Skip to main content
SpringerLink
Log in

Tortuosity Influence on the Trabecular Bone Elasticity and Mechanical Competence

  • Chapter
  • First Online:
Developments in Medical Image Processing and Computational Vision

Part of the book series: Lecture Notes in Computational Vision and Biomechanics ((LNCVB,volume 19))

Abstract

Osteoporosis is a disease characterized by a remarkable bone mass loss and trabecular bone degradation, which leads to an increase in bone fragility and a higher fracture risk. There are strong evidences that the trabecular microarchitecture degradation impacts the fracture risk. The trabecular bone structure resembles a network composed of tortuous struts and their tortuosity influences the structural stiffness. This work investigates how the trabecular volume fraction, network connectivity, trabecular tortuosity and Young modulus of elasticity can be aggregated in a unique variable to provide information about the trabecular bone fragility. The parameters are estimated for three cohorts, two from ex vivo microtomographic (μCT) images and the other one from in vivo magnetic resonance imaging (MRI); the μCT image samples are from distal radius and vertebrae, while the MRI samples are also from distal radius. The principal component analysis shows that the principal component, defined as mechanical competence parameter (MCP), can be used to grade the quality of the samples and a visual color spectrum is generated to provide a quality distribution of the samples. The results point out a prevalent direction of the tortuosity along the z direction in all cohorts, which correspond to the most frequent direction of stress and high values of MCP indicating better structured samples. In addition, a remarkable result is the strong correlation between the tortuosity in both x and y horizontal directions and the elasticity in the z vertical direction, evidencing the role that the horizontal trabecular connectivity plays to the mechanical competence of the trabecular bone structure.

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

Access this chapter

Log in via an institution
Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 84.99
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Hardcover Book
USD 109.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Notes

  1. 1.

    http://palaisdetokyo.com/fr/exposition/exposition-monographique/Henrique-Oliveira.

References

  1. Alberich-Bayarri A, Marti-Bonmati L, Perez MA, Lerma JJ, Moratal D (2010) Finite element modeling for a morphometric and mechanical characterization of trabecular bone from high resolution magnetic resonance imaging. In: Moratal D (ed) Finite element analysis. InTechOpen, pp 195–208

    Google Scholar 

  2. Alberich-Bayarri A, Marti-Bonmati L, Pérez MA, Sanz-Requena R, Lerma-Garrido JJ, García-Martí G, Moratal D (2010) Assessment of 2D and 3D fractal dimension measurements of trabecular bone from high-spatial resolution magnetic resonance images at 3 tesla. Med Phys 37:4930–4937

    Article  Google Scholar 

  3. Arcaro K (2013) Caracterização Geométrica e Topológica da Competência Mecânica no Estudo da Estrutura Trabecular. DSc. Thesis (in Portuguese). Graduate Program in Applied Mathematics, Federal University of Rio Grande do Sul, Porto Alegre, Brazil, July 2013

    Google Scholar 

  4. Argenta MA, Gebert AP, Filho ES, Felizari BA, Hecke MB (2011) Methodology for numerical simulation of trabecular bone structures mechanical behavior. CMES 79(3):159–182

    Google Scholar 

  5. Aygün H, Attenborough K, Postema M, Lauriks W, Langton CM (2009) Predictions of angle dependent tortuosity and elasticity effects on sound propagation in cancellous bone. J Acoust Soc Am 126:3286–3290

    Article  Google Scholar 

  6. Boutroy S, Van Rietbergen B, Sornay-Rendu E, Munoz F, Bouxsein ML, Delmas PD (2008) Finite element analysis based on in vivo HR-pQCT images of the distal radius is associated with wrist fracture in postmenopausal women. J Bone Miner Res 23(3):392–399

    Article  Google Scholar 

  7. Carbonare D, Giannini S (2004) Bone microarchitecture as an important determinant of bone strength. J Endocrinol Invest 27:99–105

    Article  Google Scholar 

  8. Chappard D, Basle MF, Legrand E, Audran M (2008) Trabecular bone microarchitecture: a review. Morphologie 92:162–170

    Article  Google Scholar 

  9. Chen H, Zhou X, Fujita H, Onozuka M, Kubo K-Y (2013) Age-related changes in trabecular and cortical bone microstructure. Int J Endocrinol 2013:213234

    Google Scholar 

  10. Clennell MB (1997) Tortuosity: a guide through the maze. In: Lovell MA, Harvey PK (eds) Developments in Petrophysics, vol 122. Geological Society, London, pp 299–344

    Google Scholar 

  11. Cohen A, Dempster DW, Müller R, Guo XE, Nickolas TL, Liu XS, Zhang XH, Wirth AJ, van Lenthe GH, Kohler T, McMahon DJ, Zhou H, Rubin MR, Bilezikian JP, Lappe JM, Recker RR, Shane E (2010) Assessment of trabecular and cortical architecture and mechanical competence of bone by high-resolution peripheral computed tomography: comparison with transiliac bone biopsy. Osteoporos Int 21:263–273

    Article  Google Scholar 

  12. Dempster DW (2003) Bone microarchitecture and strength. Osteoporos Int 14(Suppl 5):S54–S56

    Article  Google Scholar 

  13. Ebbesen EN, Thomsen JS, Beck-Nielsen H, Nepper-Rasmussen HJ, Mosekilde L (1999) Lumbar vertebral body compressive strength evaluated by dual-energy x-ray absorptiometry, quantitative computed tomography, and ashing. Bone 25:713–724

    Article  Google Scholar 

  14. Edwards WB, Troy KL (2012) Finite element prediction of surface strain and fracture strength at the distal radius. Med Eng Phys 34:290–298

    Article  Google Scholar 

  15. Fields AJ, Lee GL, Liu XS, Jekir MG, Guo XE, Keaveny TM (2011) Influence of vertical trabeculae on the compressive strength of the human vertebra. J Bone Miner Res 26:263–269

    Article  Google Scholar 

  16. Fields AJ, Nawathe S, Eswaran SK, Jekir MG, Adams MF, Papadopoulos P, Keaveny TM (2012) Vertebral fragility and structural redundancy. J Bone Miner Res 27:2152–2158

    Article  Google Scholar 

  17. Gefen A (2009) Finite element modeling of the microarchitecture of cancellous bone: techniques and applications. In Leondes CT (ed) Biomechanics system technology: muscular skeletal systems, vol 4, pp 73–112. World Scientific, Singapore (chapter 3)

    Google Scholar 

  18. Gomberg BR, Saha PK, Song HK, Hwang SN, Wehrli FW (2000) Topological analysis of trabecular bone MR images. IEEE T Med Imaging 19(3):166–174

    Article  Google Scholar 

  19. Gommes CJ, Bons A-J, Blacher S, Dunsmuir JH, Tsou AH (2009) Practical methods for measuring the tortuosity of porous materials from binary or gray-tone tomographic reconstructions. AIChE J 55(8):2000–2012

    Article  Google Scholar 

  20. Gong H, Zhu D, Gao J, Lv L, Zhang X (2010) An adaptation model for trabecular bone at different mechanical levels. Biomed Eng Online 9:32

    Article  Google Scholar 

  21. Gundersen HJG, Boyce RW, Nyengaard JR, Odgaard A (1993) The Conneuler: unbiased estimation of the connectivity using physical disectors under projection. Bone 14:217–222

    Article  Google Scholar 

  22. Hambli R, Bettamer A, Allaoui S (2012) Finite element prediction of proximal femur fracture pattern based on orthotropic behaviour law coupled to quasi-brittle damage. Med Eng Phys 34:202–210

    Article  Google Scholar 

  23. Hollister SJ, Fyhrie DP, Jepsen KJ, Goldstein SA (1991) Application of homogenization theory to the study of trabecular bone mechanics. J Biomech 24:825–839

    Article  Google Scholar 

  24. Homminga J, Mccreadie BR, Weinans H, Huiskes R (2002) The dependence of the elastic properties of osteoporotic cancellous bone on volume fraction and fabric. J Biomech 36:1461–1467

    Article  Google Scholar 

  25. Jolliffe IT (2002) Principal component analysis, 2nd edn. Springer, Berlin

    MATH  Google Scholar 

  26. Kapur JN, Sahoo PK, Wong ACK (1985) A new method for gray-level picture thresholding using the entropy of the histogram. Graph Mod Im Proc 29:273–285

    Article  Google Scholar 

  27. Laib A, Beuf O, Issever A, Newitt DC, Majumdar S (2001) Direct measures of trabecular bone architecture from MR images. Adv Exp Med Biol 496:37–46 (Springer US, chapter 5)

    Google Scholar 

  28. Liu XS, Sajda P, Saha PK, Wehrli FW, Bevill G, Keaveny TM, Guo XE (2008) Complete volumetric decomposition of individual trabecular plates and rods and its morphological correlations with anisotropic elastic moduli in human trabecular bone. J Bone Miner Res 23(2):223–235

    Article  Google Scholar 

  29. Manjón JV, Coupé P, Buades A, Fonov V, Louis Collins D, Robles M (2010) Non-local MRI upsampling. Med Image Anal 14:784–792

    Article  Google Scholar 

  30. Mosekilde L (1993) Vertebral structure and strength in vivo and in vitro. Calcif Tissue Int 53(Suppl 1):S121–S126

    Article  Google Scholar 

  31. Ohmura J (2011) Effects of elastic modulus on single fiber uniaxial deformation. Undergraduate Honors Thesis, The Ohio State University, 41pp

    Google Scholar 

  32. Parkinson IH, Badiei A, Stauber M, Codrington J, Müller R, Fazzalari NL (2012) Vertebral body bone strength: the contribution of individual trabecular element morphology. Osteoporos Int 23:1957–1965

    Article  Google Scholar 

  33. Portero-Muzy NR, Chavassieux PM, Milton D, Duboeuf F, Delmas PD, Meunier PJ (2007) Euler strut-cavity, a new histomorphometric parameter of connectivity reflects bone strength and speed of sound in trabecular bone from human os calcis. Calcified Tissue Int 81:92–98

    Article  Google Scholar 

  34. R Development Core Team (2010) R: a language and environment for statistical computing. R Foundation for Statistical Computing, Vienna, Austria, 2010. ISBN 3-900051-07-0

    Google Scholar 

  35. Roberts N, Reed M, Nesbitt G (1997) Estimation of the connectivity of a synthetic porous medium. J Microsc 187:110–118

    Article  Google Scholar 

  36. Roque WL, de Souza ACA, Barbieri DX (2009) The euler-poincaré characteristic applied to identify low bone density from vertebral tomographic images. Rev Bras Reumatol 49:140–152

    Article  Google Scholar 

  37. Roque WL, Arcaro K, Tabor Z (2010) An investigation of the mechanical competence of the trabecular bone. In: Dvorkin E, Goldschmit M, Storti M (eds) Mecánica computacional, vol XXIX, pp 2001–2009. AMCA, Buenos Aires

    Google Scholar 

  38. Roque WL, Arcaro K, Freytag I (2011) Tortuosidade da rede do osso trabecular a partir da reconstrução geodésica de imagens binárias tridimensionais. Anais do XI Workshop de Informática Médica, pp 1708–1717

    Google Scholar 

  39. Roque WL, Arcaro K, Alberich-Bayarri A (2012) Tortuosity and elasticity study of distal radius trabecular bone. In: Rocha A, Calvo-Manzano JA, Reis LP, Cota MP (eds) (2012) Actas de la 7a Conferencia Ibérica de Sistemas y Tecnologías de Información, vol 1. AISTI - UPM, 2012.

    Google Scholar 

  40. Roque WL, Arcaro K, Lanfredi RB (2012) Tortuosidade e conectividade da rede trabecular do rádio distal a partir de imagens micro-tomográficas. Rev Bras Eng Bio 28:116–123

    Google Scholar 

  41. Roque WL, Arcaro K, Alberich-Bayarri A (2013) Mechanical competence of bone: a new parameter to grade trabecular bone fragility from tortuosity and elasticity. IEEE T Bio-Med Eng 60:1363–1370

    Article  Google Scholar 

  42. Saha PK, Xu Y, Duan H, Heiner A, Liang G (2010) Volumetric topological analysis: a novel approach for trabecular bone classification on the continuum between plates and rods. IEEE T Med Imaging 29(11):1821–1838

    Article  Google Scholar 

  43. Sterio DC (1984) The unbiased estimation of number and sizes of arbitrary particles using the disector. J Microsc 134:127–136

    Article  Google Scholar 

  44. Tabor Z (2007) Estimating structural properties of trabecular bone from gray-level low-resolution images. Med Eng Phys 29:110–119

    Article  Google Scholar 

  45. Tabor Z (2009) On the equivalence of two methods of determining fabric tensor. Med Eng Phys 31:1313–1322

    Article  Google Scholar 

  46. Thomsen JS, Niklassen AS, Ebbesen EN, Brüel A (2013) Age-related changes of vertical and horizontal lumbar vertebral trabecular 3d bone microstructure is different in women and men. Bone 57:47–55

    Article  Google Scholar 

  47. Vogel HJ, Kretzschmar A (1996) Topological characterization of pore space in soil—sample preparation and digital image-processing. Geoderma 73:23–38

    Article  Google Scholar 

  48. Wesarg S, Erdt M, Kafchitsas Ks, Khan MF (2010) Direct visualization of regions with lowered bone mineral density in dual-energy CT images of vertebrae. In: Summers RM, Bram van Ginneken MD (eds) Medical Imaging 2011: Computer-Aided Diagnosis. SPIE Proceedings, 2010

    Google Scholar 

  49. Wolff J (1986) The law of bone remodeling. Springer-Verlag, Berlin (translation of the german 1892 edition) edition

    Book  Google Scholar 

  50. Wua YS, van Vliet LJ, Frijlink HW, Maarschalka KV (2006) The determination of relative path length as a measure for tortuosity in compacts using image analysis. Eur J Pharm Sci 28:433–440

    Article  Google Scholar 

Download references

Acknowledgements

We would like to thank Dr. K. Arcaro for several preliminary discussions and especially Dr. Z. Tabor for kindly let us make use of his μCT image samples and data. W. L. Roque thank the University for its competence in dealing with the redistribution process.

Author information

Authors and Affiliations

  1. Department of Scientific Computation, Federal University of Paraíba, João Pessoa, Brazil

    Waldir Leite Roque

  2. Biomedical Imaging Research Group, La Fe Health Research Institute, Valencia, Spain

    Angel Alberich-Bayarri

Authors
  1. Waldir Leite Roque
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Angel Alberich-Bayarri
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Waldir Leite Roque .

Editor information

Editors and Affiliations

  1. Department of mechanical engineering, Universidade do Porto, Porto, Portugal

    João Manuel R. S. Tavares

  2. Universidade do Porto, Porto, Portugal

    Renato Natal Jorge

Rights and permissions

Reprints and permissions

Copyright information

© 2015 Springer International Publishing Switzerland

About this chapter

Cite this chapter

Roque, W., Alberich-Bayarri, A. (2015). Tortuosity Influence on the Trabecular Bone Elasticity and Mechanical Competence. In: Tavares, J., Natal Jorge, R. (eds) Developments in Medical Image Processing and Computational Vision. Lecture Notes in Computational Vision and Biomechanics, vol 19. Springer, Cham. https://doi.org/10.1007/978-3-319-13407-9_11

Download citation

  • DOI: https://doi.org/10.1007/978-3-319-13407-9_11

  • Published:

  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-13406-2

  • Online ISBN: 978-3-319-13407-9

  • eBook Packages: EngineeringEngineering (R0)

Publish with us

Policies and ethics

Search

Navigation