Angiogenesis in bone fracture healing: A bioregulatory model

Ahrens, 1993, 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, 871, 10.1089/dna.1993.12.871

Ambrosi, 2004, Cell directional and chemotaxis in vascular morphogenesis, Bull. Math. Biol., 66, 1851, 10.1016/j.bulm.2004.04.004

Amir, 2006, 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, 410, 10.1111/j.1600-0501.2006.01258.x

Anderson, 1998, Continuous and discrete mathematical models of tumor-induced angiogenesis, Bull. Math. Biol., 60, 857, 10.1006/bulm.1998.0042

Bailón-Plaza, 2001, A mathematical framework to study the effects of growth factor influences on fracture healing, J. Theor. Biol., 212, 191, 10.1006/jtbi.2001.2372

Bailón-Plaza, 2003, Beneficial effects of moderate, early loading and adverse effects of delayed or excessive loading on bone healing, J. Biomech., 36, 1069, 10.1016/S0021-9290(03)00117-9

Bancroft, 2002, Fluid flow increases mineralized matrix deposition in 3D perfusion culture of marrow stromal osteoblasts in a dose-dependent manner, Proc. Natl Acad. Sci., 99, 12600, 10.1073/pnas.202296599

Barnes, 1999, Growth factor regulation of fracture repair, J. Bone Miner. Res., 14, 1805, 10.1359/jbmr.1999.14.11.1805

Bland, 1999, The expression of the fibrillar collagen genes during fracture healing: heterogeneity of the matrices and differentiation of the osteoprogenitor cells, Histochem. J., 31, 797, 10.1023/A:1003954104290

Bolander, 1992, Regulation of fracture repair by growth factors, Proc. Soc. Exp. Biol. Med., 200, 165, 10.3181/00379727-200-43410A

Bruder, 2005, Cell-based strategies for bone regeneration: from developmental biology to clinical therapy, 67

Carano, 2003, Angiogenesis and bone repair, Drug Discovery Today, 8, 980, 10.1016/S1359-6446(03)02866-6

Carter, 1998, Mechanobiology of skeletal regeneration, Clin. Orthop. Relat. Res., 355S, S41, 10.1097/00003086-199810001-00006

Chai, 1999, Osteogenic role played by fibroblasts in secondary healing of fracture, Chin. J. Traumatol., 2, 53

Claes, 1998, Effects of mechanical factors on the fracture healing process, Clin. Orthop. Relat. Res., 355S, S132, 10.1097/00003086-199810001-00015

Coffey, 1990, Pharmacokinetics of TGF beta with emphasis on effects in liver and gut, Ann. N.Y. Acad. Sci., 593, 285, 10.1111/j.1749-6632.1990.tb16120.x

Colnot, 2003, Altered fracture repair in the absence of MMP9, Development, 130, 4123, 10.1242/dev.00559

Cramer, 2004, Expression of VEGF isoforms by epiphyseal chondrocytes during low-oxygen tension is HIF-1alfa dependent, Osteoarthr. Cart., 12, 433, 10.1016/j.joca.2004.02.003

Darling, 2003, Articular cartilage bioreactors and bioprocesses, Tissue Eng., 1, 9, 10.1089/107632703762687492

Dasch, 1989, Monoclonal antibodies recognizing transforming growth factor-beta. Bioactivity neutralization and transforming growth factor beta 2 affinity purification, J. Immunol., 142, 1536, 10.4049/jimmunol.142.5.1536

Deckers, 2000, Expression of vascular endothelial growth factors and their receptors during osteoblast differentiation, Endocrinology, 141, 1667, 10.1210/endo.141.5.7458

Deckers, 2002, Dissociation of angiogenesis and osteoclastogenesis during endochondral bone formation in neonatal mice, J. Bone Miner. Res., 17, 998, 10.1359/jbmr.2002.17.6.998

Dickinson, 1993, A stochastic model for adhesion-mediated cell random motility and haptokinesis, J. Math. Biol., 31, 563, 10.1007/BF00161199

Dimitriou, 2005, Current concepts of molecular aspects of bone healing, Injury, 36, 1392, 10.1016/j.injury.2005.07.019

Edelman, 1993, Perivascular and intravenous administration of basic fibroblast growth factor: vascular and solid organ deposition, Proc. Natl Acad. Sci. USA, 90, 1513, 10.1073/pnas.90.4.1513

Ehrlich, 2002, Mechanical strain and bone cell function: a review, Osteoporos. Int., 13, 688, 10.1007/s001980200095

Einhorn, 1995, Enhancement of fracture healing, J. Bone J. Surg. Am., 77, 940, 10.2106/00004623-199506000-00016

Einhorn, 1998, The cell and molecular biology of fracture healing, Clin. Orthop. Relat. Res., 355S, S7, 10.1097/00003086-199810001-00003

Enomoto-Iwamoto, 1998, Bone morphogenetic protein signaling is required for maintenance of differentiated phenotype, control of proliferation, and hypertrophy in chondrocytes, J. Cell Biol., 140, 409, 10.1083/jcb.140.2.409

Fang, 2005, Angiogenesis is required for successful bone induction during distraction osteogenesis, J. Bone Miner. Res., 20, 1114, 10.1359/JBMR.050301

Fiedler, 2004, To go or not to go: migration of human mesenchymal progenitor cells stimulated by isoforms of PDGF, J. Cell. Biochem., 93, 990, 10.1002/jcb.20219

Fiedler, 2005, VEGF-A and PlGF-1 stimulate chemotactic migration of human mesenchymal progenitor cells, Biochem. Biophys. Res. Commun., 334, 561, 10.1016/j.bbrc.2005.06.116

Filion, 2004, A reaction–diffusion model of basic fibroblast growth factor interactions with cell surface receptors, Ann. Biomed. Eng., 32, 645, 10.1023/B:ABME.0000030231.88326.78

Friedl, 1998, Cell migration strategies in 3-d extracellular matrix: differences in morphology, cell matrix interactions, and integrin function, Microsc. Res. Tech., 43, 369, 10.1002/(SICI)1097-0029(19981201)43:5<369::AID-JEMT3>3.0.CO;2-6

Gerber, 1999, VEGF couples hypertrophic cartilage remodeling, ossification and angiogenesis during endochondral bone formation, Nat. Med., 5, 623, 10.1038/9467

Geris, 2003, Assessment of mechanobiological models for the numerical simulation of tissue differentiation around immediately loaded implants, Comp. Methods Biomech. Biomed. Eng., 6, 277, 10.1080/10255840310001634412

Geris, 2004, Numerical simulation of tissue differentiation around loaded titanium implants in a bone chamber, J. Biomech., 37, 763, 10.1016/j.jbiomech.2003.09.026

Geris, 2006, Mathematical modeling of fracture healing in mice: comparison between experimental data and numerical simulation results, Med. Biol. Eng. Comp., 44, 280, 10.1007/s11517-006-0040-6

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.

Gerisch, A., 2001. Numerical methods for the simulation of taxis–diffusion–reaction systems. Ph.D. Thesis, Martin-Luther-Universität Halle-Wittenberg, Germany.

Gerisch, 2005, Robust numerical methods for taxis–diffusion–reaction systems: applications to biomedical problems, Math. Comput. Model., 43, 49, 10.1016/j.mcm.2004.05.016

Gerisch, 2007, A finite volume spatial discretisation for taxis–diffusion–reaction systems with axi-symmetry: application to fracture healing, vol. I, 299

Gerstenfeld, 2003, Fracture healing as a post-natal developmental process: molecular, spatial, and temporal aspects of its regulation, J. Cell. Biochem., 88, 873, 10.1002/jcb.10435

Glowacki, 1998, Angiogenesis in fracture repair, Clin. Orthop. Rel. Res., 355S, S82, 10.1097/00003086-199810001-00010

Gómez-Benito, 2005, Influence of fracture gap size on the pattern of long bone healing: a computational study, J. Theor. Biol., 235, 105, 10.1016/j.jtbi.2004.12.023

Gruler, 1984, Analysis of cell movement, Blood cells, 10, 61

Guenther, 1986, Endothelial cells in culture secrete a potent bone cell active mitogen, Endocrinology, 119, 193, 10.1210/endo-119-1-193

Hadjiargyrou, 2002, Transcriptional profiling of bone regeneration, J. Biol. Chem., 277, 30177, 10.1074/jbc.M203171200

Harrison, 2003, Controlled induction of a pseudarthrosis: a study using a rodent model, J. Orthop. Trauma, 17, 11, 10.1097/00005131-200301000-00003

Hee, 2006, Influence of three-dimensional scaffold on the expression of osteogenic differentiation markers by human dermal fibroblasts, Biomaterials, 27, 875, 10.1016/j.biomaterials.2005.07.004

Helm, 2005, Synergy between interstitial flow and VEGF directs capillary morphogenesis in vitro through a gradient amplification mechanism, Proc. Natl Acad. Sci. USA, 102, 15779, 10.1073/pnas.0503681102

Henle, 2005, Matrix metalloproteinases and failed fracture healing, Bone, 37, 791, 10.1016/j.bone.2005.06.015

Hundsdorfer, 2003, vol. 33

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.

Jagodzinski, 2004, Effects of cyclic longitudinal mechanical strain and dexamethasone on osteogenic differentiation of human bone marrow stromal cells, Eur. Cell Mater., 7, 35, 10.22203/eCM.v007a04

Joyce, 1990, Role of transforming growth factor-b in fracture repair, Ann. N. Y. Acad. Sci., 593, 107, 10.1111/j.1749-6632.1990.tb16104.x

Kaspar, 2000, Dynamic cell stretching increases human osteoblast proliferation and CICP synthesis but decreases osteocalcin synthesis and alkaline phosphatase activity, J. Biomech., 33, 45, 10.1016/S0021-9290(99)00171-2

Kasperk, 1997, Endothelin-1 is a potent regulator of human bone cell metabolism in vitro, Calcif. Tissue Int., 60, 368, 10.1007/s002239900245

Knippenberg, 2005, Adipose tissue-derived mesenchymal stem cells acquire bone cell-like responsiveness to fluid shear stress on osteogenic stimulation, Tissue Eng., 11, 1780, 10.1089/ten.2005.11.1780

Kreke, 2005, Fluid flow stimulates expression of osteopontin and bone sialoprotein by bone marrow stromal cells in a temporally dependent manner, Bone, 36, 1047, 10.1016/j.bone.2005.03.008

Kuntz, 1997, Neutrophil motility in extra-cellular matrix gels: mesh size and adhesion affect speed of migration, Biophys. J., 72, 1472, 10.1016/S0006-3495(97)78793-9

Lacroix, 2002, A mechano-regulation model for tissue differentiation during fracture healing: analysis of gap size and loading, J. Biomech., 35, 1163, 10.1016/S0021-9290(02)00086-6

Laplantine, 2002, FGF signaling targets the pRb-related p107 and p130 proteins to induce chondrocyte growth arrest, J. Cell Biol., 158, 741, 10.1083/jcb.200205025

Lee, 1999, Early stages of endothelial wound repair: conversion of quiescent to migrating endothelial cells involves tyrosine phosphorylation and actin microfilament reorganization, Cell Tissue Res., 297, 435, 10.1007/s004410051370

Li, 2004, Oscillatory fluid flow affects human marrow stromal cell proliferation and differentiation, J. Orthop. Res., 22, 1283, 10.1016/j.orthres.2004.04.002

Li, 2005, rhBMP-2, rhVEGF165, rhPTN and thrombin-related peptide, TP508 induce chemotaxis of human osteoblasts and microvascular endothelial cells, J. Orthop. Res., 23, 680, 10.1016/j.orthres.2004.12.005

Lienau, 2005, Initial vascularization and tissue differentiation are influenced by fixation stability, J Orthop. Res., 23, 639, 10.1016/j.orthres.2004.09.006

Lin, 1994, Differentiation of periodontal ligament fibroblasts into osteoblasts during socket healing after tooth extraction in the rat, Anat. Rec., 240, 492, 10.1002/ar.1092400407

Lind, 1996, 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, 53, 10.1016/8756-3282(95)00423-8

Lu, 2007, Ischemia leads to delayed union during fracture healing: a mouse model, J. Orthop. Res., 25, 51, 10.1002/jor.20264

Lutolf, 2003, Synthetic matrix metalloproteinase-sensitive hydrogels for the conduction of tissue regeneration: engineering cell-invasion characteristics, Proc. Natl Acad. Sci., 100, 5413, 10.1073/pnas.0737381100

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.

Maes, 2002, Impaired angiogenesis and endochondral bone formation in mice lacking the vascular endothelial growth factor isoforms VEGF164 and VEGF188, Mech. Dev., 111, 61, 10.1016/S0925-4773(01)00601-3

Maes, 2006, Placental growth factor mediates mesenchymal cell development, cartilage turnover, and bone remodeling during fracture repair, J. Clin. Invest., 116, 1230, 10.1172/JCI26772

Maheswari, 1999, Biophysical integration of effects of epidermal growth factor and fibronectin on fibroblast migration, Biophys. J., 76, 2814, 10.1016/S0006-3495(99)77435-7

Malizos, 2005, The healing potential of the periosteum, molecular aspects, Injury, 36S, S13, 10.1016/j.injury.2005.07.030

Mayer, 2005, 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, 827, 10.1002/jcb.20462

Mayr-Wohlfart, 2002, Vascular endothelial growth factor stimulates chemotactic migration of primary human osteoblasts, Bone, 30, 472, 10.1016/S8756-3282(01)00690-1

Metheny-Barlow, 2004, Direct chemotactic action of angiopoietin-1 on mesenchymal cells in the presence of VEGF, Microvasc. Res., 68, 221, 10.1016/j.mvr.2004.08.005

Michaeli, 1994, Effect of loading on the migration of periodontal fibroblasts in the rat incisor, J Periodontal Res., 29, 25, 10.1111/j.1600-0765.1994.tb01087.x

Midy, 1994, Vasculotropin/vascular endothelial growth factor induces differentiation in cultured osteoblasts, Biochem. Biophys. Res. Commun., 199, 380, 10.1006/bbrc.1994.1240

Nagy, 2006, VEGF-A, cytoskeletal dynamics, and the pathological vascular phenotype, Exp. Cell Res., 312, 538, 10.1016/j.yexcr.2005.10.017

Nogami, 1984, Postnatal new bone formation, Clin. Orthop. Relat. Res., 184, 106, 10.1097/00003086-198404000-00013

Olsen, 1995, A mechanochemical model for adult dermal wound contraction and the permanence of the contracted tissue displacement profile, J. Theor. Biol., 177, 113, 10.1006/jtbi.1995.0230

Olsen, 1997, A mathematical model for the capillary endothelial cell-extracellular matrix interactions in wound-healing angiogenesis, IMA J. Math. Appl. Med. Biol., 14, 261, 10.1093/imammb/14.4.261

Ortega, 2004, Matrix remodeling during endochondral ossification, Trends Cell Biol., 14, 86, 10.1016/j.tcb.2003.12.003

Peng, 2002, Synergistic enhancement of bone formation and healing by stem cell-expressed VEGF and bone morphogenetic protein-4, J. Clin. Invest., 110, 751, 10.1172/JCI15153

Postlethwaite, 1987, Simulation of the chemotactic migration of human fibroblasts by transforming growth factor β, J. Exp. Med., 165, 251, 10.1084/jem.165.1.251

Pountos, 2005, Biology of mesenchymal stem cells, Injury, 36S, S8, 10.1016/j.injury.2005.07.028

Prendergast, 1997, Biophysical stimuli on cells during tissue differentiation at implant interfaces, J. Biomech., 30, 539, 10.1016/S0021-9290(96)00140-6

Pufe, 2005, The influence of biomechanical parameters on the expression of VEGF and endostatin in the bone and joint system, Ann. Anat., 187, 461, 10.1016/j.aanat.2005.06.008

Rickard, 1994, Induction of rapid osteoblast differentiation in rat bone marrow stromal cell cultures by dexamethasone and BMP-2, Dev. Biol., 161, 218, 10.1006/dbio.1994.1022

Rossi, 2002, p107 and p130 coordinately regulate proliferation, Cbfa1 expression, and hypertrophic differentiation during endochondral bone development, Dev. Biol., 247, 271, 10.1006/dbio.2002.0691

Rupnick, 1988, Quantitative analysis of human microvessel endothelial cells using a linear under-agarose assay, Lab. Invest., 59, 363

Sakai, 1998, Fluid shear stress increases transforming growth factor beta 1 expression in human osteoblast-like cells: modulation by cation channel blockades, Calcif. Tissue Int., 63, 515, 10.1007/s002239900567

Sato, 1988, Autocrine activities of basic FGF: regulation of cell movement, plasminogen activator synthesis and DNA synthesis, J. Cell. Biol., 107, 1199, 10.1083/jcb.107.3.1199

Seppä, 1982, Platelet-derived growth factor is chemotactic for fibroblasts, J. Cell Biol., 92, 584, 10.1083/jcb.92.2.584

Shefelbine, 2005, Trabecular bone fracture healing simulation with finite element analysis and fuzzy logic, J. Biomech., 38, 2440, 10.1016/j.jbiomech.2004.10.019

Sherratt, 1994, Chemotaxis and chemokinesis in eukaryotic cells: the Keller–Segel equations as an approximation to a detailed model, Bull. Math. Biol., 56, 129, 10.1007/BF02458292

Shima, 1995, Hypoxic induction of vascular endothelial growth factor (VEGF) in human epithelial cells is mediated by increases in mRNA stability, FEBS Lett., 370, 203, 10.1016/0014-5793(95)00831-S

Stokes, 1990, Chemotaxis of human microvessel endothelial cells in response to acidic fibroblast growth factor, Lab. Invest., 63, 657

Street, 2002, Vascular endothelial growth factor stimulates bone repair by promoting angiogenesis and bone turnover, Proc. Natl Acad. Sci. USA, 99, 9656, 10.1073/pnas.152324099

Taguchi, 2005, The role of bone marrow-derived cells in bone fracture repair in a green fluorescent protein chimeric mouse model, Biochem. Biophys. Res. Commun., 331, 31, 10.1016/j.bbrc.2005.03.119

Terranova, 1985, Human endothelial cells are chemotactic to endothelial cell growth factor and heparin, J. Cell Biol., 101, 2330, 10.1083/jcb.101.6.2330

Thies, 1992, Recombinant human bone morphogenetic protein-2 induces osteoblastic differentiation in W-20-17 stromal cells, Endocrinology, 130, 1318

Thorne, 2004, Diffusion of epidermal growth factor in rat brain extracellular space measured by integrative optical imaging, J. Neurophysiol., 92, 3471, 10.1152/jn.00352.2004

Vander, 1998

Villenueva, 1997, Promotion of calvarial cell osteogenesis by endothelial cells, J. Bone Miner. Res., 5, 733, 10.1002/jbmr.5650050710

Weinberg, 1985, Regulation of proliferation of bovine aortic endothelial cells, smooth muscle cells and adventitial fibroblasts in collagen lattices, J. Cell. Physiol., 122, 410, 10.1002/jcp.1041220311

Weiner, 1997, ROWMAP—a ROW-code with Krylov techniques for large stiff ODEs, Appl. Numer. Math., 25, 303, 10.1016/S0168-9274(97)00067-6

Yoshizato, 1985, Growth inhibition of human fibroblasts by reconstituted collagen fibrils, Biomed. Res., 6, 61, 10.2220/biomedres.6.61

Zaman, 2006, Migration of tumor cells in 3D matrices is governed by matrix stiffness along with cell-matrix adhesion and proteolysis, Proc. Natl Acad. Sci., 103, 10889, 10.1073/pnas.0604460103

Zhang, 2001, Osteoporosis influence the fracture healing in ovariectomized rat: ultrastructure study, Chin. Med. J., 114, 15