Computational Models of Sprouting Angiogenesis and Cell Migration: Towards Multiscale Mechanochemical Models of Angiogenesis
Math. Model. Nat. Phenom., 10 1 (2015) 108-141
Published online: 2015-02-13
Articles citing this article
The Citing articles tool gives a list of articles citing the current article.
The citing articles come from EDP Sciences database, as well as other publishers participating in CrossRef Cited-by Linking Program. You can set up your personal account to receive an email alert each time this article is cited by a new article (see the menu on the right-hand side of the abstract page).
Cited article:
This article has been cited by the following article(s):
Generating vascular network structures from real data
João Braz Simões, Rui D.M. Travasso, Tiago Baptista and Ernesto CostaExpert Systems with Applications 299 129941 (2026)
https://doi.org/10.1016/j.eswa.2025.129941
A Particle-Based Model of Endothelial Cell Dynamics in the Extracellular Matrix
Kazuma Sakai, Tatsuya Hayashi, Jun Mada and Tetsuji TokihiroComplexities 1 (1) 3 (2025)
https://doi.org/10.3390/complexities1010003
Representing unsegmented vessels using available vascular data for bioheat transfer simulation
Rohan Amare, Amir A. Bahadori and Steven EckelsFrontiers in Thermal Engineering 5 (2025)
https://doi.org/10.3389/fther.2025.1536410
Investigating Tumour Responses to Combinations of Radiotherapy and Hyperthermia
Chloé Colson, Philip K. Maini and Helen M. ByrneBulletin of Mathematical Biology 87 (8) (2025)
https://doi.org/10.1007/s11538-025-01449-7
(2025)
https://doi.org/10.1101/2025.11.20.689434
Modeling the extracellular matrix in cell migration and morphogenesis: a guide for the curious biologist
Rebecca M. Crossley, Samuel Johnson, Erika Tsingos, Zoe Bell, Massimiliano Berardi, Margherita Botticelli, Quirine J. S. Braat, John Metzcar, Marco Ruscone, Yuan Yin and Robyn ShuttleworthFrontiers in Cell and Developmental Biology 12 (2024)
https://doi.org/10.3389/fcell.2024.1354132
The Statistical Theory of the Angiogenesis Equations
Björn Birnir, Luis Bonilla, Manuel Carretero and Filippo TerragniJournal of Nonlinear Science 34 (2) (2024)
https://doi.org/10.1007/s00332-023-10006-2
Bridging scales: A hybrid model to simulate vascular tumor growth and treatment response
Tobias Duswald, Ernesto A.B.F. Lima, J. Tinsley Oden and Barbara WohlmuthComputer Methods in Applied Mechanics and Engineering 418 116566 (2024)
https://doi.org/10.1016/j.cma.2023.116566
Radiomics Multifactorial in Silico Model for Spatial Prediction of Glioblastoma Progression and Recurrence: A Proof-of-Concept
Sabino Luzzi and Abramo AgostiWorld Neurosurgery 183 e677 (2024)
https://doi.org/10.1016/j.wneu.2024.01.002
Dynamic cluster field modeling of collective chemotaxis
Aditya Shankar Paspunurwar, Adrian Moure and Hector GomezScientific Reports 14 (1) (2024)
https://doi.org/10.1038/s41598-024-75653-1
Computational Insights into the Interplay of Mechanical Forces in Angiogenesis
Ana Guerra, Jorge Belinha, Christiane Salgado, Fernando Jorge Monteiro and Renato Natal JorgeBiomedicines 12 (5) 1045 (2024)
https://doi.org/10.3390/biomedicines12051045
Long-term day-by-day tracking of microvascular networks sprouting in fibrin gels: From detailed morphological analyses to general growth rules
Katarzyna O. Rojek, Antoni Wrzos, Stanisław Żukowski, Michał Bogdan, Maciej Lisicki, Piotr Szymczak and Jan GuzowskiAPL Bioengineering 8 (1) (2024)
https://doi.org/10.1063/5.0180703
Computational modeling of angiogenesis: The importance of cell rearrangements during vascular growth
Daria Stepanova, Helen M. Byrne, Philip K. Maini and Tomás AlarcónWIREs Mechanisms of Disease 16 (2) (2024)
https://doi.org/10.1002/wsbm.1634
Modelling of chemotactic sprouting endothelial cells through an extracellular matrix
Josep Ferre-Torres, Adria Noguera-Monteagudo, Adrian Lopez-Canosa, J. Roberto Romero-Arias, Rafael Barrio, Oscar Castaño and Aurora Hernandez-MachadoFrontiers in Bioengineering and Biotechnology 11 (2023)
https://doi.org/10.3389/fbioe.2023.1145550
(2023)
https://doi.org/10.1101/2023.09.02.555959
External mechanical loading overrules cell-cell mechanical communication in sprouting angiogenesis during early bone regeneration
Chiara Dazzi, Julia Mehl, Mounir Benamar, Holger Gerhardt, Petra Knaus, Georg N. Duda, Sara Checa and Roeland M. H. MerksPLOS Computational Biology 19 (11) e1011647 (2023)
https://doi.org/10.1371/journal.pcbi.1011647
Soliton approximation in continuum models of leader-follower behavior
F. Terragni, W. D. Martinson, M. Carretero, P. K. Maini and L. L. BonillaPhysical Review E 108 (5) (2023)
https://doi.org/10.1103/PhysRevE.108.054407
Approaches to vascular network, blood flow, and metabolite distribution modeling in brain tissue
Veronika Kopylova, Stanislav Boronovskiy and Yaroslav NartsissovBiophysical Reviews 15 (5) 1335 (2023)
https://doi.org/10.1007/s12551-023-01106-0
An image-informed Cahn–Hilliard Keller–Segel multiphase field model for tumor growth with angiogenesis
A. Agosti, A. Giotta Lucifero and S. LuzziApplied Mathematics and Computation 445 127834 (2023)
https://doi.org/10.1016/j.amc.2023.127834
Tissue-growth-based synthetic tree generation and perfusion simulation
Hyun Jin Kim, Hans Christian Rundfeldt, Inpyo Lee and Seungmin LeeBiomechanics and Modeling in Mechanobiology 22 (3) 1095 (2023)
https://doi.org/10.1007/s10237-023-01703-8
Using a meshless method to assess the effect of mechanical loading in angiogenesis
Ana Guerra, Jorge Belinha and Renato Natal JorgeMathematics and Computers in Simulation 202 421 (2022)
https://doi.org/10.1016/j.matcom.2022.05.039
Systems biology of angiogenesis signaling: Computational models and omics
Yu Zhang, Hanwen Wang, Rebeca Hannah M. Oliveira, Chen Zhao and Aleksander S. PopelWIREs Mechanisms of Disease 14 (4) (2022)
https://doi.org/10.1002/wsbm.1550
A multiscale cell‐based model of tumor growth for chemotherapy assessment and tumor‐targeted therapy through a 3D computational approach
Sahar Jafari Nivlouei, Madjid Soltani, Ebrahim Shirani, Mohammad Reza Salimpour, Rui Travasso and João CarvalhoCell Proliferation 55 (3) (2022)
https://doi.org/10.1111/cpr.13187
A Method to Coarse-Grain MultiAgent Stochastic Systems with Regions of Multistability
Daria Stepanova, Helen M. Byrne, Philip K. Maini and Tomás AlarcónMultiscale Modeling & Simulation 20 (1) 404 (2022)
https://doi.org/10.1137/21M1418575
Positivity preserving high order schemes for angiogenesis models
A. Carpio and E. CebrianInternational Journal of Nonlinear Sciences and Numerical Simulation 23 (6) 917 (2022)
https://doi.org/10.1515/ijnsns-2021-0112
A vasculogenesis model based on flow-induced stresses on endothelial cells
Pooya Abdi and Bahman VahidiAIP Advances 12 (5) (2022)
https://doi.org/10.1063/5.0087884
On the role of mechanical signals on sprouting angiogenesis through computer modeling approaches
Tamer Abdalrahman and Sara ChecaBiomechanics and Modeling in Mechanobiology 21 (6) 1623 (2022)
https://doi.org/10.1007/s10237-022-01648-4
In Vitro, In Vivo, and In Silico Models of Lymphangiogenesis in Solid Malignancies
Sophie Bekisz, Louis Baudin, Florence Buntinx, Agnès Noël and Liesbet GerisCancers 14 (6) 1525 (2022)
https://doi.org/10.3390/cancers14061525
Biologically-Based Mathematical Modeling of Tumor Vasculature and Angiogenesis via Time-Resolved Imaging Data
David A. Hormuth, Caleb M. Phillips, Chengyue Wu, Ernesto A. B. F. Lima, Guillermo Lorenzo, Prashant K. Jha, Angela M. Jarrett, J. Tinsley Oden and Thomas E. YankeelovCancers 13 (12) 3008 (2021)
https://doi.org/10.3390/cancers13123008
Comparative analysis of continuum angiogenesis models
W. Duncan Martinson, Hirokazu Ninomiya, Helen M. Byrne and Philip K. MainiJournal of Mathematical Biology 82 (4) (2021)
https://doi.org/10.1007/s00285-021-01570-w
Multiscale modeling of tumor growth and angiogenesis: Evaluation of tumor-targeted therapy
Sahar Jafari Nivlouei, M. Soltani, João Carvalho, et al.PLOS Computational Biology 17 (6) e1009081 (2021)
https://doi.org/10.1371/journal.pcbi.1009081
Functional angiogenesis requires microenvironmental cues balancing endothelial cell migration and proliferation
William Y. Wang, Daphne Lin, Evan H. Jarman, William J. Polacheck and Brendon M. BakerLab on a Chip 20 (6) 1153 (2020)
https://doi.org/10.1039/C9LC01170F
Angiogenic Networks in Tumors—Insights via Mathematical Modeling
Mohsen Dorraki, Anahita Fouladzadeh, Andrew Allison, Claudine S. Bonder and Derek AbbottIEEE Access 8 43215 (2020)
https://doi.org/10.1109/ACCESS.2020.2977062
Evaluating snail-trail frameworks for leader-follower behavior with agent-based modeling
W. Duncan Martinson, Helen M. Byrne and Philip K. MainiPhysical Review E 102 (6) (2020)
https://doi.org/10.1103/PhysRevE.102.062417
Integrodifference master equation describing actively growing blood vessels in angiogenesis
Luis L. Bonilla, Manuel Carretero and Filippo TerragniInternational Journal of Nonlinear Sciences and Numerical Simulation 21 (7-8) 705 (2020)
https://doi.org/10.1515/ijnsns-2019-0094
Two dimensional soliton in tumor induced angiogenesis
L L Bonilla, M Carretero and F TerragniJournal of Statistical Mechanics: Theory and Experiment 2020 (8) 083402 (2020)
https://doi.org/10.1088/1742-5468/aba598
(2020)
https://doi.org/10.1101/2020.12.08.411603
Notch signaling and taxis mechanisms regulate early stage angiogenesis: A mathematical and computational model
Rocío Vega, Manuel Carretero, Rui D. M. Travasso, Luis L. Bonilla and Philip K MainiPLOS Computational Biology 16 (1) e1006919 (2020)
https://doi.org/10.1371/journal.pcbi.1006919
A Computational Model of the Endothelial to Mesenchymal Transition
Nathan Weinstein, Luis Mendoza and Elena R. Álvarez-BuyllaFrontiers in Genetics 11 (2020)
https://doi.org/10.3389/fgene.2020.00040
Mathematical models for chemotaxis and their applications in self-organisation phenomena
Kevin J. PainterJournal of Theoretical Biology 481 162 (2019)
https://doi.org/10.1016/j.jtbi.2018.06.019
Stochastic Dynamics Out of Equilibrium
Luis L. Bonilla, Manuel Carretero and Filippo TerragniSpringer Proceedings in Mathematics & Statistics, Stochastic Dynamics Out of Equilibrium 282 413 (2019)
https://doi.org/10.1007/978-3-030-15096-9_13
Computational Modeling to Quantify the Contributions of VEGFR1, VEGFR2, and Lateral Inhibition in Sprouting Angiogenesis
Clemens Kühn and Sara ChecaFrontiers in Physiology 10 (2019)
https://doi.org/10.3389/fphys.2019.00288
(2019)
https://doi.org/10.1101/868497
(2019)
https://doi.org/10.1101/569897
Coupled Mathematical Models for Physical and Biological Nanoscale Systems and Their Applications
Luis L. Bonilla, M. Carretero and F. TerragniSpringer Proceedings in Mathematics & Statistics, Coupled Mathematical Models for Physical and Biological Nanoscale Systems and Their Applications 232 97 (2018)
https://doi.org/10.1007/978-3-319-76599-0_6
Capillary network formation from dispersed endothelial cells: Influence of cell traction, cell adhesion, and extracellular matrix rigidity
João R. D. Ramos, Rui Travasso and João CarvalhoPhysical Review E 97 (1) (2018)
https://doi.org/10.1103/PhysRevE.97.012408
Translational models of tumor angiogenesis: A nexus of in silico and in vitro models
Shirin Soleimani, Milad Shamsi, Mehran Akbarpour Ghazani, Hassan Pezeshgi Modarres, Karolina Papera Valente, Mohsen Saghafian, Mehdi Mohammadi Ashani, Mohsen Akbari and Amir Sanati-NezhadBiotechnology Advances 36 (4) 880 (2018)
https://doi.org/10.1016/j.biotechadv.2018.01.013
Computational modelling suggests complex interactions between interstitial flow and tumour angiogenesis
Guillermo Vilanova, Miguel Burés, Ignasi Colominas and Hector GomezJournal of The Royal Society Interface 15 (146) 20180415 (2018)
https://doi.org/10.1098/rsif.2018.0415
Stem Cell Sources and Graft Material for Vascular Tissue Engineering
Dorothee Hielscher, Constanze Kaebisch, Benedikt Julius Valentin Braun, Kevin Gray and Edda TobiaschStem Cell Reviews and Reports 14 (5) 642 (2018)
https://doi.org/10.1007/s12015-018-9825-x
Study on the tumor‐induced angiogenesis using mathematical models
Takashi Suzuki, Dhisa Minerva, Koichi Nishiyama, Naohiko Koshikawa and Mark Andrew Joseph ChaplainCancer Science 109 (1) 15 (2018)
https://doi.org/10.1111/cas.13395
Angiogenic Factors produced by Hypoxic Cells are a leading driver of Anastomoses in Sprouting Angiogenesis–a computational study
Maurício Moreira-Soares, Rita Coimbra, Luís Rebelo, João Carvalho and Rui D. M. TravassoScientific Reports 8 (1) (2018)
https://doi.org/10.1038/s41598-018-27034-8
Modelling of retinal vasculature based on genetically tuned parametric L-system
Seyed Mohammad Ali Aghamirmohammadali, Ramin Bozorgmehry Boozarjomehry and Mohammad AbdekhodaieRoyal Society Open Science 5 (5) 171639 (2018)
https://doi.org/10.1098/rsos.171639
A convergent numerical scheme for integrodifferential kinetic models of angiogenesis
Luis L. Bonilla, Ana Carpio, Manuel Carretero, et al.Journal of Computational Physics 375 1270 (2018)
https://doi.org/10.1016/j.jcp.2018.09.008
Ensemble Averages, Soliton Dynamics and Influence of Haptotaxis in a Model of Tumor-Induced Angiogenesis
Luis Bonilla, Manuel Carretero and Filippo TerragniEntropy 19 (5) 209 (2017)
https://doi.org/10.3390/e19050209
A Network Model to Explore the Effect of the Micro-environment on Endothelial Cell Behavior during Angiogenesis
Nathan Weinstein, Luis Mendoza, Isidoro Gitler and Jaime KlappFrontiers in Physiology 8 (2017)
https://doi.org/10.3389/fphys.2017.00960
An angiogenesis platform using a cubic artificial eggshell with patterned blood vessels on chicken chorioallantoic membrane
Wenjing Huang, Makoto Itayama, Fumihito Arai, et al.PLOS ONE 12 (4) e0175595 (2017)
https://doi.org/10.1371/journal.pone.0175595
Constructing solutions for a kinetic model of angiogenesis in annular domains
Ana Carpio, Gema Duro and Mihaela NegreanuApplied Mathematical Modelling 45 303 (2017)
https://doi.org/10.1016/j.apm.2016.12.028
Stochastic model of tumor-induced angiogenesis: Ensemble averages and deterministic equations
F. Terragni, M. Carretero, V. Capasso and L. L. BonillaPhysical Review E 93 (2) (2016)
https://doi.org/10.1103/PhysRevE.93.022413
Hybrid Modelling in Biology: a Classification Review
A. Stéphanou, V. Volpert and V. VolpertMathematical Modelling of Natural Phenomena 11 (1) 37 (2016)
https://doi.org/10.1051/mmnp/201611103
Soliton driven angiogenesis
L. L. Bonilla, M. Carretero, F. Terragni and B. BirnirScientific Reports 6 (1) (2016)
https://doi.org/10.1038/srep31296
Solitonlike attractor for blood vessel tip density in angiogenesis
L. L. Bonilla, M. Carretero and F. TerragniPhysical Review E 94 (6) (2016)
https://doi.org/10.1103/PhysRevE.94.062415
Hybrid Modelling in Cell Biology
A. Stéphanou, V. Volpert, A. Stephanou and V. VolpertMathematical Modelling of Natural Phenomena 10 (1) 1 (2015)
https://doi.org/10.1051/mmnp/201510100
The Force at the Tip - Modelling Tension and Proliferation in Sprouting Angiogenesis
Patrícia Santos-Oliveira, António Correia, Tiago Rodrigues, et al.PLOS Computational Biology 11 (8) e1004436 (2015)
https://doi.org/10.1371/journal.pcbi.1004436