-
Previous Article
Parameter space exploration within dynamic simulations of signaling networks
- MBE Home
- This Issue
-
Next Article
Approximate smooth solutions of a mathematical model for the activation and clonal expansion of T cells
An agent-based model for elasto-plastic mechanical interactions between cells, basement membrane and extracellular matrix
1. | Politecnico di Torino, Torino, 10124, Italy |
2. | Center for Applied Molecular Medicine, Keck School of Medicine, University of Southern California, Los Angeles, 90033, CA, United States |
3. | Dipartimento di Scienze Matematiche, Politecnico di Torino, Torino, 10124, Italy |
References:
[1] |
M. Aumailley, Structure and function of basement membrane components: laminin, nidogen, collagen IV, and BM-40, Advances in Molecular and Cell Biology, 6 (1993), 183-206.
doi: 10.1016/S1569-2558(08)60202-7. |
[2] |
P. Buske, J. Galle, N. Barker, G. Aust, H. Clevers and M. Loeffler, A comprehensive model of the spatio-temporal stem cell and tissue organisation in the intestinal crypt, PLoS Comput. Biol., 7 (2011), e1001045. |
[3] |
P. Buske, J. Przybilla, M. Loeffler, N. Sachs, T. Sato, H. Clevers and J. Galle, On the biomechanics of stem cell niche formation in the gut: modelling growing organoids,, FEBS J. (2012, ().
doi: 10.1111/j.1742-4658.2012.08646.x. |
[4] |
L. M. Coussens and Z. Werb, Matrix metalloproteinases and the development of cancer, Chemistry and Biology, 3 (1996), 895-904. |
[5] |
L. M. Coussens, C. L. Tinkle, D. Hanahan and Z. Werb, MMP-9 supplied by bone marrow-derived cells contributes to skin carcinogenesis, Cell, 103 (2000), 481-490. |
[6] |
J. C. Dallon and H. G. Othmer, How cellular movement determines the collective force generated by the dictyostelium discoideum slug, J. Theor. Biol., 231 (2004), 203-222. |
[7] |
G. D'Antonio, L. Preziosi and P. Macklin, A multiscale hybrid discrete-continuum model of matrix metalloproteinase transport and basement membrane-extracellular matrix degradation, in preparation (2012). |
[8] |
S. J. Dunn, A. G. Flethcer, S. J. Chapman, D. J. Gavaghan and J. M. Osborne, Modelling the role of the basement membrane beneath a growing epithelial monolayer, J. Theor. Biol., 298 (2012), 82-91. |
[9] |
S. J. Franks, H. M. Byrne, H. S. Mudhar, J. C. E. Underwood and C. E. Lewis, Mathematical modelling of comedo ductal carcinoma in situ of the breast, Math. Med. Biol., 20 (2003), 277-308. |
[10] |
S. J. Franks, H. M. Byrne, J. C. E. Underwood and C. E. Lewis, Biological inferences from a mathematical model of comedo ductal carcinoma in situ of the breast, J. Theor. Biol., 232 (2005), 523-543. |
[11] |
P. Ghysels, G. Samaey, B. Tijskens, P. Van Liedekerke H. Ramon and D. Roose, Multi-scale simulation of plant tissue deformation using a model for individual cell mechanics, Phys. Biol., 6 (2009). |
[12] |
J. Glazier and F. Graner, Simulation of the differential adhesion driven rearrangement of biological cells, Phys. Rev. E, 47 (1993), 2128-2154.
doi: 10.1103/PhysRevE.47.2128. |
[13] |
F. Graner and J. Glazier, Simulation of biological cell sorting using a two-dimensional extended Potts model, Phys. Rev. Lett., 69 (1992), 2013-2016.
doi: 10.1103/PhysRevLett.69.2013. |
[14] |
T. Hagemann, S. C. Robinson, M. Schulz, L. Trümper, F. R. Balkwill and C. Binder, Enhanced invasiveness of breast cancer cell lines upon co-cultivation with macrophages is due to TNF-$\alpha$ dependent up-regulation of matrix metalloproteinases, Carcinogenesis, 25 (2004), 1543-1549. |
[15] |
S. Jodele, L. Blavier, J. M. Yoon and Y. A. DeClerck, Modifying the soil to affect the seed: role of stromal-derived matrix metalloproteinases in cancer progression, Cancer and Metastasis Review, 25 (2006), 35-43. |
[16] |
Y. Kim, M. A. Stolarska and H.G . Othmer, The role of the microenvironment in tumor growth and invasion, Progress in Biophysics and Molecular Biology, 106 (2011), 353-379.
doi: 10.1016/j.pbiomolbio.2011.06.006. |
[17] |
R. C. Liddington, Mapping out the basement membrane, Natural Structural Biology, 8 (2001), 573-574. |
[18] |
P. Macklin, Biological background, in "Multiscale Modeling of Cancer: An Integrated Experimental and Mathematical Modeling Approach'' (eds. V. Cristini and J. S. Lowengrub), Cambridge University Press (2010), 8-23.
doi: 10.1017/CBO9780511781452.003. |
[19] |
P. Macklin, M. E. Edgerton, J. S. Lowengrub and V. Cristini, Discrete cell modeling, in "Multiscale Modeling of Cancer: An Integrated Experimental and Mathematical Modeling Approach'' (eds. V. Cristini and J. S. Lowengrub), Cambridge University Press (2010), 88-122.
doi: 10.1017/CBO9780511781452.007. |
[20] |
P. Macklin, M. E. Edgerton, A. M. Thompson and V. Cristini, Patient-calibrated agent-based modelling of ductal carcinoma in situ (DCIS): From microscopic measurements to macroscopic predictions of clinical progression, J. Theor. Biol., 301 (2012), 122-140.
doi: 10.1016/j.jtbi.2012.02.002. |
[21] |
P. Macklin, J. Kim, G. Tomaiuolo, M. E. Edgerton and V. Cristini, Agent-based modeling of ductal carcinoma in situ: application to patient-specific breast cancer modeling, in "Computational Biology: Issues and Applications in Oncology'' (ed. T. Pham), Springer (2009), 77-112.
doi: 10.1007/978-1-4419-0811-7_4. |
[22] |
P. Macklin, S. Mumenthaler and J. Lowengrub, Modeling multiscale necrotic and calcified tissue biomechanics in cancer patients: application to ductal carcinoma in situ (DCIS), in "Multiscale Computer Modeling in Biomechanics and Biomedical Engineering'' (ed. A. Gefen), Springer (2013), in press.
doi: 10.1007/8415_2012_150. |
[23] |
K. A. Norton, M. Wininger, G. Bhanot, S. Ganesan, N. Barnard and T. Shinbrot, A 2D mechanistic model of breast ductal carcinoma in situ (DCIS). Morphology and progression, J. Theor. Biol., 263 (2010), 393-406. |
[24] |
N. Poplawski, U. Agero, J. Gens, M. Swat, J. Glazier and A. Anderson, Front instabilities and invasiveness of simulated avascular tumors, Bull. Math. Biol., 71 (2009), 1189-1227.
doi: 10.1007/s11538-009-9399-5. |
[25] |
L. Preziosi, D. Ambrosi and C. Verdier, An elasto-visco-plastic model of cell aggregates, J. Theor. Biol., 262 (2010), 35-47.
doi: 10.1016/j.jtbi.2009.08.023. |
[26] |
I. Ramis-Conde, M. A. J. Chaplain and A. R. A. Anderson, Mathematical modelling of cancer cell invasion of tissue, Math. Comp. Model., 47 (2006), 533-545. |
[27] |
B. Ribba, O. Saut, T. Colin, D. Bresch, E. Grenier and J. P. Boissel, A multiscale mathematical model of avascular tumor growth to investigate the therapeutic benefit of anti-invasive agents, J. Theor. Biol., 243 (2006), 532-541. |
[28] |
S. A. Sandersius and T. J. Newman, Modeling cell rheology with the subcellular element model, Phys. Biol., 5 (2008), 015002. |
[29] |
S. A. Sandersius, C. J. Weijer and T. J. Newman, Emergent cell and tissue dynamics from subcellular modeling of active processes, Phys. Biol., 8 (2011), 045007. |
[30] |
M. Scianna and L. Preziosi, Multiscale developments of cellular Potts models, Multiscale Model. Sim., 10 (2012), 342-382.
doi: \%2010.1137/100812951. |
[31] |
M. Scianna and L. Preziosi, "Cellular Potts Models: Multiscale Developments and Biological Applications,'' CRC/Academic Press, 2012. |
[32] |
M. Scianna, L. Preziosi and K. Wolf, A Cellular Potts Model simulating cell migration on and in matrix environments,, Math. Biosci. Eng., ().
|
[33] |
C. Verdier, J. Etienne, A. Duperray and L. Preziosi, Review: rheological properties of biological materials, Comptes Rendus Physique, 10 (2009), 790-811.
doi: 10.1016/j.crhy.2009.10.003. |
[34] |
Z. Zeng, A. M. Cohen and J. G. Guillem, Loss of basement membrane type IV collagen is associated with increased expression of metalloproteinases 2 and 9 (MMP-2 and MMP-9) during human colorectal tumorigenesis, Carcinogenesis, 20 (1999), 749-755.
doi: 10.1093/carcin/20.5.749. |
show all references
References:
[1] |
M. Aumailley, Structure and function of basement membrane components: laminin, nidogen, collagen IV, and BM-40, Advances in Molecular and Cell Biology, 6 (1993), 183-206.
doi: 10.1016/S1569-2558(08)60202-7. |
[2] |
P. Buske, J. Galle, N. Barker, G. Aust, H. Clevers and M. Loeffler, A comprehensive model of the spatio-temporal stem cell and tissue organisation in the intestinal crypt, PLoS Comput. Biol., 7 (2011), e1001045. |
[3] |
P. Buske, J. Przybilla, M. Loeffler, N. Sachs, T. Sato, H. Clevers and J. Galle, On the biomechanics of stem cell niche formation in the gut: modelling growing organoids,, FEBS J. (2012, ().
doi: 10.1111/j.1742-4658.2012.08646.x. |
[4] |
L. M. Coussens and Z. Werb, Matrix metalloproteinases and the development of cancer, Chemistry and Biology, 3 (1996), 895-904. |
[5] |
L. M. Coussens, C. L. Tinkle, D. Hanahan and Z. Werb, MMP-9 supplied by bone marrow-derived cells contributes to skin carcinogenesis, Cell, 103 (2000), 481-490. |
[6] |
J. C. Dallon and H. G. Othmer, How cellular movement determines the collective force generated by the dictyostelium discoideum slug, J. Theor. Biol., 231 (2004), 203-222. |
[7] |
G. D'Antonio, L. Preziosi and P. Macklin, A multiscale hybrid discrete-continuum model of matrix metalloproteinase transport and basement membrane-extracellular matrix degradation, in preparation (2012). |
[8] |
S. J. Dunn, A. G. Flethcer, S. J. Chapman, D. J. Gavaghan and J. M. Osborne, Modelling the role of the basement membrane beneath a growing epithelial monolayer, J. Theor. Biol., 298 (2012), 82-91. |
[9] |
S. J. Franks, H. M. Byrne, H. S. Mudhar, J. C. E. Underwood and C. E. Lewis, Mathematical modelling of comedo ductal carcinoma in situ of the breast, Math. Med. Biol., 20 (2003), 277-308. |
[10] |
S. J. Franks, H. M. Byrne, J. C. E. Underwood and C. E. Lewis, Biological inferences from a mathematical model of comedo ductal carcinoma in situ of the breast, J. Theor. Biol., 232 (2005), 523-543. |
[11] |
P. Ghysels, G. Samaey, B. Tijskens, P. Van Liedekerke H. Ramon and D. Roose, Multi-scale simulation of plant tissue deformation using a model for individual cell mechanics, Phys. Biol., 6 (2009). |
[12] |
J. Glazier and F. Graner, Simulation of the differential adhesion driven rearrangement of biological cells, Phys. Rev. E, 47 (1993), 2128-2154.
doi: 10.1103/PhysRevE.47.2128. |
[13] |
F. Graner and J. Glazier, Simulation of biological cell sorting using a two-dimensional extended Potts model, Phys. Rev. Lett., 69 (1992), 2013-2016.
doi: 10.1103/PhysRevLett.69.2013. |
[14] |
T. Hagemann, S. C. Robinson, M. Schulz, L. Trümper, F. R. Balkwill and C. Binder, Enhanced invasiveness of breast cancer cell lines upon co-cultivation with macrophages is due to TNF-$\alpha$ dependent up-regulation of matrix metalloproteinases, Carcinogenesis, 25 (2004), 1543-1549. |
[15] |
S. Jodele, L. Blavier, J. M. Yoon and Y. A. DeClerck, Modifying the soil to affect the seed: role of stromal-derived matrix metalloproteinases in cancer progression, Cancer and Metastasis Review, 25 (2006), 35-43. |
[16] |
Y. Kim, M. A. Stolarska and H.G . Othmer, The role of the microenvironment in tumor growth and invasion, Progress in Biophysics and Molecular Biology, 106 (2011), 353-379.
doi: 10.1016/j.pbiomolbio.2011.06.006. |
[17] |
R. C. Liddington, Mapping out the basement membrane, Natural Structural Biology, 8 (2001), 573-574. |
[18] |
P. Macklin, Biological background, in "Multiscale Modeling of Cancer: An Integrated Experimental and Mathematical Modeling Approach'' (eds. V. Cristini and J. S. Lowengrub), Cambridge University Press (2010), 8-23.
doi: 10.1017/CBO9780511781452.003. |
[19] |
P. Macklin, M. E. Edgerton, J. S. Lowengrub and V. Cristini, Discrete cell modeling, in "Multiscale Modeling of Cancer: An Integrated Experimental and Mathematical Modeling Approach'' (eds. V. Cristini and J. S. Lowengrub), Cambridge University Press (2010), 88-122.
doi: 10.1017/CBO9780511781452.007. |
[20] |
P. Macklin, M. E. Edgerton, A. M. Thompson and V. Cristini, Patient-calibrated agent-based modelling of ductal carcinoma in situ (DCIS): From microscopic measurements to macroscopic predictions of clinical progression, J. Theor. Biol., 301 (2012), 122-140.
doi: 10.1016/j.jtbi.2012.02.002. |
[21] |
P. Macklin, J. Kim, G. Tomaiuolo, M. E. Edgerton and V. Cristini, Agent-based modeling of ductal carcinoma in situ: application to patient-specific breast cancer modeling, in "Computational Biology: Issues and Applications in Oncology'' (ed. T. Pham), Springer (2009), 77-112.
doi: 10.1007/978-1-4419-0811-7_4. |
[22] |
P. Macklin, S. Mumenthaler and J. Lowengrub, Modeling multiscale necrotic and calcified tissue biomechanics in cancer patients: application to ductal carcinoma in situ (DCIS), in "Multiscale Computer Modeling in Biomechanics and Biomedical Engineering'' (ed. A. Gefen), Springer (2013), in press.
doi: 10.1007/8415_2012_150. |
[23] |
K. A. Norton, M. Wininger, G. Bhanot, S. Ganesan, N. Barnard and T. Shinbrot, A 2D mechanistic model of breast ductal carcinoma in situ (DCIS). Morphology and progression, J. Theor. Biol., 263 (2010), 393-406. |
[24] |
N. Poplawski, U. Agero, J. Gens, M. Swat, J. Glazier and A. Anderson, Front instabilities and invasiveness of simulated avascular tumors, Bull. Math. Biol., 71 (2009), 1189-1227.
doi: 10.1007/s11538-009-9399-5. |
[25] |
L. Preziosi, D. Ambrosi and C. Verdier, An elasto-visco-plastic model of cell aggregates, J. Theor. Biol., 262 (2010), 35-47.
doi: 10.1016/j.jtbi.2009.08.023. |
[26] |
I. Ramis-Conde, M. A. J. Chaplain and A. R. A. Anderson, Mathematical modelling of cancer cell invasion of tissue, Math. Comp. Model., 47 (2006), 533-545. |
[27] |
B. Ribba, O. Saut, T. Colin, D. Bresch, E. Grenier and J. P. Boissel, A multiscale mathematical model of avascular tumor growth to investigate the therapeutic benefit of anti-invasive agents, J. Theor. Biol., 243 (2006), 532-541. |
[28] |
S. A. Sandersius and T. J. Newman, Modeling cell rheology with the subcellular element model, Phys. Biol., 5 (2008), 015002. |
[29] |
S. A. Sandersius, C. J. Weijer and T. J. Newman, Emergent cell and tissue dynamics from subcellular modeling of active processes, Phys. Biol., 8 (2011), 045007. |
[30] |
M. Scianna and L. Preziosi, Multiscale developments of cellular Potts models, Multiscale Model. Sim., 10 (2012), 342-382.
doi: \%2010.1137/100812951. |
[31] |
M. Scianna and L. Preziosi, "Cellular Potts Models: Multiscale Developments and Biological Applications,'' CRC/Academic Press, 2012. |
[32] |
M. Scianna, L. Preziosi and K. Wolf, A Cellular Potts Model simulating cell migration on and in matrix environments,, Math. Biosci. Eng., ().
|
[33] |
C. Verdier, J. Etienne, A. Duperray and L. Preziosi, Review: rheological properties of biological materials, Comptes Rendus Physique, 10 (2009), 790-811.
doi: 10.1016/j.crhy.2009.10.003. |
[34] |
Z. Zeng, A. M. Cohen and J. G. Guillem, Loss of basement membrane type IV collagen is associated with increased expression of metalloproteinases 2 and 9 (MMP-2 and MMP-9) during human colorectal tumorigenesis, Carcinogenesis, 20 (1999), 749-755.
doi: 10.1093/carcin/20.5.749. |
[1] |
Holly Gaff. Preliminary analysis of an agent-based model for a tick-borne disease. Mathematical Biosciences & Engineering, 2011, 8 (2) : 463-473. doi: 10.3934/mbe.2011.8.463 |
[2] |
A. Chauviere, L. Preziosi, T. Hillen. Modeling the motion of a cell population in the extracellular matrix. Conference Publications, 2007, 2007 (Special) : 250-259. doi: 10.3934/proc.2007.2007.250 |
[3] |
Dieter Armbruster, Christian Ringhofer, Andrea Thatcher. A kinetic model for an agent based market simulation. Networks and Heterogeneous Media, 2015, 10 (3) : 527-542. doi: 10.3934/nhm.2015.10.527 |
[4] |
Zhiyong Sun, Toshiharu Sugie. Identification of Hessian matrix in distributed gradient-based multi-agent coordination control systems. Numerical Algebra, Control and Optimization, 2019, 9 (3) : 297-318. doi: 10.3934/naco.2019020 |
[5] |
Alessandro Giacomini. On the energetic formulation of the Gurtin and Anand model in strain gradient plasticity. Discrete and Continuous Dynamical Systems - B, 2012, 17 (2) : 527-552. doi: 10.3934/dcdsb.2012.17.527 |
[6] |
Zhengshan Dong, Jianli Chen, Wenxing Zhu. Homotopy method for matrix rank minimization based on the matrix hard thresholding method. Numerical Algebra, Control and Optimization, 2019, 9 (2) : 211-224. doi: 10.3934/naco.2019015 |
[7] |
Zhongqiang Wu, Zongkui Xie. A multi-objective lion swarm optimization based on multi-agent. Journal of Industrial and Management Optimization, 2022 doi: 10.3934/jimo.2022001 |
[8] |
Prateek Kunwar, Oleksandr Markovichenko, Monique Chyba, Yuriy Mileyko, Alice Koniges, Thomas Lee. A study of computational and conceptual complexities of compartment and agent based models. Networks and Heterogeneous Media, 2022, 17 (3) : 359-384. doi: 10.3934/nhm.2022011 |
[9] |
Sergio Conti, Georg Dolzmann, Carolin Kreisbeck. Relaxation and microstructure in a model for finite crystal plasticity with one slip system in three dimensions. Discrete and Continuous Dynamical Systems - S, 2013, 6 (1) : 1-16. doi: 10.3934/dcdss.2013.6.1 |
[10] |
Seung-Yeal Ha, Dohyun Kim, Jaeseung Lee, Se Eun Noh. Emergent dynamics of an orientation flocking model for multi-agent system. Discrete and Continuous Dynamical Systems, 2020, 40 (4) : 2037-2060. doi: 10.3934/dcds.2020105 |
[11] |
Seung-Yeal Ha, Hansol Park. Emergent behaviors of the generalized Lohe matrix model. Discrete and Continuous Dynamical Systems - B, 2021, 26 (8) : 4227-4261. doi: 10.3934/dcdsb.2020286 |
[12] |
Tomáš Roubíček. Thermodynamics of perfect plasticity. Discrete and Continuous Dynamical Systems - S, 2013, 6 (1) : 193-214. doi: 10.3934/dcdss.2013.6.193 |
[13] |
Pamela A. Marshall, Eden E. Tanzosh, Francisco J. Solis, Haiyan Wang. Response of yeast mutants to extracellular calcium variations. Discrete and Continuous Dynamical Systems - B, 2009, 12 (2) : 439-453. doi: 10.3934/dcdsb.2009.12.439 |
[14] |
Maurizio Verri, Giovanna Guidoboni, Lorena Bociu, Riccardo Sacco. The role of structural viscoelasticity in deformable porous media with incompressible constituents: Applications in biomechanics. Mathematical Biosciences & Engineering, 2018, 15 (4) : 933-959. doi: 10.3934/mbe.2018042 |
[15] |
Urszula Ledzewicz, Omeiza Olumoye, Heinz Schättler. On optimal chemotherapy with a strongly targeted agent for a model of tumor-immune system interactions with generalized logistic growth. Mathematical Biosciences & Engineering, 2013, 10 (3) : 787-802. doi: 10.3934/mbe.2013.10.787 |
[16] |
Anthony Tongen, María Zubillaga, Jorge E. Rabinovich. A two-sex matrix population model to represent harem structure. Mathematical Biosciences & Engineering, 2016, 13 (5) : 1077-1092. doi: 10.3934/mbe.2016031 |
[17] |
Marco Scianna, Luigi Preziosi, Katarina Wolf. A Cellular Potts model simulating cell migration on and in matrix environments. Mathematical Biosciences & Engineering, 2013, 10 (1) : 235-261. doi: 10.3934/mbe.2013.10.235 |
[18] |
Jian Zhao, Fang Deng, Jian Jia, Chunmeng Wu, Haibo Li, Yuan Shi, Shunli Zhang. A new face feature point matrix based on geometric features and illumination models for facial attraction analysis. Discrete and Continuous Dynamical Systems - S, 2019, 12 (4&5) : 1065-1072. doi: 10.3934/dcdss.2019073 |
[19] |
S. Sadeghi, H. Jafari, S. Nemati. Solving fractional Advection-diffusion equation using Genocchi operational matrix based on Atangana-Baleanu derivative. Discrete and Continuous Dynamical Systems - S, 2021, 14 (10) : 3747-3761. doi: 10.3934/dcdss.2020435 |
[20] |
Guimin Liu, Hongbin Lv. Bounds for spectral radius of nonnegative tensors using matrix-digragh-based approach. Journal of Industrial and Management Optimization, 2021 doi: 10.3934/jimo.2021176 |
2018 Impact Factor: 1.313
Tools
Metrics
Other articles
by authors
[Back to Top]