Search Advanced

Mathematical Biosciences and Engineering

2005, Volume 2, Issue 3: 613-624. doi: 10.3934/mbe.2005.2.613
Previous Article Next Article

Modeling Multicellular Systems Using Subcellular Elements

  • 1.
    Department of Physics & Astronomy, and School of Life Sciences, Arizona State University, Tempe, AZ 85287
  • Received: 01 April 2005 Accepted: 29 June 2018 Published: 01 August 2005

  • MSC : 92C10, 92C15, 82C31.

  • We introduce a model for describing the dynamics of large numbers of interacting cells. The fundamental dynamical variables in the model are subcellular elements, which interact with each other through phenomenological intra- and intercellular potentials. Advantages of the model include i) adaptive cell-shape dynamics, ii) flexible accommodation of additional intracellular biology, and iii) the absence of an underlying grid. We present here a detailed description of the model, and use successive mean-field approximations to connect it to more coarse-grained approaches, such as discrete cell-based algorithms and coupled partial differential equations. We also discuss efficient algorithms for encoding the model, and give an example of a simulation of an epithelial sheet. Given the biological flexibility of the model, we propose that it can be used effectively for modeling a range of multicellular processes, such as tumor dynamics and embryogenesis.

    Citation: T. J. Newman. Modeling Multicellular Systems Using Subcellular Elements[J]. Mathematical Biosciences and Engineering, 2005, 2(3): 613-624. doi: 10.3934/mbe.2005.2.613

    Related Papers:

    [1] Sharon L. Truesdell, Marnie M. Saunders . Bone remodeling platforms: Understanding the need for multicellular lab-on-a-chip systems and predictive agent-based models. Mathematical Biosciences and Engineering, 2020, 17(2): 1233-1252. doi: 10.3934/mbe.2020063
    [2] H. J. Alsakaji, F. A. Rihan, K. Udhayakumar, F. El Ktaibi . Stochastic tumor-immune interaction model with external treatments and time delays: An optimal control problem. Mathematical Biosciences and Engineering, 2023, 20(11): 19270-19299. doi: 10.3934/mbe.2023852
    [3] Denise E. Kirschner, Alexei Tsygvintsev . On the global dynamics of a model for tumor immunotherapy. Mathematical Biosciences and Engineering, 2009, 6(3): 573-583. doi: 10.3934/mbe.2009.6.573
    [4] Christian Engwer, Markus Knappitsch, Christina Surulescu . A multiscale model for glioma spread including cell-tissue interactions and proliferation. Mathematical Biosciences and Engineering, 2016, 13(2): 443-460. doi: 10.3934/mbe.2015011
    [5] Marcello Delitala, Tommaso Lorenzi . Emergence of spatial patterns in a mathematical model for the co-culture dynamics of epithelial-like and mesenchymal-like cells. Mathematical Biosciences and Engineering, 2017, 14(1): 79-93. doi: 10.3934/mbe.2017006
    [6] Samantha L Elliott, Emek Kose, Allison L Lewis, Anna E Steinfeld, Elizabeth A Zollinger . Modeling the stem cell hypothesis: Investigating the effects of cancer stem cells and TGF−β on tumor growth. Mathematical Biosciences and Engineering, 2019, 16(6): 7177-7194. doi: 10.3934/mbe.2019360
    [7] Yan Fu, Tian Lu, Meng Zhou, Dongwei Liu, Qihang Gan, Guowei Wang . Effect of color cross-correlated noise on the growth characteristics of tumor cells under immune surveillance. Mathematical Biosciences and Engineering, 2023, 20(12): 21626-21642. doi: 10.3934/mbe.2023957
    [8] Hsiu-Chuan Wei . Mathematical modeling of tumor growth: the MCF-7 breast cancer cell line. Mathematical Biosciences and Engineering, 2019, 16(6): 6512-6535. doi: 10.3934/mbe.2019325
    [9] Filippo Cacace, Valerio Cusimano, Alfredo Germani, Pasquale Palumbo, Federico Papa . Closed-loop control of tumor growth by means of anti-angiogenic administration. Mathematical Biosciences and Engineering, 2018, 15(4): 827-839. doi: 10.3934/mbe.2018037
    [10] Yuyang Xiao, Juan Shen, Xiufen Zou . Mathematical modeling and dynamical analysis of anti-tumor drug dose-response. Mathematical Biosciences and Engineering, 2022, 19(4): 4120-4144. doi: 10.3934/mbe.2022190
  • We introduce a model for describing the dynamics of large numbers of interacting cells. The fundamental dynamical variables in the model are subcellular elements, which interact with each other through phenomenological intra- and intercellular potentials. Advantages of the model include i) adaptive cell-shape dynamics, ii) flexible accommodation of additional intracellular biology, and iii) the absence of an underlying grid. We present here a detailed description of the model, and use successive mean-field approximations to connect it to more coarse-grained approaches, such as discrete cell-based algorithms and coupled partial differential equations. We also discuss efficient algorithms for encoding the model, and give an example of a simulation of an epithelial sheet. Given the biological flexibility of the model, we propose that it can be used effectively for modeling a range of multicellular processes, such as tumor dynamics and embryogenesis.


  • This article has been cited by:

    1. Timothy J. Newman, 2008, 81, 9780123742537, 157, 10.1016/S0070-2153(07)81005-2
    2. Zahra Sadat Hosseini, Seyed Mohammad Reza Hashemi Golpayegani, Esophageal epithelium modeling based on globally coupled map: an approach toward precancerous lesion diagnosis, 2020, 58, 0140-0118, 1297, 10.1007/s11517-020-02151-7
    3. Miquel Marín-Riera, Miguel Brun-Usan, 2019, Chapter 12, 978-3-030-18201-4, 251, 10.1007/978-3-030-18202-1_12
    4. Philip J. Murray, Jun-Won Kang, Gary R. Mirams, Sung-Young Shin, Helen M. Byrne, Philip K. Maini, Kwang-Hyun Cho, Modelling Spatially Regulated β-Catenin Dynamics and Invasion in Intestinal Crypts, 2010, 99, 00063495, 716, 10.1016/j.bpj.2010.05.016
    5. C.C. Antonovici, S.E.M. Boas, E.G. Rens, H. Tahir, R.M.H. Merks, 2016, 9780123947963, 122, 10.1016/B978-0-12-394447-4.40020-9
    6. Elijah Flenner, Lorant Janosi, Bogdan Barz, Adrian Neagu, Gabor Forgacs, Ioan Kosztin, Kinetic Monte Carlo and cellular particle dynamics simulations of multicellular systems, 2012, 85, 1539-3755, 10.1103/PhysRevE.85.031907
    7. Adrian Neagu, Role of computer simulation to predict the outcome of 3D bioprinting, 2017, 1, 2059-4755, 103, 10.2217/3dp-2016-0008
    8. STEFAN HOEHME, DIRK DRASDO, Biomechanical and Nutrient Controls in the Growth of Mammalian Cell Populations, 2010, 17, 0889-8480, 166, 10.1080/08898480.2010.491032
    9. Miguel Brun-Usan, Miquel Marín-Riera, Cristina Grande, Marta Truchado-Garcia, Isaac Salazar-Ciudad, A set of simple cell processes is sufficient to model spiral cleavage, 2017, 144, 0950-1991, 54, 10.1242/dev.140285
    10. Ghaidaa Kashgari, Lina Meinecke, William Gordon, Bryan Ruiz, Jady Yang, Amy Lan Ma, Yilu Xie, Hsiang Ho, Maksim V. Plikus, Qing Nie, James V. Jester, Bogi Andersen, Epithelial Migration and Non-adhesive Periderm Are Required for Digit Separation during Mammalian Development, 2020, 52, 15345807, 764, 10.1016/j.devcel.2020.01.032
    11. Anja Voss-Böhme, 2018, Chapter 19, 978-3-319-65556-7, 311, 10.1007/978-3-319-65558-1_19
    12. Daniel G. Harvey, Alexander G. Fletcher, James M. Osborne, Joe Pitt-Francis, A parallel implementation of an off-lattice individual-based model of multicellular populations, 2015, 192, 00104655, 130, 10.1016/j.cpc.2015.03.005
    13. PETROS KOUMOUTSAKOS, BASIL BAYATI, FLORIAN MILDE, GERARDO TAURIELLO, PARTICLE SIMULATIONS OF MORPHOGENESIS, 2011, 21, 0218-2025, 955, 10.1142/S021820251100543X
    14. Andras Czirok, Charles D. Little, Pattern formation during vasculogenesis, 2012, 96, 1542975X, 153, 10.1002/bdrc.21010
    15. Gareth Wyn Jones, S. Jonathan Chapman, Modeling Growth in Biological Materials, 2012, 54, 0036-1445, 52, 10.1137/080731785
    16. Andreea Robu, Roxana Aldea, Oana Munteanu, Monica Neagu, Lacramioara Stoicu-Tivadar, Adrian Neagu, Computer simulations of in vitro morphogenesis, 2012, 109, 03032647, 430, 10.1016/j.biosystems.2012.06.002
    17. Enys Mones, András Czirók, Tamás Vicsek, Anomalous segregation dynamics of self-propelled particles, 2015, 17, 1367-2630, 063013, 10.1088/1367-2630/17/6/063013
    18. Andras Czirok, Endothelial cell motility, coordination and pattern formation during vasculogenesis, 2013, 5, 19395094, 587, 10.1002/wsbm.1233
    19. Anna Mkrtchyan, Jan Åström, Mikko Karttunen, A new model for cell division and migration with spontaneous topology changes, 2014, 10, 1744-683X, 4332, 10.1039/C4SM00489B
    20. Mikahl Banwarth-Kuhn, Ali Nematbakhsh, Kevin W. Rodriguez, Stephen Snipes, Carolyn G. Rasmussen, G. Venugopala Reddy, Mark Alber, Cell-Based Model of the Generation and Maintenance of the Shape and Structure of the Multilayered Shoot Apical Meristem of Arabidopsis thaliana, 2019, 81, 0092-8240, 3245, 10.1007/s11538-018-00547-z
    21. Nikolai Bessonov, Vitaly Volpert, Deformable Cell Model of Tissue Growth, 2017, 5, 2079-3197, 45, 10.3390/computation5040045
    22. Scott Christley, Bryanna Emr, Auyon Ghosh, Josh Satalin, Louis Gatto, Yoram Vodovotz, Gary F Nieman, Gary An, Bayesian inference of the lung alveolar spatial model for the identification of alveolar mechanics associated with acute respiratory distress syndrome, 2013, 10, 1478-3967, 036008, 10.1088/1478-3975/10/3/036008
    23. Jieling Zhao, Youfang Cao, Luisa A. DiPietro, Jie Liang, Dynamic cellular finite-element method for modelling large-scale cell migration and proliferation under the control of mechanical and biochemical cues: a study of re-epithelialization, 2017, 14, 1742-5689, 20160959, 10.1098/rsif.2016.0959
    24. Ruirui Liu, Kathryn A Higley, Maciej H Swat, Mark A J Chaplain, Gibin G Powathil, James A Glazier, Development of a coupled simulation toolkit for computational radiation biology based on Geant4 and CompuCell3D, 2021, 66, 0031-9155, 045026, 10.1088/1361-6560/abd4f9
    25. Simon Tanaka, Simulation Frameworks for Morphogenetic Problems, 2015, 3, 2079-3197, 197, 10.3390/computation3020197
    26. Ramon Grima, 2008, 81, 9780123742537, 435, 10.1016/S0070-2153(07)81015-5
    27. Yilin Wu, Nan Chen, Matthew Rissler, Yi Jiang, Dale Kaiser, Mark Alber, 2006, Chapter 24, 978-3-540-40929-8, 192, 10.1007/11861201_24
    28. Watal M. Iwasaki, Hideki Innan, Arndt von Haeseler, Simulation framework for generating intratumor heterogeneity patterns in a cancer cell population, 2017, 12, 1932-6203, e0184229, 10.1371/journal.pone.0184229
    29. Yangyang Wang, Christian F. Guerrero‐Juarez, Yuchi Qiu, Huijing Du, Weitao Chen, Seth Figueroa, Maksim V. Plikus, Qing Nie, A multiscale hybrid mathematical model of epidermal‐dermal interactions during skin wound healing, 2019, 28, 0906-6705, 493, 10.1111/exd.13909
    30. Henri B. Wolff, Lance A. Davidson, Roeland M. H. Merks, Adapting a Plant Tissue Model to Animal Development: Introducing Cell Sliding into VirtualLeaf, 2019, 81, 0092-8240, 3322, 10.1007/s11538-019-00599-9
    31. Artur Cristea, Adrian Neagu, Shape changes of bioprinted tissue constructs simulated by the Lattice Boltzmann method, 2016, 70, 00104825, 80, 10.1016/j.compbiomed.2015.12.020
    32. Zhiliang Xu, Nan Chen, Malgorzata M Kamocka, Elliot D Rosen, Mark Alber, A multiscale model of thrombus development, 2008, 5, 1742-5689, 705, 10.1098/rsif.2007.1202
    33. James M. Osborne, Alexander G. Fletcher, Joe M. Pitt-Francis, Philip K. Maini, David J. Gavaghan, Qing Nie, Comparing individual-based approaches to modelling the self-organization of multicellular tissues, 2017, 13, 1553-7358, e1005387, 10.1371/journal.pcbi.1005387
    34. Elijah Flenner, Francoise Marga, Adrian Neagu, Ioan Kosztin, Gabor Forgacs, 2008, 81, 9780123742537, 461, 10.1016/S0070-2153(07)81016-7
    35. William T. Gibson, Matthew C. Gibson, 2009, 89, 9780123749024, 87, 10.1016/S0070-2153(09)89004-2
    36. Zhiliang Xu, Scott Christley, Joshua Lioi, Oleg Kim, Cameron Harvey, Wenzhao Sun, Elliot D. Rosen, Mark Alber, 2012, 110, 9780123884039, 367, 10.1016/B978-0-12-388403-9.00014-X
    37. I. González-Valverde, C. Semino, J.M. García-Aznar, Phenomenological modelling and simulation of cell clusters in 3D cultures, 2016, 77, 00104825, 249, 10.1016/j.compbiomed.2016.08.019
    38. Ricard V. Solé, Sergi Valverde, Johannes Jaeger, Before the Endless Forms: Embodied Model of Transition from Single Cells to Aggregates to Ecosystem Engineering, 2013, 8, 1932-6203, e59664, 10.1371/journal.pone.0059664
    39. Simon Tanaka, David Sichau, Dagmar Iber, LBIBCell: a cell-based simulation environment for morphogenetic problems, 2015, 31, 1367-4803, 2340, 10.1093/bioinformatics/btv147
    40. Adrian Neagu, Vladimir Mironov, Ioan Kosztin, Bogdan Barz, Monica Neagu, Ricardo A. Moreno-Rodriguez, Roger R. Markwald, Gabor Forgacs, Computational modeling of epithelial–mesenchymal transformations, 2010, 100, 03032647, 23, 10.1016/j.biosystems.2009.12.004
    41. Hammad Naveed, Sema Kachalo, , 2013, Dynamic mechanical finite element model of biological cells for studying cellular pattern formation, 978-1-4577-0216-7, 4517, 10.1109/EMBC.2013.6610551
    42. Alexander G. Fletcher, Fergus Cooper, Ruth E. Baker, Mechanocellular models of epithelial morphogenesis, 2017, 372, 0962-8436, 20150519, 10.1098/rstb.2015.0519
    43. Miquel Marin-Riera, Miguel Brun-Usan, Roland Zimm, Tommi Välikangas, Isaac Salazar-Ciudad, Computational modeling of development by epithelia, mesenchyme and their interactions: a unified model, 2015, 1367-4803, btv527, 10.1093/bioinformatics/btv527
    44. Yi Sun, Qi Wang, Modeling and simulations of multicellular aggregate self-assembly in biofabrication using kinetic Monte Carlo methods, 2013, 9, 1744-683X, 2172, 10.1039/c2sm27090k
    45. Brian Drawert, Stefan Hellander, Michael Trogdon, Tau-Mu Yi, Linda Petzold, A framework for discrete stochastic simulation on 3D moving boundary domains, 2016, 145, 0021-9606, 184113, 10.1063/1.4967338
    46. Sebastian A Sandersius, Timothy J Newman, Modeling cell rheology with the Subcellular Element Model, 2008, 5, 1478-3975, 015002, 10.1088/1478-3975/5/1/015002
    47. R. Rey, J. M. García-Aznar, A phenomenological approach to modelling collective cell movement in 2D, 2013, 12, 1617-7959, 1089, 10.1007/s10237-012-0465-9
    48. Dimas C. Belisario, Leonardo Di. G. Sigalotti, 2014, Chapter 6, 978-3-319-00190-6, 121, 10.1007/978-3-319-00191-3_6
    49. Daniel L. Barton, Silke Henkes, Cornelis J. Weijer, Rastko Sknepnek, Stanislav Shvartsman, Active Vertex Model for cell-resolution description of epithelial tissue mechanics, 2017, 13, 1553-7358, e1005569, 10.1371/journal.pcbi.1005569
    50. A Szabó, K Varga, T Garay, B Hegedűs, A Czirók, Invasion from a cell aggregate—the roles of active cell motion and mechanical equilibrium, 2012, 9, 1478-3967, 016010, 10.1088/1478-3975/9/1/016010
    51. B A Camley, W-J Rappel, Physical models of collective cell motility: from cell to tissue, 2017, 50, 0022-3727, 113002, 10.1088/1361-6463/aa56fe
    52. Philip J Murray, Alex Walter, Alexander G Fletcher, Carina M Edwards, Marcus J Tindall, Philip K Maini, Comparing a discrete and continuum model of the intestinal crypt, 2011, 8, 1478-3975, 026011, 10.1088/1478-3975/8/2/026011
    53. A. Szabó, A. Czirók, The Role of Cell-Cell Adhesion in the Formation of Multicellular Sprouts, 2010, 5, 0973-5348, 106, 10.1051/mmnp/20105105
    54. Roeland Merks, 2015, Chapter 70, 978-3-540-70528-4, 195, 10.1007/978-3-540-70529-1_70
    55. K. Aihara, Modeling and Analyzing Biological Oscillations in Molecular Networks, 2008, 96, 0018-9219, 1361, 10.1109/JPROC.2008.925448
    56. Zhan Chen, Yuting Zou, A multiscale model for heterogeneous tumor spheroid in vitro, 2017, 15, 1551-0018, 361, 10.3934/mbe.2018016
    57. Ashkan Shafiee, Jareer Kassis, Anthony Atala, Elham Ghadiri, Acceleration of tissue maturation by mechanotransduction-based bioprinting, 2021, 3, 2643-1564, 10.1103/PhysRevResearch.3.013008
    58. Zhenyu Shi, Nan Chen, Yanan Du, Ali Khademhosseini, Mark Alber, Stochastic model of self-assembly of cell-laden hydrogels, 2009, 80, 1539-3755, 10.1103/PhysRevE.80.061901
    59. Timothy J. Newman, 2007, Chapter 10, 978-3-7643-8101-1, 221, 10.1007/978-3-7643-8123-3_10
    60. P. K. Maini, R. E. Baker, 2014, Chapter 1, 978-3-319-06922-7, 1, 10.1007/978-3-319-06923-4_1
    61. John Metzcar, Yafei Wang, Randy Heiland, Paul Macklin, A Review of Cell-Based Computational Modeling in Cancer Biology, 2019, 2473-4276, 1, 10.1200/CCI.18.00069
    62. Y. Davit, J. M. Osborne, H. M. Byrne, D. Gavaghan, J. Pitt-Francis, Validity of the Cauchy-Born rule applied to discrete cellular-scale models of biological tissues, 2013, 87, 1539-3755, 10.1103/PhysRevE.87.042724
    63. Pascal F. Hagolani, Roland Zimm, Miquel Marin-Riera, Isaac Salazar-Ciudad, Cell signaling stabilizes morphogenesis against noise, 2019, 146, 0950-1991, dev179309, 10.1242/dev.179309
    64. Sebastian A. Sandersius, Manli Chuai, Cornelis J. Weijer, Timothy J. Newman, Jörg Langowski, Correlating Cell Behavior with Tissue Topology in Embryonic Epithelia, 2011, 6, 1932-6203, e18081, 10.1371/journal.pone.0018081
    65. Florian Milde, Gerardo Tauriello, Hannah Haberkern, Petros Koumoutsakos, SEM++: A particle model of cellular growth, signaling and migration, 2014, 1, 2196-4378, 211, 10.1007/s40571-014-0017-4
    66. R. M. H. Merks, P. Koolwijk, Modeling Morphogenesisin silicoandin vitro: Towards Quantitative, Predictive, Cell-based Modeling, 2009, 4, 0973-5348, 149, 10.1051/mmnp/20094406
    67. S A Sandersius, C J Weijer, T J Newman, Emergent cell and tissue dynamics from subcellular modeling of active biomechanical processes, 2011, 8, 1478-3975, 045007, 10.1088/1478-3975/8/4/045007
    68. Philip J. Murray, Carina M. Edwards, Marcus J. Tindall, Philip K. Maini, From a discrete to a continuum model of cell dynamics in one dimension, 2009, 80, 1539-3755, 10.1103/PhysRevE.80.031912
    69. Abdul N. Malmi-Kakkada, Xin Li, Himadri S. Samanta, Sumit Sinha, D. Thirumalai, Cell Growth Rate Dictates the Onset of Glass to Fluidlike Transition and Long Time Superdiffusion in an Evolving Cell Colony, 2018, 8, 2160-3308, 10.1103/PhysRevX.8.021025
    70. L.A. D'Alessandro, S. Hoehme, A. Henney, D. Drasdo, U. Klingmüller, Unraveling liver complexity from molecular to organ level: Challenges and perspectives, 2015, 117, 00796107, 78, 10.1016/j.pbiomolbio.2014.11.005
    71. William R. Holmes, Nabora Soledad Reyes de Mochel, Qixuan Wang, Huijing Du, Tao Peng, Michael Chiang, Olivier Cinquin, Ken Cho, Qing Nie, Santiago Schnell, Gene Expression Noise Enhances Robust Organization of the Early Mammalian Blastocyst, 2017, 13, 1553-7358, e1005320, 10.1371/journal.pcbi.1005320
    72. A Szabó, R Ünnep, E Méhes, W O Twal, W S Argraves, Y Cao, A Czirók, Collective cell motion in endothelial monolayers, 2010, 7, 1478-3975, 046007, 10.1088/1478-3975/7/4/046007
    73. Julien Delile, René Doursat, Nadine Peyriéras, 2014, 9780124059269, 359, 10.1016/B978-0-12-405926-9.00016-2
    74. Marco Scianna, Luigi Preziosi, A node-based version of the cellular Potts model, 2016, 76, 00104825, 94, 10.1016/j.compbiomed.2016.06.027
    75. S A Sandersius, M Chuai, C J Weijer, T J Newman, A ‘chemotactic dipole’ mechanism for large-scale vortex motion during primitive streak formation in the chick embryo, 2011, 8, 1478-3975, 045008, 10.1088/1478-3975/8/4/045008
    76. Joost H. J. van Opheusden, Jaap Molenaar, Algorithm for a particle-based growth model for plant tissues, 2018, 5, 2054-5703, 181127, 10.1098/rsos.181127
    77. Manli Chuai, Cornelis J. Weijer, 2008, 81, 9780123742537, 135, 10.1016/S0070-2153(07)81004-0
    78. Ioan Kosztin, Gordana Vunjak-Novakovic, Gabor Forgacs, Colloquium: Modeling the dynamics of multicellular systems: Application to tissue engineering, 2012, 84, 0034-6861, 1791, 10.1103/RevModPhys.84.1791
    79. Xiuxiu He, Yi Jiang, 2018, Chapter 3, 978-3-319-96841-4, 61, 10.1007/978-3-319-96842-1_3
    80. Oliver J. Maclaren, Helen M. Byrne, Alexander G. Fletcher, Philip K. Maini, Models, measurement and inference in epithelial tissue dynamics, 2015, 12, 1551-0018, 1321, 10.3934/mbe.2015.12.1321
    81. Michael Meyer-Hermann, 2008, 81, 9780123742537, 373, 10.1016/S0070-2153(07)81013-1
    82. Scott Christley, Briana Lee, Xing Dai, Qing Nie, Integrative multicellular biological modeling: a case study of 3D epidermal development using GPU algorithms, 2010, 4, 1752-0509, 10.1186/1752-0509-4-107
    83. Huijing Du, Qing Nie, William R. Holmes, Carina M Dunlop, The Interplay between Wnt Mediated Expansion and Negative Regulation of Growth Promotes Robust Intestinal Crypt Structure and Homeostasis, 2015, 11, 1553-7358, e1004285, 10.1371/journal.pcbi.1004285
    84. Qing Nie, Lingxia Qiao, Yuchi Qiu, Lei Zhang, Wei Zhao, Noise control and utility: From regulatory network to spatial patterning, 2020, 63, 1674-7283, 425, 10.1007/s11425-019-1633-1
    85. Andras Czirok, Dona Greta Isai, Cell resolved, multiparticle model of plastic tissue deformations and morphogenesis, 2014, 12, 1478-3975, 016005, 10.1088/1478-3975/12/1/016005
    86. Hermann-Georg Holzhütter, Dirk Drasdo, Tobias Preusser, Jörg Lippert, Adriano M. Henney, The virtual liver: a multidisciplinary, multilevel challenge for systems biology, 2012, 4, 19395094, 221, 10.1002/wsbm.1158
    87. Matthew McCune, Ashkan Shafiee, Gabor Forgacs, Ioan Kosztin, Predictive modeling of post bioprinting structure formation, 2014, 10, 1744-683X, 1790, 10.1039/C3SM52806E
    88. Cameron W Harvey, Faruck Morcos, Christopher R Sweet, Dale Kaiser, Santanu Chatterjee, Xiaomin Liu, Danny Z Chen, Mark Alber, Study of elastic collisions ofMyxococcus xanthusin swarms, 2011, 8, 1478-3975, 026016, 10.1088/1478-3975/8/2/026016
    89. Pavel M. Lushnikov, Nan Chen, Mark Alber, Macroscopic dynamics of biological cells interacting via chemotaxis and direct contact, 2008, 78, 1539-3755, 10.1103/PhysRevE.78.061904
    90. Sonja E. M. Boas, Roeland M. H. Merks, Tip cell overtaking occurs as a side effect of sprouting in computational models of angiogenesis, 2015, 9, 1752-0509, 10.1186/s12918-015-0230-7
    91. Ryan C Kennedy, Glen EP Ropella, C Anthony Hunt, A cell-centered, agent-based framework that enables flexible environment granularities, 2016, 13, 1742-4682, 10.1186/s12976-016-0030-9
    92. Qi Wang, In-Silico Analysis on 3D Biofabrication Using Kinetic Monte Carlo Simulations, 2017, 2, 25728490, 10.15406/atroa.2017.02.00045
    93. Helen Byrne, Dirk Drasdo, Individual-based and continuum models of growing cell populations: a comparison, 2009, 58, 0303-6812, 657, 10.1007/s00285-008-0212-0
    94. Alexander Gord, William R. Holmes, Xing Dai, Qing Nie, Computational modelling of epidermal stratification highlights the importance of asymmetric cell division for predictable and robust layer formation, 2014, 11, 1742-5689, 20140631, 10.1098/rsif.2014.0631
    95. F. J. Vermolen, Particle methods to solve modelling problems in wound healing and tumor growth, 2015, 2, 2196-4378, 381, 10.1007/s40571-015-0055-6
    96. Zixuan Cang, Yangyang Wang, Qixuan Wang, Ken W. Y. Cho, William Holmes, Qing Nie, David Umulis, A multiscale model via single-cell transcriptomics reveals robust patterning mechanisms during early mammalian embryo development, 2021, 17, 1553-7358, e1008571, 10.1371/journal.pcbi.1008571
    97. Isaac Salazar-Ciudad, Jukka Jernvall, A computational model of teeth and the developmental origins of morphological variation, 2010, 464, 0028-0836, 583, 10.1038/nature08838
    98. András Czirók, Katalin Varga, Előd Méhes, András Szabó, Collective cell streams in epithelial monolayers depend on cell adhesion, 2013, 15, 1367-2630, 075006, 10.1088/1367-2630/15/7/075006
    99. Michael Meyer-Hermann, Tilo Beyer, 2012, 3527600906, 10.1002/3527600906.mcb.201100040
    100. G. Grise, M. Meyer-Hermann, Towards Sub-cellular Modeling with Delaunay Triangulation, 2010, 5, 0973-5348, 224, 10.1051/mmnp/20083710
    101. Aboutaleb Amiri, Cameron Harvey, Amy Buchmann, Scott Christley, Joshua D. Shrout, Igor S. Aranson, Mark Alber, Reversals and collisions optimize protein exchange in bacterial swarms, 2017, 95, 2470-0045, 10.1103/PhysRevE.95.032408
    102. Mikahl Banwarth-Kuhn, Suzanne Sindi, 2020, Chapter 4, 978-1-83962-519-0, 10.5772/intechopen.88575
    103. Ramiro Magno, Verônica A Grieneisen, Athanasius FM Marée, The biophysical nature of cells: potential cell behaviours revealed by analytical and computational studies of cell surface mechanics, 2015, 8, 2046-1682, 10.1186/s13628-015-0022-x
    104. Yousef Jamali, Mohammad Azimi, Mohammad R. K. Mofrad, Nick Monk, A Sub-Cellular Viscoelastic Model for Cell Population Mechanics, 2010, 5, 1932-6203, e12097, 10.1371/journal.pone.0012097
    105. Rebecca L Klank, Steven S Rosenfeld, David J Odde, A Brownian dynamics tumor progression simulator with application to glioblastoma, 2018, 4, 2057-1739, 015001, 10.1088/2057-1739/aa9e6e
    106. Mikahl Banwarth-Kuhn, Jordan Collignon, Suzanne Sindi, Quantifying the Biophysical Impact of Budding Cell Division on the Spatial Organization of Growing Yeast Colonies, 2020, 10, 2076-3417, 5780, 10.3390/app10175780
    107. Dirk Drasdo, Stefan Hoehme, Michael Block, On the Role of Physics in the Growth and Pattern Formation of Multi-Cellular Systems: What can we Learn from Individual-Cell Based Models?, 2007, 128, 0022-4715, 287, 10.1007/s10955-007-9289-x
    108. Kana Fuji, Sakurako Tanida, Masaki Sano, Makiko Nonomura, Daniel Riveline, Hisao Honda, Tetsuya Hiraiwa, Computational approaches for simulating luminogenesis, 2022, 131, 10849521, 173, 10.1016/j.semcdb.2022.05.021
    109. C.C. Antonovici, S.E.M. Boas, E.G. Rens, H. Tahir, R.M.H. Merks, 2016, 9780128216248, 322, 10.1016/B978-0-12-821618-7.40020-9
    110. Seunghwa Kang, Simon Kahan, Jason McDermott, Nicholas Flann, Ilya Shmulevich, Biocellion : accelerating computer simulation of multicellular biological system models , 2014, 30, 1367-4811, 3101, 10.1093/bioinformatics/btu498
    111. Adrian Neagu, 2023, 9780128186534, 209, 10.1016/B978-0-12-818653-4.00009-7
    112. Ashkan Shafiee, Elham Ghadiri, Robert Langer, Fabricating human tissues: How physics can help, 2022, 75, 0031-9228, 38, 10.1063/PT.3.5138
    113. Phillip J. Brown, J. Edward F. Green, Benjamin J. Binder, James M. Osborne, A rigid body framework for multicellular modeling, 2021, 1, 2662-8457, 754, 10.1038/s43588-021-00154-4
    114. Yuchi Qiu, Lianna Fung, Thomas F. Schilling, Qing Nie, David Umulis, Multiple morphogens and rapid elongation promote segmental patterning during development, 2021, 17, 1553-7358, e1009077, 10.1371/journal.pcbi.1009077
    115. Diego Alejandro Sánchez Rodríguez, Ana Isabel Ramos-Murillo, Rubén Darío Godoy-Silva, Tissue engineering, 3D-Bioprinting, morphogenesis modelling and simulation of biostructures: Relevance, underpinning biological principles and future trends, 2021, 24, 24058866, e00171, 10.1016/j.bprint.2021.e00171
    116. Stelian Arjoca, Andreea Robu, Monica Neagu, Adrian Neagu, Mathematical and computational models in spheroid-based biofabrication, 2022, 17427061, 10.1016/j.actbio.2022.07.024
    117. Naman Merchant, Adam T. Sampson, Andrei Boiko, Ruth E. Falconer, Dense agent-based HPC simulation of cell physics and signaling with real-time user interactions, 2023, 5, 2624-9898, 10.3389/fcomp.2023.1085867
    118. Erika Tsingos, Bente Hilde Bakker, Koen A.E. Keijzer, Hermen Jan Hupkes, Roeland M.H. Merks, Hybrid cellular Potts and bead-spring modeling of cells in fibrous extracellular matrix, 2023, 00063495, 10.1016/j.bpj.2023.05.013
    119. Alireza Ramezani, Samuel Britton, Roya Zandi, Mark Alber, Ali Nematbakhsh, Weitao Chen, A multiscale chemical-mechanical model predicts impact of morphogen spreading on tissue growth, 2023, 9, 2056-7189, 10.1038/s41540-023-00278-5
    120. C.S. Dias, N.A.M. Araújo, 2024, 9780128239483, 79, 10.1016/B978-0-12-823948-3.00013-0
    121. Nilay Kumar, Jennifer Rangel Ambriz, Kevin Tsai, Mayesha Sahir Mim, Marycruz Flores-Flores, Weitao Chen, Jeremiah J. Zartman, Mark Alber, Balancing competing effects of tissue growth and cytoskeletal regulation during Drosophila wing disc development, 2024, 15, 2041-1723, 10.1038/s41467-024-46698-7
    122. Nilay Kumar, Mayesha Sahir Mim, Alexander Dowling, Jeremiah J. Zartman, Reverse engineering morphogenesis through Bayesian optimization of physics-based models, 2024, 10, 2056-7189, 10.1038/s41540-024-00375-z
    123. James M. Osborne, An adaptive numerical method for multi–cellular simulations of tissue development and maintenance, 2024, 00225193, 111922, 10.1016/j.jtbi.2024.111922
    124. R. Belousov, S. Savino, P. Moghe, T. Hiiragi, L. Rondoni, A. Erzberger, Poissonian Cellular Potts Models Reveal Nonequilibrium Kinetics of Cell Sorting, 2024, 132, 0031-9007, 10.1103/PhysRevLett.132.248401
  • Reader Comments
  • © 2005 the Author(s), licensee AIMS Press. This is an open access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0)
通讯作者: 陈斌, bchen63@163.com
  • 1. 

    沈阳化工大学材料科学与工程学院 沈阳 110142

  1. 本站搜索
  2. 百度学术搜索
  3. 万方数据库搜索
  4. CNKI搜索
Mathematical Biosciences and Engineering
3.9

Metrics

Article views(6025) PDF downloads(756) Cited by(124)

Preview PDF
Download XML
Export Citation
Article outline
Abstract

Other Articles By Authors

Related pages

Tools

Copyright © AIMS Press

/

DownLoad:  Full-Size Img  PowerPoint
Return
Return

Catalog