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Mathematically modeling PCR: An asymptotic approximation with potential for optimization
Diffusion-limited tumour growth: Simulations and analysis
1. | Center for Models of Life, Niels Bohr Institute, Blegdamsvej 17, 2200 Copenhagen O, Denmark |
2. | H. Lee Moffitt Cancer Center & Research Institute, Integrated Mathematical Oncology, 12902 Magnolia Drive, Tampa, FL 33612, United States |
[1] |
Elena Izquierdo-Kulich, Margarita Amigó de Quesada, Carlos Manuel Pérez-Amor, Magda Lopes Texeira, José Manuel Nieto-Villar. The dynamics of tumor growth and cells pattern morphology. Mathematical Biosciences & Engineering, 2009, 6 (3) : 547-559. doi: 10.3934/mbe.2009.6.547 |
[2] |
Matthias Ebenbeck, Harald Garcke, Robert Nürnberg. Cahn–Hilliard–Brinkman systems for tumour growth. Discrete and Continuous Dynamical Systems - S, 2021, 14 (11) : 3989-4033. doi: 10.3934/dcdss.2021034 |
[3] |
Russell Betteridge, Markus R. Owen, H.M. Byrne, Tomás Alarcón, Philip K. Maini. The impact of cell crowding and active cell movement on vascular tumour growth. Networks and Heterogeneous Media, 2006, 1 (4) : 515-535. doi: 10.3934/nhm.2006.1.515 |
[4] |
Vicent Caselles. An existence and uniqueness result for flux limited diffusion equations. Discrete and Continuous Dynamical Systems, 2011, 31 (4) : 1151-1195. doi: 10.3934/dcds.2011.31.1151 |
[5] |
Andrea Signori. Penalisation of long treatment time and optimal control of a tumour growth model of Cahn–Hilliard type with singular potential. Discrete and Continuous Dynamical Systems, 2021, 41 (6) : 2519-2542. doi: 10.3934/dcds.2020373 |
[6] |
R. P. Gupta, Shristi Tiwari, Shivam Saxena. The qualitative behavior of a plankton-fish interaction model with food limited growth rate and non-constant fish harvesting. Discrete and Continuous Dynamical Systems - B, 2022, 27 (5) : 2791-2815. doi: 10.3934/dcdsb.2021160 |
[7] |
Benjamin Söllner, Oliver Junge. A convergent Lagrangian discretization for $ p $-Wasserstein and flux-limited diffusion equations. Communications on Pure and Applied Analysis, 2020, 19 (9) : 4227-4256. doi: 10.3934/cpaa.2020190 |
[8] |
Sarah Bailey Frick. Limited scope adic transformations. Discrete and Continuous Dynamical Systems - S, 2009, 2 (2) : 269-285. doi: 10.3934/dcdss.2009.2.269 |
[9] |
Xiaofeng Ren. Shell structure as solution to a free boundary problem from block copolymer morphology. Discrete and Continuous Dynamical Systems, 2009, 24 (3) : 979-1003. doi: 10.3934/dcds.2009.24.979 |
[10] |
Zhaosheng Feng, Goong Chen. Traveling wave solutions in parametric forms for a diffusion model with a nonlinear rate of growth. Discrete and Continuous Dynamical Systems, 2009, 24 (3) : 763-780. doi: 10.3934/dcds.2009.24.763 |
[11] |
Matthieu Alfaro, Thomas Giletti. When fast diffusion and reactive growth both induce accelerating invasions. Communications on Pure and Applied Analysis, 2019, 18 (6) : 3011-3034. doi: 10.3934/cpaa.2019135 |
[12] |
Yilong Wang, Xuande Zhang. On a parabolic-elliptic chemotaxis-growth system with nonlinear diffusion. Discrete and Continuous Dynamical Systems - S, 2020, 13 (2) : 321-328. doi: 10.3934/dcdss.2020018 |
[13] |
Benedetto Bozzini, Deborah Lacitignola, Ivonne Sgura. Morphological spatial patterns in a reaction diffusion model for metal growth. Mathematical Biosciences & Engineering, 2010, 7 (2) : 237-258. doi: 10.3934/mbe.2010.7.237 |
[14] |
H.M. Byrne, S.M. Cox, C.E. Kelly. Macrophage-tumour interactions: In vivo dynamics. Discrete and Continuous Dynamical Systems - B, 2004, 4 (1) : 81-98. doi: 10.3934/dcdsb.2004.4.81 |
[15] |
John R. King, Judith Pérez-Velázquez, H.M. Byrne. Singular travelling waves in a model for tumour encapsulation. Discrete and Continuous Dynamical Systems, 2009, 25 (1) : 195-230. doi: 10.3934/dcds.2009.25.195 |
[16] |
Marek Bodnar, Monika Joanna Piotrowska, Urszula Foryś, Ewa Nizińska. Model of tumour angiogenesis -- analysis of stability with respect to delays. Mathematical Biosciences & Engineering, 2013, 10 (1) : 19-35. doi: 10.3934/mbe.2013.10.19 |
[17] |
Anotida Madzvamuse, Raquel Barreira. Domain-growth-induced patterning for reaction-diffusion systems with linear cross-diffusion. Discrete and Continuous Dynamical Systems - B, 2018, 23 (7) : 2775-2801. doi: 10.3934/dcdsb.2018163 |
[18] |
Kolade M. Owolabi, Kailash C. Patidar, Albert Shikongo. Efficient numerical method for a model arising in biological stoichiometry of tumour dynamics. Discrete and Continuous Dynamical Systems - S, 2019, 12 (3) : 591-613. doi: 10.3934/dcdss.2019038 |
[19] |
Hong Zhou, M. Gregory Forest. Anchoring distortions coupled with plane Couette & Poiseuille flows of nematic polymers in viscous solvents: Morphology in molecular orientation, stress & flow. Discrete and Continuous Dynamical Systems - B, 2006, 6 (2) : 407-425. doi: 10.3934/dcdsb.2006.6.407 |
[20] |
Macarena Boix, Begoña Cantó. Using wavelet denoising and mathematical morphology in the segmentation technique applied to blood cells images. Mathematical Biosciences & Engineering, 2013, 10 (2) : 279-294. doi: 10.3934/mbe.2013.10.279 |
2018 Impact Factor: 1.313
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