distinct, with the former fully colonizing the tissue whereas the latter only partially. I demonstrated that the two mutants’ tissue takeover dynamics can be recapitulated by two distinct spatial feedback rules, on the basis of response to crowding, providing a mechanistic explanation of the observed distinct growth modes. Finally, mutant competition was explored. A striking effect resulting from the spatial interaction of the two mutations in a wild-type background is that the p53 mutant cell population was always outcompeted by the Notch mutant population and appeared to shrink. Considering this consistent emergent behaviour in the competition simulations and given the paucity of Notch mutations in human cancer datasets, it is tempting to speculate that the aggressive fitness of Notch may offer a tumour-protective effect

Selection and competition of somatic mutations in normal epithelia

Tumourigenesis occurs when a series of genome alterations occur in the same group of cells and cause uncontrolled cell proliferation. Therefore, to understand the journey from healthy to cancerous tissue, it is important to study the accumulation and spread of mutations in pre- cancerous normal tissues. Recent studies have shown that apparently normal epithelium contains a high burden of mutations in cancer-associated genes. This thesis explores the behaviour of mutant clones in normal epithelium and how this affects cancer development. The nature of mutant clonal growth and competition in normal epidermis has been a subject of debate. A study found that mutant clone sizes inferred from DNA sequencing of normal human eyelid skin were consistent with a mathematical model of neutral cell dynamics, appearing to contradict a genetic analysis of the same dataset that found several genes under positive selection. I investigate this debate using computational modelling that takes into account the tissue structure and experimental tissue-sampling methods. The results show that mutant clone sizes in skin and oesophagus are consistent with non-neutral clonal competition. Further evidence for non-neutral selection in normal epithelium is found in patterns of mutations detected by DNA sequencing. By adapting a statistical method used for driver gene discovery, I look for enrichment or depletion of structural categories of missense mutations and find biologically meaningful patterns of selection in several proteins. The method can associate changes to protein structure or function with cell fitness, even in the absence of hotspot mutations and in the presence of passenger mutations. I demonstrate how the method is flexible and could be widely applicable, but can also produce misleading results if confounding sources of selection are not accounted for. Clonal competition in normal oesophageal epithelium is dominated by Notch1 loss-of- function mutations. I fit stochastic models of clonal dynamics to lineage tracing data to show that haploinsufficiency greatly accelerates Notch1 mutant expansion and that the loss of the second Notch1 allele provides a further strong selective advantage, consistent with the high frequency of NOTCH1 loss-of-heterozygosity events observed in human oesophagus. Finally, I examine a consequence of the spread of these highly fit mutant clones in the normal tissue. I use a mathematical model to analyse the results of a series of experiments in mutagen-treated mouse oesophagus, finding that microscopic tumours can be eliminated by highly fit clones in the surrounding normal tissue.Harrison Watson Fund at Clare College, Cambridg