A multiphase model for tissue construct growth in a perfusion bioreactor

Mathematical Medicine and Biology

Volumn 27, Issue 2, 2009, Pages 95-127

  O'Dea, R D ^a   Waters, S L ^a,b   Byrne, H M ^a  

^a UNIVERSITY OF NOTTINGHAM   (United Kingdom)

^b UNIVERSITY OF OXFORD   (United Kingdom)

Author keywords

Mechanotransduction; Multiphase; Tissue growth

Indexed keywords

BIOCONVERSION; CELL CULTURE; CELL PROLIFERATION; CONTINUUM MECHANICS; POPULATION STATISTICS; SCAFFOLDS (BIOLOGY); SHEAR FLOW; SHEAR STRESS; TISSUE;

CELL POPULATIONS; CULTURE MEDIUM; MECHANOTRANSDUCTION; MULTIPHASE MODELING; MULTIPHASES; PERFUSION BIOREACTOR; POROUS SCAFFOLD; THREE PHASIS; TISSUE CONSTRUCTS; TISSUE GROWTH;

BIOREACTORS;

CITRUS LIMON;

EID: 77955651654     PISSN: 14778599     EISSN: 14778602     Source Type: Journal    
DOI: 10.1093/imammb/dqp003     Document Type: Article

References (54)

1. ARAUJO, R. P. & MCELWAIN, D. L. S. (2004) A history of the study of solid tumour growth: the contribution of mathematical modelling. Bull. Math. Biol., 66, 1039-1091.
2. ARAUJO, R. P. & MCELWAIN, D. L. S. (2005) A mixture theory for the genesis of residual stresses in growing tissues I: a general formulation. SIAM J. Appl. Math., 65, 1261-1284.
3. BAKKER, A., KLEIN-NULEND, J. & BURGER, E. (2004) Shear stress inhibits while disuse promotes osteocyte apoptosis. Biochem. Biophys. Res. Commun., 320, 1163-1168.
4. BITTIG, T., WARTLICK, O., KICHEVA, A., GONZÁLEZ-GAITÁ N, M. & JÜLICHER, F. (2008) Dynamics of anisotropic tissue growth. New J. Phys., 10, 63001-63011.
5. BREWARD, C. J. W., BYRNE, H. M. & LEWIS, C. E. (2002) The role of cell-cell interactions in a two-phase model for avascular tumour growth. J. Math. Biol., 45, 125-152.
6. BYRNE, H. M., KING, J. R., MCELWAIN, D. L. S. & PREZIOSI, L. (2003) A two-phase model of solid tumour growth. Appl. Math. Lett., 16, 567-573.
7. BYRNE, H. M. & PREZIOSI, L. (2003) Modelling solid tumour growth using the theory of mixtures. Math. Med. Biol., 20, 341-366.
8. CARTMELL, S. H. & EL HAJ, A. J. (2005) Mechanical bioreactors for tissue engineering. Bioreactors for Tissue Engineering: Principles, Design and Operation (J. Chaudhuri & M. Al-Rubeai eds), Chapter 8. Dordrecht: Springer, pp. 193-209.
9. CHAPLAIN, M. A. J., GRAZIANO, L. & PREZIOSI, L. (2006) Mathematical modelling of the loss of tissue compression responsiveness and its role in solid tumour development. Math. Med. Biol., 23, 197.
10. COLETTI, F., MACCHIETTO, S. & ELVASSORE, N. (2006) Mathematical modeling of three-dimensional cell cultures in perfusion bioreactors. Ind. Eng. Chem. Res., 45, 8158-8169.
11. COWIN, S. C. (2000) How is a tissue built? J. Biomech. Eng., 122, 553.
12. COWIN, S. C. (2004) Tissue growth and remodeling. Ann. Rev. Biomed. Eng., 6, 77-107.
13. CURTIS, A. & RIEHLE, M. (2001) Tissue engineering: the biophysical background. Phys. Med. Biol., 46, 47-65.
14. DREW, D. A. (1983) Mathematical modelling of two-phase flow. Annu. Rev. Fluid Mech., 15, 261-291.
15. DREW, D. A. & SEGEL, L. A. (1971) Averaged equations for two-phase flows. Stud. Appl. Math., 50, 205-231.
16. EL-HAJ, A. J., MINTER, S. L., RAWLINSON, S. C., SUSWILLO, R. & LANYON, L. E. (1990) Cellular responses to mechanical loading in vitro. J. Bone Miner. Res., 5, 923-932.
17. FRANKS, S. J. (2002) Mathematical modelling of tumour growth and stability. Ph.D. Thesis, University of Nottingham, Nottingham, UK.
18. FRANKS, S. J., BYRNE, H. M., KING, J. R., UNDERWOOD, J. C. E. & LEWIS, C. E. (2003) Modelling the early growth of ductal carcinoma in situ of the breast. J. Math. Biol., 47, 424-452.
19. FRANKS, S. J. & KING, J. R. (2003) Interactions between a uniformly proliferating tumour and its surroundings: uniform material properties. Math. Med. Biol., 20, 47-89.
20. FREYRIA, A. M., YANG, Y., CHAJRA, H., ROUSSEAU, C. F., RONZIERE, M. C., HERBAGE, D. & EL HAJ, A. J. (2005) Optimization of dynamic culture conditions: effects on biosynthetic activities of chondrocytes grown in collagen sponges. Tissue Eng., 11, 674-684.
21. FUNG, Y. C. (1991) What are residual stresses doing in our blood vessels? Ann. Biomed. Eng., 19, 237-249.
22. HAN, Y., COWIN, S. C., SCHAFFLER, M. B. & WEINBAAUM, S. (2004) Mechanotransduction and strain amplification in osteocyte cell processes. Proc. Natl. Acad. Sci. USA, 101, 16689-16694.
23. HASKIN, C., CAMERON, I. & ATHANASIOU, K. (1993) Physiological levels of hydrostatic pressure alter morphology and organization of cytoskeletal and adhesion proteins in MG-63 osteosarcoma cells. Biochem. Cell Biol., 71, 27-35.
24. JAECQUES, S. V. N., VAN-OOSTERWYCK, H., MURARU, L., VAN-CLEYNBREUGEL, T., DE-SMET, E., WEVERS, M., NAERT, I. & VANDER-SLOTEN, J. (2004) Individualised, micro CT-based finite element modelling as a tool for biomechanical analysis relating to tissue engineering of bone. Biomat., 25, 1683-1696.
25. KING, J. R. & FRANKS, S. J. (2004) Mathematical analysis of some multi-dimensional tissue growth models. Eur. J. Appl. Math., 15, 273-295.
26. KLEIN-NULEND, J., HELFRICH, M. H., STERCK, J. G. H., MACPHERSON, H., JOLDERSMA, M., RALSTON, S. H., SEMEINS, C. M. & BURGER, E. H. (1998) Nitric oxide response to shear stress by human bone cell cultures is endothelial nitric oxide synthase dependent. Biochem. Biophys. Res. Commun., 250, 108-114.
27. KLEIN-NULEND, J., ROELOFSEN, J., STERCK, J. G., SEMEINS, C. M. & BURGER, E. H. (1995a) Mechanical loading stimulates the release of transforming growth factor-beta activity by cultured mouse calvariae and periosteal cells. J. Cell Phys., 163, 115-119.
28. KLEIN-NULEND, J., VAN DER PLAS, A., SEMEINS, C. M., AJUBI, N. E., FRANGOS, J. A., NIJWEIDE, P. J. & BURGER, E. H. (1995b) Sensitivity of osteocytes to biomechanical stress in vitro. FASEB, 9, 441-445.
29. KOLEV, N. I. (2002) Multiphase Flow Dynamics, Volume 1-Fundamentals. Berlin: Springer.
30. LANDMAN, K. A. & PLEASE, C. P. (2001) Tumour dynamics and necrosis: surface tension and stability. IMA J. Math. Appl. Med. Biol., 18, 131-158.
31. LEMON, G. & KING, J. R. (2007) Multiphase modelling of cell behaviour on artificial scaffolds: effects of nutrient depletion and spatially nonuniform porosity. Math. Med. Biol., 24, 57.
32. LEMON, G., KING, J. R., BYRNE, H. M., JENSEN, O. E. & SHAKESHEFF, K. (2006) Multiphase modelling of tissue growth using the theory of mixtures. J. Math. Biol., 52, 571-594.
33. LEWIS, M. C., MACARTHUR, B. D., MALDA, J., PETTET, G. & PLEASE, C. P. (2005) Heterogeneous proliferation within engineered cartilaginous tissue: the role of oxygen tension. Biotech. Bioeng., 91, 607-615.
34. MALDA, J., ROUWKEMA, J., MARTENS, D. E., LE COMTE, E. P., KOOY, F. K., TRAMPER, J., VAN BLITTERSWIJK, C. A. & RIESLE, J. (2004) Oxygen gradients in tissue-engineered PEGT/PBT cartilaginous constructs: measurement and modelling. Biotech. Bioeng., 86, 9-18.
35. MARTIN, I., WENDT, D. & HEBERER, M. (2004) The role of bioreactors in tissue engineering. Trends Biotechnol., 22, 80-86.
36. MCGARRY, J. G., KLEIN-NULEND, J., MULLENDER, M. G. & PRENDERGAST, P. J. (2005) A comparison of strain and fluid shear stress in simulating bone cell responses-a computation and experimental study. FASEB, 19, 482-484.
37. O'DEA, R. D. (2008) Multiphase modelling of tissue growth in dynamic culture conditions. Ph.D. Thesis, University of Nottingham, Nottingham, UK.
38. O'DEA, R. D., WATERS, S. L. & BYRNE, H. M. (2008) A two-fluid model for tissue growth within a dynamic flow environment. Eur. J. Appl. Math. (accepted for publication).
39. OWAN, I., BURR, D. B., TURNER, C. H., QIU, J., TU, Y., ONYIA, J. E. & DUNCAN, R. L. (1997) Mechanotransduction in bone: osteoblasts are more responsive to fluid forces than mechanical strain. Am. J. Physiol. Cell Physiol., 273, 810-815.
40. PEIRCE, S. M., SKALAK, T. C. & PAPIN, J. A. (2006) Multiscale biosystems integration: coupling intracellular network analysis with tissue-patterning simulations. Syst. Biol., 50, 601-615.
41. PEREGRINE, D. H. (1967) Long waves on a beach. J. Fluid Mech., 27, 815-827.
42. PORTER, B., ZAUEL, R., STOCKMAN, H., GULDBERG, R. & FYHRIE, D. (2005) 3-D computational modeling of media flow through scaffolds in a perfusion bioreactor. J. Biomech., 38, 543-549.
43. RAIMONDI, M. T. (2004) The effect of media perfusion on three-dimensional cultures of human chondrocytes: integration of experimental and computational approaches. Biorheology, 41, 401-410.
44. ROELOFSEN, J., KLEIN-NULEND, J. & BURGER, E. H. (1995) Mechanical stimulation by intermittent hydrostatic compression promotes bone-specific gene expression in vitro. J. Biomech., 28, 1493-1503.
45. ROOSE, T., NETI, P. A., MUNN, L. L., BOUCHER, Y. & JAIN, R. K. (2003) Solid stress generated by spheroid growth estimated using a poroelasticity model. Microvasc. Res., 66, 204-212.
46. SIPE, J. D. (2002) Tissue engineering and reparative medicine. Ann. N. Y. Acad. Sci., 961, 1-9.
47. TRACQUI, P. & OHAYON, J. (2004) Transmission of mechanical stresses within the cytoskeleton of adherent cells: a theoretical analysis based on a multi-component cell model. Acta Biotheor., 52, 323-341.
48. WEINBAUM, S., COWIN, S. C. & ZENG, Y. (1994) A model for the excitation of osteocytes by mechanical loading-induced bone fluid shear stresses. J. Biomech., 27, 339-360.
49. WILSON, D. J., KING, J. R. & BYRNE, H. M. (2007) Modelling scaffold occupation by a growing, nutrient-rich tissue. Math. Models Methods Appl. Sci., 17, 1721.
50. WOOD, M. A., MARSHALL, G., YANG, Y. & EL HAJ, A. (2003) Seeding efficiency and distribution of primary osteoblasts in 3D porous poly (L-lactide) scaffolds. Eur. Cells Mater., 6, 58.
51. WOOD, M. A., YANG, Y., THOMAS, P. B. M. & HAJ, A. J. E. (2006) Using dihydropyridine-release strategies to enhance load effects in engineered human bone constructs. Tissue Eng., 12, 2489-2497.
52. YOU, J., YELLOWLEY, C. E., DONAHUE, H. J., ZHANG, Y., CHEN, Q. & JACOBS, C. R. (2000) Substrate deformation levels associated with routine physical activity are less stimulatory to bone cells relative to loadinginduced oscillatory fluid flow. J. Biomech. Eng., 122, 377-393.
53. YOU, L., COWIN, S. C., SCHAFFLER, M. B. & WEINBAUM, S. (2001) A model for strain amplification in the actin cytoskeleton of osteocytes due to fluid drag on pericellular matrix. J. Biomech., 34, 1375-1386.
54. ZAUDERER, E. (1989) Partial Differential Equations of Applied Mathematics, 2nd edn. New York: Wiley Interscience.