Hybrid Equation/Agent-Based Model of Ischemia-Induced Hyperemia and Pressure Ulcer Formation Predicts Greater Propensity to Ulcerate in Subjects with Spinal Cord Injury

Pressure ulcers are costly and life-threatening complications for people with spinal cord injury (SCI). People with SCI also exhibit differential blood flow properties in non-ulcerated skin. We hypothesized that a computer simulation of the pressure ulcer formation process, informed by data regarding skin blood flow and reactive hyperemia in response to pressure, could provide insights into the pathogenesis and effective treatment of post-SCI pressure ulcers. Agent-Based Models (ABM) are useful in settings such as pressure ulcers, in which spatial realism is important. Ordinary Differential Equation-based (ODE) models are useful when modeling physiological phenomena such as reactive hyperemia. Accordingly, we constructed a hybrid model that combines ODEs related to blood flow along with an ABM of skin injury, inflammation, and ulcer formation. The relationship between pressure and the course of ulcer formation, as well as several other important characteristic patterns of pressure ulcer formation, was demonstrated in this model. The ODE portion of this model was calibrated to data related to blood flow following experimental pressure responses in non-injured human subjects or to data from people with SCI. This model predicted a higher propensity to form ulcers in response to pressure in people with SCI vs. non-injured control subjects, and thus may serve as novel diagnostic platform for post-SCI ulcer formation. © 2013 Solovyev et al

Evolutionary Games with Affine Fitness Functions: Applications to Cancer

We analyze the dynamics of evolutionary games in which fitness is defined as an affine function of the expected payoff and a constant contribution. The resulting inhomogeneous replicator equation has an homogeneous equivalent with modified payoffs. The affine terms also influence the stochastic dynamics of a two-strategy Moran model of a finite population. We then apply the affine fitness function in a model for tumor-normal cell interactions to determine which are the most successful tumor strategies. In order to analyze the dynamics of concurrent strategies within a tumor population, we extend the model to a three-strategy game involving distinct tumor cell types as well as normal cells. In this model, interaction with normal cells, in combination with an increased constant fitness, is the most effective way of establishing a population of tumor cells in normal tissue.Comment: The final publication is available at http://www.springerlink.com, http://dx.doi.org/10.1007/s13235-011-0029-

Elongation, proliferation & migration differentiate endothelial cell phenotypes and determine capillary sprouting

<p>Abstract</p> <p>Background</p> <p>Angiogenesis, the growth of capillaries from preexisting blood vessels, has been extensively studied experimentally over the past thirty years. Molecular insights from these studies have lead to therapies for cancer, macular degeneration and ischemia. In parallel, mathematical models of angiogenesis have helped characterize a broader view of capillary network formation and have suggested new directions for experimental pursuit. We developed a computational model that bridges the gap between these two perspectives, and addresses a remaining question in angiogenic sprouting: how do the processes of endothelial cell elongation, migration and proliferation contribute to vessel formation?</p> <p>Results</p> <p>We present a multiscale systems model that closely simulates the mechanisms underlying sprouting at the onset of angiogenesis. Designed by agent-based programming, the model uses logical rules to guide the behavior of individual endothelial cells and segments of cells. The activation, proliferation, and movement of these cells lead to capillary growth in three dimensions. By this means, a novel capillary network emerges out of combinatorially complex interactions of single cells. Rules and parameter ranges are based on literature data on endothelial cell behavior in vitro. The model is designed generally, and will subsequently be applied to represent species-specific, tissue-specific in vitro and in vivo conditions.</p> <p>Initial results predict tip cell activation, stalk cell development and sprout formation as a function of local vascular endothelial growth factor concentrations and the Delta-like 4 Notch ligand, as it might occur in a three-dimensional in vitro setting. Results demonstrate the differential effects of ligand concentrations, cell movement and proliferation on sprouting and directional persistence.</p> <p>Conclusion</p> <p>This systems biology model offers a paradigm closely related to biological phenomena and highlights previously unexplored interactions of cell elongation, migration and proliferation as a function of ligand concentration, giving insight into key cellular mechanisms driving angiogenesis.</p

Introduction of an agent-based multi-scale modular architecture for dynamic knowledge representation of acute inflammation

<p>Abstract</p> <p>Background</p> <p>One of the greatest challenges facing biomedical research is the integration and sharing of vast amounts of information, not only for individual researchers, but also for the community at large. Agent Based Modeling (ABM) can provide a means of addressing this challenge via a unifying translational architecture for dynamic knowledge representation. This paper presents a series of linked ABMs representing multiple levels of biological organization. They are intended to translate the knowledge derived from in vitro models of acute inflammation to clinically relevant phenomenon such as multiple organ failure.</p> <p>Results and Discussion</p> <p>ABM development followed a sequence starting with relatively direct translation from in-vitro derived rules into a cell-as-agent level ABM, leading on to concatenated ABMs into multi-tissue models, eventually resulting in topologically linked aggregate multi-tissue ABMs modeling organ-organ crosstalk. As an underlying design principle organs were considered to be functionally composed of an epithelial surface, which determined organ integrity, and an endothelial/blood interface, representing the reaction surface for the initiation and propagation of inflammation. The development of the epithelial ABM derived from an in-vitro model of gut epithelial permeability is described. Next, the epithelial ABM was concatenated with the endothelial/inflammatory cell ABM to produce an organ model of the gut. This model was validated against in-vivo models of the inflammatory response of the gut to ischemia. Finally, the gut ABM was linked to a similarly constructed pulmonary ABM to simulate the gut-pulmonary axis in the pathogenesis of multiple organ failure. The behavior of this model was validated against in-vivo and clinical observations on the cross-talk between these two organ systems</p> <p>Conclusion</p> <p>A series of ABMs are presented extending from the level of intracellular mechanism to clinically observed behavior in the intensive care setting. The ABMs all utilize cell-level agents that encapsulate specific mechanistic knowledge extracted from in vitro experiments. The execution of the ABMs results in a dynamic representation of the multi-scale conceptual models derived from those experiments. These models represent a qualitative means of integrating basic scientific information on acute inflammation in a multi-scale, modular architecture as a means of conceptual model verification that can potentially be used to concatenate, communicate and advance community-wide knowledge.</p

Migration rules: tumours are conglomerates of self-metastases

Tumours are heterogeneous populations composed of different cells types: stem cells with the capacity for self-renewal and more differentiated cells lacking such ability. The overall growth behaviour of a developing neoplasm is determined largely by the combined kinetic interactions of these cells. By tracking the fate of individual cancer cells using agent-based methods in silico, we apply basic rules for cell proliferation, migration and cell death to show how these kinetic parameters interact to control, and perhaps dictate defining spatial and temporal tumour growth dynamics in tumour development. When the migration rate is small, a single cancer stem cell can only generate a small, self-limited clone because of the finite life span of progeny and spatial constraints. By contrast, a high migration rate can break this equilibrium, seeding new clones at sites outside the expanse of older clones. In this manner, the tumour continually ‘self-metastasises'. Counterintuitively, when the proliferation capacity is low and the rate of cell death is high, tumour growth is accelerated because of the freeing up of space for self-metastatic expansion. Changes to proliferation and cell death that increase the rate at which cells migrate benefit tumour growth as a whole. The dominating influence of migration on tumour growth leads to unexpected dependencies of tumour growth on proliferation capacity and cell death. These dependencies stand to inform standard therapeutic approaches, which anticipate a positive response to cell killing and mitotic arrest