Papers
Topics
Authors
Recent
Search
2000 character limit reached

An in-silico approach to meniscus tissue regeneration: Modeling, numerical simulation, and experimental analysis

Published 9 Mar 2024 in q-bio.TO, cs.NA, math.AP, math.NA, q-bio.CB, and q-bio.QM | (2403.05909v1)

Abstract: We develop a model the dynamics of human mesenchymal stem cells (hMSCs) and chondrocytes evolving in a nonwoven polyethylene terephtalate (PET) scaffold impregnated with hyaluron and supplied with a differentiation medium. The scaffold and the cells are assumed to be contained in a bioreactor with fluid perfusion. The differentiation of hMSCs into chondrocytes favors the production of extracellular matrix (ECM) and is influenced by fluid stress. The model takes deformations of ECM and PET scaffold into account. The scaffold structure is explicitly included by statistical assessment of the fibre distribution from CT images. The effective macroscopic equations are obtained by appropriate upscaling from dynamics on lower (microscopic and mesoscopic) scales and feature in the motility terms an explicit cell diffusion tensor encoding the assessed anisotropic scaffold structure. Numerical simulations show its influence on the overall cell and tissue dynamics.

Definition Search Book Streamline Icon: https://streamlinehq.com
References (77)
  1. “Cell differentiation by mechanical stress” In The FASEB Journal 16.2 Wiley Online Library, 2002, pp. 1–13
  2. “A Lagrange multiplier method for a Stokes–Biot fluid–poroelastic structure interaction model” In Numerische Mathematik 140.2 Springer ScienceBusiness Media LLC, 2018, pp. 513–553 DOI: 10.1007/s00211-018-0967-1
  3. A Andreykiv, F Van Keulen and PJ Prendergast “Simulation of fracture healing incorporating mechanoregulation of tissue differentiation and dispersal/proliferation of cells” In Biomechanics and modeling in mechanobiology 7 Springer, 2008, pp. 443–461
  4. “Multiphase Models of Tumour Growth” In Selected Topics in Cancer Modeling: Genesis - Evolution - Immune Competition - Therapy Springer, 2008, pp. 1–31 DOI: 10.1007/978-0-8176-4713-1˙9
  5. Adam C AufderHeide and Kyriacos A Athanasiou “Mechanical stimulation toward tissue engineering of the knee meniscus” In Annals of biomedical engineering 32 Springer, 2004, pp. 1163–1176
  6. Alicia Bailón-Plaza and Marjolein C.H. Meulen “A Mathematical Framework to Study the Effects of Growth Factor Influences on Fracture Healing” In Journal of Theoretical Biology 212.2 Elsevier BV, 2001, pp. 191–209 DOI: 10.1006/jtbi.2001.2372
  7. V. H. Barocas and R. T. Tranquillo “An Anisotropic Biphasic Theory of Tissue-Equivalent Mechanics: The Interplay Among Cell Traction, Fibrillar Network Deformation, Fibril Alignment, and Cell Contact Guidance” In Journal of Biomechanical Engineering 119.2 ASME International, 1997, pp. 137–145 DOI: 10.1115/1.2796072
  8. V. H. Barocas and R. T. Tranquillo “Biphasic Theory and In Vitro Assays of Cell-Fibril Mechanical Interactions in Tissue-Equivalent Gels” In Cell Mechanics and Cellular Engineering Springer New York, 1994, pp. 185–209 DOI: 10.1007/978-1-4613-8425-0˙12
  9. Victor H Barocas and Robert T Tranquillo “An anisotropic biphasic theory of tissue-equivalent mechanics: the interplay among cell traction, fibrillar network deformation, fibril alignment, and cell contact guidance”, 1997
  10. “A quest towards a mathematical theory of living systems” Springer, 2017
  11. “Toward a mathematical theory of Keller–Segel models of pattern formation in biological tissues” In Mathematical Models and Methods in Applied Sciences 25.09 World Scientific, 2015, pp. 1663–1763
  12. Edoardo Borgiani, Georg N. Duda and Sara Checa “Multiscale Modeling of Bone Healing: Toward a Systems Biology Approach” In Frontiers in Physiology 8 Frontiers Media SA, 2017 DOI: 10.3389/fphys.2017.00287
  13. “Partitioning strategies for the interaction of a fluid with a poroelastic material based on a Nitsche’s coupling approach” In Computer Methods in Applied Mechanics and Engineering 292 Elsevier BV, 2015, pp. 138–170 DOI: 10.1016/j.cma.2014.10.047
  14. Kelly Campbell, Shailesh Naire and Jan Herman Kuiper “A mathematical model of cartilage regeneration after chondrocyte and stem cell implantation – I: the effects of growth factors” In Journal of Tissue Engineering 10 SAGE Publications, 2019, pp. 204173141982779 DOI: 10.1177/2041731419827791
  15. Kelly Campbell, Shailesh Naire and Jan Herman Kuiper “A mathematical model of cartilage regeneration after chondrocyte and stem cell implantation – II: the effects of co-implantation” In Journal of Tissue Engineering 10 SAGE Publications, 2019, pp. 204173141982779 DOI: 10.1177/2041731419827792
  16. “Mathematical models for cell migration: a non-local perspective” In Philosophical Transactions of the Royal Society B: Biological Sciences 375.1807 The Royal Society, 2020, pp. 20190379 DOI: 10.1098/rstb.2019.0379
  17. “Stochastic geometry and its applications” John Wiley & sons, 2013
  18. “Mathematical modeling of glioma invasion and therapy approaches via kinetic theory of active particles” In Mathematical Models and Methods in Applied Sciences World Scientific, 2023, pp. 1–43
  19. “Mathematical modeling of glioma invasion: acid-and vasculature mediated go-or-grow dichotomy and the influence of tissue anisotropy” In Applied Mathematics and Computation 407 Elsevier, 2021, pp. 126305
  20. “Modeling glioma invasion with anisotropy-and hypoxia-triggered motility enhancement: From subcellular dynamics to macroscopic PDEs with multiple taxis” In Mathematical Models and Methods in Applied Sciences 31.01 World Scientific, 2021, pp. 177–222
  21. “Multiscale modeling of glioma invasion: from receptor binding to flux-limited macroscopic PDEs” In Multiscale Modeling & Simulation 20.2 SIAM, 2022, pp. 685–713
  22. “Ridges for image analysis” In J. Mathematical Imaging and Vision 4.4, 1994, pp. 353–373. https://doi.org/10.1007/BF01262402 DOI: 10.1007/BF01262402
  23. “Nonlocal and local models for taxis in cell migration: a rigorous limit procedure” In Journal of Mathematical Biology 81 Springer, 2020, pp. 1251–1298
  24. “Glioma follow white matter tracts: a multiscale DTI-based model” In Journal of mathematical biology 71 Springer, 2015, pp. 551–582
  25. Christian Engwer, Alexander Hunt and Christina Surulescu “Effective equations for anisotropic glioma spread with proliferation: a multiscale approach and comparisons with previous settings” In Mathematical medicine and biology: a journal of the IMA 33.4 Oxford University Press, 2016, pp. 435–459
  26. “Mathematical Analysis of Two Competing Cancer Cell Migration Mechanisms Driven by Interstitial Fluid Flow” In Journal of Nonlinear Science 30.4 Springer ScienceBusiness Media LLC, 2020, pp. 1809–1847 DOI: 10.1007/s00332-020-09625-w
  27. Niamh Fahy, Mauro Alini and Martin J Stoddart “Mechanical stimulation of mesenchymal stem cells: Implications for cartilage tissue engineering” In Journal of Orthopaedic Research 36.1 Wiley Online Library, 2018, pp. 52–63
  28. N. I. Fisher, Toby Lewis and B. J. J. Embleton “Statistical Analysis of Spherical Data” Cambridge [Cambridgeshire] ; New York: Cambridge University Press, 1987
  29. “Toward scaffold-based meniscus repair: effect of human serum, hyaluronic acid and TGF-ß3 on cell recruitment and re-differentiation” In Osteoarthritis and Cartilage 21.5 Elsevier, 2013, pp. 773–781
  30. “Angiogenesis in bone fracture healing: a bioregulatory model” In Journal of theoretical biology 251.1 Elsevier, 2008, pp. 137–158
  31. “Structural properties of scaffolds: crucial parameters towards stem cells differentiation” In World journal of stem cells 7.4 Baishideng Publishing Group Inc, 2015, pp. 728
  32. E. Grosjean, B. Simeon and C. Surulescu “A mathematical model for meniscus cartilage regeneration” In PAMM 23.3 Wiley, 2023 DOI: 10.1002/pamm.202300261
  33. “Influence of fracture gap size on the pattern of long bone healing: a computational study” In Journal of Theoretical Biology 235.1 Elsevier BV, 2005, pp. 105–119 DOI: 10.1016/j.jtbi.2004.12.023
  34. “A mathematical analysis for indentation tests of articular cartilage” In Journal of Biomechanics 5.5 Elsevier BV, 1972, pp. 541–551 DOI: 10.1016/0021-9290(72)90010-3
  35. “A multiphase multiscale model for nutrient-limited tissue growth, part II: a simplified description” In The ANZIAM Journal 61.4 Cambridge University Press (CUP), 2019, pp. 368–381 DOI: 10.1017/s1446181119000130
  36. “A biomechanical regulatory model for periprosthetic fibrous-tissue differentiation” In Journal of materials science: Materials in medicine 8.12 Springer-Verlag, Tiergartenstrasse 17 Heidelberg 69121 Germany, 1997, pp. 785–788
  37. Trachette L Jackson and Helen M Byrne “A mechanical model of tumor encapsulation and transcapsular spread” In Mathematical biosciences 180.1-2 Elsevier, 2002, pp. 307–328
  38. Paul A Janmey and Christopher A McCulloch “Cell mechanics: integrating cell responses to mechanical stimuli” In Annu. Rev. Biomed. Eng. 9 Annual Reviews, 2007, pp. 1–34
  39. “An overview of multiphase cartilage mechanical modelling and its role in understanding function and pathology” In journal of the mechanical behavior of biomedical materials 62 Elsevier, 2016, pp. 139–157
  40. “Modeling multiple taxis: tumor invasion with phenotypic heterogeneity, haptotaxis, and unilateral interspecies repellence” In Discr. Cont. Dyn. Syst. B 26, 2021, pp. 443–481
  41. Pawan Kumar, Jing Li and Christina Surulescu “Multiscale modeling of glioma pseudopalisades: contributions from the tumor microenvironment” In Journal of Mathematical Biology 82 Springer, 2021, pp. 1–45
  42. Pawan Kumar, Christina Surulescu and Anna Zhigun “Multiphase modelling of glioma pseudopalisading under acidosis” In arXiv preprint arXiv:2106.15241, 2021
  43. “The influence of mechanical stimuli on articular cartilage tissue engineering” In Topics in tissue engineering 2.2 Expertissues Oulu, Finland, 2006
  44. “Travelling-wave behaviour in a multiphase model of a population of cells in an artificial scaffold” In Journal of Mathematical Biology 55 Springer, 2007, pp. 449–480
  45. “Mathematical modelling of engineered tissue growth using a multiphase porous flow mixture theory” In Journal of Mathematical Biology 52.5 Springer ScienceBusiness Media LLC, 2006, pp. 571–594 DOI: 10.1007/s00285-005-0363-1
  46. “On a class of multiscale cancer cell migration models: Well-posedness in less regular function spaces” In Mathematical Models and Methods in Applied Sciences 24.12 World Scientific Pub Co Pte Lt, 2014, pp. 2383–2436 DOI: 10.1142/s0218202514500249
  47. “Regional multilineage differentiation potential of meniscal fibrochondrocytes: implications for meniscus repair” In The Anatomical Record: Advances in Integrative Anatomy and Evolutionary Biology: Advances in Integrative Anatomy and Evolutionary Biology 290.1 Wiley Online Library, 2007, pp. 48–58
  48. “Chemotaxis of human articular chondrocytes and mesenchymal stem cells” In Journal of Orthopaedic Research 26.10 Wiley Online Library, 2008, pp. 1407–1412
  49. Shimi Chettiparambil Mohanan, Nishith Mohan and Christina Surulescu “On a mathematical model for tissue regeneration” In arXiv:2403.04516, 2024 DOI: 10.48550/arXiv.2403.04516
  50. Seyed Jamaleddin Mousavi and Mohamed Hamdy Doweidar “Role of mechanical cues in cell differentiation and proliferation: a 3D numerical model” In PloS one 10.5 Public Library of Science San Francisco, CA USA, 2015, pp. e0124529
  51. Van C. Mow and R. Huiskes “Structure and function of articular cartilage and meniscus” In Basic Orthopaedic Biomechanics & Mechano-Biology. Philadelphia: Lippincott Williams & Wilkins, 2005, pp. 182–257
  52. “3d Images of Materials Structures – Processing and Analysis” Weinheim: Wiley VCH, 2009
  53. Felix Ospald “Contributions to the Simulation and Optimization of the Manufacturing Process and the Mechanical Properties of Short Fiber-Reinforced Plastic Parts”, 2019
  54. Hans G. Othmer and Thomas Hillen “The Diffusion Limit of Transport Equations Derived from Velocity-Jump Processes” In SIAM J. Appl. Math. 61, 2000, pp. 751–775
  55. N. Otsu “A threshold selection method from gray level histograms” In IEEE Trans. Systems, Man and Cybernetics 9, 1979, pp. 62–66
  56. “A multiscale analysis of nutrient transport and biological tissue growthin vitro” In Mathematical Medicine and Biology 32.3 Oxford University Press (OUP), 2014, pp. 345–366 DOI: 10.1093/imammb/dqu015
  57. “Mathematical modelling of glioma growth: the use of diffusion tensor imaging (DTI) data to predict the anisotropic pathways of cancer invasion” In Journal of theoretical biology 323 Elsevier, 2013, pp. 25–39
  58. “Rfast: A Collection of Efficient and Extremely Fast R Functions” R package version 2.0.8, 2023 URL: https://CRAN.R-project.org/package=Rfast
  59. Jong-Hoon Park, Takashi Ushida and Takayuki Akimoto “Control of cell differentiation by mechanical stress” In The journal of physical fitness and sports medicine 2.1 The Japanese Society of Physical FitnessSports Medicine, 2013, pp. 49–62
  60. Daniele Antonio Di Pietro and Alexandre Ern “Mathematical Aspects of Discontinuous Galerkin Methods” Springer Berlin Heidelberg, 2012 DOI: 10.1007/978-3-642-22980-0
  61. “Comparison and error estimation of 3D fibre orientation analysis of computed tomography image data for fibre reinforced composites” In NDT & E Int. 95. https://doi.org/10.1016/j.ndteint.2018.01.001, 2018 DOI: 10.1016/j.ndteint.2018.01.001
  62. Ramón G. Plaza “Derivation of a bacterial nutrient-taxis system with doubly degenerate cross-diffusion as the parabolic limit of a velocity-jump process” In Journal of Mathematical Biology 78.6 Springer ScienceBusiness Media LLC, 2019, pp. 1681–1711 DOI: 10.1007/s00285-018-1323-x
  63. J. V. Pohlmeyer and L. J. Cummings “Cyclic Loading of Growing Tissue in a Bioreactor: Mathematical Model and Asymptotic Analysis” In Bulletin of Mathematical Biology 75.12 Springer ScienceBusiness Media LLC, 2013, pp. 2450–2473 DOI: 10.1007/s11538-013-9902-x
  64. P.J. Prendergast, R. Huiskes and K. Søballe “Biophysical stimuli on cells during tissue differentiation at implant interfaces” In Journal of Biomechanics 30.6 Elsevier BV, 1997, pp. 539–548 DOI: 10.1016/s0021-9290(96)00140-6
  65. “In silico Mechano-Chemical Model of Bone Healing for the Regeneration of Critical Defects: The Effect of BMP-2” In PLOS ONE 10.6 Public Library of Science (PLoS), 2015, pp. e0127722 DOI: 10.1371/journal.pone.0127722
  66. “Magnetic-Responsive Carbon Nanotubes Composite Scaffolds for Chondrogenic Tissue Engineering” In Advanced Healthcare Materials Wiley, 2023 DOI: 10.1002/adhm.202301787
  67. “Osteoarthritis-Related Degeneration Alters the Biomechanical Properties of Human Menisci Before the Articular Cartilage” In Frontiers in Bioengineering and Biotechnology 9 Frontiers Media SA, 2021 DOI: 10.3389/fbioe.2021.659989
  68. “Stress-relaxation response of human menisci under confined compression conditions” In Journal of the Mechanical Behavior of Biomedical Materials 26 Elsevier BV, 2013, pp. 68–80 DOI: 10.1016/j.jmbbm.2013.05.027
  69. “Electromechanical probe and automated indentation maps are sensitive techniques in assessing early degenerated human articular cartilage” In Journal of Orthopaedic Research 35.4 Wiley, 2016, pp. 858–867 DOI: 10.1002/jor.23330
  70. Christian Stinner, Christina Surulescu and Aydar Uatay “Global existence for a go-or-grow multiscale model for tumor invasion with therapy” In Mathematical Models and Methods in Applied Sciences 26.11 World Scientific, 2016, pp. 2163–2201
  71. Christian Stinner, Christina Surulescu and Michael Winkler “Global weak solutions in a PDE-ODE system modeling multiscale cancer cell invasion” In SIAM Journal on Mathematical Analysis 46.3 SIAM, 2014, pp. 1969–2007
  72. David E. Tyler “Statistical analysis for the angular central Gaussian distribution on the sphere” In Biometrika 74.3 Oxford University Press (OUP), 1987, pp. 579–589 DOI: 10.1093/biomet/74.3.579
  73. S. L. Waters, L. J. Schumacher and A. J. El Haj “Regenerative medicine meets mathematical modelling: developing symbiotic relationships” In npj Regenerative Medicine 6.1 Springer ScienceBusiness Media LLC, 2021 DOI: 10.1038/s41536-021-00134-2
  74. “Estimating Fibre Direction Distributions of Reinforced Composites from Tomographic Images” In Image Anal. Stereol. 35.3, 2016, pp. 167–179 http://dx.doi.org/10.5566/ias.1489 DOI: http://dx.doi.org/10.5566/ias.1489
  75. “A novel derivation of rigorous macroscopic limits from a micro-meso description of signal-triggered cell migration in fibrous environments” In SIAM Journal on Applied Mathematics 82.1 SIAM, 2022, pp. 142–167
  76. Anna Zhigun, Christina Surulescu and Alexander Hunt “A strongly degenerate diffusion-haptotaxis model of tumour invasion under the go-or-grow dichotomy hypothesis” In Mathematical Methods in the Applied Sciences 41.6 Wiley Online Library, 2018, pp. 2403–2428
  77. Anna Zhigun, Christina Surulescu and Aydar Uatay “Global existence for a degenerate haptotaxis model of cancer invasion” In Zeitschrift für angewandte Mathematik und Physik 67 Springer, 2016, pp. 1–29
Citations (2)

Summary

No one has generated a summary of this paper yet.

Paper to Video (Beta)

No one has generated a video about this paper yet.

Whiteboard

No one has generated a whiteboard explanation for this paper yet.

Open Problems

We found no open problems mentioned in this paper.

Continue Learning

We haven't generated follow-up questions for this paper yet.

Collections

Sign up for free to add this paper to one or more collections.