Skip to main content

Advertisement

SpringerLink
Log in

The Influence of Expansion Rates on Mandibular Distraction Osteogenesis: A Computational Analysis

  • Published:
Annals of Biomedical Engineering Aims and scope Submit manuscript

Abstract

Mandibular distraction osteogenesis is a clinical procedure used for modifying the mandibular geometry when problems of dental overcrowding and arch shrinkage occur. The objective of this study is to use a computational model of tissue differentiation to examine the influence of the rate of distraction on bone re-growth within the fracture callus of a human mandible submitted to symphyseal distraction osteogenesis. A 3D model of the mandible is reconstructed from CT scan data and meshed into finite elements. Two different mastication loadings have been investigated: a ‘full’ mastication load and a ‘reduced’ mastication load where the action of each muscle was reduced by 70%. Four different distraction rates were analyzed: 0.6, 1.2, 2, and 3 mm/day, allowing a total displacement of 6 mm. In the early stages of the distraction process it is predicted that there is a decrease in the amount of bone tissue forming within the center of the fracture gap for all distraction rates. After the initial phases of expansion, the bone tissue within the callus increases for the slower rate of distraction or continues to decrease at the faster rates of distraction. At the end of the simulated maturation period, 47% of the distracted callus was predicted to consist of bone tissue for a distraction rate of 0.6 mm/day, decreasing to 22% for a distraction rate of 3 mm/day. Significantly higher amounts of bone formation were predicted for all distraction rates for the case of reduced mastication loading. Disparities between the model predictions and what is observed in vivo were found. For instance, during the latency period, the distraction period and beyond, the model is predicting larger than expected amounts of cartilage tissue formation within the callus. This and other limitations of the proposed model are discussed and possible specific explanations for these disparities are provided in the paper. The model predicts a distraction rate of around 1.2 mm/day to be optimal as higher rates produce less bone tissue while the risk of a premature bone union is greater at slower rates of distraction because in the latter stages of the distraction process bone tissue is predicted to form between the left and right side of the bone callus.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Figure 1
Figure 2
Figure 3
Figure 4
Figure 5
Figure 6
Figure 7
Figure 8
Figure 9
Figure 10
Figure 11
Figure 12
Figure 13
Figure 14

Similar content being viewed by others

References

  1. Anderson, C. B. Mechanics of fluids. In: Marks’ Saturated Handbook of Mechanical Engineers, edited by T. Baumeister. New York: MacGraw-Hill, 1967, pp. 3.48–3.76

  2. Andreykiv A., Prendergast P. J., van Keulen F., Swieszkowski W., Rozing P. M. (2005) Bone ingrowth simulation for a concept glenoid component design. J. Biomech. 38: 1023–1033

    Article  PubMed  CAS  Google Scholar 

  3. Bailon-Plaza A., van der Meulen M. C. (2001) A mathematical framework to study the effects of growth factor influences on fracture healing. J. Theor. Biol. 212: 191–209

    Article  PubMed  CAS  Google Scholar 

  4. Basciftci F. A., Korkmaz H. H., Işeri H., Malkoç S. (2004) Biomechanical evaluation of mandibular midline distraction osteogenesis by using finite element method. Am. J. Orthod. Dentofac. 125: 706–715

    Article  Google Scholar 

  5. Beek M., Koolstra J. H., Van Ruijven L. J., Van Eijden T. M. G. J. (2000) Three-dimensional finite element analysis of the human temporomandibular joint disc. J. Biomech. 33: 307–316

    Article  PubMed  CAS  Google Scholar 

  6. Boccaccio, A., L. Lamberti, C. Pappalettere, M. Cozzani, and G. Siciliani. Comparison of different orthodontic devices for mandibular symphyseal distraction osteogenesis: a finite element study. Am. J. Orthod. Dentofac. 2006 (in press)

  7. Boccaccio A., Lamberti L., Pappalettere C., Carano A., Cozzani M. (2006) Mechanical behaviour of an osteotomized mandible with distraction orthodontic devices. J. Biomech. 39: 2907–2918

    Article  PubMed  CAS  Google Scholar 

  8. Carter D. R., Blenman P. R., Beaupré G. S. (1998) Correlations between mechanical stress history and tissue differentiation in initial fracture healing. J. Orthop. Res. 6: 736–748

    Article  Google Scholar 

  9. Claes L. E., Heigele C. A. (1999) Magnitudes of local stress and strain along bony surfaces predict the course and type of fracture healing. J. Biomech. 32: 255–266

    Article  PubMed  CAS  Google Scholar 

  10. Conley R., Legan H. (2003) Mandibular symphyseal distraction osteogenesis: diagnosis and treatment planning considerations. Angle Orthod. 73: 3–11

    PubMed  Google Scholar 

  11. Conley R., Legan H. (2006) Correction of severe obstructive sleep apnea with bimaxillary transverse distraction osteogenesis and maxillomandibular advancement. Am. J. Orthod. Dentofac. 129: 283–292

    Article  Google Scholar 

  12. Cowin S. C. (1999) Bone poroelasticity. J. Biomech. 32: 217–238

    Article  PubMed  CAS  Google Scholar 

  13. Del Santo M., Guerrero C. A., Buschang P. H., English J., Samchukov L., Bell W. (2000) Long-term skeletal and dental effects of mandibular symphyseal distraction osteogenesis. Am. J. Orthod. Dentofac. 118: 485–493

    Article  Google Scholar 

  14. Faulkner M. G., Hatcher D. C., Hay A. (1987) A three-dimensional investigation of temporomandibular joint loading. J. Biomech. 20: 997–1002

    Article  PubMed  CAS  Google Scholar 

  15. Guerrero, C. A. Expansion mandibular quirurgica. Revista Venezolana de Ortodoncia 1:48–50, 1990 (In Spanish) English translation “Rapid mandibular expansion”

  16. Guerrero C. A., Bell W. H., Contasti G. I., Rodriguez A. M. (1997) Mandibular widening by intraoral distraction osteogenesis. Brit. J. Oral Max. Surg. 35: 383–392

    Article  CAS  Google Scholar 

  17. Gòmez-Benito M. J., Garcìa-Aznar J. M., Kuiper J. H., Doblaré M. (2005) Influence of fracture gap size on the pattern of long bone healing: a computational study. J. Theor. Biol. 235: 105–109

    Article  PubMed  Google Scholar 

  18. Hibbit, Karlsson & Sorensen, ABAQUS® 6.4 User’s Manual, 2004

  19. Hori R. Y., Lewis J. L. (1982) Mechanical properties of the fibrous tissue found at the bone cement interface following total joint replacement. J. Biomed. Mater. Res. 16: 911–927

    Article  PubMed  CAS  Google Scholar 

  20. Huiskes R., van Driel W. D., Prendergast P. J., Søballe K. (1997) A biomechanical regulatory model of periprosthetic tissue differentiation. J. Mater. Sci. Mater. Med. 8: 785–788

    Article  PubMed  CAS  Google Scholar 

  21. Imola, J. M. Craniofacial distraction osteogenesis. http://www.emedicine.com/ent/topic702.htm, 2004

  22. Isaksson, H., C. C. van Donkelaar, R. Huiskes, and K. Ito. Corroboration of mechano-regulatory algorithms for tissue differentiation during fracture healing: comparison with in vivo results. J. Orthop. Res. 24(5):898–907, 2006

    Google Scholar 

  23. Karp N. S., McCarthy J. G., Schreiber J. S., Sisson H. A., Thorne C. H. (1992) Membranous bone lengthening: a serial histological study. Ann. Plast. Surg. 29: 2

    Article  PubMed  CAS  Google Scholar 

  24. Kelly D. J., Prendergast P. J. (2005) Mechano-regulation of stem cell differentiation and tissue regeneration in osteochondral defects. J. Biomech. 38: 1413–1422

    Article  PubMed  CAS  Google Scholar 

  25. Komuro Y., Takato T., Harii K. (1994) The histologic analysis of distraction osteogenesis of the mandible in rabbits. Plast. Reconst. Surg. 94:152

    Article  PubMed  CAS  Google Scholar 

  26. Lacroix D., Prendergast P. J. (2002) A mechano-regulation model for tissue differentiation during fracture healing: analysis of gap size and loading. J. Biomech. 35: 1163–1171

    Article  PubMed  CAS  Google Scholar 

  27. Loboa E. G., Fang T. D., Parker D. W., Warren S. M., Fong K. D., Longaker M. T., Carter D. R. (2005) Mechanobiology of mandibular distraction osteogenesis: finite element analyses with a rat model. J. Orthop. Res. 23: 663–670

    Article  PubMed  Google Scholar 

  28. Loboa E. G., Fang T. D., Warren S. M., Lindsey D. P., Fong K. D., Longaker M. T., Carter D. R. (2004) Mechanobiology of mandibular distraction osteogenesis: experimental analyses with a rat model. Bone 34: 336–343

    Article  PubMed  Google Scholar 

  29. Martin I., Obradovic B., Treppo S., Grodzinsky A. J., Langer R., Freed L. E., Vunjak-Novakovic G. (2000) Modulation of the mechanical properties of tissue engineered cartilage. Biorheology 37: 141–147

    PubMed  CAS  Google Scholar 

  30. Mauck R. L., Soltz M. A., Wang C. C., Wong D. D., Chao P. H., Valhmu W. B., Hung C. T., Ateshian G. A. (2000) Functional tissue engineering of articular cartilage through dynamic loading of chondrocyte-seeded agarose gels. J. Biomech. Eng. 122: 252–260

    Article  PubMed  CAS  Google Scholar 

  31. Meyer U., Kleinheinz J., Joos U. (2004) Biomechanical and clinical implications of distraction osteogenesis in craniofacial surgery. J. Cranio Maxill. Surg. 32: 140–149

    Article  Google Scholar 

  32. Meyer U., Kruse-Lösler B., Wiesmann H. P. (2006) Principles of bone formation driven by biophysical forces in craniofacial surgery. Brit. J. Oral Max. Surg. 44: 289–295

    Article  CAS  Google Scholar 

  33. Meyer U., Meyer T., Wiesmann H. P., Kruse-Lösler B., Vollmer D., Stratmann U., Joos U. (2001) Mechanical tension in distraction osteogenesis regulates chondrocytic differentiation. Int. J. Oral Max. Surg. 30: 522–530

    Article  CAS  Google Scholar 

  34. Mora G., Forriol F. (2000) Mechanical analysis of the healing of different osteotomies fixed externally. Int. Orthop. 24: 295–298

    Article  PubMed  CAS  Google Scholar 

  35. Paccione M. F., Mehrara B. J., Warren S. M., Greenwald J. A., Spector J. A., Luchs J. S., et al. (2001) Rat mandibular distraction osteogenesis: latency, rate and rhythm determine the adaptive response. J. Cranio Maxill. Surg. 12: 175–182

    Article  CAS  Google Scholar 

  36. Pauwels, F. Eine neue theorie über den einfluβ mechanischer reize auf die differenzierung der stützgewebe. Z Anat Entwickl. Gesch. 121:478–515, 1960. Translated as A new theory concerning the influence of mechanical stimuli on the differentiation of the supporting tissues. In: Bioechanics of the Locomotor Apparatus, edited by P. Maquet and R. Furlong. Springer, Berlin, 1980, pp. 375–407

  37. Prendergast P. J., Huiskes R., Søballe K. (1997) Biophisical stimuli on cells during tissue differentiation at implant interfaces. J. Biomech. 30: 539–548

    Article  PubMed  CAS  Google Scholar 

  38. Richardson J. B., Kenwright J., Cunningham J. L. (1992) Fracture stiffness measurement in the assessment and management of tibial fractures. J. Clin. Biomech. 7: 75–79

    Article  Google Scholar 

  39. Schaffer M. B., Burr D. B. (1988) Stiffness of compact bone: effects of porosity and density. J. Biomech. 21: 13–16

    Article  Google Scholar 

  40. Schwartz-Dabney C. L., Dechow P. C. (2003) Variations in cortical material properties throughout the human dentate mandible. Am. J. Phys. Anthropol. 120: 252–277

    Article  PubMed  CAS  Google Scholar 

  41. Stewart K. J., Lvoff G. O., White S. A., Bonar S. F., Walsh W. R., Smart R. C., Poole M. D. (1998) Mandibular distraction osteogenesis: a comparison of distraction rates in the rabbit model. J. Cranio Maxill. Surg. 26: 43–49

    Article  CAS  Google Scholar 

  42. Tavakoli K., Walsh W. R., Bonar F., Smart R., Wulf S., Poole M. D. (1998) The role of latency in mandibular osteodistraction. J. Cranio Maxill. Surg. 26: 209–219

    Article  CAS  Google Scholar 

  43. Weil T. S., Van Sickles J., Payne J. (1997) Distraction osteogenesis for correction of transverse mandibular deficiency: a preliminary report. J. Oral. Maxillofac. Surg. 55: 953–960

    Article  PubMed  CAS  Google Scholar 

  44. Yazawa M., Kishi K., Nakajima H., Nakajima T. (2003) Expression of bone morphogenetic proteins during mandibular distraction osteogenesis in rabbits. J.Oral Maxillofac. Surg. 61: 587–592

    Article  PubMed  Google Scholar 

  45. Zimmermann C. E., Thurmüller P., Troulis M. J., Perrot D. H., Rahn B., Kaban L. B. (2005) Histology of the porcine mandibular distraction wound. Int. J. Oral Max. Surg. 34: 411–419

    Article  CAS  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Dipartimento di Ingegneria Meccanica e Gestionale, Politecnico di Bari, Bari, 70126, Italy

    A. Boccaccio & C. Pappalettere

  2. Trinity Centre for Bioengineering, School of Engineering, Trinity College Dublin, Dublin, 2, Ireland

    A. Boccaccio & D. J. Kelly

Authors
  1. A. Boccaccio
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. C. Pappalettere
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. D. J. Kelly
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to D. J. Kelly.

Appendix A

Appendix A

Evaluation of the Reaction Force Acting on the Bone Callus

The boundary and loading conditions acting on the mandibular arch may be schematized with the simplified structure S1 illustrated in Fig. A1. The domain indicated with LA represents the left arm of the mandible while the BC and RA domains represent the bone callus and the right arm respectively. The unilateral occlusion is schematized with the UO supports. We assume, for simplicity, that the UO supports prevent displacements in all three coordinate directions. (In the FE model, the constraint simulating the unilateral occlusion only prevents displacement along the 3 direction, while the other two degrees of freedom are restrained due to the elastic element simulating the temporo-mandibular joint.) Let F mL and F mR be the vertical components (which are the most significant component) of the resultant forces developed by the mastication muscles on the left and on the right side and let b be the distance of the action line of F mL force with respect to the bone callus domain; c is the thickness of the BC bone callus.

Figure A1
figure a

Evaluation of the reaction force acting on the left and on the right side of the bone callus

Full size image

Let us suppose RA and LA to be rigid structures. This allows us to model the S1 structure as shown in structure S2. The action of the F mL force on the left side of BC is given by the same F mL force and a moment M L on the left hand side of the callus is given by: M L  = F mL *b. The moment on the right hand side is given by M R  = M L  + F mL *c = F mL *(b + c). Therefore in general, the reaction force acting on the right side of the callus is bigger than the left side.

As is clear, the real boundary and loading conditions of the mandible are more complicated than those schematized in S1. In fact, we neglect the effect of the constraint simulating the temporo-mandibular joint and we introduce the simplification that the support modeling the unilateral occlusion prevents displacement in all the three coordinate directions. However, the hypothesis made should not affect the validity of the conclusion.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Boccaccio, A., Pappalettere, C. & Kelly, D.J. The Influence of Expansion Rates on Mandibular Distraction Osteogenesis: A Computational Analysis. Ann Biomed Eng 35, 1940–1960 (2007). https://doi.org/10.1007/s10439-007-9367-x

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10439-007-9367-x

Keywords

Search

Navigation