23 research outputs found
A new ghost cell/level set method for moving boundary problems:application to tumor growth
In this paper, we present a ghost cell/level set method for the evolution of interfaces whose normal velocity depend upon the solutions of linear and nonlinear quasi-steady reaction-diffusion equations with curvature-dependent boundary conditions. Our technique includes a ghost cell method that accurately discretizes normal derivative jump boundary conditions without smearing jumps in the tangential derivative; a new iterative method for solving linear and nonlinear quasi-steady reaction-diffusion equations; an adaptive discretization to compute the curvature and normal vectors; and a new discrete approximation to the Heaviside function. We present numerical examples that demonstrate better than 1.5-order convergence for problems where traditional ghost cell methods either fail to converge or attain at best sub-linear accuracy. We apply our techniques to a model of tumor growth in complex, heterogeneous tissues that consists of a nonlinear nutrient equation and a pressure equation with geometry-dependent jump boundary conditions. We simulate the growth of glioblastoma (an aggressive brain tumor) into a large, 1 cm square of brain tissue that includes heterogeneous nutrient delivery and varied biomechanical characteristics (white matter, gray matter, cerebrospinal fluid, and bone), and we observe growth morphologies that are highly dependent upon the variations of the tissue characteristics—an effect observed in real tumor growth
Independence before conservatism Transparency, politics and central bank design
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Large scale fiscal retrenchments Long-run lessons from the stability pact
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Labour market reform and monetary policy in EMU Do asymmetries matter?
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EMU and the external value of the Euro
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Fiscal deficit reductions in line with the Maastricht criteria for monetary union
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The cost of heterogeneity in a monetary union
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EMU in reality The effect of a common monetary policy on economies with different transmission mechanisms
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The European Monetary System Achievements and survival
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The impact of exchange rate uncertainty on the level of investment
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