Optimal planar flow network designs for tissue engineered constructs with built-in vasculature

Annals of Biomedical Engineering

Volumn 35, Issue 3, 2007, Pages 337-347

  Janakiraman, Vijayakumar ^a   Mathur, Kamlesh ^b   Baskaran, Harihara ^a  

^a Case Western Reserve University   (United States)

^b CASE WESTERN RESERVE UNIVERSITY   (United States)

Author keywords

Duct flow; Flow networks; Mass transport; Mathematical modeling; Microfabrication; Microvascular engineering; Nutrient transport; Optimization; Tissue engineering; Vascular engineering

Indexed keywords

ALGORITHMS; BIFURCATION (MATHEMATICS); GROWTH KINETICS; MASS TRANSPORTATION; OPTIMIZATION; PROBLEM SOLVING;

DUCT FLOW; FLOW NETWORKS; MICROFABRICATION; MICROVASCULAR ENGINEERING; NUTRIENT TRANSPORT; VASCULAR ENGINEERING;

TISSUE CULTURE;

ARTICLE; BIOLOGICAL MODEL; MICROCIRCULATION; PHYSIOLOGY; POROSITY; TISSUE ENGINEERING;

MICROCIRCULATION; MODELS, BIOLOGICAL; POROSITY; TISSUE ENGINEERING;

EID: 33847273873     PISSN: 00906964     EISSN: 15739686     Source Type: Journal    
DOI: 10.1007/s10439-006-9235-0     Document Type: Article

References (40)

1. Baba, K., T. Kawamura, M. Shibata, M. Sohirad, and A. Kamiya. Capillary-tissue arrangement in the skeletal muscle optimized for oxygen transport in all mammals. Microvasc. Res. 49(2): 163-179, 1995.
2. Bentley, G., and R. B. Greer 3rd. Homotransplantation of isolated epiphyseal and articular cartilage chondrocytes into joint surfaces of rabbits. Nature 230(5293):385-388, 1971.
3. Chu, T. M., D. G. Orton, S. J. Hollister, S. E. Feinberg, and J. W. Halloran. Mechanical and in vivo performance of hydroxyapatite implants with controlled architectures. Biomaterials 23(5): 1283-1293, 2002.
4. Constantinescu, V. N. Laminar Viscous FlowSpringer, New York.
5. Dantzer, E., and F. M. Braye. Reconstructive surgery using an artificial dermis (Integra): results with 39 grafts. Br. J. Plast. Surg. 54(8):659-664, 2001.
6. Dunn, J. C., M. L. Yarmush, H. G. Koebe, and R. G. Tompkins. Hepatocyte function and extracellular matrix geometry: long-term culture in a sandwich configuration. Faseb J. 3(2):174-177, 1989.
7. Fitton, A. R., P. Drew, and W. A. Dickson. The use of a bilaminate artificial skin substitute (Integra) in acute resurfacing of burns: an early experience. Br. J. Plast. Surg. 54(3):208-212, 2001.
8. Freitas, R. A. NanomedicineLandes Bioscience, Austin, TX.
9. Gafiychuk, V. V., and I. A. Lubashevsky. On the principles of the vascular network branching. J. Theor. Biol. 212(1):1-9, 2001.
10. Ganong, W. F. Review of Medical PhysiologyAppleton and Lange, Norwalk.
11. Godde, R., and H. Kurz. Structural and biophysical simulation of angiogenesis and vascular remodeling. Dev. Dyn. 220(4):387-401, 2001.
12. Griffith, L. G. and G. Naughton. Tissue engineering - current challenges and expanding opportunities. Science 295(5557):1009-1014, 2002.
13. Guyton, A. C. and J. E. Hall. Textbook of Medical Physiology. W.B. Saunders Company, Philadelphia.
14. Hutmacher, D. W. Scaffolds in tissue engineering bone and cartilage Biomaterials 21(24):2529-2543, 2000.
15. Kaihara, S., J. Borenstein, R. Koka, S. Lalan, E. R. Ochoa, M. Ravens, H. Pien, B. Cunningham, and J. P. Vacanti. Silicon micromachining to tissue engineer branched vascular channels for liver fabrication. Tissue Eng. 6(2): 105-117, 2000.
16. Karch, R., F. Neumann, M. Neumann, and W. Schreiner. Staged growth of optimized arterial model trees. Ann. Biomed. Eng. 28(5):495-511, 2000.
17. Klarbring, A., J. Petersson, B. Torstenfelt, and M. Karlsson. Topology optimization of flow networks. Comput. Methods Appl. Mech. Eng. 192(35-36):3909-3932, 2003.
18. Ko, I. K. and H. Iwata. An approach to constructing three-dimensional tissue. Ann. NY Acad. Sci. 944:443-455, 2001.
19. Langer, R. and J. P. Vacanti. Tissue engineering. Science 260(5110):920-926, 1993.
20. Lasdon, L. S., A. D. Waren, A. Jain, and M. Ratner. Design and testing of a generalized reduced gradient code for nonlinear programming. ACM Trans. Math. Software 4(1):34-50, 1978.
21. Ma, P. X. and R. Zhang. Microtubular architecture of biodegradable polymer scaffolds. J. Biomed. Mater. Res. 56(4):469-477, 2001.
22. Mantzaris, N. V., S. Webb, and H. G. Othmer. Mathematical modeling of tumor-induced angiogenesis. J. Math. Biol. 49(2):111-187, 2004.
23. McDougall, S. R., A. R. Anderson, and M. A. Chaplain. Mathematical modelling of dynamic adaptive tumourinduced angiogenesis: clinical implications and therapeutic targeting strategies. J. Theor. Biol. 241(3):564-589, 2006.
24. McDougall, S. R., A. R. Anderson, M. A. Chaplain, and J. A. Sherratt. Mathematical modelling of flow through vascular networks: implications for tumour-induced angiogenesis and chemotherapy strategies. Bull. Math. Biol. 64(4):673-702, 2002.
25. Merchant, F. A., K. R. Diller, S. J. Aggarwal, and A. C. Bovik. Angiogenesis in cultured and cryopreserved pancreatic islet grafts. Transplantation 63(11):1652-1660, 1997.
26. Murphy, W. L., M. C. Peters, D. H. Kohn, and D. J. Mooney. Sustained release of vascular endothelial growth factor from mineralized poly(lactide-co-glycolide) scaffolds for tissue engineering. Biomaterials 21(24):2521-2527, 2000.
27. Neumann, T., B. S. Nicholson, and J. E. Sanders. Tissue engineering of perfused microvessels. Microvasc. Res. 66(1):59-67, 2003.
28. Porter, B. D., J. B. Oldham, S. L. He, M. E. Zobitz, R. G. Payne, K. N. An, B. L. Currier, A. G. Mikos, and M. J. Yaszemski. Mechanical properties of a biodegradable bone regeneration scaffold. J. Biomech. Eng, 122(3):286-288, 2000.
29. Powers, M. J., K. Domansky, M. R. Kaazempur-Mofrad, A. Kalezi, A. Capitano, A. Upadhyaya, P. Kurzawski, K. E. Wack, D. B. Stolz, R. Kamm, and L. G. Griffith. A microfabricated array bioreactor for perfused 3D liver culture. Biotechnol. Bioeng. 78(3):257-269, 2002.
30. Powers, M. J., D. M. Janigian, K. E. Wack, C. S. Baker, D. Beer Stolz, and L. G. Griffith. Functional behavior of primary rat liver cells in a three-dimensional perfused microarray bioreactor. Tissue Eng. 8(3):499-513, 2002.
31. Richardson, T. P., M. C. Peters, A. B. Ennett, and D. J. Mooney. Polymeric system for dual growth factor delivery. Nat. Biotechnol. 19(11): 1029-1034, 2001.
32. Scheuplein, R. J. and I. H. Blank. Permeability of the skin. Physiol. Rev. 51(4):702-747, 1971.
33. Schmidt, R. F. and G. Thews. Human Physiology (2nd ed.). Springer-Verlag, New York.
34. Schreiner, W. Computer generation of complex arterial tree modelsJ. Biomed. Eng. 15(2):148-150, 1993.
35. Schreiner, W., R. Karch, M. Neumann, F. Neumann, S. M. Roedler, and G. Heinze. Heterogeneous perfusion is a consequence of uniform shear stress in optimized arterial tree models. J. Theor. Biol. 220(3):285-301, 2003.
36. Toyota, E., K. Fujimoto, Y. Ogasawara, T. Kajita, F. Shigeto, T. Matsumoto, M. Goto, and F. Kajiya. Dynamic changes in three-dimensional architecture and vascular volume of transmural coronary microvasculature between diastolic- and systolic-arrested rat hearts. Circulation 105(5):621-626, 2002.
37. Vacanti, C. A. and J. Upton. Tissue-engineered morphogenesis of cartilage and bone by means of cell transplantation using synthetic biodegradable polymer matrices. Clin. Plast. Surg. 21(3):445-462, 1994.
38. VanBavel, E. and J. A. Spaan. Branching patterns in the porcine coronary arterial tree. Estimation of flow heterogeneity. Circ. Res. 71(5):1200-1212, 1992.
39. Wechsatol, W., S. Lorente, and A. Bejan. Optimal tree-shaped networks for fluid flow in a disc-shaped body. Int. J. Heat Mass Transfer 45(25):4911-4924, 2002.
40. West, G. B., J. H. Brown, and B. J. Enquist. A general model for the origin of allometric scaling laws in biology. Science 276(5309): 122-126, 1997.