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We present a new third-order, semidiscrete, central method for approximating solutions to multidimensional systems of hyperbolic conservation laws, convection-diffusion equations, and related problems. Our method is a high-order extension of the recently proposed second-order, semidiscrete method in [A. Kurgonov and E. Tadmor, J. Comput Phys., 160 (2000)(More)
Recent mathematical models have been developed to study the dynamics of chronic myelogenous leukemia (CML) under imatinib treatment. None of these models incorporates the anti-leukemia immune response. Recent experimental data show that imatinib treatment may promote the development of anti-leukemia immune responses as patients enter remission. Using these(More)
We present a new third-order central scheme for approximating solutions of systems of conservation laws in one and two space dimensions. In the spirit of Godunov-type schemes, our method is based on reconstructing a piecewisepolynomial interpolant from cell-averages which is then advanced exactly in time. In the reconstruction step, we introduce a new(More)
We develop a mathematical framework for modeling regulatory mechanisms in the immune system. The model describes dynamics of key components of the immune network within two compartments: lymph node and tissue. We demonstrate using numerical simulations that our system can eliminate virus-infected cells, which are characterized by a tendency to increase(More)
We derive a model for describing the dynamics of imatinib-treated chronic myelogenous leukemia (CML). This model is a continuous extension of the agent-based CML model of Roeder et al. (Nat. Med. 12(10), 1181-1184, 2006) and of its recent formulation as a system of difference equations (Kim et al. in Bull. Math. Biol. 70(3), 728-744, 2008). The new model is(More)
We develop a model for describing the dynamics of imatinib-treated chronic myelogenous leukemia. Our model is based on replacing the recent agent-based model of Roeder et al. (Nat. Med. 12(10):1181-1184, 2006) by a system of deterministic difference equations. These difference equations describe the time-evolution of clusters of individual agents that are(More)
We present new thirdand fifth-order Godunov-type central schemes for approximating solutions of the Hamilton-Jacobi (HJ) equation in an arbitrary number of space dimensions. These are the first central schemes for approximating solutions of the HJ equations with an order of accuracy that is greater than two. In two space dimensions we present two versions(More)
Tumor necrosis factor (TNF)-stimulated gene 14 (TSG-14, also termed PTX3) encodes a secreted glycoprotein whose carboxy-terminal half shares sequence similarity with the pentraxin family of acute phase proteins (C-reactive protein and serum amyloid P component). We compared TSG-14 mRNA expression in cultures of murine BALB/c 3T3 fibroblasts and(More)
We present a new algorithm for segmenting organs in CT scans for radiotherapy treatment planning. Given a contour of an organ that is segmented in one image, our algorithm proceeds to segment contours that identify the same organ in the consecutive images. Our technique combines partial diferential equations-based morphing active contours with algorithms(More)