3D characterization of bone strains in the rat tibia loading model

  • Antonia Torcasio
  • Xiaolei Zhang
  • Joke Duyck
  • G. Harry van Lenthe
Original Paper

Abstract

Bone strain is considered one of the factors inducing bone tissue response to loading. Nevertheless, where animal studies can provide detailed data on bone response, they only offer limited information on experimental bone strains. Including micro-CT-based finite element (micro FE) models in the analysis represents a potent methodology for quantifying strains in bone. Therefore, the main objective of this study was to develop and validate specimen-specific micro FE models for the assessment of bone strains in the rat tibia compression model. Eight rat limbs were subjected to axial compression loading; strain at the medio-proximal site of the tibiae was measured by means of strain gauges. Specimen-specific micro FE models were created and analyzed. Repeated measurements on each limb indicated that the effect of limb positioning was small (COV = 6.45 ± 2.27 %). Instead, the difference in the measured strains between the animals was high (54.2%). The computational strains calculated at the strain gauge site highly correlated to the measured strains (R2 = 0.95). Maximum peak strains calculated at exactly 25% of the tibia length for all specimens were equal to 435.11 ± 77.88 microstrains (COV = 17.19%). In conclusion, we showed that strain gauge measurements are very sensitive to the exact strain gauge location on the bone; hence, the use of strain gauge data only is not recommended for studies that address at identifying reliable relationships between tissue response and local strains. Instead, specimen-specific micro FE models of rat tibiae provide accurate estimates of tissue-level strains.

Keywords

Tissue-level strains Micro-CT Voxel-based finite element models Rat tibia compression loading Strain gauge measurements 

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References

  1. Adams M (2002) Evaluation of three unstructured multigrid methods on 3D finite element problems in solid mechanics. Int J Numer Meth Eng 55: 519–534MATHCrossRefGoogle Scholar
  2. Akhter MP, Raab DM, Turner CH, Kimmel DB, Recker RR (1992) Characterization of in vivo strain in the rat tibia during external application of a four-point bending load. J Biomech 25(10): 1241–1246CrossRefGoogle Scholar
  3. Arbenz P, van Lenthe GH, Mennel U, Müller R, Sala M (2008) A scalable multi-level preconditioner for matrix-free μ-finite element analysis of human bone structures. Int J Numer Meth Eng 73: 927–947MATHCrossRefGoogle Scholar
  4. Bouxsein ML, Boyd SK, Christiansen BA, Guldberg RE, Jepsen KJ, Müller R (2010) Guidelines for assessment of bone microstructure in Rodents using micro-computed tomography. J Bone Miner Res 25(7): 1468–1486CrossRefGoogle Scholar
  5. Boyd SK, Muller R, Zernicke RF (2002) Mechanical and architectural bone adaptation in early stage experimental osteoarthritis. J Bone Miner Res 17(4): 687–694CrossRefGoogle Scholar
  6. Chennimalai KN, Dantzig JA, Jasiuk IM, Robling AG, Turner CH (2010) Numerical modeling of long bone adaptation due to mechanical loading: correlation with experiments. Ann Biomed Eng 38(3): 594–604CrossRefGoogle Scholar
  7. Frost HM (2003) Bone’s mechanostat: a 2003 update. Anat Rec A Discov Mol Cell Evol Biol 275(2): 1081–1101MathSciNetCrossRefGoogle Scholar
  8. Hsieh YF, Robling AG, Ambrosius WT, Burr DB, Turner CH (2001) Mechanical loading of diaphyseal bone in vivo: the strain threshold for an osteogenic response varies with location. J Bone Miner Res 16(12): 2291–2297CrossRefGoogle Scholar
  9. Hsieh YF, Wang T, Turner CH (1999) Viscoelastic response of the rat loading model: implications for studies of strain-adaptive bone formation. Bone 25: 379–382CrossRefGoogle Scholar
  10. Huang TH, Lin SC, Chang FL, Hsieh SS, Liu SH, Yang RS (2003) Effects of different exercise modes on mineralization, structure, and biomechanical properties of growing bone. J Appl Physiol 95(1): 300–307Google Scholar
  11. Kotha SP, Hsieh YF, Strigel RM, Muller R, Silva MJ (2004) Experimental and finite element analysis of the rat ulnar loading model-correlations between strain and bone formation following fatigue loading. J Biomech 37(4): 541–548CrossRefGoogle Scholar
  12. Kuruvilla SJ, Fox SD, Cullen DM, Akhter MP (2008) Site specific bone adaptation response to mechanical loading. J Musculoskelet Neuronal Interact 8(1): 71–78Google Scholar
  13. LaMothe JM, Hamilton NH, Zernicke RF (2005) Strain rate influences periosteal adaptation in mature bone. Med Eng Phys 27: 277–284CrossRefGoogle Scholar
  14. LaMothe JM, Zernicke RF (2004) Rest insertion combined with high-frequency loading enhances osteogenesis. J Appl Physiol 96: 1788–1793CrossRefGoogle Scholar
  15. Robling AG, Turner CH (2002) Mechanotransduction in bone: genetic effects on mechanosensitivity in mice. Bone 31(5): 562–569CrossRefGoogle Scholar
  16. Rubin CT, Lanyon LE (1984) Regulation of bone formation by applied dynamic loads. J Bone Joint Surg Am 66(3): 397–402Google Scholar
  17. Schriefer JL, Robling AG, Warden SJ, Fournier AJ, Mason JJ, Turner CH (2005a) A comparison of mechanical properties derived from multiple skeletal sites in mice. J Biomech 38(3): 467–475CrossRefGoogle Scholar
  18. Schriefer JL, Warden SJ, Saxon LK, Robling AG, Turner CH (2005b) Cellular accommodation and the response of bone to mechanical loading. J Biomech 38(9): 1838–1845CrossRefGoogle Scholar
  19. Stadelmann VA, Hocke J, Verhelle J, Forster V, Merlini F, Terrier A, Pioletti DP (2009) 3D strain map of axially loaded mouse tibia: a numerical analysis validated by experimental measurements. Comput Methods Biomech Biomed Eng 12(1): 95–100CrossRefGoogle Scholar
  20. Torcasio A, van Oosterwyck H, van Lenthe GH (2008) The systematic errors in tissue modulus of murine bones when estimated from three-point bending. J Biomech 41: S14CrossRefGoogle Scholar
  21. Turner CH, Forwood MR, Otter MW (1994) Mechanotransduction in bone: do bone cells act as sensors of fluid flow. FASEB J 8(11): 875–878Google Scholar
  22. Uthgenannt BA, Silva MJ (2007) Use of the rat forelimb compression model to create discrete levels of bone damage in vivo. J Biomech 40(2): 317–324CrossRefGoogle Scholar
  23. van Lenthe GH, Kohler T, Voide R, Donahue LR, Müller R (2004) Functional phenomics in bone: high-throughput assessment of genetic differences in murine inbred strains. J Bone Miner Res 19((1): S390Google Scholar
  24. van Lenthe GH, Voide R, Boyd SK, Muller R (2008) Tissue modulus calculated from beam theory is biased by bone size and geometry: implications for the use of three-point bending tests to determine bone tissue modulus. Bone 43(4): 717–723CrossRefGoogle Scholar
  25. van Lenthe GH, Muller R (2006) Prediction of failure load using micro-finite element analysis models: toward in vivo strength assessment. Drug Discov Today Technol 3: 221–229CrossRefGoogle Scholar
  26. van Rietbergen B, Weinans H, Huiskes R, Odgaard A (1995) A new method to determine trabecular bone elastic properties and loading using micromechanical finite-element models. J Biomech 28(1): 69–81CrossRefGoogle Scholar
  27. Voide R, van Lenthe GH, Muller R (2008) Femoral stiffness and strength critically depend on loading angle: a parametric study in a mouse-inbred strain. Biomed Tech (Berl) 53(3): 122–129CrossRefGoogle Scholar
  28. Xie L, Jacobson JM, Choi ES, Busa B, Donahue LR, Miller LM, Rubin CT, Judex S (2006) Low-level mechanical vibrations can influence bone resorption and bone formation in the growing skeleton. Bone 39: 1059–1066CrossRefGoogle Scholar
  29. Zhang P, Tanaka SM, Jiang H, Su M, Yokota H (2006) Diaphyseal bone formation in murine tibiae in response to knee loading. J Appl Physiol 100: 1452–1459CrossRefGoogle Scholar

Copyright information

© Springer-Verlag 2011

Authors and Affiliations

  • Antonia Torcasio
    • 1
  • Xiaolei Zhang
    • 2
  • Joke Duyck
    • 2
  • G. Harry van Lenthe
    • 1
    • 3
  1. 1.Division of Biomechanics and Engineering Design, Department of Mechanical EngineeringK.U.LeuvenLeuvenBelgium
  2. 2.BIOMAT, Department of Prosthetic DentistryK.U.LeuvenLeuvenBelgium
  3. 3.Institute for BiomechanicsETH ZurichZurichSwitzerland

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