Tissue growth in a rotating bioreactor. Part I: Mechanical stability

Mathematical Medicine and Biology

Volumn 23, Issue 4, 2006, Pages 311-337

  Waters, Sarah L ^a   Cummings, L J ^a   Shakesheff, K M ^a   Rose, F R A J ^a  

^a UNIVERSITY OF NOTTINGHAM   (United Kingdom)

Author keywords

Linear stability; Rotating bioreactor; Rotating Hele Shaw; Rotating Stokes flow; Tissue construct

Indexed keywords

ASPECT RATIO; BIOREACTORS; CELL CULTURE; CELL PROLIFERATION; MECHANICAL STABILITY; ROTATION RATE; TISSUE;

CRITICAL VALUE; CULTURE MEDIUM; HELE-SHAW; LINEAR STABILITY; ROTATING BIOREACTOR; ROTATING HELE-SHAW; ROTATION RATE; TISSUE CONSTRUCTS; TISSUE GROWTH; VISCOUS FLUIDS;

VISCOSITY;

COLLAGEN;

APOPTOSIS; ARTICLE; BIOREACTOR; BIOREACTOR DESIGN; CELL AGGREGATION; CELL CULTURE; CELL PROLIFERATION; CELL STRAIN MCF 7; COMPUTATIONAL FLUID DYNAMICS; HUMAN; HUMAN CELL; MATHEMATICAL ANALYSIS; MATHEMATICAL MODEL; MECHANICAL STRESS; ROTATION; TISSUE ENGINEERING; TISSUE GROWTH; VELOCITY;

EID: 33845414425     PISSN: 14778599     EISSN: 14778602     Source Type: Journal    
DOI: 10.1093/imammb/dql013     Document Type: Article

References (22)

1. ABBOTT, A. (2003) Biology's new dimension. Nature, 424, 870-872.
2. ALVAREZ-LACALLE, L., PAUNE, E., CASADEMUNT, J. & ORTIN, J. (2003) Systematic weakly nonlinear analysis of radial viscous fingering. Phys. Rev. E, 68, 016302.
3. BATCHELOR, G. K. (1967) An Introduction to Fluid Dynamics. Cambridge: Cambridge University Press.
4. BEGLEY, C. M. & KLEIS, S. J. (2000) The fluid dynamic and shear environment in the NASA/JSC rotating-wall perfused-vessel bioreactor. Biotechnol. Bioeng., 70, 32-40.
5. BENSIMON, D., KADANOFF, L. P., LIANG, S., SHRAIMAN, B. I. & TANG, C. (1986) Viscous flows in two dimensions. Rev. Mod. Phys., 58, 977-999.
6. CARRILLO, L.,MAGDALENO, F. X., CASADEMUNT, J. & ORTIN, J. (1996) Experiments in a rotating Hele-Shaw cell. Phys. Rev. E, 54, 6260-6267.
7. CARRILLO, L., SORIANO, J. & ORTIN, J. (1998) Radial displacement of a fluid annulus in a rotating Hele-Shaw cell. Phys. Fluids, 11, 778-785.
8. CARRILLO, L., SORIANO, J. & ORTIN, J. (2000) Interfacial instabilities of a fluid annulus in a rotating Hele-Shaw cell. Phys. Fluids, 12, 1685-1698.
9. CASADEMUNT, J. (2004) Viscous fingering as a paradigm of interfacial pattern formation: Recent results and new challenges. Chaos, 14, 809-824.
10. CUMMINGS, L. J. & WATERS, S. L. Tissue growth in a rotating bioreactor. Part II: Flow and nutrient transport problems. Math. Med. Biol. (submitted).
11. ENTOV, V.M., ETINGOF, P. I. & KLEINBOCK, D. Y. (1995) On nonlinear interface dynamics in Hele-Shaw flows. Eur. J. Appl. Math., 6, 399-420.
12. GADELHA, H. & MIRANDA, J. A. (2004) Finger competition dynamics in rotating Hele-Shaw cells. Phys. Rev. E, 70, 066308.
13. HAMMOND, T. G. & HAMMOND, J. M. (2001) Optimised suspension culture: The rotating-wall vessel. Am. J. Physiol. Renal Physiol., 281, F12-F25.
14. HOMSY, G. M. (1987) Viscous fingering in porous media. Annu. Rev. Fluid Mech., 19, 271-311.
15. LAPPA, M. (2003) Organic tissues in rotating bioreactors: fluid-mechanical aspects, dynamic growth models and morphological evolution. Biotechnol. Bioeng., 84, 518-532.
16. MARTIN, I.,WENDT, D. & HEBERER, M. (2004) The role of bioreactors in tissue engineering. Trends Biotechnol., 17, 1949-1964.
17. PARK, C.-W & HOMSY, G. W. (1984) Two-phase displacement in Hele-Shaw cells: Theory. J. Fluid Mech., 139, 291.
18. PATERSON, L. (1981) Radial fingering in a Hele Shaw cell. J. Fluid Mech., 113, 513-529.
19. SAFFMAN, P. & TAYLOR, G. (1958) The penetration of a fluid into a porous medium or Hele-Shaw cell containing a more viscous fluid. Proc. R. Soc. Lond. A, 245, 312.
20. SCHWARTZ, L. W. (1988) Instability and fingering in a rotating Hele-Shaw cell or porous medium. Phys. Fluids, 1, 167-169.
21. WATERS, S. L. & CUMMINGS, L. J. (2005) Coriolis effects in a rotating Hele-Shaw cell. Phys. Fluids, 17, 048101.
22. WORRALL, L. K., ROSE, F. R. A. J., BRADSHAW, T. D., STEVENS, M. F. G. & SHAKESHEFF, K. M. (2005) Real-time monitoring of a 3D cancer model in the RCCS. Int. J. Exp. Pathol., 86, A26-A26.