Cited by 100Cellular Mechanics and InteractionsMathematical Biology Tumor GrowthCancer Cells and Metastasis

The DOI matches its Crossref record; 65 of the 67 references it cites were found in a registry or an index.

Multi-scale models of cell and tissue dynamics

Open access

Stolarska, Magdalena A., Kim, Yangjin, Othmer, Hans G.·2009·Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences

DOI 10.1098/rsta.2009.0095PMC PMC3263796

Open this paper in CoChat — free account

Abstract

Cell and tissue movement are essential processes at various stages in the life cycle of most organisms. The early development of multi-cellular organisms involves individual and collective cell movement; leukocytes must migrate towards sites of infection as part of the immune response; and in cancer, directed movement is involved in invasion and metastasis. The forces needed to drive movement arise from actin polymerization, molecular motors and other processes, but understanding the cell- or tissue-level organization of these processes that is needed to produce the forces necessary for directed movement at the appropriate point in the cell or tissue is a major challenge. In this paper, we present three models that deal with the mechanics of cells and tissues: a model of an arbitrarily deformable single cell, a discrete model of the onset of tumour growth in which each cell is treated individually, and a hybrid continuum-discrete model of the later stages of tumour growth. While the models are different in scope, their underlying mechanical and mathematical principles are similar and can be applied to a variety of biological systems.

Integrity signals

Registry

Crossref · 10.1098/rsta.2009.0095

Cites

65 of 65 references verified0 citation errors · 0 not checkable

Statistics

Recomputing p-values needs the paper’s full text.

Claims the paper makes

We couldn’t retrieve this paper’s full text, so its claims and self-check weren’t run. The registry and citation checks still apply.

Claims other papers make about this one

Each is checked against this paper’s own text: does it say what the citing paper says it does?

Molecular Biology of the Cell
Alberts, B., Johnson, A., Lewis, J. H., Morgan, D. O., RAFF, M. C., Roberts, K. J., & Walter, P. (2017) · W.W. Norton eBooks · doi:10.1201/9781315735368 · Cited by 7,937
Tumour-cell invasion and migration: diversity and escape mechanisms
Friedl, P., & Wolf, K. (2003) · Nature reviews. Cancer · doi:10.1038/nrc1075 · Cited by 3,350
Cell Movement Is Guided by the Rigidity of the Substrate
Lo, C.-M., Wang, H.-B., Dembo, M., & Wang, Y.-L. (2000) · Biophysical Journal · doi:10.1016/s0006-3495(00)76279-5 · Cited by 3,289
Nonlinear Solid Mechanics: A Continuum Approach for Engineering
Holzapfel, G. A. (2000) · Cited by 2,733
Focal adhesion kinase: in command and control of cell motility.
Mitra, S. K., Hanson, D. A., & Schlaepfer, D. D. (2005) · Nature Reviews Molecular Cell Biology · doi:10.1038/nrm1549 · Cited by 2,335
Contact Problems in Elasticity
Kikuchi, N., & Oden, J. T. (1988) · Society for Industrial and Applied Mathematics eBooks · doi:10.1137/1.9781611970845 · Cited by 2,292
Molecular Mechanisms Controlling Actin Filament Dynamics in Nonmuscle Cells
Pollard, T. D., Blanchoin, L., & Mullins, R. D. (2000) · Annual Review of Biophysics and Biomolecular Structure · doi:10.1146/annurev.biophys.29.1.545 · Cited by 1,559
Actin-Based Cell Motility and Cell Locomotion
Mitchison, T. J., & Cramer, L. P. (1996) · Cell · doi:10.1016/s0092-8674(00)81281-7 · Cited by 1,556
Stress-dependent finite growth in soft elastic tissues
Rodriguez, E. K., Hoger, A., & McCulloch, A. D. (1994) · Journal of Biomechanics · doi:10.1016/0021-9290(94)90021-3 · Cited by 1,464
Cost of Migration: Invasion of Malignant Gliomas and Implications for Treatment
Giese, A., Bjerkvig, R., Berens, M. E., & Westphal, M. (2003) · Journal of Clinical Oncology · doi:10.1200/jco.2003.05.063 · Cited by 1,216

Show all 67 references

Research works printed but not linked: 2

Skalak R., 1981, Proc. IUTAM Symp. on Finite Elasticity
10.1023/A:1011082712497 · DOI

Nonlinear modelling of cancer: bridging the gap between cells and tumours
Lowengrub, J. S., Frieboes, H. B., Jin, F., Chuang, Y.-L., Li, X., Macklin, P., Wise, S. M., & Vittorio Cristini, C. (2009) · Nonlinearity · doi:10.1088/0951-7715/23/1/r01 · Cited by 565
Multiscale Cancer Modeling
Deisboeck, T. S., Wang, Z., Macklin, P., & Vittorio Cristini, C. (2011) · Annual Review of Biomedical Engineering · doi:10.1146/annurev-bioeng-071910-124729 · Cited by 477
Hybrid models of tumor growth
Rejniak, K. A., & Anderson, A. R. A. (2010) · WIREs Systems Biology and Medicine · doi:10.1002/wsbm.102 · Cited by 302
Three-dimensional multispecies nonlinear tumor growth—II: Tumor invasion and angiogenesis
Frieboes, H. B., Jin, F., Chuang, Y.-L., Wise, S. M., Lowengrub, J. S., & Vittorio Cristini, C. (2010) · Journal of Theoretical Biology · doi:10.1016/j.jtbi.2010.02.036 · Cited by 236
Model for self-polarization and motility of keratocyte fragments
Ziebert, F., Swaminathan, S., & Aranson, I. S. (2011) · Journal of The Royal Society Interface · doi:10.1098/rsif.2011.0433 · Cited by 205
The role of the microenvironment in tumor growth and invasion
Kim, Y., Stolarska, M., & Othmer, H. G. (2011) · Progress in Biophysics and Molecular Biology · doi:10.1016/j.pbiomolbio.2011.06.006 · Cited by 181
Self-citation
A Review of Computational Methods in Materials Science: Examples from Shock-Wave and Polymer Physics
Steinhauser, M. O., & Hiermaier, S. J. (2009) · International Journal of Molecular Sciences · doi:10.3390/ijms10125135 · Cited by 152
Glioma follow white matter tracts: a multiscale DTI-based model
Engwer, C., Hillen, T., Knappitsch, M., & Surulescu, C. (2014) · Journal of Mathematical Biology · doi:10.1007/s00285-014-0822-7 · Cited by 115
An adaptive multigrid algorithm for simulating solid tumor growth using mixture models
Wise, S. M., Lowengrub, J. S., & Vittorio Cristini, C. (2010) · Mathematical and Computer Modelling · doi:10.1016/j.mcm.2010.07.007 · Cited by 103
Modeling the Mechanics of Cancer: Effect of Changes in Cellular and Extra-Cellular Mechanical Properties
Katira, P., Bonnecaze, R. T., & Zaman, M. H. (2013) · Frontiers in Oncology · doi:10.3389/fonc.2013.00145 · Cited by 104
Review: Rheological properties of biological materials
Claude Verdier, A., Etienne, J., Alain Duperray, B., & Preziosi, L. (2009) · Comptes Rendus Physique · doi:10.1016/j.crhy.2009.10.003 · Cited by 97
ON THE ASYMPTOTIC THEORY FROM MICROSCOPIC TO MACROSCOPIC GROWING TISSUE MODELS: AN OVERVIEW WITH PERSPECTIVES
Bellomo, N., Bellouquid, A., Nieto, J., & Soler, J. (2011) · Mathematical Models and Methods in Applied Sciences · doi:10.1142/s0218202512005885 · Cited by 96
Airway smooth muscle in asthma: Linking contraction and mechanotransduction to disease pathogenesis and remodelling
Noble, P. B., Pascoe, C. D., Lan, B., Ito, S., Kistemaker, L. E. M., Tatler, A. L., Pera, T., Brook, B. S., Gosens, R., & West, A. R. (2014) · Pulmonary Pharmacology & Therapeutics · doi:10.1016/j.pupt.2014.07.005 · Cited by 88
Geometry-Driven Cell Organization Determines Tissue Growths in Scaffold Pores: Consequences for Fibronectin Organization
Joly, P., Duda, G. N., Schöne, M., Welzel, P. B., Freudenberg, U., Werner, C., & Petersen, A. (2013) · PLoS ONE · doi:10.1371/journal.pone.0073545 · Cited by 88
A unified rheological model for cells and cellularised materials
Bonfanti, A., Fouchard, J., Khalilgharibi, N., Charras, G., & Kabla, A. (2020) · Royal Society Open Science · doi:10.1098/rsos.190920 · Cited by 70
Multiscale modelling of cancer response to oncolytic viral therapy
Alzahrani, T. A., Eftimie, R., & Trucu, D. (2019) · Mathematical Biosciences · doi:10.1016/j.mbs.2018.12.018 · Cited by 69
How Changes in Cell Mechanical Properties Induce Cancerous Behavior
Katira, P., Zaman, M. H., & Bonnecaze, R. T. (2012) · Physical Review Letters · doi:10.1103/physrevlett.108.028103 · Cited by 64
The effects of cell compressibility, motility and contact inhibition on the growth of tumor cell clusters using the Cellular Potts Model
Li, J. F., & Lowengrub, J. S. (2013) · Journal of Theoretical Biology · doi:10.1016/j.jtbi.2013.10.008 · Cited by 61
A numerical analysis of multicellular environment for modeling tissue electroporation
Mezeme, M. E., Pucihar, G., Pavlin, M., Brosseau, C., & Damijan Miklavčič, A. (2012) · Applied Physics Letters · doi:10.1063/1.3700727 · Cited by 54
Comparison of cell migration mechanical strategies in three-dimensional matrices: a computational study
Zhu, J., & Mogilner, A. (2016) · Interface Focus · doi:10.1098/rsfs.2016.0040 · Cited by 52
Role of extracellular matrix and microenvironment in regulation of tumor growth and LAR-mediated invasion in glioblastoma
Kim, Y., Kang, H., Powathil, G., Kim, H., Trucu, D., Lee, W., Lawler, S. E., & Chaplain, M. A. J. (2018) · PLoS ONE · doi:10.1371/journal.pone.0204865 · Cited by 51
Self-citation
Multiscale Cancer Modeling
Fletcher, A. G., Mirams, G. R., Murray, P. J., Walter, A., Kang, J. W., Cho, K. H., Maini, P. K., & Byrne, H. M. (2010) · CRC Press eBooks · doi:10.1201/b10407 · Cited by 52
Mechanisms of cell propulsion by active stresses
Carlsson, A. E. (2011) · New Journal of Physics · doi:10.1088/1367-2630/13/7/073009 · Cited by 48
From kinetic models of multicellular growing systems to macroscopic biological tissue models
Bellouquid, A., & Angelis, E. D. (2010) · Nonlinear Analysis Real World Applications · doi:10.1016/j.nonrwa.2010.09.005 · Cited by 46
Choindroitinase ABC I-Mediated Enhancement of Oncolytic Virus Spread and Anti Tumor Efficacy: A Mathematical Model
Kim, Y., Lee, H. G., Dmitrieva, N., Kim, J., Kaur, B., & Friedman, A. (2014) · PLoS ONE · doi:10.1371/journal.pone.0102499 · Cited by 41
Self-citation
Mathematical models of wound healing and closure: a comprehensive review
Jorgensen, S., & Sanders, J. R. (2015) · Medical & Biological Engineering & Computing · doi:10.1007/s11517-015-1435-z · Cited by 39
A hybrid model for cell proliferation and migration in glioblastoma
Kim, Y., & Roh, S. (2013) · Discrete and Continuous Dynamical Systems - B · doi:10.3934/dcdsb.2013.18.969 · Cited by 39
Self-citation
‘Run-and-tumble’ or ‘look-and-run’? A mechanical model to explore the behavior of a migrating amoeboid cell
Allena, R., & Aubry, D. (2012) · Journal of Theoretical Biology · doi:10.1016/j.jtbi.2012.03.041 · Cited by 37
Dynamic density functional theory of solid tumor growth: Preliminary models
Chauviere, A. H., Hatzikirou, H., Kevrekidis, I. G., Lowengrub, J. S., & Vittorio Cristini, C. (2012) · AIP Advances · doi:10.1063/1.3699065 · Cited by 36
Modeling tumor growth with peridynamics
Lejeune, E., & Linder, C. (2017) · Biomechanics and Modeling in Mechanobiology · doi:10.1007/s10237-017-0876-8 · Cited by 37
An Integrated Computational/Experimental Model of Lymphoma Growth
Frieboes, H. B., Smith, B. R., Chuang, Y.-L., Ito, K., Roettgers, A. M., Gambhir, S. S., & Vittorio Cristini, C. (2013) · PLoS Computational Biology · doi:10.1371/journal.pcbi.1003008 · Cited by 35
A poroelastic model for cell crawling including mechanical coupling between cytoskeletal contraction and actin polymerization
Taber, L. A., Shi, Y., Yang, L., & Bayly, P. V. (2011) · Journal of mechanics of materials and structures · doi:10.2140/jomms.2011.6.569 · Cited by 35
Fundamental constraints to the logic of living systems
Solé, R., Kempes, C. P., Corominas-Murtra, B., De Domenico, M., Kolchinsky, A., Lachmann, M., Libby, E., Saavedra, S., Smith, E., & Wolpert, D. (2024) · Interface Focus · doi:10.1098/rsfs.2024.0010 · Cited by 34
Integrative physical oncology
Hatzikirou, H., Chauvière, A., Bauer, A. L., Leier, A., Lewis, M. T., Macklin, P., Marquez‐Lago, T. T., Bearer, E. L., & Vittorio Cristini, C. (2011) · WIREs Systems Biology and Medicine · doi:10.1002/wsbm.158 · Cited by 32
Role of neutrophil extracellular traps in regulation of lung cancer invasion and metastasis: Structural insights from a computational model
Lee, J.-H., Lee, D., Lawler, S. E., & Kim, Y. (2021) · PLoS Computational Biology · doi:10.1371/journal.pcbi.1008257 · Cited by 31
Self-citation
Differentiated cell behavior: a multiscale approach using measure theory
Colombi, A., Scianna, M., & Tosin, A. (2014) · Journal of Mathematical Biology · doi:10.1007/s00285-014-0846-z · Cited by 29
Cell Migration with Multiple Pseudopodia: Temporal and Spatial Sensing Models
Allena, R. (2013) · Bulletin of Mathematical Biology · doi:10.1007/s11538-012-9806-1 · Cited by 29
Hybrid models of cell and tissue dynamics in tumor growth
Othmer, H. G., & Kim, Y. (2015) · Mathematical Biosciences & Engineering · doi:10.3934/mbe.2015.12.1141 · Cited by 30
Self-citation
A Computational Model for Collective Cellular Motion in Three Dimensions: General Framework and Case Study for Cell Pair Dynamics
Frascoli, F., Hughes, B. D., Zaman, M. H., & Landman, K. A. (2013) · PLoS ONE · doi:10.1371/journal.pone.0059249 · Cited by 22
Quantifying the relationship between cell division angle and morphogenesis through computational modeling
Lejeune, E., & Linder, C. (2017) · Journal of Theoretical Biology · doi:10.1016/j.jtbi.2017.01.026 · Cited by 21
Optimal regulation of tumour-associated neutrophils in cancer progression
Reyes, A. A. D. L., V, & Kim, Y. (2022) · Royal Society Open Science · doi:10.1098/rsos.210705 · Cited by 21
Self-citation
Multiscale modeling of solid stress and tumor cell invasion in response to dynamic mechanical microenvironment
Chen, H., Cai, Y., Chen, Q., & Li, Z. (2019) · Biomechanics and Modeling in Mechanobiology · doi:10.1007/s10237-019-01231-4 · Cited by 21
The Mathematical Analysis of Biological Aggregation and Dispersal: Progress, Problems and Perspectives
Othmer, H. G., & Xue, C. (2013) · Lecture notes in mathematics · doi:10.1007/978-3-642-35497-7_4 · Cited by 20
Self-citation
A Measure-Theoretic Model for Collective Cell Migration and Aggregation
Colombi, A., Scianna, M., & Preziosi, L. (2014) · Mathematical Modelling of Natural Phenomena · doi:10.1051/mmnp/201510101 · Cited by 20
Thermo-elastic properties of random particulate nano-materials for various models of interphase
Nazarenko, L., Stolarski, H. K., & Altenbach, H. (2017) · International Journal of Mechanical Sciences · doi:10.1016/j.ijmecsci.2017.03.021 · Cited by 19
Synergistic Effects of Bortezomib-OV Therapy and Anti-Invasive Strategies in Glioblastoma: A Mathematical Model
Kim, Y., Lee, J.-H., Lee, D., & Othmer, H. G. (2019) · Cancers · doi:10.3390/cancers11020215 · Cited by 18
Self-citation
Strategies in regulating glioblastoma signaling pathways and anti-invasion therapy
Jung, E., Reyes, A. A. D. L., V, Pumares, K. J. A., & Kim, Y. (2019) · PLoS ONE · doi:10.1371/journal.pone.0215547 · Cited by 18
Self-citation
Navigating Multi-Scale Cancer Systems Biology Towards Model-Driven Clinical Oncology and Its Applications in Personalized Therapeutics
Gondal, M. N., & Chaudhary, S. U. (2021) · Frontiers in Oncology · doi:10.3389/fonc.2021.712505 · Cited by 19
Various Mathematical Models of Tumor Growth with Reference to Cancer Stem Cells: A Review
Rivaz, A., Azizian, M., & Soltani, M. (2019) · Iranian Journal of Science and Technology Transactions A Science · doi:10.1007/s40995-019-00681-w · Cited by 18
Generative models of morphogenesis in developmental biology
Stillman, N., & Mayor, R. (2023) · Seminars in Cell and Developmental Biology · doi:10.1016/j.semcdb.2023.02.001 · Cited by 17
Multi-scale interactions in Dictyostelium discoideum aggregation
Dixon, J. A., & Kelty‐Stephen, D. G. (2012) · Physica A Statistical Mechanics and its Applications · doi:10.1016/j.physa.2012.07.001 · Cited by 16
Modeling chemotaxis from $L^2$--closure moments in kinetic theory of active particles
Bellomo, N., Bellouquid, A., Nieto, J., & Soler, J. (2013) · Discrete and Continuous Dynamical Systems - B · doi:10.3934/dcdsb.2013.18.847 · Cited by 14
Modeling the Role of TGF-β in Regulation of the Th17 Phenotype in the LPS-Driven Immune System
Lee, S., Hwang, H. J., & Kim, Y. (2014) · Bulletin of Mathematical Biology · doi:10.1007/s11538-014-9946-6 · Cited by 14
Self-citation
Computational multiscale modeling of embryo development
Krupinski, P., Chickarmane, V. S., & Peterson, C. (2012) · Current Opinion in Genetics & Development · doi:10.1016/j.gde.2012.08.006 · Cited by 14
Validity of the Cauchy-Born rule applied to discrete cellular-scale models of biological tissues
Davit, Y., Osborne, J. M., Byrne, H. M., Gavaghan, D. J., & Pitt‐Francis, J. (2013) · Physical Review E · doi:10.1103/physreve.87.042724 · Cited by 13
Cell resolved, multiparticle model of plastic tissue deformations and morphogenesis
Czirók, A., & Isai, D. G. (2014) · Physical Biology · doi:10.1088/1478-3975/12/1/016005 · Cited by 11
A cell based modelling framework for skeletal tissue engineering applications
Geris, L., Liedekerke, P. V., Smeets, B., Tijskens, E., & Ramón, H. (2009) · Journal of Biomechanics · doi:10.1016/j.jbiomech.2009.11.010 · Cited by 11
Data-driven spatio-temporal modelling of glioblastoma
Jørgensen, A. C. S., Hill, C. S., Sturrock, M., Tang, W., Karamched, S. R., Gorup, D., Lythgoe, M. F., Parrinello, S., Marguerat, S., & Shahrezaei, V. (2023) · Royal Society Open Science · doi:10.1098/rsos.221444 · Cited by 12
Simulation of lamellipodial fragments
Oelz, D., & Schmeiser, C. (2011) · Journal of Mathematical Biology · doi:10.1007/s00285-011-0421-9 · Cited by 10
Equation-Based Models of Wound Healing and Collective Cell Migration
Arciero, J. C., & David Swigon, A. (2013) · Springer eBooks · doi:10.1007/978-1-4614-8008-2_11 · Cited by 10
Modeling Morphodynamic Phenotypes and Dynamic Regimes of Cell Motion
Enculescu, M., & Falcke, M. (2011) · Advances in experimental medicine and biology · doi:10.1007/978-1-4419-7210-1_20 · Cited by 9
Modelling Keloids Dynamics: A Brief Review and New Mathematical Perspectives
Eftimie, R., Rolin, G., Adebayo, O. E., Urcun, S., Chouly, F., & Bordas, S. (2023) · Bulletin of Mathematical Biology · doi:10.1007/s11538-023-01222-8 · Cited by 9
Computational mechano-chemo-biology: a tool for the design of tissue scaffolds
García‐Aznar, J. M., Valero, C., Borau, C., & Garijo, N. (2016) · Biomanufacturing Reviews · doi:10.1007/s40898-016-0002-1 · Cited by 8
TISON: a next-generation multi-scale modeling theatre for in silico systems oncologyPreprint
Gondal, M. N., Sultan, M. U., Arif, A., Basharat, A. R., Awan, H. A., Arshad, Z., Ahmed, W., Chaudhary, M. F., Khan, S., Tanveer, Z. B., et al. (2021) · bioRxiv (Cold Spring Harbor Laboratory) · doi:10.1101/2021.05.04.442539 · Cited by 7
Role of senescent tumor cells in building a cytokine shield in the tumor microenvironment: mathematical modeling
Kim, Y., Lee, J.-H., Lee, C., & Lawler, S. E. (2022) · Journal of Mathematical Biology · doi:10.1007/s00285-022-01850-z · Cited by 7
Self-citation
Mathematical and Physical Modeling of Actin Dynamics in Motile Cells
Carlsson, A. E., & Mogilner, A. (2010) · Springer eBooks · doi:10.1007/978-90-481-9301-1_16 · Cited by 6
Capturing the Dynamics of a Hybrid Multiscale Cancer Model with a Continuum Model
Joshi, T. V., Avitabile, D., & Owen, M. R. (2018) · Bulletin of Mathematical Biology · doi:10.1007/s11538-018-0406-6 · Cited by 6
Biomechanical modelling of tumor growth with chemotherapeutic treatment: a review
Xu, J., Wang, Y., Gómez, H., & Feng, X. (2023) · Smart Materials and Structures · doi:10.1088/1361-665x/acf79a · Cited by 6
Interactive Visualization Tool for Planning Cancer Treatment
Wcisło, R., Dzwinel, W., Gosztyła, P., Yuen, D. A., & Czech, W. (2013) · Lecture notes in earth system sciences · doi:10.1007/978-3-642-16405-7_38 · Cited by 6
A multiscale model for heterogeneous tumor spheroid in vitro
Chen, Z., & Zou, Y. (2017) · Mathematical Biosciences & Engineering · doi:10.3934/mbe.2018016 · Cited by 7
The role of the microenvironment in regulation of CSPG-driven invasive and non-invasive tumor growth in glioblastoma
Lee, H. G., & Kim, Y. (2015) · Japan Journal of Industrial and Applied Mathematics · doi:10.1007/s13160-015-0188-2 · Cited by 7
Self-citation
Traveling Waves in a One-Dimensional Elastic Continuum Model of Cell Layer Migration with Stretch-Dependent Proliferation
Stepien, T. L., & David Swigon, A. (2014) · SIAM Journal on Applied Dynamical Systems · doi:10.1137/130941407 · Cited by 5
Mechanical irreversibility of active deformations: analytical and numerical analyses
Allena, R. (2026) · Mathematics and Mechanics of Complex Systems · doi:10.2140/memocs.2026.14.181 · Cited by 4
Field models in low-frequency bioelectromagnetics
Mognaschi, M. E. (2016) · PRZEGLĄD ELEKTROTECHNICZNY · doi:10.15199/48.2016.12.01 · Cited by 4
Broad-tailed force distributions and velocity ordering in a heterogeneous membrane model for collective cell migration
Bameta, T., Das, D., Sarkar, S., Das, D., & Inamdar, M. M. (2012) · Europhysics Letters (EPL) · doi:10.1209/0295-5075/99/18004 · Cited by 4
Bayesian Uncertainty Quantification for Particle-Based Simulation of Lipid Bilayer Membranes
Bowman, C., Larson, K. A., Roitershtein, A., Stein, D., & Anastasios Matzavinos, A. (2018) · Modeling and simulation in science, engineering & technology · doi:10.1007/978-3-319-96842-1_4 · Cited by 4
Modeling biological materials with peridynamics
Lejeune, E., & Linder, C. (2021) · Elsevier eBooks · doi:10.1016/b978-0-12-820069-8.00005-6 · Cited by 4
Verruciform xanthoma of the earlobe in an immunosuppressed patient.
Aldabagh, B., Al‐Dabagh, A., Usmani, A. S., & Puri, P. K. (2013) · PubMed · Cited by 4
“Active” drops as phantom models for living cells: a mesoscopic particle-based approach
Dallavalle, M., Lugli, F., Rapino, S., & Zerbetto, F. (2016) · Soft Matter · doi:10.1039/c5sm02686e · Cited by 3
An enzyme kinetics model of tumor dormancy, regulationof secondary metastases
Kim, Y., & Boushaba, K. (2011) · Discrete and Continuous Dynamical Systems - S · doi:10.3934/dcdss.2011.4.1465 · Cited by 2
Self-citation
Morphogenesis modelization of a fractone-based model
Chyba, M., & Tamura-Sato, A. (2016) · Discrete and Continuous Dynamical Systems - B · doi:10.3934/dcdsb.2017002 · Cited by 2
Selected aspects of avascular tumor growth reproduced by a hybrid model of cell dynamics and chemical kinetics
Scianna, M. (2024) · Mathematical Biosciences · doi:10.1016/j.mbs.2024.109168 · Cited by 2
The role of contact inhibition in intratumoral heterogeneity: An off-lattice individual based modelPreprint
Gallaher, J. A., & Anderson, A. R. A. (2016) · bioRxiv (Cold Spring Harbor Laboratory) · doi:10.1101/036467 · Cited by 2
Elementary Concepts and Definitions
Brosseau, C. (2023) · Studies in mechanobiology, tissue engineering and biomaterials · doi:10.1007/978-3-031-37981-9_2 · Cited by 2
Neural networks for emergent behavior in biological microstructures
Kumar, M., Sgarrella, J., & Peco, C. (2024) · Engineering Computations · doi:10.1108/ec-11-2023-0792 · Cited by 1
Simulated embryonic and fetal cellular dynamics inside structured biomaterials
Green, D. W., Watson, G. S., Watson, J. A., Lee, J., & Jung, H.-S. (2018) · Applied Materials Today · doi:10.1016/j.apmt.2017.12.007 · Cited by 1
A multiscale computational framework for the development of spines in molluscan shells
Moulton, D. E., Aubert-Kato, N., Almet, A. A., & Sato, A. (2024) · PLoS Computational Biology · doi:10.1371/journal.pcbi.1011835 · Cited by 1
Multi-scale based software for effective analysis of anticancer drug efficacy in a computer simulated target environment
Sheraton, V. M. (2019) · DR-NTU (Nanyang Technological University) · doi:10.32657/10356/105587 · Cited by 1
Actin Cytoskeleton, Multi-scale Modeling
Othmer, H. G. (2015) · Springer eBooks · doi:10.1007/978-3-540-70529-1_60 · Cited by 1
Self-citation
Multi-scale whole-plant model of arabidopsis growth to flowering
Chew, Y. H. (2013) · ERA · Cited by 1
Self-Organization in Cells II: Reaction-Diffusion Models
Bressloff, P. C. (2014) · Interdisciplinary applied mathematics · doi:10.1007/978-3-319-08488-6_9
Evaluation of material mechanical properties influence on single cell mechanics
Panzetta, V. (2011)
Efficient and extendible class scheme for the combined reaction–diffusion of multiple molecular species
Stella, S., Chignola, R., & Milotti, E. (2013) · Computer Physics Communications · doi:10.1016/j.cpc.2013.11.014
Mechanical Sensing of Living Systems — From Statics to Dynamics
Argoul, F., Audit, B., & Arnéodo, A. (2015) · InTech eBooks · doi:10.5772/60883
A Hybrid Cellular Automata Model for the Role of Reactive Oxygen Species in Novel Tumour Treatments Strategies
May, B. (2015) · UWSpace (University of Waterloo)
An Effective Numerical Calculation Method for Multi-Time-Scale Mathematical Models in Systems Biology
Motomura, Y., Hamada, H., & Okamoto, M. (2016) · Applied Mathematics · doi:10.4236/am.2016.717178
Multiscale phenomena and patterns in biological systems: special issue in honour of Hans Othmer
Hillen, T., Painter, K. J., Stolarska, M., & Xue, C. (2020) · Journal of Mathematical Biology · doi:10.1007/s00285-020-01473-2
Self-citation
Cell Migration, Biomechanics
Preziosi, L. (2015) · Springer eBooks · doi:10.1007/978-3-540-70529-1_69
Modern Modeling of Single-Cell Migration: From Membrane Tension and Galvanotaxis to Machine LearningPreprint
Shi, W., & Mogilner, A. (2025) · Cold Spring Harbor Perspectives in Biology · doi:10.1101/cshperspect.a041745
Receptor-structured modelling of EGFR-driven tumor initiation: from spatially resolved cell-based simulations to reduced population dynamicsPreprint
Qasim, R., & Bouchnita, A. (2026) · bioRxiv (Cold Spring Harbor Laboratory) · doi:10.64898/2026.06.05.730529

Authors: Stolarska, M. A., Kim, Y., & Othmer, H. G.
Affiliations: University of St. Thomas - Minnesota (US)
Corresponding author: Othmer, Hans G.
ORCID: Stolarska, Magdalena A.
Kim, Yangjin
Othmer, Hans G.
Venue: Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences
Publisher: The Royal Society
Published: 2009-09-13
Volume: 367
Issue: 1902
Pages: 3525-3553
ISSN: 1364-503X (ISSN-L)
1471-2962
DOI: 10.1098/rsta.2009.0095
PMC: PMC3263796
OpenAlex: W2101405933
Cited by: 100
References: 67
Citations by year: 2026: 2 · 2025: 1 · 2024: 4 · 2023: 5 · 2022: 2 · 2021: 4 · 2020: 2 · 2019: 6 · 2018: 4 · 2017: 4 · 2016: 7 · 2015: 7 · 2014: 9 · 2013: 15 · 2012: 7
FWCI: 4.15
Type: journal article
Language: en
Open access: green
www.ncbi.nlm.nih.gov
Licence: royalsociety.org/journals/ethics-policies/data-sharing-mining/ (tdm)
Locations: Philosophical Transactions of the Royal Society A Mathematical Physical and Engineering Sciences (publishedVersion)
PubMed Central (publishedVersion)
PubMed (publishedVersion)
Topics: Life Sciences › Biochemistry, Genetics and Molecular Biology › Cell Biology › Cellular Mechanics and Interactions
Physical Sciences › Mathematics › Modeling and Simulation › Mathematical Biology Tumor Growth
Health Sciences › Medicine › Oncology › Cancer Cells and Metastasis
Keywords: cell mechanics, tissue mechanics, collective cell migration, tumor growth, discrete cell model, actin polymerization, molecular motors, tumor invasion and metastasis, leukocyte migration, multiscale modeling
MeSH terms: Animals, Biomechanical Phenomena, Cell Movement, Elasticity, Humans, Models, Biological, Neoplasms, Mechanotransduction, Cellular, Cell Proliferation

About these checks

Registry, retraction, Cites and statistics results are computed, not judged, with one exception: a printed reference that no index lists is read once by a model before it counts as a citation error. Claims are extracted by a model and kept only when their quote appears verbatim in the text; each cited source is then checked, with a model’s help, for whether it says what the claim relies on. Those verdicts can be wrong — read the claim’s quote and the cited source before relying on one.

Statistics and arithmetic are recomputed, not judged.

Confidence bands are shown only for fields calibrated on our annotated test set. None is calibrated yet, so no band is shown.

What counts as a claim ›How we measure confidence ›How we check this ›

Are you an author, or do you see a problem with this page? Request a review

Multi-scale models of cell and tissue dynamics

Abstract

Overview

Integrity signals

Verification

Claims the paper makes

Claims other papers make about this one

Citations

Cites

Cited by

Related

Metadata

Record

About these checks