Biomechanics and Modeling in Mechanobiology

, Volume 15, Issue 5, pp 1079–1090 | Cite as

Multiscale modelling of solid tumour growth: the effect of collagen micromechanics

  • Peter A. Wijeratne
  • Vasileios Vavourakis
  • John H. Hipwell
  • Chrysovalantis Voutouri
  • Panagiotis Papageorgis
  • Triantafyllos Stylianopoulos
  • Andrew Evans
  • David J. Hawkes
Original Paper


Here we introduce a model of solid tumour growth coupled with a multiscale biomechanical description of the tumour microenvironment, which facilitates the explicit simulation of fibre–fibre and tumour–fibre interactions. We hypothesise that such a model, which provides a purely mechanical description of tumour–host interactions, can be used to explain experimental observations of the effect of collagen micromechanics on solid tumour growth. The model was specified to mouse tumour data, and numerical simulations were performed. The multiscale model produced lower stresses than an equivalent continuum-like approach, due to a more realistic remodelling of the collagen microstructure. Furthermore, solid tumour growth was found to cause a passive mechanical realignment of fibres at the tumour boundary from a random to a circumferential orientation. This is in accordance with experimental observations, thus demonstrating that such a response can be explained as purely mechanical. Finally, peritumoural fibre network anisotropy was found to produce anisotropic tumour morphology. The dependency of tumour morphology on the peritumoural microstructure was reduced by adding a load-bearing non-collagenous component to the fibre network constitutive equation.


Tumour mechanics Microenvironment  Fibre remodelling Finite element analysis 


  1. Ambrosi D, Mollica F (2002) On the mechanics of a growing tumor. Int J Eng Sci 40:1297–1316MathSciNetCrossRefMATHGoogle Scholar
  2. Ambrosi D, Mollica F (2004) The role of stress in the growth of a multicell spheroid. J Math Biol 48:477–499MathSciNetCrossRefMATHGoogle Scholar
  3. Ambrosi D, Preziosi L (2009) Cell adhesion mechanisms and stress relaxation in the mechanics of tumours. Biomech Model Mechanobiol 8:397–413CrossRefGoogle Scholar
  4. Balay S, Gropp WD, McInnes LC, Smith BF (1997) Efficient management of parallelism in object oriented numerical software libraries. In: Bruaset AM, Langtangen HP, Arge E (eds) Modern software tools in scientific computing. Birkhäuser Press, Berlin, pp 163–202CrossRefGoogle Scholar
  5. Barocas V, Tranquillo R (1997) An anisotropic biphasic theory of tissue-equivalent mechanics: the interplay among cell traction, fibrillar network deformation, fibril alignment, and cell contact guidance. J Biomech Eng 119:137–145CrossRefGoogle Scholar
  6. Bathe KJ (1996) Finite element procedures. Prentice Hall, Upper Saddle River, NJMATHGoogle Scholar
  7. Billiar KL, Sacks MS (2000a) Biaxial mechanical properties of the native and glutaraldehyde-treated aortic valve cusp: part I—experimental results. J Biomech Eng 122:23–30CrossRefGoogle Scholar
  8. Billiar KL, Sacks MS (2000b) Biaxial mechanical properties of the native and glutaraldehyde-treated aortic valve cusp: part II—a structural constitutive model. J Biomech Eng 122:327–335CrossRefGoogle Scholar
  9. Butcher DT, Alliston T, Weaver V (2009) A tense situation: forcing tumour progression. Nature 9:108–122Google Scholar
  10. Byrne H (2010) Dissecting cancer through mathematics: from the cell to the animal model. Nat Rev Cancer 10:221–230CrossRefGoogle Scholar
  11. Casciari J, Sotirchos S, Sutherland R (1992) Variations in tumor cell growth rates and metabolism with oxygen concentration, glucose concentration, and extracellular pH. J Cell Physiol 151:386–394CrossRefGoogle Scholar
  12. Chandran PL, Barocas VH (2006) Affine versus non-affine fibril kinematics in collagen networks: theoretical studies of network behavior. J Biomech Eng 128:259–270CrossRefGoogle Scholar
  13. Chandran PL, Barocas VH (2007) Deterministic material-based averaging theory model of collagen gel micromechanics. J Biomech Eng 129:137–147CrossRefGoogle Scholar
  14. Chen CS, Mrksich M, Huang S, Whitesides GM, Ingber DE (1997) Geometric control of cell life and death. Science 276:1425–1428CrossRefGoogle Scholar
  15. Cheng G, Tse J, Jain RK, Munn LL (2009) Micro-environmental mechanical stress controls tumor spheroid size and morphology by suppressing proliferation and inducing apoptosis in cancer cells. PLoS One 4:e4632CrossRefGoogle Scholar
  16. Conklin MW, Keely PJ (2012) Why the stroma matters in breast cancer. Cell Adhes Migration 6:249–260CrossRefGoogle Scholar
  17. Cristini V, Lowengrub J (2010) Multiscale modeling of cancer: an integrated experimental and mathematical modeling approach, chaps 1 and 3, 1st edn. Cambridge University Press, CambridgeCrossRefGoogle Scholar
  18. Discher DE, Janmey P, Wang YL (2005) Tissue cells feel and respond to the stiffness of their substrate. Science 310:1139–1143CrossRefGoogle Scholar
  19. Frieboes H, Chaplain M, Thompson A, Bearer E, Lowengrub J, Cristini V (2011) Physical oncology: a bench-to-bedside quantitative and predictive approach. Cancer Res 71:298–302CrossRefGoogle Scholar
  20. Helmlinger G, Netti PA, Lichtenbeld HC, Melder RJ, Jain RK (1997) Solid stress inhibits the growth of multicellular tumor spheroids. Nat Biotechnol 15:778–783CrossRefGoogle Scholar
  21. Hori M, Nemat-Nasser S (1999) On two micromechanics theories for determining micro–macro relations in heterogeneous solids. Mech Mater 31:667–682CrossRefGoogle Scholar
  22. Hughes TJR (2000) The finite element method: linear static and dynamic finite element analysis, 1st edn. Mineola, NY, Dover PublicationsMATHGoogle Scholar
  23. Jackson TL, Byrne H (2002) A mechanical model of tumor encapsulation and transcapsular spread. Math Biosci 180:307–328MathSciNetCrossRefMATHGoogle Scholar
  24. Jain RK, Martin JD, Stylianopoulos T (2014) The role of mechanical forces in tumor progression and therapy. Ann Rev Biomed Eng 16:321–346CrossRefGoogle Scholar
  25. Janmey PA (1998) The cytoskeleton and cell signaling: component localization and mechanical coupling. Physiol Rev 78:763–781Google Scholar
  26. Kam Y, Rejniak K, Anderson A (2012) Cellular modeling of cancer invasion: integration of in silico and in vitro approaches. J Cell Physiol 227:431–438CrossRefGoogle Scholar
  27. Kim Y, Stolarska MA, Othmer HG (2011) The role of the microenvironment in tumor growth and invasion. Prog Biophys Mol Biol 106:353–379CrossRefGoogle Scholar
  28. Kirk BS, Peterson JW, Stogner RH, Carey GF (2006) libMesh: A C++ library for parallel adaptive mesh refinement/coarsening simulations. Eng Comput 22(3–4):237–254CrossRefGoogle Scholar
  29. Kroon M, Holzapfel GA (2008) A new constitutive model for multi-layered collagenous tissues. J Biomech 41:2766–2771CrossRefGoogle Scholar
  30. Liotta LA, Kohn EC (2001) The microenvironment of the tumour-host interface. Nature 411:375–379CrossRefGoogle Scholar
  31. Lubarda VA, Hoger A (2002) On the mechanics of solids with a growing mass. Int J Solids Struct 39:4627–4664CrossRefMATHGoogle Scholar
  32. Malvern LE (1977) Introduction to the mechanics of a continuous medium, 1st edn. Prentice Hall, Upper Saddle River, NJGoogle Scholar
  33. Mpekris F, Angeli S, Pirentis A, Stylianopoulos T (2015) Stress-mediated progression of solid tumors: effect of mechanical stress on tissue oxygenation, cancer cell proliferation, and drug delivery. Biomech Model Mechanobiol.
  34. Netti PA, Berk DA, Swartz MA, Grodzinsky AJ, Jain RK (2000) Role of extracellular matrix assembly in interstitial transport in solid tumors. Cancer Res 60:2497–2503Google Scholar
  35. Papageorgis P, Lambert A, Ozturk S, Gao F, Pan H, Manne U, Alekseyev Y, Thiagalingam A, Abdolmaleky H, Lenburg M, Thiagalingam S (2010) Smad signaling is required to maintain epigenetic silencing during breast cancer progression. Cancer Res 70:1916–1930CrossRefGoogle Scholar
  36. Paszek MJ, Zahir N, Johnson KR, Lakins JN, Rozenberg GI, Gefen A, Reinhart-King CA, Margulies SS, Dembo M, Boettiger D, Hammer DA, Weaver VM (2005) Tensional homeostasis and the malignant phenotype. Cancer Cell 8:241–254CrossRefGoogle Scholar
  37. Pelham RJ, Wang YL (1997) Cell locomotion and focal adhesions are regulated by substrate flexibility. PNAS 94:13661–13665CrossRefGoogle Scholar
  38. Preziosi L, Ambrosi D, Verdier C (2010) An elasto-visco-plastic model of cell aggregates. J Theor Biol 262:35–47MathSciNetCrossRefGoogle Scholar
  39. Provenzano PP, Eliceiri KW, Campbell JM, Inman DR, White JG, Keely PJ (2006) Collagen reorganization at the tumor-stromal interface facilitates local invasion. BMC Med 4:38CrossRefGoogle Scholar
  40. Rodriguez EK, Hoger A, McCulloch AD (1994) Stress-dependent finite growth in soft elastic tissues. J Biomech 27:455–467CrossRefGoogle Scholar
  41. Santner SJ, Dawson PJ, Tait L, Soule HD, Eliason J, Mohamed AN, Wolman SR, Heppner GH, Miller FR (2001) Malignant MCF10CA1 cell lines derived from premalignant human breast epithelial MCF10AT cells. Breast Cancer Res Treat 65:101–110CrossRefGoogle Scholar
  42. Silver FH, Horvath I, Foran DJ (2001) Viscoelasticity of the vessel wall: the role of collagen and elastin fibers. Crit Rev Biomed Eng 29:279–301CrossRefGoogle Scholar
  43. Stylianopoulos T, Martin JD, Chauhan VP, Jain SR, Diop-Frimpong B, Bardeesy N, Smith BL, Ferrone CR, Hornicek FJ, Boucher Y, Munn LL, Jain RK (2012) Causes, consequences, and remedies for growth-induced solid stress in murine and human tumors. PNAS 109:15101–15108CrossRefGoogle Scholar
  44. Stylianopoulos T, Martin JD, Snuderi M, Mpekris F, Jain SR, Jain RK (2013) Coevolution of solid stress and interstitial fluid pressure in tumors during progression: implications for vascular collapse. Cancer Res 73:3833–3841CrossRefGoogle Scholar
  45. Stylianopoulos T, Barocas VH (2007) Volume-averaging theory for the study of the mechanics of collagen networks. Comput Methods Appl Mech Eng 196:2981–2990MathSciNetCrossRefMATHGoogle Scholar
  46. Veis A (1982) Collagen fibrillogenesis. Connect Tissue Res 10:11–24CrossRefGoogle Scholar
  47. Voutouri C, Mpekris F, Papageorgis P, Odysseos AD, Stylianopoulos T (2014) Role of constitutive behavior and tumor-host mechanical interactions in the state of stress and growth of solid tumors. PLoS One 9(e104):717Google Scholar
  48. Yeung T, Georges PC, Flanagan LA, Marg B, Ortiz M, Funaki M, Zahir N, Ming W, Weaver V, Janmey PA (2005) Effects of substrate stiffness on cell morphology, cytoskeletal structure and adhesion. Cell Motil Cytoskelet 60:24–34CrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2015

Authors and Affiliations

  • Peter A. Wijeratne
    • 1
  • Vasileios Vavourakis
    • 1
  • John H. Hipwell
    • 1
  • Chrysovalantis Voutouri
    • 2
  • Panagiotis Papageorgis
    • 2
  • Triantafyllos Stylianopoulos
    • 2
  • Andrew Evans
    • 3
  • David J. Hawkes
    • 1
  1. 1.Department of Medical Physics and Bioengineering, Centre for Medical Image ComputingUniversity College London, Engineering Front Building, Malet PlaceLondonUK
  2. 2.Cancer Biophysics Laboratory, Department of Mechanical and Manufacturing EngineeringUniversity of CyprusNicosiaCyprus
  3. 3.Ninewells Medical SchoolDundeeUK

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