Module-based multiscale simulation of angiogenesis in skeletal muscle. Theor Biol Med Model 8:6

Systems Biology Laboratory, Department of Biomedical Engineering, School of Medicine, Johns Hopkins University, Baltimore, MD 21205, USA.
Theoretical Biology and Medical Modelling (Impact Factor: 0.95). 04/2011; 8(1):6. DOI: 10.1186/1742-4682-8-6
Source: PubMed


Mathematical modeling of angiogenesis has been gaining momentum as a means to shed new light on the biological complexity underlying blood vessel growth. A variety of computational models have been developed, each focusing on different aspects of the angiogenesis process and occurring at different biological scales, ranging from the molecular to the tissue levels. Integration of models at different scales is a challenging and currently unsolved problem.
We present an object-oriented module-based computational integration strategy to build a multiscale model of angiogenesis that links currently available models. As an example case, we use this approach to integrate modules representing microvascular blood flow, oxygen transport, vascular endothelial growth factor transport and endothelial cell behavior (sensing, migration and proliferation). Modeling methodologies in these modules include algebraic equations, partial differential equations and agent-based models with complex logical rules. We apply this integrated model to simulate exercise-induced angiogenesis in skeletal muscle. The simulation results compare capillary growth patterns between different exercise conditions for a single bout of exercise. Results demonstrate how the computational infrastructure can effectively integrate multiple modules by coordinating their connectivity and data exchange. Model parameterization offers simulation flexibility and a platform for performing sensitivity analysis.
This systems biology strategy can be applied to larger scale integration of computational models of angiogenesis in skeletal muscle, or other complex processes in other tissues under physiological and pathological conditions.

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Available from: Feilim Mac Gabhann, Oct 07, 2015
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    • "For decades, mathematical models have been employed to help address some of the pressing questions associated with tumor angiogenesis. As discussed in detail in Jackson and Zheng (2010), Zheng et al. (2013), existing models of tumor-induced angiogenesis can be characterized as continuous approaches (Balding and McElwain, 1985; Byrne and Chaplain, 1995, 1996; Anderson and Chaplain, 1998a,b; Holmes and Sleeman, 2000; Levine et al., 2001; Arakelyan et al., 2002; Sleeman and Wallis, 2002; Manoussaki, 2003; Plank and Sleeman, 2003, 2004; Plank et al., 2004; Levine and Nilsen-Hamilton, 2006; Schugart et al., 2008; Billy et al., 2009; Xue et al., 2009; Travasso et al., 2011), wherein cells are assumed to have a continuous distribution; discrete or hybrid models (Stokes and Lauffenburger, 1991; Anderson and Chaplain, 1998b; Tong and Yuan, 2001; Plank and Sleeman, 2003, 2004; Sun et al., 2005; Bartha and Rieger, 2006; Gevertz and Torquato, 2006; Frieboes et al., 2007; Milde et al., 2008; Capasso and Morale, 2009; Owen et al., 2009; Perfahl et al., 2011), wherein cells are modeled as individual agents and diffusible chemicals are modeled as a continuum; and cell-based formulations (Peirce et al., 2004; Bauer et al., 2007; Bentley et al., 2009; Qutub and Popel, 2009; Wcislo et al., 2009; Jackson and Zheng, 2010; Liu et al., 2011) wherein explicit incorporation of different properties of individual cells allows collective behavior of cell clusters to be predicted from the behavior and interactions of individual cells. Reviews of these models that appeared in or before 2009 can be found in Mantzaris et al. (2004), Peirce (2008), Qutub et al. (2009). "
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    Frontiers in Oncology 05/2013; 3:102. DOI:10.3389/fonc.2013.00102
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    • "Multi-scale simulations of sprout extension can couple the VEGF dynamics at the cellular scale with tissue-level models of VEGF sources. In this approach, vascular sprouts are treated as stochastic units (Liu et al., 2011): sprouts invade into the tissue led by a tip cell that follows VEGF gradients. Stalk cells, in turn, are assumed to elongate and proliferate. "
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    ABSTRACT: Vasculogenesis, the assembly of the first vascular network, is an intriguing developmental process that yields the first functional organ system of the embryo. In addition to being a fundamental part of embryonic development, vasculogenic processes also have medical importance. To explain the organizational principles behind vascular patterning, we must understand how morphogenesis of tissue level structures can be controlled through cell behavior patterns that, in turn, are determined by biochemical signal transduction processes. Mathematical analyses and computer simulations can help conceptualize how to bridge organizational levels and thus help in evaluating hypotheses regarding the formation of vascular networks. Here, we discuss the ideas that have been proposed to explain the formation of the first vascular pattern: cell motility guided by extracellular matrix alignment (contact guidance), chemotaxis guided by paracrine and autocrine morphogens, and sprouting guided by cell-cell contacts.
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    ABSTRACT: Tumor growth is dependent on angiogenesis, a process whereby new capillaries are formed from pre-existing microvasculature. Inhibition of tumor-induced angiogenesis has proven to be an effective therapeutic strategy for several drugs currently in the clinic (1). One of the key molecules involved in tumor angiogenesis is vascular endothelial growth factor A (VEGF-A, commonly referred to as VEGF). Thus, an understanding of how VEGF is expressed, diffuses, and interacts with other important regulators such as VEGF receptors at molecular, cellular and tissue levels is critical to the evaluation of therapeutic effects (4). Computational modeling of these angiogenic events at multiple scales of biological organization provides a means to explore the regulatory mechanisms underlying the complex process. We have developed a number of computational models to investigate how VEGF transport events are linked with receptor signaling at the molecular scale, with cellular behavior and cell phenotypes at the cellular scale, and how these events combine to regulate angiogenesis at tissue and whole body levels (5, 6, 9). First, we apply an in vivo hemorheological model to simulate the distribution of blood flow and hematocrit in all the microvessels. We then use this distribution in a 3D convection-diffusion model to describe how oxygen is delivered by microvascular blood flow and its diffusion and utilization through the tissue. The oxygen transport model is important, as VEGF secretion by muscle and tumor cells is mediated by insufficient oxygen supply to the cell, in turn resulting in hypoxia or low partial pressure of oxygen (PO2); low PO2 is sensed by a transcription factor hypoxia-inducible factor HIF1alpha that activates hundreds of genes including VEGF (8). Next, we developed a reaction-diffusion model to predict molecular distribution of VEGF in the interstitial space and on the surface of endothelial and parenchymal cells (e.g. myocytes and tumor cells). The model describes the secretion of two major VEGF isoforms, VEGF121 and VEGF165, molecular transport of each isoform in the interstitial space, VEGF binding to heparan sulfate proteoglycans in the extracellular matrix (ECM), VEGF binding to receptors VEGFR1, VEGFR2 and co-receptors neuropilin-1 (NRP1) and neuropilin-2 (NRP2) on the surface of endothelial cells, myocytes, and tumor cells, and internalization of the ligand-receptor complexes. Next, a cellular agent-based model was developed to describe how capillary 6-3 Interdisciplinary Transport Phenomena VII, Dresden, Germany, 2011 Paper No.: ITP-2011-49 endothelial cells respond to stimuli, specifically VEGF concentration and gradients, during the time course of capillary sprout formation (7). The model applies logical rules, based on extensive experimental data, to define cell activation, elongation, migration and proliferation events, which in turn dynamically affect VEGF transport and gradients. In addition, a module-based istrategy was developed to integrate the computer models of the major steps of angiogenesis from the molecular to tissue levels, starting from blood flow, to oxygen transport, to HIF1alpha expression, to VEGF secretion and transport, to capillary growth (3). In order to understand the effect of VEGF concentration in the multiple tissues in the body and be able to simulate systemic administration of anti-VEGF therapeutic agents, we developed a whole-body compartmental model of VEGF transport (10, 12-14). The model is comprised of three compartments: normal tissue represented by skeletal muscle, the vascular or blood compartment, and tumor compartment; tissue interstitial space compartments are further subdivided into ECM, and endothelial and parenchymal basement membranes. The model includes the molecular interactions of VEGF121 and VEGF165, receptors VEGFR1, VEGFR2, and co-receptors NRP1 and NRP2. The density of VEGF receptors and co-receptors is determined experimentally using quantitative flow cytometry (2). We then add an anti-VEGF compound to the model, specifically bevacizumab, an anti-VEGF antibody used clinically for different types of cancer (11). Intercompartment transport of VEGF, anti-VEGF and their products includes vascular permeability and lymph flow. These molecules intravasate and extravasate via transendothelial macromolecular permeability, and can be convected from the normal tissue into the blood via lymphatic drainage, and they are removed from the blood via clearance. The compartmental model predicts the spatially-averaged interstitial concentration of VEGF and anti-VEGF, as well as ligand-receptor binding in different compartments. The model is used to investigate the effect of various therapies that target VEGF-mediated angiogenesis.
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