Abstract
A common technique for in vitro cartilage regeneration is to seed a porous matrix with cartilage cells and to culture the construct in static conditions or under medium perfusion in a bioreactor. An essential step toward the development of functional cartilage is to understand and control the tissue growth phenomenon in such systems. The growth process depends on various space- and time-varying biophysical variables of the environment surrounding the cartilage cells, primarily mass transport and mechanical variables, all involved in the cell biological response. Moreover, the growth process is inherently multiscale, since cell size (10 μm), scaffold pore size (100 μm), and cellular construct size (10 mm) pertain to three separate spatial scales. To obtain a quantitative understanding of cartilage growth in this complex multiphysics and multiscale system, advanced mathematical models and efficient scientific computing techniques have been developed. In this chapter, we discuss the existing knowledge in this field and we present the most recent advancements for the numerical simulation of cartilage tissue engineering.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
References
Boschetti, F., Raimondi, M.T., Migliavacca, F., Dubini, G.: Prediction of the micro-fluid dynamic environment imposed to three-dimensional engineered cell systems in bioreactors. J. Biomech. 39(3), 418–425 (2006)
Botchwey, E.A., Pollack, S.R., El-Amin, S., Levine, E.M., Tuan, R.S., Laurencin, C.T.: Human osteoblast-like cells in three-dimensional culture with fluid flow. Biorheology 40, 299–306 (2003)
Botchwey, E.A., Dupree, M.A., Pollack, S.R., Levine, E.M., Laurencin, C.T.: Tissue-engineered bone: measurement of nutrient transport in three-dimensional matrices. J. Biomed. Mater. Res. A 67(1), 357–367 (2003)
Burman, E., Hansbo. P.: Fictitious domain finite element methods using cut elements: II. A stabilized Nitsche method. Appl. Numer. Math. (2011). doi:10.1016/j.apnum.2011.01.008
Burman, E., Zunino, P.: Numerical approximation of large contrast problems with the unfitted Nitsche method, frontiers in numerical analysis––Durham 2010. In: Blowey, J., Jensen, M. (eds.) Lecture Notes in Computational Science and Engineering, vol. 85, Springer, Heidelberg, Germany, (2012). ISBN 978-3-642-23913-7
Byrne, H.M., King, J.R., McElwain, D.L.S., Preziosi, L.: A two-phase model of solid tumor growth. Appl. Math. Lett. 16(4), 567–573 (2003)
Cheng, G., Youssef, B.B., Markenscoff, P., Zygourakis, K.: Cell population dynamics modulate the rates of tissue growth processes. Biophys. J. 90(3), 713–724 (2006)
Chung, C.A., Yang, C.W., Chen, C.W.: Analysis of cell growth and diffusion in a scaffold for cartilage tissue engineering. Biotechnol. Bioeng. 94(6), 1138–1146 (2006)
Chung, C.A., Chen, C.W., Chen, C.P., Tseng, C.S.: Enhancement of cell growth in tissue-engineering constructs under direct perfusion: modeling and simulation. Biotechnol. Bioeng. 97(6), 1603–1616 (2007)
Cioffi, M., Boschetti, F., Raimondi, M.T., Dubini, G.: Modeling evaluation of the fluid-dynamic microenvironment in tissue-engineered constructs: a micro-CT based model. Biotechnol. Bioeng. 93(3), 500–510 (2006)
Cioffi, M., Küffer, J., Ströbel, S., Dubini, G., Martin, I., Wendt, D.: Computational evaluation of oxygen and shear stress distributions in 3D perfusion culture systems: macro-scale and micro-structured models. J. Biomech. 41(14), 2918–2925 (2008)
D’Angelo, C., Zunino, P.: Robust numerical approximation of coupled Stokes and Darcy flows applied to vascular hemodynamics and biochemical transport. ESAIM: Math. Model. Numer. Anal. (M2AN) 45(3), 447–476 (2011)
DiMicco, M.A., Sah, R.L.: Dependence of cartilage matrix composition on biosynthesis, diffusion, and reaction. Transp. Porous Media 50(1–2), 57–73 (2003)
El Haj, A.J., Wood, M.A., Thomas, P., Yang, Y.: Controlling cell biomechanics in orthopaedic tissue engineering and repair. Pathol. Biol. 53(10), 581–589 (2005)
Galban, C.J., Locke, B.R.: Analysis of cell growth kinetics and substrate diffusion in a polymer scaffold. Biotech. Bioeng. 65(2), 121–132 (1999)
Galbusera, F., Cioffi, M., Raimondi, M.T., Pietrabissa, R.: Computational modelling of combined cell population dynamics and oxygen transport in engineered tissue subject to interstitial perfusion. Comput. Methods. Biomech. Biomed. Eng. 10(4), 279–287 (2007)
Galbusera, F., Cioffi, M., Raimondi, M.T.: An in silico bioreactor for simulating laboratory experiments in tissue engineering. Biomed. Microdevice 10(4), 547–554 (2008)
Glowinski, R., Pan, T.W., Périaux, J.: A fictitious domain method for Dirichlet problem and applications. Comput. Methods Appl. Mech. Eng. 111(3-4), 283–303 (1994)
Hansbo, A., Hansbo, P.: An unfitted finite element method, based on Nitsche’s method for elliptic interface problems. Comput. Methods Appl. Mech. Eng. 191(47-48), 5537–5552 (2002)
Hsu, C.T., Cheng, P.: Thermal dispersion in a porous medium. Int. J. Heat Mass Transfer 33(8), 1587–1597 (1990)
Klein, T.J., Sah, R.L.: Modulation of depth-dependent properties in tissue-engineered cartilage with a semi-permeable membrane and perfusion: a continuum model of matrix metabolism and transport. Biomech. Model Mechanobiol. 6, 21–32 (2007)
Laganà, M., Raimondi, M.T.: (2011) A miniaturized, optically accessible bioreactor for systematic 3D tissue engineering research. Biomedical Microdevices. doi:10.1007/s10544-011-9600-0
Lemon, G., King, J.R., Byrne, H.M., Jensen, O.E., Shakesheff, K.M.: Mathematical modelling of engineered tissue growth using a multiphase porous flow mixture theory. J. Math. Biol. 52(5), 571–594 (2006)
Marle, C.: On macroscopic equations governing multiphase flow with diffusion and chemical reactions in porous media. Int. J. Eng. Sci. 20(5), 643–662 (1982)
Mizuno, S., Tateishi, T., Ushida, T., Glowacki, J.: Hydrostatic fluid pressure enhances matrix synthesis and accumulation by bovine chondrocytes in three-dimensional culture. J. cell physiol. 193, 319–327 (2002)
Moretti, M., Freed, L.E., Padera, R.F., Laganà, K., Boschetti, F., Raimondi, M.T.: An integrated experimental–computational approach for the study of engineered cartilage constructs subjected to combined regimens of hydrostatic pressure and interstitial perfusion. Bio-Med. Mater. Eng. 18(4–5), 273–278 (2008)
Obradovic, B., Meldon, J.H., Lisa, E.F., Vunjak-Novakovic, G.: Glycosaminoglycan deposition in engineered cartilage: experiments and mathematical model. AIChE J. 46, 1860–1871 (2000)
Palsson, E.: A three-dimensional model of cell movement in multicellular systems. Future Gener. Comput. Sys. 17, 835–852 (2001)
Pisu, M., Lai, N., Cincotti, A., Concas, A., Cao, G.: Modeling of engineered cartilage growth in rotating bioreactors. Chem. Eng. Sci. 59, 5035–5040 (2004)
Plank, M.J., Sleeman, B.D., Jones, P.F.: A mathematical model of tumour angiogenesis, regulated by vascular endothelial growth factor and the angiopoietins. J. Theor. Biol. 229(4), 435–454 (2004)
Porter, B., Zauel, R., Stockman, H., Guldberg, R., Fyhrie, D.: 3-D computational modeling of media flow through scaffolds in a perfusion bioreactor. J. Biomech. 38(3), 543–549 (2005)
Potter, H.G., Linklater, J.M., Allen, A.A., Hannafin, J., Haas, S.: Magnetic resonance imaging of articular cartilage in the knee. An evaluation with use of fast-spin-echo imaging. J. Bone Joint Surg. (Am.) 80, 1276–1284 (1998)
Quarteroni, A., Valli, A.: Domain Decomposition Methods for Partial Differential Equations. Numerical Mathematics and Scientific Computation. Oxford Science Publications, The Clarendon Press, Oxford University Press, New York (1999), ISBN: 0-19-850178-1
Quarteroni, A., Veneziani, A., Zunino, P.: Mathematical and numerical modelling of solute dynamics in blood flow and arterial walls. SIAM J. Numer. Anal 39(2), 1488–1511 (2002)
Quarteroni, A., Veneziani, A., Zunino, P.: Domain decomposition methods for blood solute dynamics. SIAM J. Sci. Comput. 23(6), 1959–1980 (2002)
Raimondi, M.T., Boschetti, F., Falcone, L., Fiore, G.B., Remuzzi, A., Marinoni, E., Marazzi, M., Pietrabissa, R.: Mechanobiology of engineered cartilage cultured under a quantified fluid-dynamic environment. Biomech. Model. Mechanobiol. 1, 69–82 (2002)
Raimondi, M.T., Boschetti, F., Falcone, L., Migliavacca, F., Remuzzi, A., Dubini, G.: The effect of media perfusion on three-dimensional cultures of human chondrocytes: integration of experimental and computational approaches. Biorheology 41(3–4), 401–410 (2004)
Raimondi, M.T.: Engineered tissue as a model to study cell and tissue function from a biophysical perspective. Curr. Drug Discov. Technol. 3(4), 245–268 (2006a)
Raimondi, M.T., Moretti, M., Cioffi, M., Giordano, C., Boschetti, F., Laganà, K., Pietrabissa, R.: The effect of hydrodynamic shear on 3D engineered chondrocyte systems subject to direct perfusion. Biorheology 43(3–4), 215–222 (2006b)
Raimondi, M.T., Candiani, G., Cabras, M., Cioffi, M., Laganà, K., Moretti, M., Pietrabissa, R.: Engineered cartilage constructs subject to very low regimens of interstitial perfusion. Biorheology 45(3–4), 471–478 (2008)
Raimondi, M.T., Bridgen, D.T., Laganà, M., Tonnarelli, B., Cioffi, M., Boschetti, F., Wendt, D.: In-tegration of experimental and computational microfluidics in 3D tissue engineering. In: Berthiaume, F., Morgan, J. (eds.) Methods in Bioengineering––3D Tissue Engineering. Artech House, Boston, London (2010). ISBN: 978-1-59693-458
Raimondi, M.T., Bonacina, E., Candiani, G., Laganà, M., Rolando, E., Talò, G., Pezzoli, D., D’Anchise, R., Pietrabissa, R., Moretti, M.: Comparative chondrogenesis of human cells in a 3D integrated experimental-computational mechanobiology model. Biomech. Model. Mechanobiol. 10(2), 259–268 (2011a)
Raimondi, M.T., Causin, P., Mara, A., Nava, M., Laganà, M., Sacco, R.: Breakthroughs in computational modeling of cartilage regeneration in perfused bioreactors. IEEE Trans. Biomed. Eng. 58(12) (2011b). doi:10.1109/TBME.2011.2163405
Sacco, R., Causin, P., Zunino, P., Raimondi, M.T.: A multiphysics/multiscale numerical simulation of scaffold-based cartilage regeneration under interstitial perfusion in a bioreactor. Biomech. Model. Mechanobiol. 10(4), 577–589 (2011)
Sengers, B.G., van Donkelaar, C.C., Oomens, C.W., Baaijens, F.P.: Computational study of culture conditions and nutrient supply in cartilage tissue engineering. Biotechnol. Prog. 21(4), 1252–1261 (2005)
Schulz, R.M., Bader, A.: Cartilage tissue engineering and bioreactor systems for the cultivation and stimulation of chondrocytes. Eur. Biophys. J. 36, 539–568 (2007)
Singh, H., Teoh, S.H., Low, H.T., Hutmacher, D.W.: Flow modeling within a scaffold under the influence of uni-axial and bi-axial bioreactor rotation. J. Biotechnol. 119, 181–196 (2005)
Whitaker, S.: The Method of Volume Averaging Theory and Application of Transport in Porous Media. Kluwer Academic Publishers, Dordrecht (1999)
Williams, K.A., Saini, S., Wick, T.M.: Computational fluid dynamics modeling of steady-state momentum and mass transport in a bioreactor for cartilage tissue engineering. Biotechnol. Prog. 18(5), 951–963 (2002)
Wood, B.D., Quintard, M., Whitaker, S.: Calculation of effective diffusivities for bio films and tissues. Biotech. Bioeng. 77(5), 495–514 (2002)
Acknowledgments
This research is funded by Politecnico di Milano, under grant 5 per Mille Junior 2009 CUPD41J10000490001 “Computational Models for Heterogeneous Media. Application to Micro Scale Analysis of Tissue-engineered Constructs”, by the Italian Institute of Technology (IIT-Genoa), under grant “Biosensors and Artificial Bio-systems”, and by the Cariplo Foundation (Milano), under grant 2010 “3D Micro structuring and Functionalisation of Polymeric Materials for Scaffolds in Regenerative Medicine”.
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2011 Springer-Verlag Berlin Heidelberg
About this chapter
Cite this chapter
Raimondi, M.T., Causin, P., Laganà, M., Zunino, P., Sacco, R. (2011). Multiphysics Computational Modeling in Cartilage Tissue Engineering. In: Geris, L. (eds) Computational Modeling in Tissue Engineering. Studies in Mechanobiology, Tissue Engineering and Biomaterials, vol 10. Springer, Berlin, Heidelberg. https://doi.org/10.1007/8415_2011_112
Download citation
DOI: https://doi.org/10.1007/8415_2011_112
Published:
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-32562-5
Online ISBN: 978-3-642-32563-2
eBook Packages: EngineeringEngineering (R0)