Modeling and simulation: Examples in Biomedicine

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Mathematical modeling and simulation examples in Biomedicine: Bacterial biofilms, resistance to antibiotics, metastatic migration in epithelial tissue, angiogenesis, nerve impulse propagation, mechanical behavior of modular proteins, imaging.
[1] A Carpio, LL Bonilla, Depinning transitions in discrete reaction-diffusion equations, SIAM Journal on Applied Mathematics 63 (3), 1056-1082, 2003 [2] A Carpio, LL Bonilla, Pulse propagation in discrete systems of coupled excitable cells, SIAM Journal on Applied Mathematics 63 (2), 619-635, 2003 [3] A Carpio, Asymptotic construction of pulses in the discrete Hodgkin-Huxley model for myelinated nerves, Physical Review E 72 (1), 011905, 2005 [4] A Carpio, Wave trains, self-oscillations and synchronization in discrete media, Physica D: Nonlinear Phenomena 207 (1-2), 117-136, 2005 [5] A Carpio, ML Rapún, Domain reconstruction using photothermal techniques, Journal of Computational Physics 227 (17), 8083-8106, 2008 [6] A Carpio, BT Johansson, ML Rapún, Determining planar multiple sound-soft obstacles from scattered acoustic fields, Journal of Mathematical Imaging and Vision 36 (2), 185-199, 2010 [7] A Carpio, I Peral, Propagation failure along myelinated nerves, Journal of nonlinear science 21 (4), 499-520, 2011 [8] LL Bonilla, A Carpio, A Prados, RR Rosales, Ripples in a string coupled to Glauber spins, Physical Review E 85 (3), 031125, 2012 [9] A Prados, A Carpio, LL Bonilla, Spin-oscillator model for the unzipping of biomolecules by mechanical force, Physical Review E 86 (2), 021919, 2012 [10] A Carpio, ML Rapún, Hybrid topological derivative and gradient-based methods for electrical impedance tomography, Inverse Problems 28 (9), 095010, 2012 [11] D Rodriguez, B Einarsson, A Carpio, Biofilm growth on rugose surfaces, Physical Review E 86 (6), 061914, 2012 [12] A Prados, A Carpio, LL Bonilla, Sawtooth patterns in force-extension curves of biomolecules: An equilibrium-statistical-mechanics theory, Physical Review E 88 (1), 012704, 2013 [13] LL Bonilla, A Carpio, A Prados, Protein unfolding and refolding as transitions through virtual states, EPL (Europhysics Letters) 108 (2), 28002, 2014 [14] DR Espeso, A Carpio, B Einarsson, Differential growth of wrinkled biofilms, Physical Review E 91 (2), 022710, 2015 [15] LL Bonilla, A Carpio, A Prados, Theory of force-extension curves for modular proteins and DNA hairpins, Physical Review E 91 (5), 052712, 2015 [16] DR Espeso, A Carpio, E Martínez-García, V De Lorenzo, Stenosis triggers spread of helical Pseudomonas biofilms in cylindrical flow systems, Scientific reports 6, 27170, 2016 [17] A. Carpio, B. Einarsson, D.R. Espeso, In G Russo, V Capasso, G Nicosia, Romano, V. (eds) Progress in Industrial Mathematics at ECMI 2014. Mathematics in Industry, vol 22. Springer, 2016 [18] A Carpio, TG Dimiduk, ML Rapún, V Selgás, Noninvasive imaging of three-dimensional micro and nanostructures by topological methods, SIAM Journal on Imaging Sciences 9 (3), 1324-1354, 2016 [19] A Carpio, G Duro, Well posedness of an angiogenesis related integrodifferential diffusion model, Applied Mathematical Modelling 40 (9-10), 5560-5575, 2016 [20] A Carpio, G Duro, Well posedness of an integrodifferential kinetic model of Fokker–Planck type for angiogenesis, Nonlinear Analysis: Real World Applications 30, 184-212, 2016 [21] A Carpio, G Duro, M Negreanu, Constructing solutions for a kinetic model of angiogenesis in annular domains, Applied Mathematical Modelling 45, 303-322, 2017 [22] B Birnir, A Carpio, E Cebrián, P Vidal, Dynamic energy budget approach to evaluate antibiotic effects on biofilms, Communications in Nonlinear Science and Numerical Simulation 54, 70-83, 2018 [23] A Carpio, TG Dimiduk, V Selgás, P Vidal, Optimization methods for in-line holography, SIAM Journal on Imaging Sciences 11, 923-956, 2018 [24]DR Espeso, E Martínez-García, A Carpio, V de Lorenzo, Dynamics of Pseudomonas putida biofilms in an upscale experimental framework Journal of Industrial Microbiology and Biotechnology 45 (10), 899-911, 2018 [25] A. Carpio, E. Cebrian, D. R. Espeso, P. Vidal, Biofilm mechanics and patterns, in Coupled Mathematical Models for Physical and Biological Nanoscale Systems and Their Applications, Springer Proceedings in Mathematics & Statistics 232, Springer Nature 2018 [26] LL Bonilla, A Carpio, M Carretero, G Duro, M Negreanu, F Terragni, A convergent numerical scheme for integrodifferential kinetic models of angiogenesis, Journal of Computational Physics 375, 1270-1294, 2018 [27] A Carpio, E Cebrián, P Vidal, Biofilms as poroelastic materials, International Journal of Non-Linear Mechanics 109, 1-8, 2019 [28] A Carpio, TG Dimiduk, F Le Louër, ML Rapún, When topological derivatives met regularized Gauss-Newton iterations in holographic 3D imaging, Journal of Computational Physics 388, 224-251, 2019 [29] A Carpio, E Cebrián, Incorporating Cellular Stochasticity in Solid–Fluid Mixture Biofilm Models, Entropy 22 (2), 188, 2020 [30] A Carpio, S Iakunin, G Stadler, Bayesian approach to inverse scattering with topological priors, Inverse Problems 36 (10), 105001, 2020 [31] LL Bonilla, A Carpio, C Trenado, Tracking collective cell motion by topological data analysis, PLOS Computational Biology 16 (12), e1008407, 2020 [32] A Carpio, E Cebrian, Positivity preserving high order schemes for angiogenesis models, International Journal of Nonlinear Sciences and Numerical Simulation, 2021 [33] A Carpio, M Pena, ML Rapún, Processing the 2D and 3D Fresnel experimental databases via topological derivative methods, Inverse Problems 37 (10), 105012, 2021