Numerical simulation of vascular tumour growth under antiangiogenic treatment: addressing the paradigm of single-agent bevacizumab therapy with the use of experimental data

Background: Antiangiogenic agents have been recently added to the oncological armamentarium with bevacizumab probably being the most popular representative in current clinical practice. The elucidation of the mode of action of these agents is a prerequisite for personalized prediction of antiangiogenic treatment response and selection of patients who may benefit from this kind of therapy. To this end, having used as a basis a preexisting continuous vascular tumour growth model which addresses the targeted nature of antiangiogenic treatment, we present a paper characterized by the following three features. First, the integration of a two-compartmental bevacizumab specific pharmacokinetic module into the core of the aforementioned preexisting model. Second, its mathematical modification in order to reproduce the asymptotic behaviour of tumour volume in the theoretical case of a total destruction of tumour neovasculature. Third, the exploitation of a range of published animal datasets pertaining to antitumour efficacy of bevacizumab on various tumour types (breast, lung, head and neck, colon).Results: Results for both the unperturbed growth and the treatment module reveal qualitative similarities with experimental observations establishing the biologically acceptable behaviour of the model. The dynamics of the untreated tumour has been studied via a parameter analysis, revealing the role of each relevant input parameter to tumour evolution. The combined effect of endogenous proangiogenic and antiangiogenic factors on the angiogenic potential of a tumour is also studied, in order to capture the dynamics of molecular competition between the two key-players of tumoural angiogenesis. The adopted methodology also allows accounting for the newly recognized direct antitumour effect of the specific agent.Conclusions: Interesting observations have been made, suggesting a potential size-dependent tumour response to different treatment modalities and determining the relative timing of cytotoxic versus antiangiogenic agents administration. Insight into the comparative effectiveness of different antiangiogenic treatment strategies is revealed. The results of a series of in vivo experiments in mice bearing diverse types of tumours (breast, lung, head and neck, colon) and treated with bevacizumab are successfully reproduced, supporting thus the validity of the underlying model.Reviewers: This article was reviewed by L. Hanin, T. Radivoyevitch and L. Edler

Modeling Three-dimensional Invasive Solid Tumor Growth in Heterogeneous Microenvironment under Chemotherapy

A systematic understanding of the evolution and growth dynamics of invasive solid tumors in response to different chemotherapy strategies is crucial for the development of individually optimized oncotherapy. Here, we develop a hybrid three-dimensional (3D) computational model that integrates pharmacokinetic model, continuum diffusion-reaction model and discrete cell automaton model to investigate 3D invasive solid tumor growth in heterogeneous microenvironment under chemotherapy. Specifically, we consider the effects of heterogeneous environment on drug diffusion, tumor growth, invasion and the drug-tumor interaction on individual cell level. We employ the hybrid model to investigate the evolution and growth dynamics of avascular invasive solid tumors under different chemotherapy strategies. Our simulations reproduce the well-established observation that constant dosing is generally more effective in suppressing primary tumor growth than periodic dosing, due to the resulting continuous high drug concentration. In highly heterogeneous microenvironment, the malignancy of the tumor is significantly enhanced, leading to inefficiency of chemotherapies. The effects of geometrically-confined microenvironment and non-uniform drug dosing are also investigated. Our computational model, when supplemented with sufficient clinical data, could eventually lead to the development of efficient in silico tools for prognosis and treatment strategy optimization.Comment: 41 pages, 8 figure

Cellular Potts Model: Applications to Vasculogenesis and Angiogenesis

The cellular Potts model (CPM, a.k.a. Glazier–Graner–Hogeweg or GGH model) is a somewhat liberal extension of probabilistic cellular automata. The model is derived from the Ising and Potts models and represents biological cells as domains of CA-sites of the same state. A Hamiltonian energy is used to describe the balance of forces that the biological cells apply onto one another and their local environment. A Metropolis algorithm iteratively copies the state from one site into one of the adjacent sites, thus shifting the domain interfaces and moving the biological cells along the lattice. The approach is commonly used in applications of developmental biology, where the CPM often interacts with systems of ordinary-differential equations that model the intracellular chemical kinetics and partial-differential equations that model the extracellular chemical signal dynamics to constitute a hybrid and multiscale description of the biological system. In this chapter we will introduce the cellular Potts model and discuss its use in developmental biology, focusing on the development of blood vessels, a process called vascular morphogenesis. We will start by introducing a range of models focusing on uncovering the basic mechanisms of vascular morphogenesis: network formation and sprouting and then show how these models are extended with models of intracellular regulation and with interactions with the extracellular micro-environment. We then briefly review the integration of models of vascular morphogenesis in several examples of organ development in health and disease, including development, cancer, and age-related macular degeneration. We end by discussing the computational efficiency of the CPM and the available strategies for the validation of CPM-based simulation models.Analysis and Stochastic

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

Distribution and metabolism of antibodies and macromolecules in tumor tissue

Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Chemical Engineering, 2008.Vita.Includes bibliographical references.Tumor targeting drugs that selectively treat cancerous tissue are promising agents for lowering the morbidity and mortality of cancer. Within this field, antibody treatments for cancer are currently being developed for both imaging and therapeutic applications. A major limitation with this class of drugs is the poor distribution and low uptake in tumor tissue. Poor distribution leaves some cells completely devoid of treatment, while others experience marginally toxic concentrations that could foster drug resistance. The low overall uptake in vascularized tumors constrains the therapeutic index and lowers signal to noise ratios for imaging applications. Since antibody therapies are currently used to treat both bulk tumors and residual disease, an understanding of the limitations in targeting prevascular metastases and vascularized tumors is required. In order to circumvent the current limitations with antibody therapies, the underlying causes must first be determined. In this thesis, the various steps in tumor localization of antibodies are analyzed in order to determine which steps are limiting uptake and distribution. Mathematical models are developed that indicate the distance antibodies and other binding macromolecules will penetrate into tumors and micrometastases. These models can also estimate the maximum uptake and time course of antibody concentration in tumors. The experimental distribution of a CEA binding antibody is measured in tumor spheroids and a mouse xenograft system to validate the model predictions. Using dimensional analysis of the fundamental transport rates that occur in tumors and micrometastases, two main groups determine the distance antibodies will penetrate in tumor tissue.(cont.) The clearance modulus indicates whether antibody persistence in the blood is sufficient to allow the drug to reach all cells in the micrometastasis or vascularized tumor. The Thiele modulus, defined for antibody transport in tumors, relates the internalization and catabolism of bound antibodies on cancer cells to the maximum distance the antibodies will reach in the tissue. These groups are related to the overall time course and maximum uptake in tumors, indicating when all cells will be targeted, and what factors determine this limit. These models can aid in experimental design, data interpretation, and strategies to improve uptake.by Greg M. Thurber.Ph.D

Selected Topics on Mathematical Models in Immunology and Medicine

In 1988 the new IIASA project on System Immunology was inaugurated. The new activity focuses theoretical and experimental research in immunology and system mathematics to experimental planning and prediction for relevant disease applications and systematic understanding of immunology. IIASA analysis and simulation should lead to an effective plan of successive experiments to identify and to quantify particularly sensitive parameters in this most complex system of information processing, decision and control. The integration of such diverse disciplines is extremely difficult but some basis has already been established. For several years IIASA has sponsored international workshops dealing with dynamical systems and their applications to biology. These include: (1) The conference on "Dynamics of Macrosystems"; (2) The Working Conference on "Theoretical Immunology"; (3) The Workshop on "Selected Topics in Biomathematics"; The present volume contains the proceedings of the latest Workshop "Mathematical Modelling in Immunology and Medicine", Part 1 deals with the mathematical models of autoimmune, infectious diseases and AIDS. The models are studied with the intent to establish a basis for more effective treatment. In Part 2, questions of computer simulation and data analysis in cancer research are analyzed. Part 3 is devoted to the models for antibody binding, immunoassay dynamics and immunogenetic systems. The problems of system analysis and medical decision making are discussed in Part 4