Investigating biocomplexity through the agent-based paradigm.

Capturing the dynamism that pervades biological systems requires a computational approach that can accommodate both the continuous features of the system environment as well as the flexible and heterogeneous nature of component interactions. This presents a serious challenge for the more traditional mathematical approaches that assume component homogeneity to relate system observables using mathematical equations. While the homogeneity condition does not lead to loss of accuracy while simulating various continua, it fails to offer detailed solutions when applied to systems with dynamically interacting heterogeneous components. As the functionality and architecture of most biological systems is a product of multi-faceted individual interactions at the sub-system level, continuum models rarely offer much beyond qualitative similarity. Agent-based modelling is a class of algorithmic computational approaches that rely on interactions between Turing-complete finite-state machines--or agents--to simulate, from the bottom-up, macroscopic properties of a system. In recognizing the heterogeneity condition, they offer suitable ontologies to the system components being modelled, thereby succeeding where their continuum counterparts tend to struggle. Furthermore, being inherently hierarchical, they are quite amenable to coupling with other computational paradigms. The integration of any agent-based framework with continuum models is arguably the most elegant and precise way of representing biological systems. Although in its nascence, agent-based modelling has been utilized to model biological complexity across a broad range of biological scales (from cells to societies). In this article, we explore the reasons that make agent-based modelling the most precise approach to model biological systems that tend to be non-linear and complex

Modelling angiogenesis in three dimensions

The process through which new blood vessels are formed within the body is known as angiogenesis. An essential part of our survival, it has also been implicated more recently in many diseases both in terms of induced growth, and abnormal vascular structure. Angiogenesis is characterized as two processes, the development of a vascular network during embryonic growth and the production of new blood vessels. This work focuses on the latter, and seeks to develop a robust, three-dimensional model for simulating blood vessel growth and the attendant processes of blood flow and mass transfer within the simulated system. A system was developed which utilises medical imaging scan data (specifically, MicroCT) as the initial conditions from which a network of vessels is grown. This is combined with GPU accelerated simulations of fluid dynamics, with the intention of providing a technique for future use in predictive medicine and therapeutic simulation

Cellular dynamics models of angiogenesis

Mención Internacional en el título de doctorCancer kills 26.4% of Spanish people. It is the second cause of death, just behind diseases of the circulatory system, 28.3% [1]. The growth of new blood vessels from the existing vasculature in response to chemical signals from a tumor is called tumorinduced angiogenesis and it is closely related to cancer and metastasis. The growth rate of a tumor is considerably increased in its vascular stage compared to its avascular and solid stage, therefore treating cancer turns excessively difficult and the survival rates rapidly decrease [2]. Among diseases that cause disability but not substantial mortality, age-related macular degeneration may cause severe loss of vision or blindness in many people, particularly the elderly. It is projected that 196 million people will be affected by age-related macular degeneration in 2020, increasing to 288 million by 2040 [3], which is likely an underestimation [4]. With age, Bruch’s membrane gets thicker and some damaged cells in the retina become inflamed. The secretion of chemical signals from those cells due to their inflammation induces angiogenesis, but the new blood vessels are disorganized and leaky causing the loss of vision. John Hunter was the pioneer in describing the vessel formation process in 1787 [5], but the first person who coined the word “angiogenesis” was Arthur T. Hertig in 1935 [6]. He was studying the formation of new blood vessel in the primary placenta of the macaque monkey when this word was used for the first time. Years later, in 1971, Judah Folkman hypothesized that tumors emit Tumor Angiogenic Factors (TAF) to attract blood vessels to them [7]. This investigation triggered the research field of angiogenesis in cancer and in 1989 one of the most important angiogenic factors was discovered: the Vascular Endothelial Growth Factor (VEGF). Since then, drugs with antiangiogenic effects have been investigated for cancer, age-related macular degeneration and other diseases, as it is involved in more than seventy different diseases. However, angiogenesis also occurs in normal and vital processes such as wound healing or the growth of a fetus. The difference between physiological and pathological angiogenic processes is a matter of balance. In a healthy process, angiogenesis develops to its proper extent and then stops, while in pathological processes angiogenesis does not stop or it does not develop sufficiently. Angiogenesis keeps the number of blood vessels needed in balance: few blood vessels cause tissue death, while uncontrolled vascular proliferation can lead to cancer, macular degeneration and other diseases. Angiogenesis is a complex, multistep and well regulated process where biochemistry and physics are intertwined. The process entails signaling in vessel cells being driven by both chemical and mechanical mechanisms that result in vascular cell movement, deformation and proliferation. In a later stage of angiogenesis, vessel cells rearrange to form lumen and allow the perfusion of the blood inside the sprout. Depending on what induces the angiogenesis, different environments and cells should be considered, for instance in the retina. A detailed review of the processes involved in angiogenesis from the biological point of view is given in section 1.1. Beyond experimental investigations, mathematical models of angiogenesis try to help in understanding the process and how the relevant mechanisms of angiogenesis interact. The approach of some models focus on a single scale or a single process of those involved to deepen the knowledge about it. Others span multiple scales or the whole process to give an idea about how to prevent or favor angiogenesis. In section 1.2, we briefly review the mathematical models of angiogenesis that have been used to date as well as those when angiogenesis occurs in the retina and models of lumen formation, the late stage of angiogenesis. A crucial question about modeling is how to integrate the multiple scales and mechanisms present in angiogenesis in a mathematical model. A model is expected to be useful to explore methods for promoting and inhibiting angiogenesis. However, answering this question with this expectation is not a simple task. Assembling all the processes involved with their different time and length scales requires to develop a cellular dynamics model combined with models for the continuum fields. We achieved this objective by developing a hybrid cellular Potts model of early stage angiogenesis, given in chapter 2. In contrast to recent models, this mathematical and computational model is able to explore the role of biochemical signaling and tissue mechanics. A exhaustive description of the results of the numerical simulations complete the chapter 2. The advantages of discovering the reasons why angiogenesis starts in the retina or inhibitory mechanisms are innumerable. Unraveling the causes of neovascularization in the retina and giving possible solutions for age-related macular degeneration are our motivation to adapt the angiogenesis model of chapter 2 to the retina. In chapter 3, we present the model and the numerical results. If mathematical models of angiogenesis that incorporate multiple scales and cellular signaling processes are not that common, those that also include lumen formation are almost nonexistent. In chapter 4, we describe two models of lumen formation and their results. The lumen formation in the first model takes place in a already developed sprout. Although some restrictions in the model make its applications and possibilities limited, its study is convenient to establish the basis of the second proposed model. In this second model, the lumenization occurs while the sprout is developing and the pressure of the blood is involved, following recent experiments of lumen formation during angiogenesis. This model is work in progress, but we believe that showing the preliminary results in chapter 4 may be interesting. A critical step in the development of a mathematical and computational model is to analyze the viability of its simulations. The simulations of the model in chapter 2 have been carried out thanks to the parallel computing on Graphics Processing Units (GPUs), as well as simulations of chapters 3 and 4. The large amount of square elements of the grid, nodes, cells and sprouts make this type of computation suitable for these models. The way they have been implemented is explained in chapter 5. Finally, conclusions of this thesis and future work are drawn in the last chapter 6. This chapter highlights and summarizes the research that has been carried out and proposes future extensions and applications of this work.La investigación de esta tesis ha sido financiada por los proyectos de investigación del Ministerio de Economía y Competitividad (ahora FEDER/Ministerio de Ciencia, Innovación y Universidades–Agencia Estatal de Investigación) No. MTM2014-56948-C2-2-P y No. MTM2017-84446-C2-2-R.Programa de Doctorado en Ingeniería Matemática por la Universidad Carlos III de MadridPresidente: Ana María Carpio Rodríguez.- Secretario: Filippo Terragni.- Vocal: Stephen W. Teitswort

Modelling angiogenesis in three dimensions

The process through which new blood vessels are formed within the body is known as angiogenesis. An essential part of our survival, it has also been implicated more recently in many diseases both in terms of induced growth, and abnormal vascular structure. Angiogenesis is characterized as two processes, the development of a vascular network during embryonic growth and the production of new blood vessels. This work focuses on the latter, and seeks to develop a robust, three-dimensional model for simulating blood vessel growth and the attendant processes of blood flow and mass transfer within the simulated system. A system was developed which utilises medical imaging scan data (specifically, MicroCT) as the initial conditions from which a network of vessels is grown. This is combined with GPU accelerated simulations of fluid dynamics, with the intention of providing a technique for future use in predictive medicine and therapeutic simulation

Multi-level agent-based modeling - A literature survey

During last decade, multi-level agent-based modeling has received significant and dramatically increasing interest. In this article we present a comprehensive and structured review of literature on the subject. We present the main theoretical contributions and application domains of this concept, with an emphasis on social, flow, biological and biomedical models.Comment: v2. Ref 102 added. v3-4 Many refs and text added v5-6 bibliographic statistics updated. v7 Change of the name of the paper to reflect what it became, many refs and text added, bibliographic statistics update

GPGPU Computing for Microscopic Simulations of Crowd Dynamics

We compare GPGPU implementations of two popular models of crowd dynamics. Specifically, we consider a continuous social force model, based on differential equations (molecular dynamics) and a discrete social distances model based on non-homogeneous cellular automata. For comparative purposes both models have been implemented in two versions: on the one hand using GPGPU technology, on the other hand using CPU only. We compare some significant characteristics of each model, for example: performance, memory consumption and issues of visualization. We also propose and test some possibilities for tuning the proposed algorithms for efficient GPU computations

Dynamic Load Balancing Strategy for Parallel Tumor Growth Simulations

In this paper, we propose a parallel cellular automaton tumor growth model that includes load balancing of cells distribution among computational threads with the introduction of adjusting parameters. The obtained results show a fair reduction in execution time and improved speedup compared with the sequential tumor growth simulation program currently referenced in tumoral biology. The dynamic data structures of the model can be extended to address additional tumor growth characteristics such as angiogenesis and nutrient intake dependencies