level set method; curvature based growth; tissue engineering; scaffold design
Abstract :
[en] Three dimensional (3D) open porous scaffolds are commonly used in tissue engineering (TE) applications to provide an initial template for cell attachment and subsequent cell growth and construct development. The macroscopic geometry of the scaffold is key in determining the kinetics of cell growth and thus in vitro ‘tissue’ formation. In this study we developed a computational framework based on the level set methodology to predict curvature-dependent growth of the cell/extracellular matrix domain within TE constructs. Scaffolds with various geometries (hexagonal, square, triangular) and pore sizes (500 and 1000 µm) were produced in house by additive manufacturing, seeded with human periosteum-derived cells and cultured under static conditions for 14 days. Using the projected tissue area as an output measure, the comparison between the experimental and the numerical results demonstrated a good qualitative and quantitative behavior of the framework. The model in its current form is able to provide important spatio-temporal information on final shape and speed of pore-filling of tissue engineered constructs by cells and extracellular matrix during static culture.
Disciplines :
Engineering, computing & technology: Multidisciplinary, general & others
Author, co-author :
Guyot, Yann ; Université de Liège - ULiège > Département d'aérospatiale et mécanique > Génie biomécanique
papantoniou, Ioannis; KULeuven > Skeletal Biology and Engineering Research Center
Chai, Yoke Chin; KULeuven > Skeletal Biology and Engineering Research Center
Van Bael, Simon; Katholieke Universiteit Leuven - KUL > Division of Production engineering
Schrooten, Jan; Katholieke Universiteit Leuven - KUL > Departement of Mechanical engineering
Geris, Liesbet ; Université de Liège - ULiège > Département d'aérospatiale et mécanique > Génie biomécanique
Language :
English
Title :
A computational model for cell/ECM growth on 3D surfaces using the level set method: a bone tissue engineering case study
Publication date :
April 2014
Journal title :
Biomechanics and Modeling in Mechanobiology
ISSN :
1617-7959
eISSN :
1617-7940
Publisher :
Springer, Germany
Peer reviewed :
Peer Reviewed verified by ORBi
European Projects :
FP7 - 279100 - BRIDGE - Biomimetic process design for tissue regeneration: from bench to bedside via in silico modelling
Funders :
F.R.S.-FNRS - Fonds de la Recherche Scientifique ERC - European Research Council FWO - Fonds Wetenschappelijk Onderzoek Vlaanderen CE - Commission Europ�enne
AlMomani T, Udaykumar HS, Marshall JS, Chandran KB (2008) Micro-scale dynamic simulation of erythrocyte–platelet interaction in blood flow. Ann Biomed Eng 36(6):905–920. doi:10.1007/s10439-008-9478-z
Bidan CM, Kommareddy KP, Rumpler M, Kollmannsberger P, Brechet YJM, Fratzl P, Dunlop JWC (2012) How linear tension converts to curvature: geometric control of bone tissue growth. PloS One 7(5). doi:10.1371/journal.pone.0036336
Bidan CM, Kommareddy KP, Rumpler M, Kollmannsberger P, Fratzl P, Dunlop JW (2013a) Geometry as a factor for tissue growth: towards shape optimization of tissue engineering scaffolds. Adv Healthc Mater 2(1):186–194. doi:10.1002/adhm.201200159
Bidan CM, Wang FM, Dunlop JW (2013) A three-dimensional model for tissue deposition on complex surfaces. Comput Methods Biomech Biomed Eng. doi:10.1080/10255842.2013.774384
Bochev PB, Gunzburger MD, Shadid JN (2004) Stability of the SUPG finite element method for transient advection-diffusion problems. Comput Method Appl Mech 193(23–26):2301–2323. doi:10.1016/j.cma.2004.01.026
Chai YC, Kerckhofs G, Roberts SJ, Van Bael S, Schepers E, Vleugels J, Luyten FP, Schrooten J (2012) Ectopic bone formation by 3D porous calcium phosphate-Ti6Al4V hybrids produced by perfusion electrodeposition. Biomaterials 33(16):4044–4058. doi:10.1016/j.biomaterials.2012.02.026
Chai YC, Roberts SJ, Van Bael S, Chen Y, Luyten FP, Schrooten J (2012b) Multi-level factorial analysis of Ca2+/Pi supplementation as bio-instructive media for in vitro biomimetic engineering of three-dimensional osteogenic hybrids. Tissue Eng Part C Methods 18(2):90–103. doi:10.1089/ten.TEC.2011.0248
De Bari C, Dell’Accio F, Vanlauwe J, Eyckmans J, Khan IM, Archer CW, Jones EA, McGonagle D, Mitsiadis TA, Pitzalis C, Luyten FP (2006) Mesenchymal multipotency of adult human periosteal cells demonstrated by single-cell lineage analysis. Arthr Rheum 54(4):1209–1221. doi:10.1002/art.21753
Dunlop JWC, Fischer FD, Gamsjager E, Fratzl P (2010) A theoretical model for tissue growth in confined geometries. J Mech Phys Solids 58(8):1073–1087. doi:10.1016/j.jmps.2010.04.008
Eyckmans J, Boudou T, Yu X, Chen CS (2011) A Hitchhiker’s guide to mechanobiology. Dev Cell 21(1):35–47. doi:10.1016/j.devcel.2011.06.015
Gamsjager E, Bidan CM, Fischer FD, Fratzl P, Dunlop JW (2013) Modelling the role of surface stress on the kinetics of tissue growth in confined geometries. Acta Biomater 9(3):5531–5543. doi:10.1016/j.actbio.2012.10.020
Grayson WL, Ma T, Bunnell B (2004) Human mesenchymal stem cells tissue development in 3D PET matrices. Biotechnol Progr 20(3):905–912. doi:10.1021/bp034296z
Hecht F (2012) New development in freefem++. J Numer Math 20(3–4):251–265. doi:10.1515/jnum-2012-0013
Higuchi A, Ling QD, Chang Y, Hsu ST, Umezawa A (2013) Physical cues of biomaterials guide stem cell differentiation fate. Chem Rev 113(5):3297–3328. doi:10.1021/cr300426x
Hogea CS, Murray BT, Sethian JA (2006) Simulating complex tumor dynamics from avascular to vascular growth using a general level-set method. J Math Biol 53(1):86–134. doi:10.1007/s00285-006-0378-2
Hollister SJ, Maddox RD, Taboas JM (2002) Optimal design and fabrication of scaffolds to mimic tissue properties and satisfy biological constraints. Biomaterials 23(20):4095–4103
Javierre E, Vuik C, Vermolen F, Segal A, van der Zwaag S (2006) The level set method for solid-solid phase transformations. Numer Math Adv Appl 712–719. doi:10.1007/978-3-540-34288-5_69
Knychala J, Bouropoulos N, Catt CJ, Katsamenis OL, Please CP, Sengers BG (2013) Pore geometry regulates early stage human bone marrow cell tissue formation and organisation. Ann Biomed Eng 41(5):917–930. doi:10.1007/s10439-013-0748-z
Kommareddy KP, Lange C, Rumpler M, Dunlop JWC, Manjubala I, Cui J, Kratz K, Lendlein A, Fratzl P (2010) Two stages in three-dimensional in vitro growth of tissue generated by osteoblastlike cells. Biointerphases 5(2):45–52. doi:10.1116/1.3431524
Lappa M (2003a) The growth and the fluid dynamics of protein crystals and soft organic tissues: models and simulations, similarities and differences. J Theor Biol 224(2):225–240. doi:10.1016/S0022-5193(03)00160-7
Lappa M (2003b) Organic tissues in rotating bioreactors: fluid-mechanical aspects, dynamic growth models, and morphological evolution. Biotechnol Bioeng 84(5):518–532. doi:10.1002/bit.10821
Lappa M (2005) A CFD level-set method for soft tissue growth: theory and fundamental equations. J Biomech 38(1):185–190. doi:10.1016/j.jbiomech.2004.02.037
Lutolf MP, Hubbell JA (2005) Synthetic biomaterials as instructive extracellular microenvironments for morphogenesis in tissue engineering. Nat Biotechnol 23(1):47–55. doi:10.1038/nbt1055
Machacek M, Danuser G (2006) Morphodynamic profiling of protrusion phenotypes. Biophys J 90(4):1439–1452. doi:10.1529/biophysj.105.070383
Melchels FP, Barradas AM, van Blitterswijk CA, de Boer J, Feijen J, Grijpma DW (2010) Effects of the architecture of tissue engineering scaffolds on cell seeding and culturing. Acta Biomater 6(11):4208–4217
Melchels FP, Tonnarelli B, Olivares AL, Martin I, Lacroix D, Feijen J, Wendt DJ, Grijpma DW (2011) The influence of the scaffold design on the distribution of adhering cells after perfusion cell seeding. Biomaterials 32(11):2878–2884. doi:10.1016/j.biomaterials.2011.01.023
Nelson CM, Jean RP, Tan JL, Liu WF, Sniadecki NJ, Spector AA, Chen CS (2005) Emergent patterns of growth controlled by multicellular form and mechanics. Proc Natl Acad Sci USA 102(33):11594–11599. doi:10.1073/pnas.0502575102
Papantoniou I, Sonnaert M, Geris L, Luyten FP, Schrooten J, Kerckhofs G (2013a) Three dimensional characterization of tissue-engineered constructs by contrast enhanced nanofocus computed tomography. Tissue Eng Part C Methods. doi:10.1089/ten.TEC.2013.0041
Papantoniou II, Chai YC, Luyten FP, Schrooten JI (2013b) Process quality engineering for bioreactor-driven manufacturing of tissue-engineered constructs for bone regeneration. Tissue Eng Part C Methods. doi:10.1089/ten.TEC.2012.0526
Polyanin ADZ VF, Moussiaux A (2002) Handbook of first order partial differential equations. Taylor & Francis, London
Rumpler M, Woesz A, Dunlop JWC, van Dongen JT, Fratzl P (2008) The effect of geometry on three-dimensional tissue growth. J R Soc Interface 5(27):1173–1180. doi:10.1098/rsif.2008.0064
Sethian JA (1999) Fast marching methods. Siam Rev 41(2):199–235. doi:10.1137/S0036144598347059
Shraiman BI (2005) Mechanical feedback as a possible regulator of tissue growth. Proc Natl Acad Sci USA 102(9):3318–3323. doi:10.1073/pnas.0404782102
Sobral JM, Caridade SG, Sousa RA, Mano JF, Reis RL (2011) Three-dimensional plotted scaffolds with controlled pore size gradients: effect of scaffold geometry on mechanical performance and cell seeding efficiency. Acta Biomater 7(3):1009–1018. doi:10.1016/j.actbio.2010.11.003
Van Bael S, Chai YC, Truscello S, Moesen M, Kerckhofs G, Van Oosterwyck H, Kruth IP, Schrooten J (2012) The effect of pore geometry on the in vitro biological behavior of human periosteum-derived cells seeded on selective laser-melted Ti6Al4V bone scaffolds. Acta Biomater 8(7):2824–2834. doi:10.1016/j.actbio.2012.04.001
Van Bael S, Chai YC, Truscello S, Moesen M, Kerckhofs G, Van Oosterwyck H, Kruth JP, Schrooten J (2012) The effect of pore geometry on the in vitro biological behavior of human periosteum-derived cells seeded on selective laser-melted Ti6Al4V bone scaffolds. Acta Biomater 8(7):2824–2834. doi:10.1016/j.actbio.2012.04.001
Van Bael S, Kerckhofs G, Moesen M, Pyka G, Schrooten J, Kruth JP (2011) Micro-CT-based improvement of geometrical and mechanical controllability of selective laser melted Ti6Al4V porous structures. Mater Sci Eng A Struct 528(24):7423–7431. doi:10.1016/j.msea.2011.06.045
van Lenthe GH, Hagenmuller H, Bohner M, Hollister SJ, Meinel L, Muller R (2007) Nondestructive micro-computed tomography for biological imaging and quantification of scaffold-bone interaction in vivo. Biomaterials 28(15):2479–2490
Voronov RS, Vangordon SB, Shambaugh RL, Papavassiliou DV, Sikavitsas VI (2012) 3D Tissue engineered construct analysis via conventional high resolution MicroCT without X-ray contrast. Tissue Eng Part C Methods. doi:10.1089/ten.TEC.2011.0612
Zeltinger J, Landeen LK, Alexander HG, Kidd ID, Sibanda B (2001a) Development and characterization of tissue-engineered aortic valves. Tissue Eng 7(1):9–22. doi:10.1089/107632701300003250
Zeltinger J, Sherwood JK, Graham DA, Mueller R, Griffith LG (2001b) Effect of pore size and void fraction on cellular adhesion, proliferation, and matrix deposition. Tissue Eng 7(5):557–572. doi:10.1089/107632701753213183