Medical Imaging in the Diagnosis of Osteoporosis and Estimation of the Individual Bone Fracture Risk

  • Chapter
  • First Online:
Medical Image Processing

Part of the book series: Biological and Medical Physics, Biomedical Engineering ((BIOMEDICAL))

Abstract

Osteoporosis is a degenerative disease of the bone. In an advanced state, bone weakened by osteoporosis may fracture spontaneously with debilitating consequences. Beginning osteoporosis can be treated with exercise and calcium/vitamin D supplement, whereas osteoclast-inhibiting drugs are used in advanced stages. Choosing the proper treatment requires accurate diagnosis of the degree of osteoporosis. The most commonly used measurement of bone mineral content or bone mineral density provides a general orientation, but is insufficient as a predictor for load fractures or spontaneous fractures. There is wide agreement that the averaging nature of the density measurement does not take into account the microarchitectural deterioration, and imaging methods that provide a prediction of the load-bearing quality of the trabecular network are actively investigated. Studies have shown that X-ray projection images, computed tomography (CT) images, and magnetic resonance images (MRI) contain texture information that relates to the trabecular density and connectivity. In this chapter, image analysis methods are presented which allow to quantify the degree of microarchitectural deterioration of trabecular bone and have the potential to predict the load-bearing capability of bone.

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

Access this chapter

Subscribe and save

Springer+ Basic
EUR 32.99 /Month
  • Get 10 units per month
  • Download Article/Chapter or Ebook
  • 1 Unit = 1 Article or 1 Chapter
  • Cancel anytime
Subscribe now

Buy Now

Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 129.00
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 169.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free ship** worldwide - see info
Hardcover Book
USD 169.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free ship** worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Similar content being viewed by others

References

  1. Klibanski, A., Adams-Campbell, L., Bassford, T., Blair, S.N., Boden, S.D., Dickersin, K., et al.: Osteoporosis prevention, diagnosis, and therapy. J. Am. Med. Assoc 285(6), 785–795 (2001)

    Article  Google Scholar 

  2. Hernandez, C.J., Keaveny, T.M.: A biomechanical perspective on bone quality. Bone 39(6), 1173–1181 (2006)

    Article  Google Scholar 

  3. Holroyd, C., Cooper, C., Dennison, E.: Epidemiology of osteoporosis. Best Pract. Res. Clin. Endocrinol. Metabol. 22(5), 671–685 (2008)

    Article  Google Scholar 

  4. Ritchie, R.O.: How does human bone resist fracture? Ann. New York Acad. Sci. 1192, 72–80 (2010)

    Article  Google Scholar 

  5. Small, R.E.: Uses and limitations of bone mineral density measurements in the management of osteoporosis. Medsc. Gen. Med. 7(2), 3 (2005)

    Google Scholar 

  6. Gennari, C.: Calcium and vitamin D nutrition and bone disease of the elderly. Publ. Health Nutr. 4, 547–559 (2001)

    Google Scholar 

  7. Rittweger, J.: Can exercise prevent osteoporosis? J. Musculosceletal Neuronal Interact. 6(2), 162 (2006)

    Google Scholar 

  8. Felsenberg, D., Boonen, S.: The bone quality framework: Determinants of bone strength and their interrelationships, and implications for osteoporosis management. Clin. Therapeut. 27(1), 1–11 (2005)

    Article  Google Scholar 

  9. Frost, H.M.: Dynamics of bone remodeling. Bone Biodynamics 315 (1964)

    Google Scholar 

  10. Wolff, I., Van Croonenborg, J.J., Kemper, H.C.G., Kostense, P.J., Twisk, J.W.R.: The effect of exercise training programs on bone mass: a meta-analysis of published controlled trials in pre-and postmenopausal women. Osteoporos. Int. 9(1), 1–12 (1999)

    Article  Google Scholar 

  11. Karlsson, M.K., Nordqvist, A., Karlsson, C.: Physical activity, muscle function, falls and fractures. Food Nutr. Res. 52 (2008)

    Google Scholar 

  12. Meunier, P.J., Sebert, J.L., Reginster, J.Y., Briancon, D., Appelboom, T., Netter, P., et al.: Fluoride salts are no better at preventing new vertebral fractures than calcium-vitamin D in postmenopausal osteoporosis: the FAVOStudy. Osteoporos. Int. 8(1), 4–12 (1998)

    Article  Google Scholar 

  13. Riggs, B.L., Hodgson, S.F., O’Fallon, W.M., Chao, E., Wahner, H.W., Muhs, J.M., et al.: Effect of fluoride treatment on the fracture rate in postmenopausal women with osteoporosis. Obstet. Gynecol. Surv. 45(8), 542 (1990)

    Article  Google Scholar 

  14. McCreadie, B.R., Goldstein, S.A.: Biomechanics of fracture: Is bone mineral density sufficient to assess risk? J. Bone Miner. Res. 15(12), 2305–2308 (2000)

    Article  Google Scholar 

  15. Rockoff, S.D., Sweet, E., Bleustein, J.: The relative contribution of trabecular and cortical bone to the strength of human lumbar vertebrae. Calcif. Tissue Int. 3(1), 163–175 (1969)

    Article  Google Scholar 

  16. Fields, A.J., Eswaran, S.K., Jekir, M.G., Keaveny, T.M.: Role of trabecular microarchitecture in whole-vertebral body biomechanical behavior. J. Bone Miner. Res. 24(9), 1523–1530 (2009)

    Article  Google Scholar 

  17. Keaveny, T.M., Morgan, E.F., Niebur, G.L., Yeh, O.C.: Biomechanics of trabecular bone. Annu. Rev. Biomed. Eng. 3(1), 307–333 (2001)

    Article  Google Scholar 

  18. Hernandez, C.J.: How can bone turnover modify bone strength independent of bone mass? Bone 42(6), 1014–1020 (2008)

    Article  Google Scholar 

  19. Ammann, P., Rizzoli, R.: Bone strength and its determinants. Osteoporos. Int. 14(S3), 13–18 (2003)

    Google Scholar 

  20. Chappard, D., Baslé, M.F., Legrand, E., Audran, M.: Trabecular bone microarchitecture: A review. Morphologie 92(299), 162–170 (2008)

    Google Scholar 

  21. Svendsen, O.L., Haarbo, J., Hassager, C., Christiansen, C.: Accuracy of measurements of body composition by dual-energy x-ray absorptiometry in vivo. Am. J. Clin. Nutr. 57(5), 605 (1993)

    Google Scholar 

  22. Lang, T.F.: Quantitative computed tomography. Radiol. Clin. N. Am. 48(3), 589–600 (2010)

    Article  Google Scholar 

  23. Bushberg, J., Seibert, J., Leidholdt, Jr. E.M., Boone, J.M.: The essential Physics of medical imaging. Lippincott Williams & Wilkins, New York (2002)

    Google Scholar 

  24. Njeh, C.F., Boivin, C.M., Langton, C.M.: The role of ultrasound in the assessment of osteoporosis: a review. Osteoporos. Int. 7(1), 7–22 (1997)

    Article  Google Scholar 

  25. Liu, X.S., Sajda, P., Saha, P.K., Wehrli, F.W., Bevill, G., Keaveny, T.M., et al.: 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 (2008)

    Article  Google Scholar 

  26. Parfitt, A.M.: Bone histomorphometry: standardization of nomenclature, symbols and units (summary of proposed system). Bone 9(1), 67–69 (1988)

    Article  Google Scholar 

  27. Hildebrand, T., Laib, A., Müller, R., Dequeker, J., Rüegsegger, P.: Direct three dimensional morphometric analysis of human cancellous bone: microstructural data from Spine, Femur, Iliac Crest, and Calcaneus. J. Bone Miner. Res. 14(7), 1167–1174 (1999)

    Article  Google Scholar 

  28. Hernandez, C.J., Beaupre, G.S., Keller, T.S., Carter, D.R.: The influence of bone volume fraction and ash fraction on bone strength and modulus. Bone 29(1), 74–78 (2001)

    Article  Google Scholar 

  29. Hildebrand, T., Rüegsegger, P.: A new method for the model-independent assessment of thickness in three-dimensional images. J. Microsc. 185(1), 67–75 (1997)

    Article  Google Scholar 

  30. Cortet, B., Bourel, P., Dubois, P., Boutry, N., Cotten, A., Marchandise, X.: CT scan texture analysis of the distal radius: influence of age and menopausal status. Rev. Rhum. (English edn.) 65(2), 109 (1998)

    Google Scholar 

  31. Ito, M., Ohki, M., Hayashi, K., Yamada, M., Uetani, M., Nakamura, T.: Trabecular texture analysis of CT images in the relationship with spinal fracture. Radiology 194(1), 55 (1995)

    Google Scholar 

  32. Thomsen, J.S., Ebbesen, E.N., Mosekilde, L.: Relationships between static histomorphometry and bone strength measurements in human iliac crest bone biopsies. Bone 22(2), 153–163 (1998)

    Article  Google Scholar 

  33. Saha, P.K., Gomberg, B.R., Wehrli, F.W.: Three-dimensional digital topological characterization of cancellous bone architecture. Int. J. Imag. Syst. Tech. 11(1), 81–90 (2000)

    Article  Google Scholar 

  34. Le, H.M., Holmes, R.E., Shors, E.C., Rosenstein, D.A.: Computerized quantitative analysis of the interconnectivity of porous biomaterials. Acta. Stereologica. 11, 267–267 (1992)

    Google Scholar 

  35. Vesterby, A., Gundersen, H.J.G., Melsen, F.: Star volume of marrow space and trabeculae of the first lumbar vertebra: sampling efficiency and biological variation. Bone 10(1), 7–13 (1989)

    Article  Google Scholar 

  36. Hahn, M., Vogel, M., Pompesius-Kempa, M., Delling, G.: Trabecular bone pattern factor–a new parameter for simple quantification of bone microarchitecture. Bone 13(4), 327–330 (1992)

    Article  Google Scholar 

  37. Laib, A., Hildebrand, T., Häuselmann, H.J., Rüegsegger, P.: Ridge number density: a new parameter for in vivo bone structure analysis. Bone 21(6), 541–546 (1997)

    Article  Google Scholar 

  38. Hildebrand, T., Rüegsegger, P.: Quantification of bone microarchitecture with the structure model index. Comput. Meth. Biomech. Biomed. Eng. 1(1), 15–23 (1997)

    Article  Google Scholar 

  39. Haidekker, M.A.: Advanced Biomedical Image Analysis. Wiley, Hoboken, NJ (2011)

    MATH  Google Scholar 

  40. Dougherty, G.: Image enhancement in the spatial domain. In: Digital image processing for medical applications, p. 170–188. Cambridge University Press, New York (2009)

    Google Scholar 

  41. Caldwell, C.B., Willett, K., Cuncins, A.V., Hearn, T.C.: Characterization of vertebral strength using digital radiographic analysis of bone structure. Med. Phys. 22, 611 (1995)

    Article  Google Scholar 

  42. Lespessailles, E., Gadois, C., Kousignian, I., Neveu, J.P., Fardellone, P., Kolta, S., et al.: Clinical interest of bone texture analysis in osteoporosis: a case control multicenter study. Osteoporos. Int. 19(7), 1019–1028 (2008)

    Article  Google Scholar 

  43. Haidekker, M.A., Andresen, R., Evertsz, C.J., Banzer, D., Peitgen, H.O.: Issues of threshold selection when determining the fractal dimension in HRCT slices of lumbar vertebrae. Br. J. Radiol. 73(865), 69 (2000)

    Google Scholar 

  44. Haralick, R.M., Shanmugam, K., Dinstein, I.H.: Textural features for image classification. IEEE Trans. Syst. Man. Cybern. Syst. Hum. 3(6), 610–621 (1973)

    Article  Google Scholar 

  45. Laws, K.I.: Texture energy measures. Proc DARPA Image Unerstanding Workshop, pp. 47–51 (1979)

    Google Scholar 

  46. Lee, R.L., Dacre, J.E., Hart, D.J., Spector, T.D.: Femoral neck trabecular patterns predict osteoporotic fractures. Med. Phys. 29, 1391 (2002)

    Article  Google Scholar 

  47. Lespessailles, E., Gadois, C., Lemineur, G., Do-Huu, J.P., Benhamou, L.: Bone texture analysis on direct digital radiographic images: precision study and relationship with bone mineral density at the os calcis. Calcif. Tissue Int. 80(2), 97–102 (2007)

    Article  Google Scholar 

  48. Rachidi, M., Marchadier, A., Gadois, C., Lespessailles, E., Chappard, C., Benhamou, C.L.: Laws’ masks descriptors applied to bone texture analysis: an innovative and discriminant tool in osteoporosis. Skeletal. Radiol. 37(6), 541–548 (2008)

    Article  Google Scholar 

  49. Vokes, T., Lauderdale, D., Ma, S.L., Chinander, M., Childs, K., Giger, M.: Radiographic texture analysis of densitometric calcaneal images: Relationship to clinical characteristics and to bone fragility. J. Bone Miner. Res. 25(1), 56–63 (2010)

    Article  Google Scholar 

  50. Wilkie, J.R., Giger, M.L., Engh, Sr. C.A., Hopper, Jr. R.H., Martell, J.M.: Radiographic texture analysis in the characterization of trabecular patterns in periprosthetic osteolysis1. Acad. Radiol. 15(2), 176–185 (2008)

    Article  Google Scholar 

  51. Chappard, C., Brunet-Imbault, B., Lemineur, G., Giraudeau, B., Basillais, A., Harba, R., et al.: Anisotropy changes in post-menopausal osteoporosis: characterization by a new index applied to trabecular bone radiographic images. Osteoporos. Int. 16(10), 1193–1202 (2005)

    Article  Google Scholar 

  52. Brunet-Imbault, B., Lemineur, G., Chappard, C., Harba, R., Benhamou, C.L.: A new anisotropy index on trabecular bone radiographic images using the fast Fourier transform. BMC Med. Imag. 5(1), 4 (2005)

    Article  Google Scholar 

  53. Peitgen, H.O., Jürgens, H., Saupe, D.: Chaos and fractals: new frontiers of science. Springer, New York (2004)

    MATH  Google Scholar 

  54. Mandelbrot, B.B.: The Fractal Geometry of Nature. Freeman, USA (1982)

    MATH  Google Scholar 

  55. Martínez-Lopez, F., Cabrerizo-Vílchez, M., Hidalgo-Alvarez, R.: A study of the different methods usually employed to compute the fractal dimension1. Phys. Stat. Mech. Appl. 311, 411–428 (2002)

    Article  MATH  Google Scholar 

  56. Saupe, D.: Algorithms for random fractals. In: Peitgen, H.-O., and Saupe, D. (eds.), The Science of Fractal Images, pp. 71–136. Springer, New York (1988)

    Google Scholar 

  57. Stein, M.C.: Nonparametric estimation of fractal dimension, vol. 1001 of Society of Photo-Optical Instrumentation Engineers (SPIE) Conference Series. SPIE (1988)

    Google Scholar 

  58. Chung, H.W., Chu, C.C., Underweiser, M., Wehrli, F.W.: On the fractal nature of trabecular structure. Med. Phys. 21, 1535 (1994)

    Article  Google Scholar 

  59. Dubuc, B., Zucker, S., Tricot, C., Quiniou, J., Wehbi, D.: Evaluating the fractal dimension of surfaces. Proc. Roy. Soc. Lond. Math. Phys. Sci. 425(1868), 113–127 (1989)

    Article  MathSciNet  MATH  Google Scholar 

  60. Huang, Q., Lorch, J.R., Dubes, R.C.: Can the fractal dimension of images be measured? Pattern Recogn. 27(3), 339–349 (1994)

    Article  Google Scholar 

  61. Geraets, W.G., Van Der Stelt, P.F.: Fractal properties of bone. Dentomaxillofacial Radiology 29(3), 144 (2000)

    Google Scholar 

  62. Lopes, R., Betrouni, N.: Fractal and multifractal analysis: A review. Med. Image. Anal. 13(4), 634–649 (2009)

    Article  Google Scholar 

  63. Lundahl, T., Ohley, W., Kuklinski, W.: Analysis and interpolation of angiographic images by use of fractals. Computers in Cardiology, p. 355. Linko**, Sweden (1985)

    Google Scholar 

  64. Ruttimann, U.E., Webber, R.L., Hazelrig, J.B.: Fractal dimension from radiographs of peridental alveolar bone:: A possible diagnostic indicator of osteoporosis. Oral. Surg. Oral. Med. Oral. Pathol. 74(1), 98–110 (1992)

    Article  Google Scholar 

  65. Webber, R., Underhill, T., Horton, R., Dixon, R., Pope, Jr. T.: Predicting osseous changes in ankle fractures. IEEE Eng. Med. Biol. Mag. 12(1), 103–110 (2002)

    Article  Google Scholar 

  66. Majumdar, S., Weinstein, R.S., Prasad, R.R.: Application of fractal geometry techniques to the study of trabecular bone. Med. Phys. 20, 1611 (1993)

    Article  Google Scholar 

  67. Southard, T.E., Southard, K.A.: Detection of simulated osteoporosis in maxillae using radiographic texture analysis. IEEE Trans. Biomed. Eng. 43(2), 123–132 (2002)

    Article  Google Scholar 

  68. Veenland, J., Grashuis, J., Van der Meer, F., Beckers, A., Gelsema, E.: Estimation of fractal dimension in radiographs. Med. Phys. 23, 585 (1996)

    Article  Google Scholar 

  69. Fortin, C., Kumaresan, R., Ohley, W., Hoefer, S.: Fractal dimension in the analysis of medical images. IEEE Eng. Med. Biol. Mag. 11(2), 65–71 (2002)

    Article  Google Scholar 

  70. Messent, E., Buckland-Wright, J., Blake, G.: Fractal analysis of trabecular bone in knee osteoarthritis (OA) is a more sensitive marker of disease status than bone mineral density (BMD). Calcif. Tissue Int. 76(6), 419–425 (2005)

    Article  Google Scholar 

  71. Dougherty, G., Henebry, G.M.: Fractal signature and lacunarity in the measurement of the texture of trabecular bone in clinical CT images. Med. Eng. Phys. 23(6), 369–380 (2001)

    Article  Google Scholar 

  72. Dong, P.: Test of a new lacunarity estimation method for image texture analysis. Int. J. Rem. Sens. 21(17), 3369–3373 (2000)

    Article  Google Scholar 

  73. Plotnick, R.E., Gardner, R.H., Hargrove, W.W., Prestegaard, K., Perlmutter, M.: Lacunarity analysis: a general technique for the analysis of spatial patterns. Phys. Rev. E 53(5), 5461–5468 (1996)

    Article  Google Scholar 

  74. Dougherty, G., Henebry, G.M.: Lacunarity analysis of spatial pattern in CT images of vertebral trabecular bone for assessing osteoporosis. Med. Eng. Phys. 24(2), 129–138 (2002)

    Article  Google Scholar 

  75. Zaia, A., Eleonori, R., Maponi, P., Rossi, R., Murri, R.: MR imaging and osteoporosis: Fractal lacunarity analysis of trabecular bone. IEEE Trans. Inform. Tech. Biomed. 10(3), 484–489 (2006)

    Article  Google Scholar 

  76. Panagiotopoulou, O.: Finite element analysis (FEA): applying an engineering method to functional morphology in anthropology and human biology. Ann. Hum. Biol. 36(5), 609–623 (2009)

    Article  Google Scholar 

  77. Vesterby, A., Mosekilde, L., Gundersen, H.J.G., Melsen, F., Holme, K., Sørensen, S.: Biologically meaningful determinants of the in vitro strength of lumbar vertebrae. Bone 12(3), 219–224 (1991)

    Article  Google Scholar 

  78. Jones, A.C., Wilcox, R.K.: Finite element analysis of the spine: Towards a framework of verification, validation and sensitivity analysis. Med. Eng. Phys. 30(10), 1287–1304 (2008)

    Article  Google Scholar 

  79. Lavaste, F., Skalli, W., Robin, S., Roy-Camille, R., Mazel, C.: Three-dimensional geometrical and mechanical modelling of the lumbar spine. J. Biomech. 25(10), 1153–1164 (1992)

    Article  Google Scholar 

  80. Kuo, C.S., Hu, H.T., Lin, R.M., Huang, K.Y., Lin, P.C., Zhong, Z.C., et al.: Biomechanical analysis of the lumbar spine on facet joint force and intradiscal pressure-a finite element study. BMC Muscoskel. Disord. 11, 151 (2010)

    Article  Google Scholar 

  81. Gibson, L.J.: The mechanical behaviour of cancellous bone. J. Biomech. 18(5), 317–328 (1985)

    Article  Google Scholar 

  82. Jensen, K.S., Mosekilde, L.: A model of vertebral trabecular bone architecture and its mechanical properties. Bone 11(6), 417–423 (1990)

    Article  Google Scholar 

  83. Hollister, S.J., Brennan, J.M., Kikuchi, N.: A homogenization sampling procedure for calculating trabecular bone effective stiffness and tissue level stress. J. Biomech. 27(4), 433–444 (1994)

    Article  Google Scholar 

  84. Müller, R., Rüegsegger, P.: Three-dimensional finite element modelling of non-invasively assessed trabecular bone structures. Med. Eng. Phys. 17(2), 126–133 (1995)

    Article  Google Scholar 

  85. Magland, J., Vasilic, B., Wehrli, F.W.: Fast Low Angle Dual Spin Echo (FLADE): A new robust pulse sequence for structural imaging of trabecular bone. Magn. Reson. Med. 55(3), 465–471 (2006)

    Article  Google Scholar 

  86. Karjalainen, J.P., Toyras, J., Riekkinen, O., Hakulinen, M., Jurvelin, P.S.: Ultrasound backscatter imaging provides frequency-dependent information on structure, composition and mechanical properties of human trabecular bone. Ultrasound Med. Biol. 35(8), 1376–1384 (2009)

    Article  Google Scholar 

  87. Haïat, G., Padilla, F., Svrcekova, M., Chevalier, Y., Pahr, D., Peyrin, F., et al.: Relationship between ultrasonic parameters and apparent trabecular bone elastic modulus: A numerical approach. J. Biomech. 42(13), 2033–2039 (2009)

    Article  Google Scholar 

  88. Hosokawa, A.: Effect of porosity distribution in the propagation direction on ultrasound waves through cancellous bone. IEEE Trans. Ultrason. Ferroelectrics Freq. Contr. 57(6), 1320–1328 (2010)

    Article  Google Scholar 

  89. Davison, K.S., Kendler, D.L., Ammann, P., Bauer, D.C., Dempster, D.W., Dian, L., et al.: Assessing fracture risk and effects of osteoporosis drugs: bone mineral density and beyond. Am. J. Med. 122(11), 992–997 (2009)

    Article  Google Scholar 

  90. Resch, H., Libanati, C., Farley, S., Bettica, P., Schulz, E., Baylink, D.J.: Evidence that fluoride therapy increases trabecular bone density in a peripheral skeletal site. J. Clin. Endocrinol. Metabol. 76(6), 1622 (1993)

    Article  Google Scholar 

  91. Grynpas, M.D.: Fluoride effects on bone crystals. J. Bone Miner. Res. 5(S1), S169–S175 (1990)

    Google Scholar 

  92. Jiang, Y., Zhao, J., Liao, E.Y., Dai, R.C., Wu, X.P., Genant, H.K.: Application of micro-CT assessment of 3-D bone microstructure in preclinical and clinical studies. J. Bone Miner. Metabol. 23, 122–131 (2005)

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Mark A. Haidekker .

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 2011 Springer Science+Business Media, LLC

About this chapter

Cite this chapter

Haidekker, M.A., Dougherty, G. (2011). Medical Imaging in the Diagnosis of Osteoporosis and Estimation of the Individual Bone Fracture Risk. In: Dougherty, G. (eds) Medical Image Processing. Biological and Medical Physics, Biomedical Engineering. Springer, New York, NY. https://doi.org/10.1007/978-1-4419-9779-1_9

Download citation

Publish with us

Policies and ethics

Navigation