An Integrated Finite-Element Approach to Mechanics, Transport and Biosynthesis in Tissue Engineering

[+] Author and Article Information
Bram G. Sengers, Cees W. J. Oomens, Frank P. T. Baaijens

Eindhoven University of Technology, Department of Biomedical Engineering, P.O. Box 513, 5600 MB Eindhoven, The Netherlands

J Biomech Eng 126(1), 82-91 (Mar 09, 2004) (10 pages) doi:10.1115/1.1645526 History: Received August 01, 2002; Revised August 20, 2003; Online March 09, 2004
Copyright © 2004 by ASME
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Freed,  L. E., Martin,  I., and Vunjak-Novakovic,  G., 1999, “Frontiers in Tissue Engineering: In Vitro Modulation of Chondrogenesis,” Clin. Orthop., 367S, pp. S46–S58.
Freed,  L. E., and Vunjak-Novakovic,  G., 1998, “Culture of Organized Cell Communities,” Advanced Drug Delivery Reviews, 33, pp. 15–30.
Rodriguez, A. M., and Vacanti, C. A., 1998, “Tissue Engineering of Cartilage,” Frontiers in tissue engineering, C. W. Patrick, A. G. Mikos, and L. V. McIntire, eds., Pergamon, Amsterdam, pp. 400–409.
LeBaron,  R. G., and Athanasiou,  K. A., 2000, “Ex Vivo Synthesis of Articular Cartilage,” Biomaterials, 21, pp. 2575–2587.
Freed,  L. E., Langer,  R., Martin,  I., Pellis,  N. R., and Vunjak-Novakovic,  G., 1997, “Tissue Engineering of Cartilage in Space,” Proceedings of the National Academy of Sciences of the United States of America, 94, pp. 13885–13890.
Martin,  I., Obradovic,  B., Treppo,  S., Grodzinsky,  A. J., Langer,  R., Freed,  L. E., and Vunjak-Novakovic,  G., 2000, “Modulation of the Mechanical Properties of Tissue Engineered Cartilage,” Biorheology, 37, pp. 141–147.
Butler,  D. L., Goldstein,  S. A., and Guilak,  F., 2000, “Functional Tissue Engineering: The Role of Biomechanics,” J. Biomech. Eng., 122, pp. 570–575.
Mauck,  R. L., Soltz,  M. A., Wang,  C. C. B., Wong,  D. D., Chao,  P. H. G., Valhmu,  W. B., Hung,  C. T., and Athesian,  G. A., 2000, “Functional Tissue Engineering of Articular Cartilage Through Dynamic Loading of Chondrocyte-Seeded Agarose Gels,” J. Biomech. Eng., 122, pp. 252–260.
Vunjak-Novakovic,  G., Martin,  I., Obradovic,  B., Treppo,  S., Grodzinsky,  A. J., Langer,  R., and Freed,  L. E., 1999, “Bioreactor Cultivation Conditions Modulate the Composition and Mechanical Properties of Tissue-Engineered Cartilage,” J. Orthop. Res., 17, pp. 130–138.
Gooch,  K. J., Kwon,  J. H., Blunk,  T., Langer,  R., Freed,  L. E., and Vunjak-Novakovic,  G., 2001, “Effects of Mixing Intensity on Tissue-Engineered Cartilage,” Biotechnol. Bioeng., 72, pp. 402–407.
Freed,  L. E., Vunjak-Novakovic,  G., Marquis,  J. C., and Langer,  R., 1994, “Kinetics of Chondrocyte Growth in Cell-Polymer Implants,” Biotechnol. Bioeng., 43, pp. 597–604.
Freed,  L. E., Marquis,  J. C., Vunjak-Novakovic,  G., Emmanual,  J., and Langer,  R., 1994, “Composition of Cell-Polymer Cartilage Implants,” Biotechnol. Bioeng., 43, pp. 605–614.
Obradovic,  B., Carrier,  R. L., Vunjak-Novakovic,  G., and Freed,  L. E., 1999, “Gas Exchange is Essential for Bioreactor Cultivation of Tissue Engineered Cartilage,” Biotechnol. Bioeng., 63, pp. 197–205.
Lee,  R. B., and Urban,  J. P. G., 1997, “Evidence for a Negative Pasteur Effect in Articular Cartilage,” Biochem. J., 321, pp. 95–102.
Ellis,  S. J., Velayutham,  M., Velan,  S. S., Petersen,  E. F., Zweier,  J. L., Kuppusamy,  P., and Spencer,  R. G. S., 2001, “EPR Oxygen Mapping (EPROM) of Engineered Cartilage Grown in a Hollow-Fiber Bioreactor,” Magn. Reson. Med., 46, pp. 819–826.
Vunjak-Novakovic,  G., Obradovic,  B., Martin,  I., Bursac,  P. M., Langer,  R., and Freed,  L. E., 1998, “Dynamic Cell Seeding of Polymer Scaffolds for Cartilage Tissue Engineering,” Biotechnol. Prog., 14, pp. 193–202.
Gooch, K. J., Blunk, T., Tennant, C. T., Vunjak-Novakovic, G., Langer, R., and Freed, L. E., 1998, “Mechanical Forces and Growth Factors Utilized in Tissue Engineering,” Frontiers in Tissue Engineering, C. W. Patrick, A. G. Mikos, and L. V. McIntire, eds., Pergamon, Amsterdam, pp. 61–82.
Blunk,  T., Sieminski,  A. L., Gooch,  K. J., Courter,  D. L., Hollander,  A. P., Nahir,  A. M., Langer,  R., Vunjak-Novakovic,  G., and Freed,  L. E., 2002, “Differential Effects of Growth Factors on Tissue-Engineered Cartilage,” Tissue Eng., 8(1), pp. 73–84.
Gooch,  K. J., Blunk,  T., Courter,  D. L., Sieminski,  A. L., Bursac,  P. M., Vunjak-Novakovic,  G., and Freed,  L. E., 2001, “IGF-I and Mechanical Environment Interact to Modulate Engineered Cartilage Development,” Biochem. Biophys. Res. Commun., 286, pp. 909–915.
Bonassar,  L. J., Grodzinsky,  A. J., Frank,  E. H., Davila,  S. G., Bhaktav,  N. R., and Trippel,  S. B., 2001, “The Effect of Dynamic Compression on the Response of Articular Cartilage to Insulin-like Growth Factor-I,” J. Orthop. Res., 19, pp. 11–17.
O’Hara,  B. P., Urban,  J. P. G., and Maroudas,  A., 1990, “Influence of Cyclic Loading on the Nutrition of Articular Cartilage,” Ann. Rheum. Dis., 49, pp. 536–539.
Grodzinsky, A. J., Kamm, R. D., and Lauffenburger, D. A., 1997, “Quantitative Aspects of Tissue Engineering: Basic Issues in Kinetics Transport and Mechanics,” Principles of tissue engineering, R. Lanza, R. Langer, and W. Chick, eds., Academic Press, London, pp. 193–207.
Garcia,  A. M., Frank,  E. H., Grimshaw,  P. E., and Grodzinsky,  A. J., 1996, “Contributions of Fluid Convection and Electrical Migration to Transport in Cartilage: Relevance to Loading,” Arch. Biochem. Biophys., 333, pp. 317–325.
Bursac,  P. M., Freed,  L. E., Biron,  R. J., and Vunjak-Novakovic,  G., 1996, “Mass Transfer Studies of Tissue Engineered Cartilage,” Tissue Eng., 2(2), pp. 141–150.
Buschmann,  M. D., Gluzband,  Y. A., Grodzinsky,  A. J., and Hunziker,  E. B., 1995, “Mechanical Compression Modulates Matrix Biosynthesis in Chondrocyte/Agarose Culture,” J. Cell. Sci., 108, pp. 1497–1508.
Urban,  J. P. G., 2000, “Present Perspectives on Cartilage and Chondrocyte Mechanobiology,” Biorheology, 37, pp. 185–190.
Lee,  D. A., Noguchi,  T., Knight,  M. M., O’Donnell,  L., Bentley,  G., and Bader,  D. L., 1998, “Response of Chondrocyte Subpopulations Cultured within Unloaded and Loaded Agarose,” J. Orthop. Res., 16, pp. 726–733.
Nehring,  D., Adamietz,  P., Meenen,  N. M., and Pörtner,  R., 1999, “Perfusion Cultures and Modeling of Oxygen Uptake with Three-Dimensional Chondrocyte Pellets,” Biotechnol. Tech., 13, pp. 701–706.
Galban,  C. J., and Locke,  B. R., 1997, “Analysis of Cell Growth in a Polymer Scaffold Using a Moving Boundary Approach,” Biotechnol. Bioeng., 56, pp. 422–432.
Galban,  C. J., and Locke,  B. R., 1999, “Analysis of Cell Growth Kinetics and Substrate Diffusion in a Polymer Scaffold,” Biotechnol. Bioeng., 65, pp. 121–132.
Galban,  C. J., and Locke,  B. R., 1999, “Effects of Spatial Variation of Cells and Nutrient and Product Concentrations Coupled with Product Inhibition on Cell Growth in a Polymer Scaffold,” Biotechnol. Bioeng., 64, pp. 633–643.
Obradovic,  B., Meldon,  J. H., Freed,  L. E., and Vunjak-Novakovic,  G., 2000, “Glycosaminoglycan Deposition in Engineered Cartilage: Experiments and Mathematical Model,” AIChE J., 46(9), pp. 1860–1871.
Haselgrove,  J. C., Shapiro,  I. M., and Silverton,  S. F., 1993, “Computer Modeling of the Oxygen Supply and Demand of Cells of the Avian Growth Cartilage,” Am. J. Physiol., 265, pp. c497–c506.
Boderke,  P., Schittkowski,  K., Wolf,  M., and Merkle,  H. P., 2000, “Modeling of Diffusion and Concurrent Metabolism in Cutaneous Tissue,” J. Theor. Biol., 204, pp. 393–407.
Stangeby,  D. K., and Ethier,  C. R., 2002, “Computational Analysis of Coupled Blood-Wall Arterial LDL Transport,” J. Biomech. Eng., 124, pp. 1–8.
Maseide,  K., and Rofstad,  E. K., 2000, “Mathematical Modeling of Chronical Hypoxia in Tumors Considering Potential Doubling Time and Hypoxic Cell Lifetime,” Radiother. Oncol., 54, pp. 171–177.
Netti,  P. A., Baxter,  L. T., Boucher,  Y., Skalak,  R., and Jain,  R. K., 1997, “Macro- and Microscopic Fluid Transport in Living Tissues: Application to Solid Tumors,” Bioengineering Food and Natural Products, 43(3), pp. 818–834.
Bailey, J. E., and Ollis, D. F., 1986, Biochemical Engineering Fundamentals, McGraw-Hill, New York.
Tziampazis,  E., and Sambanis,  A., 1994, “Modeling of Cell Culture Processes,” Cytotechnology, 14, pp. 191–204.
Gallo,  C., and Manzini,  G., 1998, “A Mixed Finite Element/Finite Volume Approach for Solving Biodegradation Transport in Groundwater,” Int. J. Numer. Methods Fluids, 26, pp. 533–556.
Chawla,  S., and Lenhart,  S. M., 2000, “Application of Optimal Control Theory to Bioremediation,” J. Comput. Appl. Math., 114, pp. 81–102.
Tervo,  J., Vauhkonen,  M., Vauhkonen,  P. J., and Kaipio,  J. P., 2000, “A Three-Dimensional Finite Element Model for the Control of certain Non-Linear Bioreactors,” Mathematical Methods in the Applied Sciences, 23, pp. 357–377.
Prendergast,  P. J., Huiskes,  R., and Soballe,  K., 1997, “Biophysical Stimuli on Cells During Tissue Differentiation at Implant Interfaces,” J. Biomech., 30(6), pp. 539–548.
Carter,  D. R., Beaupre,  G. S., Giori,  N. J., and Helms,  J. A., 1998, “Mechanobiology of Skeletal Regeneration,” Clin. Orthop., 355S, pp. S41–S55.
Sah,  R. L. Y., Doong,  J. Y. H., Grodzinsky,  A. J., Plaas,  A. H. K., and Sandy,  J. D., 1991, “Effects of Compression on the Loss of Newly Synthesized Proteoglycans and Proteins from Cartilage Explants,” Arch. Biochem. Biophys., 286(1), pp. 20–29.
Bowen,  R. M., 1980, “Incompressible Porous Media Models by use of the Theory of Mixtures,” International Journal of Engineering Science, 18, pp. 1129–1148.
Almeida,  E. S., and Spilker,  R. L., 1997, “Mixed and Penalty Finite Element Models for the Nonlinear Behavior of Biphasic Soft Tissues in Finite Deformation: Part I—Alternate Formulations,” Computer Methods in Biomechanics and Biomedical Engineering, 1(1), pp. 25–46.
Frijns, A. J. H., 2000, “A Four-Component Mixture Theory Applied to Cartilaginous Tissues,” Ph.D. thesis, Eindhoven University of Technology, Eindhoven, The Netherlands.
Huyghe,  J. M., and Janssen,  J. D., 1997, “Quadriphasic Mechanics of Swelling Incompressible Porous Media,” International Journal of Engineering Science, 35(8), pp. 793–802.
Sun,  D. N., Gu,  W. Y., Guo,  X. E., Lai,  W. M., and Mow,  V. C., 1999, “A Mixed Finite Element Formulation of Triphasic Mechano-Electrochemical Theory for Charged, Hydrated Biological Soft Tissues,” Int. J. Numer. Methods Eng., 45, pp. 1375–1402.
Pluen,  A., Netti,  P. A., Jain,  R. K., and Berk,  D. A., 1999, “Diffusion of Macromolecules in Agarose Gels: Comparison of Linear and Globular Configurations,” Biophys. J., 77, pp. 542–552.
Quinn,  T. M., Morel,  V., and Meister,  J. J., 2001, “Static Compression of Articular Cartilage can Reduce Solute Diffusivity and Partitioning: Implications for the Chondrocyte Biological Response,” J. Biomech., 34, pp. 1463–1469.
Levenston,  M. E., Frank,  E. H., and Grodzinsky,  A. J., 1998, “Variationally Derived 3-Field Finite Element Formulations for Quasistatic Poroelastic Analysis of Hydrated Biological Tissues,” Comput. Methods Appl. Mech. Eng., 156, pp. 231–246.
Almeida,  E. S., and Spilker,  R. L., 1997, “Mixed and Penalty Finite Element Models for the Nonlinear Behavior of Biphasic Soft Tissues in Finite Deformation: Part II—Nonlinear Examples,” Computer Methods in Biomechanics and Biomedical Engineering, 1(2), pp. 151–170.
Wang,  H., Liang,  D., Ewing,  R. E., Lyons,  S. L., and Qin,  G., 2000, “An Approximation to Miscible Fluid Flows in Porous Media with Point Sources and Sinks by an Eulerian-Lagrangian Localized Adjoint Method and Mixed Finite Element Methods,” SIAM J. Sci. Comput. (USA), 22(2), pp. 561–581.
Segal, G., 2000, SEPRAN User’s Manual, Ingenieursbureau SEPRA, Leidschendam, The Netherlands.
Strang,  G., 1968, “On the Construction and Comparison of Difference Schemes,” SIAM J. Sci. Comput. (USA), 5, pp. 506–517.
Lanser,  D., and Verwer,  J. G., 1999, “Analysis of Operator Splitting for Advection-Diffusion-Reaction Problems from Air Pollution Modelling,” Journal of Computational and Applied Mathematics, 11, pp. 201–216.
Hundsdorfer,  W., and Verwer,  J. G., 1995, “A Note on Splitting Errors for Advection-Reaction Equations,” Applied Numerical Mathematics, 18, pp. 191–199.
Morshed,  J., and Kaluarachchi,  J. J., 1995, “Critical Assessment of the Operator-Splitting Technique in Solving the Advection-Dispersion-Reaction Equation: 2. Monod Kinetics and Coupled Transport,” Adv. Water Resour., 18(2), pp. 101–110.
Comper,  W. D., and Williams,  R. P. W., 1987, “Hydrodynamics of Concentrated Proteoglycan Solutions,” J. Biol. Chem., 262(28), pp. 13464–13471.
Freed,  L. E., Hollander,  A. P., Martin,  I., Barry,  J. R., Langer,  R., and Vunjak-Novakovic,  G., 1998, “Chondrogenesis in a Cell-Polymer-Bioreactor System,” Exp. Cell Res., 240, pp. 58–65.
Wong,  M., Ponticiello,  M., Kovanen,  V., and Jurvelin,  J. S., 2000, “Volumetric Changes of Articular Cartilage during Stress Relaxation in Unconfined Compression,” J. Biomech., 33, pp. 1049–1054.
Lundberg,  P., and Kuchel,  P. W., 1997, “Diffusion of Solutes in Agarose and Alginate Gels: 1H and 23Na PFGSE and 23Na TQF NMR Studies,” Magn. Reson. Med., 37(1), pp. 44–52.
Davisson,  T., Kunig,  S., Chen,  A., Sah,  R., and Ratcliffe,  A., 2002, “Static and Dynamic Compression Modulate Matrix Metabolism in Tissue Engineered Cartilage,” J. Orthop. Res., 20, pp. 842–848.
Suh,  J. K., 1996, “Dynamic Unconfined Compression of Articular Cartilage under a Cyclic Compressive Load,” Biorheology, 33(45), pp. 289–304.
Suh,  J. K., Li,  Z., and Woo,  S. L. Y., 1995, “Dynamic Behavior of a Biphasic Cartilage Model under Cyclic Compressive Loading,” J. Biomech., 28(4), pp. 357–364.
Quinn,  T. M., Studer,  C., Grodzinsky,  A. J., and Meister,  J. J., 2002, “Preservation and Analysis of Nonequilibrium Solute Concentration Distributions within Mechanically Compressed Cartilage Explants,” J. Biochem. Biophys. Methods, 52, pp. 83–95.
Ishihara,  H., and Urban,  J. P. G., 1999, “Effects of Low Oxygen Concentrations and Metabolic Inhibitors on Proteoglycan and Protein Synthesis Rates in the Intervertebral Disc,” J. Orthop. Res., 17, pp. 829–835.
Martin,  I., Obradovic,  B., Freed,  L. E., and Vunjak-Novakovic,  G., 1999, “Method for Quantitative Analysis of Glycosaminoglycan Distribution in Cultured Natural and Engineered Cartilage,” Ann. Biomed. Eng., 27, pp. 656–662.
Gu,  W. Y., Lai,  W. M., and Mow,  V. C., 1998, “A Mixture Theory for Charged-Hydrated Soft Tissues Containing Multi-Electrolytes: Passive Transport and Swelling Behaviors,” J. Biomech. Eng., 120, pp. 169–180.
Schäfer,  D., Schäfer,  W., and Kinzelbach,  W., 1998, “Simulation of Reactive Processes related to Biodegradation in Aquifers 1. Structure of the Three-Dimensional Reactive Transport Model,” J. Contam. Hydrol., 31, pp. 167–186.
MacQuarrie,  K. T. B., and Sudicky,  E. A., 2001, “Multicomponent Simulation of Wastewater-Derived Nitrogen and Carbon in Shallow Unconfined Aquifers I. Model Formulation and Performance,” J. Contam. Hydrol., 47, pp. 53–84.


Grahic Jump Location
Schematic representation of the modeling approach, showing the coupling between the different model components and the model inputs. Outputs are defined as the concentration of functional tissue components. Dashed routes will not be considered in the current study.
Grahic Jump Location
(a) Unconfined compression setup. (b) Finite element mesh containing 24 elements.
Grahic Jump Location
Maximum local fluid velocity induced by dynamic loading in the last cycle before t=4000 s, plotted in the undeformed geometry.
Grahic Jump Location
Desorption of an initially homogeneous concentration for different loading conditions and dispersion parameters. (a), (b): Dd=0 mm. (c), (d): Dd=0.01 mm. (e), (f): Dd=0.1 mm. Left: Matrix component concentration profiles after 4000 s. Right: Evolution of total matrix component content in time.
Grahic Jump Location
(a) Steady state concentration profile resulting from diffusion and uptake for both the small and large solute. (b) Large solute concentration profiles at t=87000 for different loading frequencies and dispersion parameters.
Grahic Jump Location
Matrix component profiles at t=87000 for different loading frequencies and dispersion parameters. (a) Synthesis independent of transport. (b) Synthesis limited by a small solute. (c) Synthesis limited by a large solute.
Grahic Jump Location
Integrated effect of different loading frequencies and dispersion parameters on total biosynthesis at t=87000. The white bar represents the total synthesis. The black bar represents the fraction retained in the construct. (a) Synthesis independent of transport. (b) Synthesis limited by a small solute. (c) Synthesis limited by a large solute.



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