[en] Both mechanical and biological factors play an important role in normal as well as impaired fracture healing. This study aims to provide a mathematical framework in which both regulatory mechanisms are included. Mechanics and biology are coupled by making certain parameters of a previously established bioregulatory model dependent on local mechanical stimuli. To illustrate the potential added value of such a framework, this coupled model was applied to investigate whether local mechanical stimuli influencing only the angiogenic process can explain normal healing as well as overload-induced nonunion development. Simulation results showed that mechanics acting directly on angiogenesis alone was not able to predict the formation of overload-induced onunions. However, the direct action of mechanics on both angiogenesis and osteogenesis was able to predict overload-induced nonunion formation, confirming
the hypotheses of several experimental studies investigating the interconnection between angiogenesis and osteogenesis. This study shows that mathematical models can assist in testing hypothesis on the nature of the interaction between biology
and mechanics.
Aaron AD (1996) Bone healing and grafting. In: Kasser JR (eds) Orthopaedic Knowledge Update 5. American Academy of Orthopaedic Surgeons. J.R. Rosemont, IL, USA, pp 21-28
D Ambard P Swider 2006 A predictive mechano-biological model of the bone-implant healing Europ J Mech - A/Solids 25 6 927 937 1110.74040 10.1016/j.euromechsol.2006.02.006 (Pubitemid 44633685)
An YH, Friedman RJ, Draughn RA (1999) Animal models of fracture or osteotomy. In: An YH, Friedman RJ (eds) Animal models in orthopaedic research. CRC Press, Boca Raton, FL, USA, pp 197-218
Andreykiv A, van Keulen F, Prendergast PJ (2007) Simulation of fracture healing incorporating mechanoregulation of tissue differentiation and dispersal/proliferation of cells. Biomechan Model Mechanobiol doi: 10.1007/s10237-007-0108-8
CG Armstrong VC Mow 1982 Variations in the intrinsic mechanical properties of human articular cartilage with age, degeneration and water content J Bone Joint Surg 64A 88 94
A Bailón-Plaza MCH van der Meulen 2003 Beneficial effects of moderate, early loading and adverse effects of delayed or excessive loading on bone healing J Biomech 36 1069 1077 10.1016/S0021-9290(03)00117-9 (Pubitemid 36794102)
GL Barnes PJ Kostenuik LC Gerstenfeld TA Einhorn 1999 Growth factor regulation of fracture repair J Bone Miner Res 14 11 1805 1815 10.1359/jbmr.1999.14.11.1805 (Pubitemid 29521774)
EH Burger J Klein-Nulend 1999 Mechanotransduction in bone-role of the lacuno-canalicular network FASEB J 13 S101 S112
J Caňadell F Forriol 1997 The external fixator in the treatment of infected pseudoarthrosis and bone defects Osteosynth Int 5 221 225
DR Carter PR Blenman GS Beaupré 1988 Correlations between mechanical stress history and tissue differentiation in initial fracture healing J Orthop Res 6 5 736 748 10.1002/jor.1100060517
EYS Chao N Inoue JJ Elias H Aro 1998 Enhancement of fracture healing by mechanical and surgical intervention Clin Orthop Rel Res 355S 163 178 10.1097/00003086-199810001-00018
EJ Cheal KA Mansmann AM III DiGioia WC Hayes SM Perren 1991 Role of interfragmentary strain in fracture healing: ovine model of a healing osteotomy J Orthop Res 9 1 131 142 10.1002/jor.1100090116
S Checa PJ Prendergast 2009 A mechanobiological model for tissue differentiation that includes angiogenesis: a lattice-based modeling approach Ann Biomed Eng 37 1 129 145 10.1007/s10439-008-9594-9
LE Claes CA Heigele C Neidlinger-Wilke D Kaspar W Seidl KJ Margevicius P Augat 1998 Effects of mechanical factors on the fracture healing process Clin Orthop Rel Res 355S S132 S147 10.1097/00003086-199810001-00015
LE Claes CA Heigele 1999 Magnitudes of local stress and strain along bony surfaces predict the course and type of fracture healing J Biomech 32 3 255 266 10.1016/S0021-9290(98)00153-5 (Pubitemid 29125449)
L Claes K Eckert-Hübner P Augat 2002 The effect of mechanical stability on local vascularization and tissue differentiation in callus healing J Orthop Res 20 5 1099 1105 10.1016/S0736-0266(02)00044-X
R Dimitriou E Tsiridis PV Giannoudis 2005 Current concepts of molecular aspects of bone healing Injury 36 12 1392 1404 10.1016/j.injury.2005.07.019 (Pubitemid 41618169)
H Dinopoulos PV Giannoudis 2007 The use of bone morphogenetic proteins (BMPs) in long-bone non-unions Curr Orthop 21 268 279 10.1016/j.cuor.2007.07.007 (Pubitemid 47495968)
TA Einhorn 1998 The cell and molecular biology of fracture healing Clin Orthop Relat Res 355S S7 S21 10.1097/00003086-199810001-00003
BD Elder KA Athanasiou 2009 Hydrostatic pressure in articular cartilage tissue engineering: from chondrocytes to tissue regeneration Tis Eng B 15 1 43 53 10.1089/ten.teb.2008.0435
DR Epari J Lienau H Schell F Witt GN Duda 2008 Pressure, oxygen tension and temperature in the periosteal callus during bone healing-an in vivo study in sheep Bone 43 4 734 739 10.1016/j.bone.2008.06.007
TD Fang A Salim W Xia RP Nacamuli S Guccione HM Song RA Carano EH Filvaroff MD Bednarski AJ Giaccia MT Longaker 2005 Angiogenesis is required for successful bone induction during distraction osteogenesis J Bone Miner Res 20 7 1114 1124 10.1359/JBMR.050301 (Pubitemid 40863799)
L Geris A Gerisch C Maes G Carmeliet R Weiner J Vander Sloten H Van Oosterwyck 2006 Mathematical modeling of fracture healing in mice: Comparison between experimental data and numerical simulation results Med Biol Eng Comp 44 4 280 289 10.1007/s11517-006-0040-6 (Pubitemid 43949704)
L Geris A Gerisch J Vander Sloten R Weiner H Van Oosterwyck 2008 Angiogenesis in bone fracture healing: a bioregulatory model J Theor Biol 251 1 137 158 10.1016/j.jtbi.2007.11.008
Geris L, Reed AAC, Vander Sloten J, Simpson AHRW, Van Oosterwyck H (2010a) Potential treatment strategies for atrophic non-unions. Submitted
Geris L, Schugart R, Van Oosterwyck H, (2010b) In silico design of treatment strategies in wound healing and bone fracture healing. Philos Trans R Soc A (accepted)
A Gerisch MAJ Chaplain 2006 Robust numerical methods for taxis-diffusion-reaction systems: applications to biomedical problems Math Comput Model 43 49 75 1086.92025 10.1016/j.mcm.2004.05.016 2197403 (Pubitemid 43294569)
LC Gerstenfeld DM Cullinane GL Barnes DT Graves TA Einhorn 2003 Fracture healing as a post-natal developmental process: molecular, spatial, and temporal aspects of its regulation J Cell Biochem 88 873 884 10.1002/jcb.10435 (Pubitemid 36337032)
J Glowacki 1998 Angiogenesis in fracture repair Clin Orthop Rel Res 355 S82 S89
MJ Gómez-Benito JM GarcIa-Aznar JH Kuiper M Doblaré 2005 Influence of fracture gap size on the pattern of long bone healing: a computational study J Theor Biol 235 105 119 10.1016/j.jtbi.2004.12.023 (Pubitemid 40514428)
AE Goodship J Kenwright 1985 The influence of induced micromovement upon the healing of experimental tibial fractures J Bone Joint Surg Br 67B 650 655
AE Goodship JL Cunningham J Kenwright 1998 Strain rate and timing of stimulation in mechanical modulation of fracture healing Clin Orthop Rel Res 355S 105 115 10.1097/00003086-199810001-00012
RY Hori JL Lewis 1982 Mechanical properties of the fibrous tissue found at the bone-cement interface following total joint replacement J Biomed Mater Res 16 911 927 10.1002/jbm.820160615 (Pubitemid 13202637)
TL Hsu FY Chiu CM Chen TH Chen 2005 Treatment of nonunion of humeral shaft fracture with dynamic compression plate and cancellous bone graft J Chin Med Assoc 68 2 73 76 10.1016/S1726-4901(09)70138-8
A Hulth 1989 Current concepts of fracture healing Clin Orthop 249 265 284
R Huiskes WD Van Driel PJ Prendergast K Søballe 1997 A biomechanical regulatory model for periprosthetic fibrous-tissue differentiation J Mater Sci Mat Med 8 785 788 10.1023/A:1018520914512 (Pubitemid 28005915)
H Isaksson W Wilson CC van Donkelaar R Huiskes K Ito 2006 Comparison of biophysical stimuli for mechano-regulation of tissue differentiation during fracture healing J Biomech 39 8 1507 1516 10.1016/j.jbiomech.2005.01.037
H Isaksson CC van Donkelaar R Huiskes K Ito 2008 A mechano-regulatory bone-healing model incorporating cell-phenotype specific activity J Theor Biol 252 2 230 246 10.1016/j.jtbi.2008.01.030
H Isaksson CC van Donkelaar K Ito 2009 Sensitivity of tissue differentiation and bone healing predictions to tissue properties J Biomech 42 5 555 564 10.1016/j.jbiomech.2009.01.001
JS Jurvelin MD Buschmann EB Hunziker 1997 Optical and mechanical determination of Poisson's ratio of adult bovine humeral articular cartilage J Biomech 30 235 241 10.1016/S0021-9290(96)00133-9 (Pubitemid 27077495)
J Kenwright T Gardner 1998 Mechanical influences on tibial fracture healing Clin Orthop Rel Res 355S 179 190 10.1097/00003086-199810001-00019
ME Kirchen KM O'Connor HE Gruber JR Sweeney IA Fras SJ Stover A Sarmiento GJ Marshall 1995 Effects of microgravity on bone healing in a rat fibular osteotomy model Clin Orthop Relat Res 318 231 242
D Lacroix PJ Prendergast 2002 A mechano-regulation model for tissue differentiation during fracture healing: analysis of gap size and loading J Biomech 35 1163 1171 10.1016/S0021-9290(02)00086-6 (Pubitemid 34879736)
PS Landry 2000 Effect of soft-tissue trauma on the early periosteal response of bone to injury J Trauma 48 479 483 10.1097/00005373-200003000-00018
AX Le T Miclau D Hu JA Helms 2001 Molecular aspects of healing in stabilized and non-stabilized fractures J Orthop Res 19 1 78 84 10.1016/S0736-0266(00)00006-1 (Pubitemid 32288639)
P Leucht JB Kim R Wazen JA Currey A Nanci JB Brunski JA Helms 2007 Effect of mechanical stimuli on skeletal regeneration around implants Bone 40 4 919 930 10.1016/j.bone.2006.10.027 (Pubitemid 46389645)
J Lienau H Schell GN Duda P Seebeck S Muchow HJ Bail 2005 Initial vascularization and tissue differentiation are influenced by fixation stability J Orthop Res 23 3 639 645 10.1016/j.orthres.2004.09.006 (Pubitemid 40631337)
C Lu T Miclau D Hu RS Marcucio 2007 Ischemia leads to delayed union during fracture healing: a mouse model J Orthop Res 25 1 51 61 10.1002/jor.20264 (Pubitemid 46070731)
C Maes L Coenegrachts I Stockmans E Daci A Luttun A Petryk R Gopalakrishnan K Moermans N Smets CM Verfaillie P Carmeliet R Bouillon G Carmeliet 2006 Placental growth factor mediates mesenchymal cell development, cartilage turnover, and bone remodeling during fracture repair J Clin Invest 116 1230 1242 10.1172/JCI26772
Marsh D, Buckwalter JA, McCollister-Evarts C (1994) Delayed union, nonunion, malunion and avascular necrosis. In: Epps CH (eds) Complications in orthopaedic surgery. JB Lippinscott, Philadelphia, USA, pp 183-211
D Marsh 1998 Concepts of fracture union, delayed union, and nonunion Clin Orthop S355 S22 S30
B McKibbin 1978 The biology of fracture healing in long bones J Bone Joint Surg Br 60-B 150 162
D Moukoko M Pithioux P Chabrand 2007 Temporal evolution of mechanical properties of skeletal tissue regeneration in rabbits: an experimental study Med Biol Eng Comput 45 10 989 995 10.1007/s11517-007-0237-3 (Pubitemid 47423288)
MG Mullender R Huiskes 1997 Osteocytes and bone lining cells: which are the best candidates for mechano-sensors in cancellous bone? Bone 20 6 527 532 10.1016/S8756-3282(97)00036-7 (Pubitemid 27270466)
Murray JD (2002) Mathematical biology: I. An introduction. 3. Springer, New York, USA
Ochoa JA, Hillberry BM (1992) Permeability of bovine cancellous bone. Trans 38th Orthop Res Soc, p 162
S Olson D Hahn 2006 Surgical treatment of non-unions: a case for internal fixation Injury 37 681 690 10.1016/j.injury.2004.11.039 (Pubitemid 44066972)
OO Oni H Stafford PJ Gregg 1989 An experimental study of the patterns of periosteal and endosteal damage in tibial shaft fractures using a rabbit trauma model J Orthop Trauma 3 142 147 10.1097/00005131-198906000-00009
I Owan DB Burr CH Turner J Qiu Y Tu JE Onyia RL Duncan 1997 Mechanotransduction in bone: osteoblasts are more responsive to fluid force than mechanical strain Am J Phys 273 C810 C815
SH Park K O'Connor R Sung H McKellop A Sarmiento 1999 Comparison of healing process in open osteotomy model and closed fracture model J Orthop Trauma 13 114 120 10.1097/00005131-199902000-00008
VR Patel DK Menon RD Pool RB Simonis 2000 Nonunion of the humerus after failure of surgical treatment: management using the Ilizarov circular fixator J Bone Joint Surg Br B82 977 983 10.1302/0301-620X.82B7.10180
PJ Prendergast R Huiskes K Søballe 1997 Biophysical stimuli on cells during tissue differentiation at implant interfaces J Biomech 30 6 539 548 10.1016/S0021-9290(96)00140-6 (Pubitemid 27214187)
EC Rodriguez-Merchan F Forriol 2004 Nonunion: general principles and experimental data Clin Orthop Rel Res 419 4 12 10.1097/00003086-200402000-00003
A Sarmiento JF Schaeffer L Beckerman LL Latta JE Enis 1977 Fracture healing in rat femora as affected by functional weight-bearing J Bone Joint Surg Am 59 3 369 375
SJ Shefelbine P Augat L Claes U Simon 2005 Trabecular bone fracture healing simulation with finite element analysis and fuzzy logic J Biomech 38 12 2440 2450 10.1016/j.jbiomech.2004.10.019 (Pubitemid 41427238)
R Smalt FT Mitchell RL Howard TJ Chambers 1997 Induction of NO and prostaglandin E2 in osteoblasts by wall-shear stress but not mechanical strain Am J Phys 273 E751 E758
LL Southwood DD Frisbie CE Kawcak CW McIlwraith 2004 Delivery of growth factors using gene therapy to enhance bone healing Vet Surg 33 565 578 10.1111/j.1532-950x.2004.04080.x (Pubitemid 41754966)
SM Tanaka HB Sun RK Roeder DB Burr CH Turner H Yokota 2005 Osteoblast responses one hour after load-induced fluid flow in a three-dimensional porous matrix Calcif Tissue Int 76 4 261 271 10.1007/s00223-004-0238-2 (Pubitemid 40991397)
Z Thompson T Miclau D Hu JA Helms 2002 A model for intramembranous ossification during fracture healing J Orthop Res 20 5 1091 1098 10.1016/S0736-0266(02)00017-7
MCH van der Meulen R Huiskes 2002 Why mechanobiology? J Biomech 35 401 414 10.1016/S0021-9290(01)00184-1 (Pubitemid 34273633)
LA Whiteside 1978 The effects of extraperiosteal and subperiosteal dissection. II. On fracture healing J Bone Joint Surg Am 60 26 30
L You SC Cowin MB Schaffler S Weinbaum 2001 A model for strain amplification in the actin cytoskeleton of osteocytes due to fluid drag on pericellular matrix J Biomech 34 1375 1386 10.1016/S0021-9290(01)00107-5 (Pubitemid 32970752)
