Multiscale Agent-based Model of Tumor Angiogenesis (original) (raw)
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Simulating cancer growth with multiscale agent-based modeling
Seminars in cancer biology, 2015
There have been many techniques developed in recent years to in silico model a variety of cancer behaviors. Agent-based modeling is a specific discrete-based hybrid modeling approach that allows simulating the role of diversity in cell populations as well as within each individual cell; it has therefore become a powerful modeling method widely used by computational cancer researchers. Many aspects of tumor morphology including phenotype-changing mutations, the adaptation to microenvironment, the process of angiogenesis, the influence of extracellular matrix, reactions to chemotherapy or surgical intervention, the effects of oxygen and nutrient availability, and metastasis and invasion of healthy tissues have been incorporated and investigated in agent-based models. In this review, we introduce some of the most recent agent-based models that have provided insight into the understanding of cancer growth and invasion, spanning multiple biological scales in time and space, and we furthe...
AN AGENT-BASED HYBRID MODEL FOR AVASCULAR TUMOR GROWTH
Tumor development is a complex and multi-faceted process that cannot be captured in a single formula, yet the ability to predict a maturing tumor's magnitude and direction of growth would provide significant clinical benefits. In-vitro trials provide only limited predictive data since it is nearly impossible to chemically reproduce the exact environmental conditions surrounding a tumor. Moreover, each trial is necessarily unique to a specific tumor and cannot be quickly modified to satisfy the requirements of another. Mathematical models provide a virtual solution to this problem by implementing the core processes of tumor development in software. We present a model for tumor development from the single-cell stage to early microinvasion. An overlying nutrient field determines a cell's status as living, quiescent, or nonviable. Interactions between tumor cells are simulated using a competing exponential function and nutrient influx is modeled using the diffusion equation. The model may be applied to a variety of emerging tumors by carefully defining the set of constants that determines the tumor's development pathway.
Microvascular Research
The mechanisms involved in tumor growth mainly occur at the microenvironment, where the interactions between the intracellular, intercellular and extracellular scales mediate the dynamics of tumor. In this work, we present a multi-scale model of solid tumor dynamics to simulate the avascular and vascular growth as well as tumor-induced angiogenesis. The extracellular and intercellular scales are modeled using partial differential equations and cellular Potts model, respectively. Also, few biochemical and biophysical rules control the dynamics of intracellular level. On the other hand, the growth of melanoma tumors is modeled in an animal in-vivo study to evaluate the simulation. The simulation shows that the model successfully reproduces a completed image of processes involved in tumor growth such as avascular and vascular growth as well as angiogenesis. The model incorporates the phenotypes of cancerous cells including proliferating, quiescent and necrotic cells, as well as endothelial cells during angiogenesis. The results clearly demonstrate the pivotal effect of angiogenesis on the progression of cancerous cells. Also, the model exhibits important events in tumor-induced angiogenesis like anastomosis. Moreover, the computational trend of tumor growth closely follows the observations in the experimental study.
A Multiscale Model for Avascular Tumor Growth
Biophysical Journal, 2005
The desire to understand tumor complexity has given rise to mathematical models to describe the tumor microenvironment. We present a new mathematical model for avascular tumor growth and development that spans three distinct scales. At the cellular level, a lattice Monte Carlo model describes cellular dynamics (proliferation, adhesion, and viability). At the subcellular level, a Boolean network regulates the expression of proteins that control the cell cycle. At the extracellular level, reaction-diffusion equations describe the chemical dynamics (nutrient, waste, growth promoter, and inhibitor concentrations). Data from experiments with multicellular spheroids were used to determine the parameters of the simulations. Starting with a single tumor cell, this model produces an avascular tumor that quantitatively mimics experimental measurements in multicellular spheroids. Based on the simulations, we predict: 1), the microenvironmental conditions required for tumor cell survival; and 2), growth promoters and inhibitors have diffusion coefficients in the range between 10 ÿ6 and 10 ÿ7 cm 2 /h, corresponding to molecules of size 80-90 kDa. Using the same parameters, the model also accurately predicts spheroid growth curves under different external nutrient supply conditions.
Simulation of angiogenesis in a multiphase tumor growth model
Computer Methods in Applied Mechanics and Engineering, 2016
This is a PDF file of an unedited manuscript that has been accepted for publication. As a service to our customers we are providing this early version of the manuscript. The manuscript will undergo copyediting, typesetting, and review of the resulting proof before it is published in its final form. Please note that during the production process errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain. Highlights We introduce in our multiphase model for avascular tumor growth two new species. The new species are the tumor angiogenic factor (TAF) and endothelial cells (EC). Their diffusion and interaction simulates angiogenesis. Two numerical simulations of angiogenesis are proposed. The new capillary network will allow for simulating the chemotherapeutic agents delivery Highlights (for review)
A Multiple Scale Model for Tumor Growth
Multiscale Modeling & Simulation, 2005
We present a physiologically structured lattice model for vascular tumor growth which accounts for blood flow and structural adaptation of the vasculature, transport of oxygen, interaction between cancerous and normal tissue, cell division, apoptosis, vascular endothelial growth factor release, and the coupling between these processes. Simulations of the model are used to investigate the effects of nutrient heterogeneity, growth and invasion of cancerous tissue, and emergent growth laws.
Conference proceedings : ... Annual International Conference of the IEEE Engineering in Medicine and Biology Society. IEEE Engineering in Medicine and Biology Society. Annual Conference, 2004
There have been many efforts to explain and simulate tumor growth with mathematical and computational models. However, none have systematically examined the behaviors of tumor spheroids during growth. The interactions among tumor cells during growth are also not well understood. We have implemented an agent-based computational approach to study the macro- and micro- behaviors of avascular tumor spheroids during growth. Our simulations of tumor spheroid growth begin with a single tumor cell in optimal environmental conditions. We observe an initial phase of rapid growth, during which the shape of the collective approximates a spheroid. Subsequently a characteristic layered structure develops, consisting of an outermost proliferating cell layer, an intermediate quiescent cell layer, and a central necrotic core. These behaviors of our in silico spheroids map well to experimental in vitro observations.
Multiscale Models of Breast Cancer Progression
Annals of Biomedical Engineering, 2012
Breast cancer initiation, invasion and metastasis span multiple length and time scales. Molecular events at short length scales lead to an initial tumorigenic population, which left unchecked by immune action, acts at increasingly longer length scales until eventually the cancer cells escape from the primary tumor site. This series of events is highly complex, involving multiple cell types interacting with (and shaping) the microenvironment. Multiscale mathematical models have emerged as a powerful tool to quantitatively integrate the convective-diffusion-reaction processes occurring on the systemic scale, with the molecular signaling processes occurring on the cellular and subcellular scales. In this study, we reviewed the current state of the art in cancer modeling across multiple length scales, with an emphasis on the integration of intracellular signal transduction models with pro-tumorigenic chemical and mechanical microenvironmental cues. First, we reviewed the underlying biomolecular origin of breast cancer, with a special emphasis on angiogenesis. Then, we summarized the development of tissue engineering platforms which could provide highfidelity ex vivo experimental models to identify and validate multiscale simulations. Lastly, we reviewed top-down and bottom-up multiscale strategies that integrate subcellular networks with the microenvironment. We present models of a variety of cancers, in addition to breast cancer specific models. Taken together, we expect as the sophistication of the simulations increase, that multiscale modeling and bottom-up agent-based models in particular will become an increasingly important platform technology for basic scientific discovery, as well as the identification and validation of potentially novel therapeutic targets.
Mathematical Models of Tumor Growth and Angiogenesis
In this paper we present several mathematical models of tumor growth and angiogenesis expressed by systems of ODE’s encoding the most essential observations and assumptions about the complex hierarchical interactive processes of tumor neo-vascularization (angiogenesis). The simplest modeling option presented merely captures the three independent variables mentioned earlier-tumor size N, total vessel volume V and the amount of protein P. We modify this model assuming that the protein is additionally consumed by growing vessels and obtain a model with protein consumption. Next models with time-delays are introduced. To make our models more realistic, two more compartments representing more complex vascularity and protein effects are introduced. Hence five dimensional models are obtained.