Angiogenesis in bone fracture healing: A bioregulatory model

Journal of Theoretical Biology

Volumn 251, Issue 1, 2008, Pages 137-158

  Geris, Liesbet ^a   Gerisch, Alf ^b   Sloten, Jos Vander ^a   Weiner, Rüdiger ^b   Oosterwyck, Hans Van ^a  

^a UNIVERSITY OF LEUVEN   (Belgium)

^b MARTIN LUTHER UNIVERSITY HALLE WITTENBERG   (Germany)

Author keywords

Angiogenesis; Bone regeneration; Cell migration; Fracture healing; Mathematical model

Indexed keywords

GROWTH FACTOR;

BIOCHEMISTRY; BONE; COMPARATIVE STUDY; EXPERIMENTAL STUDY; NUMERICAL MODEL; RODENT; SENSITIVITY ANALYSIS; SPATIOTEMPORAL ANALYSIS;

ANGIOGENESIS; ARTICLE; BONE REGENERATION; CELL MIGRATION; FRACTURE; FRACTURE HEALING; MATHEMATICAL ANALYSIS; PRIORITY JOURNAL; SIMULATION; TISSUE DISTRIBUTION;

ANIMALS; BONE REGENERATION; CELL MOVEMENT; COMPUTER SIMULATION; FRACTURE HEALING; FRACTURES, BONE; INTERCELLULAR SIGNALING PEPTIDES AND PROTEINS; MODELS, ANIMAL; MODELS, BIOLOGICAL; NEOVASCULARIZATION, PHYSIOLOGIC; OSTEOBLASTS; RATS;

RODENTIA;

EID: 39149101807     PISSN: 00225193     EISSN: 10958541     Source Type: Journal    
DOI: 10.1016/j.jtbi.2007.11.008     Document Type: Article

References (113)

1. Ahrens M., Ankenbauer T., Schroder D., Hollnagel A., Mayer H., and Gross G. Expression of human bone morphogenetic proteins-2 or -4 in murine mesenchymal progenitor C3H10T1/2 cells induces differentiation into distinct mesenchymal cell lineages. DNA Cell Biol. 12 10 (1993) 871-880
2. Ambrosi D., Gamba A., and Serini G. Cell directional and chemotaxis in vascular morphogenesis. Bull. Math. Biol. 66 (2004) 1851-1873
3. Amir L.R., Becking A.G., Jovanovic A., Perdijk F.B., Everts V., and Bronckers A.L. Formation of new bone during vertical distraction osteogenesis of the human mandible is related to the presence of blood vessels. Clin. Oral Implants Res. 17 4 (2006) 410-416
4. Anderson A.R.A., and Chaplain M.A.J. Continuous and discrete mathematical models of tumor-induced angiogenesis. Bull. Math. Biol. 60 (1998) 857-900
5. Bailón-Plaza A., and van der Meulen M.C.H. A mathematical framework to study the effects of growth factor influences on fracture healing. J. Theor. Biol. 212 (2001) 191-209
6. Bailón-Plaza A., and van der Meulen M.C.H. Beneficial effects of moderate, early loading and adverse effects of delayed or excessive loading on bone healing. J. Biomech. 36 (2003) 1069-1077
7. Bancroft G.N., Sikavitsas V.I., van den Dolder J., Sheffield T.L., Ambrose C.G., Jansen J.A., and Mikos A.G. Fluid flow increases mineralized matrix deposition in 3D perfusion culture of marrow stromal osteoblasts in a dose-dependent manner. Proc. Natl Acad. Sci. 99 20 (2002) 12600-12605
8. Barnes G.L., Kostenuik P.J., Gerstenfeld L.C., and Einhorn T.A. Growth factor regulation of fracture repair. J. Bone Miner. Res. 14 11 (1999) 1805-1815
9. Bland Y.S., Critchlow M.A., and Ashhurst D.E. The expression of the fibrillar collagen genes during fracture healing: heterogeneity of the matrices and differentiation of the osteoprogenitor cells. Histochem. J. 31 (1999) 797-809
10. Bolander M.E. Regulation of fracture repair by growth factors. Proc. Soc. Exp. Biol. Med. 200 (1992) 165-170
11. Bruder S.P., and Scaduto T. Cell-based strategies for bone regeneration: from developmental biology to clinical therapy. In: Lieberman J.R., and Friedlaender G.E. (Eds). Bone Regeneration and Repair: Biology and Clinical Applications (2005), Humana Press Inc, Otowa, NJ 67-92
12. Carano R.A.D., and Filvaroff E.H. Angiogenesis and bone repair. Drug Discovery Today 8 21 (2003) 980-989
13. Carter D.R., Beaupré G.S., Giori N.J., and Helms J.A. Mechanobiology of skeletal regeneration. Clin. Orthop. Relat. Res. 355S (1998) S41-S55
14. Chai B., Tang X., and Li H. Osteogenic role played by fibroblasts in secondary healing of fracture. Chin. J. Traumatol. 2 (1999) 53-56
15. Claes L.E., Heigele C.A., Neidlinger-Wilke C., Kaspar D., Seidl W., Margevicius K.J., and Augat P. Effects of mechanical factors on the fracture healing process. Clin. Orthop. Relat. Res. 355S (1998) S132-S147
16. Coffey R.J., Russell W.E., and Barnard J.A. Pharmacokinetics of TGF beta with emphasis on effects in liver and gut. Ann. N.Y. Acad. Sci. 593 (1990) 285-291
17. Colnot C., Thompson Z., Miclau T., Werb Z., and Helms J.A. Altered fracture repair in the absence of MMP9. Development 130 (2003) 4123-4133
18. Cramer T., Schipani E., Johnson R.S., Swoboda B., and Pfander D. Expression of VEGF isoforms by epiphyseal chondrocytes during low-oxygen tension is HIF-1alfa dependent. Osteoarthr. Cart. 12 (2004) 433-439
19. Darling E.M., and Athanasiou K.A. Articular cartilage bioreactors and bioprocesses. Tissue Eng. 1 (2003) 9-26
20. Dasch J.R., Pace D.R., Waegell W., Inenaga D., and Ellingsworth L. Monoclonal antibodies recognizing transforming growth factor-beta. Bioactivity neutralization and transforming growth factor beta 2 affinity purification. J. Immunol. 142 (1989) 1536-1541
21. Deckers M.M., Karperien M., van der Bent C., Yamashita T., Papapoulos S.E., and Lowik C.W. Expression of vascular endothelial growth factors and their receptors during osteoblast differentiation. Endocrinology 141 5 (2000) 1667-1674
22. Deckers M.M., van Beek E.R., van der Pluijm G., Wetterwald A., van der Wee-Pals L.J.A., Cecchini M.G., Papapoulos S.E., and Lowik C.W. Dissociation of angiogenesis and osteoclastogenesis during endochondral bone formation in neonatal mice. J. Bone Miner. Res. 17 (2002) 998-1007
23. Dickinson R.B., and Tranquillo R.T. A stochastic model for adhesion-mediated cell random motility and haptokinesis. J. Math. Biol. 31 (1993) 563-600
24. Dimitriou R., Tsiridis E., and Giannoudis P.V. Current concepts of molecular aspects of bone healing. Injury 36 12 (2005) 1392-1404
25. Edelman E.R., Nugent M.A., and Karnovsky M.J. Perivascular and intravenous administration of basic fibroblast growth factor: vascular and solid organ deposition. Proc. Natl Acad. Sci. USA 90 (1993) 1513-1517
26. Ehrlich P.J., and Lanyon L.E. Mechanical strain and bone cell function: a review. Osteoporos. Int. 13 (2002) 688-700
27. Einhorn T.A. Enhancement of fracture healing. J. Bone J. Surg. Am. 77 (1995) 940-956
28. Einhorn T.A. The cell and molecular biology of fracture healing. Clin. Orthop. Relat. Res. 355S (1998) S7-S21
29. Enomoto-Iwamoto M., Iwamoto M., Mukudai Y., Kawakami Y., Nohno T., Higuchi Y., Takemoto S., Ohuchi H., Noji S., and Kurisu K. Bone morphogenetic protein signaling is required for maintenance of differentiated phenotype, control of proliferation, and hypertrophy in chondrocytes. J. Cell Biol. 140 (1998) 409-418
30. Fang T.D., Salim A., Xia W., Nacamuli R.P., Guccione S., Song H.M., Carano R.A., Filvaroff E.H., Bednarski M.D., Giaccia A.J., and Longaker M.T. Angiogenesis is required for successful bone induction during distraction osteogenesis. J. Bone Miner. Res. 20 7 (2005) 1114-1124
31. Fiedler J., Etzel N., and Brenner R. To go or not to go: migration of human mesenchymal progenitor cells stimulated by isoforms of PDGF. J. Cell. Biochem. 93 (2004) 990-998
32. Fiedler J., Leucht F., Waltenberger J., Dehio C., and Brenner R.E. VEGF-A and PlGF-1 stimulate chemotactic migration of human mesenchymal progenitor cells. Biochem. Biophys. Res. Commun. 334 (2005) 561-568
33. Filion R.J., and Popel A.S. A reaction-diffusion model of basic fibroblast growth factor interactions with cell surface receptors. Ann. Biomed. Eng. 32 (2004) 645-663
34. Friedl P., Zänker K.S., and Bröcker E.B. Cell migration strategies in 3-d extracellular matrix: differences in morphology, cell matrix interactions, and integrin function. Microsc. Res. Tech. 43 (1998) 369-378
35. Gerber H.-P., Vu T.H., Ryan A.M., Kowalski J., Werb Z., and Ferrara N. VEGF couples hypertrophic cartilage remodeling, ossification and angiogenesis during endochondral bone formation. Nat. Med. 5 (1999) 623-628
36. Geris L., Van Oosterwyck H., Vander Sloten J., Duyck J., and Naert I. Assessment of mechanobiological models for the numerical simulation of tissue differentiation around immediately loaded implants. Comp. Methods Biomech. Biomed. Eng. 6 (2003) 277-288
37. Geris L., Andreykiv A., Van Oosterwyck H., Vander Sloten J., van Keulen F., Duyckc J., and Naert I. Numerical simulation of tissue differentiation around loaded titanium implants in a bone chamber. J. Biomech. 37 (2004) 763-769
38. Geris L., Gerisch A., Maes C., Carmeliet G., Weiner R., Vander Sloten J., and Van Oosterwyck H. Mathematical modeling of fracture healing in mice: comparison between experimental data and numerical simulation results. Med. Biol. Eng. Comp. 44 4 (2006) 280-289
39. Geris, L., Vandamme, K., Naert, I., Vander Sloten, J., Duyck, J., Van Oosterwyck, H., 2007. Application of mechanoregulatory models to simulate peri-implant tissue formation in an in vivo bone chamber. J. Biomech. doi:10.1016/j.jbiomech.2007.07.008.
40. Gerisch, A., 2001. Numerical methods for the simulation of taxis-diffusion-reaction systems. Ph.D. Thesis, Martin-Luther-Universität Halle-Wittenberg, Germany.
41. Gerisch A., and Chaplain M.A.J. Robust numerical methods for taxis-diffusion-reaction systems: applications to biomedical problems. Math. Comput. Model. 43 (2005) 49-75
42. Gerisch A., and Geris L. A finite volume spatial discretisation for taxis-diffusion-reaction systems with axi-symmetry: application to fracture healing. In: Deutsch A., Brusch L., Byrne H., de Vries G., and Herzel H.P. (Eds). Advances in Mathematical Modeling of Biological Systems vol. I (2007), Birkhäuser, Boston 299-311
43. Gerstenfeld L.C., Cullinane D.M., Barnes G.L., Graves D.T., and Einhorn T.A. Fracture healing as a post-natal developmental process: molecular, spatial, and temporal aspects of its regulation. J. Cell. Biochem. 88 (2003) 873-884
44. Glowacki J. Angiogenesis in fracture repair. Clin. Orthop. Rel. Res. 355S (1998) S82-S89
45. Gómez-Benito M.J., García-Aznar J.M., Kuiper J.H., and Doblaré M. Influence of fracture gap size on the pattern of long bone healing: a computational study. J. Theor. Biol. 235 (2005) 105-119
46. Gruler H., and Bültmann B.D. Analysis of cell movement. Blood cells 10 (1984) 61-77
47. Guenther H.L., Fleisch H., and Sorgente N. Endothelial cells in culture secrete a potent bone cell active mitogen. Endocrinology 119 (1986) 193-201
48. Hadjiargyrou M., Lombardo F., Zhao S., Ahrens W., Joo J., Ahn H., Jurman M., White D.W., and Rubin C.T. Transcriptional profiling of bone regeneration. J. Biol. Chem. 277 33 (2002) 30177-30182
49. Harrison L.J., Cunningham J.L., Strömberg L., and Goodship A.E. Controlled induction of a pseudarthrosis: a study using a rodent model. J. Orthop. Trauma 17 (2003) 11-21
50. Hee C.K., Jonikas M.A., and Nicoll S.B. Influence of three-dimensional scaffold on the expression of osteogenic differentiation markers by human dermal fibroblasts. Biomaterials 27 6 (2006) 875-884
51. Helm C.E., Fleury M.E., Zisch A.H., Boschetti F., and Swartz M.A. Synergy between interstitial flow and VEGF directs capillary morphogenesis in vitro through a gradient amplification mechanism. Proc. Natl Acad. Sci. USA 102 (2005) 15779-15784
52. Henle P., Zimmermann G., and Weiss S. Matrix metalloproteinases and failed fracture healing. Bone 37 (2005) 791-798
53. Hundsdorfer W., and Verwer J.G. Numerical solution of time-dependent advection-diffusion-reaction equations. Springer Series in Computational Mathematics vol. 33 (2003), Springer, Berlin
54. Isaksson, H., Comas, O., van Donkelaar, C., Mediavilla, J., Wilson, W., Huiskes, R., Ito, K., 2006. Bone regeneration during distraction osteogenesis: mechano-regulation by shear strain and fluid velocity. J. Biomech, available online.
55. Jagodzinski M., Drescher M., Zeichen J., Hankemeier S., Krettek C., Bosch U., and van Griensven M. Effects of cyclic longitudinal mechanical strain and dexamethasone on osteogenic differentiation of human bone marrow stromal cells. Eur. Cell Mater. 7 (2004) 35-41
56. Joyce M.E., Terek R.M., Jingushi S., and Bolander M.E. Role of transforming growth factor-b in fracture repair. Ann. N. Y. Acad. Sci. 593 (1990) 107-123
57. Kaspar D., Seidl W., Neidlinger-Wilke C., Ignatius A., and Claes L. Dynamic cell stretching increases human osteoblast proliferation and CICP synthesis but decreases osteocalcin synthesis and alkaline phosphatase activity. J. Biomech. 33 (2000) 45-51
58. Kasperk C.H., Börcsök I., Schairer H.U., Schneider U., Nawroth P.P., Niethard F.U., and Ziegler R. Endothelin-1 is a potent regulator of human bone cell metabolism in vitro. Calcif. Tissue Int. 60 (1997) 368-374
59. Knippenberg M., Helder M.N., Doulabi B.Z., Semeins C.M., Wuisman P.I., and Klein-Nulend J. Adipose tissue-derived mesenchymal stem cells acquire bone cell-like responsiveness to fluid shear stress on osteogenic stimulation. Tissue Eng. 11 11-12 (2005) 1780-1788
60. Kreke M.R., Huckle W.R., and Goldstein A.S. Fluid flow stimulates expression of osteopontin and bone sialoprotein by bone marrow stromal cells in a temporally dependent manner. Bone 36 6 (2005) 1047-1055
61. Kuntz R.M., and Saltzman W.M. Neutrophil motility in extra-cellular matrix gels: mesh size and adhesion affect speed of migration. Biophys. J. 72 3 (1997) 1472-1480
62. Lacroix D., and Prendergast P.J. A mechano-regulation model for tissue differentiation during fracture healing: analysis of gap size and loading. J. Biomech. 35 (2002) 1163-1171
63. Laplantine E., Rossi F., Sahni M., Basilico C., and Cobrinik D. FGF signaling targets the pRb-related p107 and p130 proteins to induce chondrocyte growth arrest. J. Cell Biol. 158 (2002) 741-750
64. Lee T.-Y.J., and Gotlieb A.I. Early stages of endothelial wound repair: conversion of quiescent to migrating endothelial cells involves tyrosine phosphorylation and actin microfilament reorganization. Cell Tissue Res. 297 (1999) 435-450
65. Li Y.J., Batra N.N., You L., Meier S.C., Coe I.A., Yellowley C.E., and Jacobs C.R. Oscillatory fluid flow affects human marrow stromal cell proliferation and differentiation. J. Orthop. Res. 22 (2004) 1283-1289
66. Li G., Cui Y., McIlmurray L., Allen W.A., and Wang H. rhBMP-2, rhVEGF165, rhPTN and thrombin-related peptide, TP508 induce chemotaxis of human osteoblasts and microvascular endothelial cells. J. Orthop. Res. 23 (2005) 680-685
67. Lienau J., Schell H., Duda G.N., Seebeck P., Muchow S., and Bail H.J. Initial vascularization and tissue differentiation are influenced by fixation stability. J Orthop. Res. 23 3 (2005) 639-645
68. Lin W.L., McCulloch C.A., and Cho M.I. Differentiation of periodontal ligament fibroblasts into osteoblasts during socket healing after tooth extraction in the rat. Anat. Rec. 240 4 (1994) 492-506
69. Lind M., Eriksen E.F., and Bünger C. Bone morphogenetic protein-2 but not bone morphogenetic protein-4 and -6 stimulates chemotactic migration of human osteoblasts, human marrow osteoblasts, and U2-OS cells. Bone 18 (1996) 53-57
70. Lu C., Miclau T., Hu D., and Marcucio R.S. Ischemia leads to delayed union during fracture healing: a mouse model. J. Orthop. Res. 25 1 (2007) 51-61
71. Lutolf M.P., Lauer-Fields J.L., Schmoekel H.G., Metters A.T., Weber F.E., Fields G.B., and Hubbell J.A. Synthetic matrix metalloproteinase-sensitive hydrogels for the conduction of tissue regeneration: engineering cell-invasion characteristics. Proc. Natl Acad. Sci. 100 9 (2003) 5413-5418
72. Maes, C., 2004. Angiogenesis and bone: the role of the vascular endothelial growth factor family in bone development and repair. Ph.D. Thesis (Acta Biomedica Lovaniensia 310), Leuven University Press, Leuven, Belgium.
73. Maes C., Carmeliet P., Moermans K., Stockmans I., Smets N., Collen D., Bouillon R., and Carmeliet G. Impaired angiogenesis and endochondral bone formation in mice lacking the vascular endothelial growth factor isoforms VEGF164 and VEGF188. Mech. Dev. 111 (2002) 61-73
74. Maes C., Coenegrachts L., Stockmans I., Daci E., Luttun A., Petryk A., Gopalakrishnan R., Moermans K., Smets N., Verfaillie C.M., Carmeliet P., Bouillon R., and Carmeliet G. Placental growth factor mediates mesenchymal cell development, cartilage turnover, and bone remodeling during fracture repair. J. Clin. Invest. 116 (2006) 1230-1242
75. Maheswari G., Wells A., Griffith L.G., and Lauffenburger D.A. Biophysical integration of effects of epidermal growth factor and fibronectin on fibroblast migration. Biophys. J. 76 (1999) 2814-2823
76. Malizos K.N., and Papatheodorou L.K. The healing potential of the periosteum, molecular aspects. Injury 36S (2005) S13-S19
77. Mayer H., Bertram H., Lindenmaier W., Korff T., Weber H., and Weich H. Vascular endothelial growth factor (VEGF-A) expression in human mesenchymal stem cells: autocrine and paracrine role on osteoblastic and endothelial differentiation. J. Cell. Biochem. 95 (2005) 827-839
78. Mayr-Wohlfart U., Waltenberger J., Hausser H., Kessler S., Günther K.-P., Dehio C., Puhl W., and Brenner R.E. Vascular endothelial growth factor stimulates chemotactic migration of primary human osteoblasts. Bone 30 (2002) 472-477
79. Metheny-Barlow L.J., Tian S., Hayes A.J., and Li L.Y. Direct chemotactic action of angiopoietin-1 on mesenchymal cells in the presence of VEGF. Microvasc. Res. 68 (2004) 221-230
80. Michaeli Y., Shamir D., Weinreb M., and Steigman S. Effect of loading on the migration of periodontal fibroblasts in the rat incisor. J Periodontal Res. 29 1 (1994) 25-34
81. Midy V., and Plouet J. Vasculotropin/vascular endothelial growth factor induces differentiation in cultured osteoblasts. Biochem. Biophys. Res. Commun. 199 (1994) 380-386
82. Nagy J.A., and Senger D.R. VEGF-A, cytoskeletal dynamics, and the pathological vascular phenotype. Exp. Cell Res. 312 (2006) 538-548
83. Nogami H., and Oohira A. Postnatal new bone formation. Clin. Orthop. Relat. Res. 184 (1984) 106-113
84. Olsen L., Sherratt J., and Maini P. A mechanochemical model for adult dermal wound contraction and the permanence of the contracted tissue displacement profile. J. Theor. Biol. 177 (1995) 113-128
85. Olsen L., Sherratt J., Maini P., and Arnold F. A mathematical model for the capillary endothelial cell-extracellular matrix interactions in wound-healing angiogenesis. IMA J. Math. Appl. Med. Biol. 14 (1997) 261-281
86. Ortega N., Behonick D.J., and Werb Z. Matrix remodeling during endochondral ossification. Trends Cell Biol. 14 2 (2004) 86-93
87. Peng H., Wright V., Usas A., Gearhart B., Shen H.C., Cummins J., and Huard J. Synergistic enhancement of bone formation and healing by stem cell-expressed VEGF and bone morphogenetic protein-4. J. Clin. Invest. 110 6 (2002) 751-759
88. Postlethwaite A.E., Keski-Oja J., Moses H.L., and Kang A.H. Simulation of the chemotactic migration of human fibroblasts by transforming growth factor β. J. Exp. Med. 165 (1987) 251-256
89. Pountos I., and Giannoudis P.V. Biology of mesenchymal stem cells. Injury 36S (2005) S8-S12
90. Prendergast P.J., Huiskes R., and Søballe K. Biophysical stimuli on cells during tissue differentiation at implant interfaces. J. Biomech. 30 (1997) 539-548
91. Pufe T., Kurz B., Petersen W., Varoga D., Mentlein R., Kulow S., Lemke A., and Tillmann B. The influence of biomechanical parameters on the expression of VEGF and endostatin in the bone and joint system. Ann. Anat. 187 5-6 (2005) 461-472
92. Rickard D.J., Sullivan T.A., Shenker B.J., Leboy P.S., and Kazhdan I. Induction of rapid osteoblast differentiation in rat bone marrow stromal cell cultures by dexamethasone and BMP-2. Dev. Biol. 161 1 (1994) 218-228
93. Rossi F., MacLean H.E., Yuan W., Francis R.O., Semenova E., Lin C.S., Kronenberg H.M., and Cobrinik D. p107 and p130 coordinately regulate proliferation, Cbfa1 expression, and hypertrophic differentiation during endochondral bone development. Dev. Biol. 247 (2002) 271-285
94. Rupnick M.A., Stokes C.L., Williams S.K., and Lauffenburger D.A. Quantitative analysis of human microvessel endothelial cells using a linear under-agarose assay. Lab. Invest. 59 (1988) 363-372
95. Sakai K., Mohtai M., and Iwamoto Y. Fluid shear stress increases transforming growth factor beta 1 expression in human osteoblast-like cells: modulation by cation channel blockades. Calcif. Tissue Int. 63 6 (1998) 515-520
96. Sato Y., and Rifkin D.B. Autocrine activities of basic FGF: regulation of cell movement, plasminogen activator synthesis and DNA synthesis. J. Cell. Biol. 107 (1988) 1199-1205
97. Seppä H., Grotendorst G., Seppä S., Schiffmann E., and Martin G.R. Platelet-derived growth factor is chemotactic for fibroblasts. J. Cell Biol. 92 (1982) 584-588
98. Shefelbine S.J., Augat P., Claes L., and Simon U. Trabecular bone fracture healing simulation with finite element analysis and fuzzy logic. J. Biomech. 38 12 (2005) 2440-2450
99. Sherratt J. Chemotaxis and chemokinesis in eukaryotic cells: the Keller-Segel equations as an approximation to a detailed model. Bull. Math. Biol. 56 (1994) 129-146
100. Shima D.T., Deutsch U., and D'Amore P.A. Hypoxic induction of vascular endothelial growth factor (VEGF) in human epithelial cells is mediated by increases in mRNA stability. FEBS Lett. 370 (1995) 203-208
101. Stokes C.L., Rupnick M.A., Williams S.K., and Lauffenburger D.A. Chemotaxis of human microvessel endothelial cells in response to acidic fibroblast growth factor. Lab. Invest. 63 (1990) 657-668
102. Street J., Bao M., deGuzman L., Bunting S., Peale Jr. F.V., Ferrara N., Steinmetz H., Hoeffel J., Cleland J.L., Daugherty A., van Bruggen N., Redmond H.P., Carano R.A.D., and Filvaroff E.H. Vascular endothelial growth factor stimulates bone repair by promoting angiogenesis and bone turnover. Proc. Natl Acad. Sci. USA 99 15 (2002) 9656-9661
103. Taguchi K., Ogawa R., Migita M., Hanawa H., Ito H., and Orimo H. The role of bone marrow-derived cells in bone fracture repair in a green fluorescent protein chimeric mouse model. Biochem. Biophys. Res. Commun. 331 (2005) 31-36
104. Terranova V.P., Diflorio R., Lyall R.M., Hic S., Friesel R., and Maciag T. Human endothelial cells are chemotactic to endothelial cell growth factor and heparin. J. Cell Biol. 101 (1985) 2330-2334
105. Thies R.S., Bauduy M., Ashton B.A., Kurtzberg L., Wozney J.M., and Rosen V. Recombinant human bone morphogenetic protein-2 induces osteoblastic differentiation in W-20-17 stromal cells. Endocrinology 130 3 (1992) 1318-1324
106. Thorne R.G., Hrabetova S., and Nicholson C. Diffusion of epidermal growth factor in rat brain extracellular space measured by integrative optical imaging. J. Neurophysiol. 92 (2004) 3471-3481
107. Vander A., Sherman J., and Luciano D. Human Physiology: The Mechanisms of Body Function (1998), WCB McGraw-Hill, Boston, MA
108. Villenueva J.E., and Nimni M.E. Promotion of calvarial cell osteogenesis by endothelial cells. J. Bone Miner. Res. 5 (1997) 733-739
109. Weinberg C.B., and Bell E. Regulation of proliferation of bovine aortic endothelial cells, smooth muscle cells and adventitial fibroblasts in collagen lattices. J. Cell. Physiol. 122 (1985) 410-414
110. Weiner R., Schmitt B.A., and Podhaisky H. ROWMAP-a ROW-code with Krylov techniques for large stiff ODEs. Appl. Numer. Math. 25 (1997) 303-319
111. Yoshizato K., Taira T., and Yamamoto N. Growth inhibition of human fibroblasts by reconstituted collagen fibrils. Biomed. Res. 6 (1985) 61-71
112. Zaman M.H., Trapani L.M., Sieminski A.L., MacKellar D., Gong H., Kamm R.D., Wells A., Lauffenburger D.A., and Matsudaira P. Migration of tumor cells in 3D matrices is governed by matrix stiffness along with cell-matrix adhesion and proteolysis. Proc. Natl Acad. Sci. 103 29 (2006) 10889-10894
113. Zhang X., Sui S., Bao K., and Zeng B. Osteoporosis influence the fracture healing in ovariectomized rat: ultrastructure study. Chin. Med. J. 114 (2001) 15-21