Time Dependent Behaviour of Trabecular Bone at Multiple Load Levels

Annals of Biomedical Engineering, Jan 2017

The deformation of bone when subjected to loads is not instantaneous but varies with time. To investigate this time-dependent behaviour sixteen bovine trabecular bone specimens were subjected to compressive loading, creep, unloading and recovery at multiple load levels corresponding to apparent strains of 2000–25,000 με. We found that: the time-dependent response of trabecular bone comprises of both recoverable and irrecoverable strains; the strain response is nonlinearly related to applied load levels; and the response is linked to bone volume fraction. Although majority of strain is recovered after the load-creep-unload-recovery cycle some residual strain always exists. The analysis of results indicates that trabecular bone becomes stiffer initially and then experiences stiffness degradation with the increasing load levels. Steady state creep rate was found to be dependent on applied stress level and bone volume fraction with a power law relationship.

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Time Dependent Behaviour of Trabecular Bone at Multiple Load Levels

Time Dependent Behaviour of Trabecular Bone at Multiple Load Levels A. HAMISH R. W. SIMPSON 0 1 PANKAJ PANKAJ 1 0 Department of Orthopaedics, The University of Edinburgh , Chancellor's Building, Edinburgh EH16 4SB , UK 1 engineering, School of Engineering, The University of Edinburgh , King's Buildings, Edinburgh EH9 3DW , UK. Electronic mail: 2 Institute for Bioengineering, School of Engineering, The University of Edinburgh , King's Buildings, Edinburgh EH9 3DW , UK -The deformation of bone when subjected to loads is not instantaneous but varies with time. To investigate this time-dependent behaviour sixteen bovine trabecular bone specimens were subjected to compressive loading, creep, unloading and recovery at multiple load levels corresponding to apparent strains of 2000-25,000 le. We found that: the time-dependent response of trabecular bone comprises of both recoverable and irrecoverable strains; the strain response is nonlinearly related to applied load levels; and the response is linked to bone volume fraction. Although majority of strain is recovered after the load-creep-unloadrecovery cycle some residual strain always exists. The analysis of results indicates that trabecular bone becomes stiffer initially and then experiences stiffness degradation with the increasing load levels. Steady state creep rate was found to be dependent on applied stress level and bone volume fraction with a power law relationship. Creep-recovery; Viscoelastic; Bone volume fraction; Steady state creep rate; Creep compliance - Trabecular bone, a composite cellular material with hierarchical structure, is generally treated as time-independent in biomechanical models.24 But in reality its response to mechanical loads is known to be time-dependent.5,13,19,23,29 Study of this time-dependent behaviour is important in several contexts such as: to understand energy dissipation ability of bone; to understand the age related non-traumatic fractures,26 to predict implant loosening due to cyclic load,30 to understand progressive vertebral deformity,25 and preclinical evaluation of total joint replacements.30 Consequently, trabecular bone’s time-dependent behaviour has great clinical relevance, but it has received relatively little attention. A few studies have attempted to relate the creep behaviour with micro-architecture of bone. Kim et al. conducted one cycle of load-creep-unload-recovery experiments in which they applied a load corresponding to 2000le and found that the samples with thinner trabeculae and greater connectivity were associated with increased logarithmic creep rate.13 Novitskaya et al. reported the changes in micro-architectural indices evaluated from micro computed tomography (lCT) before and after the creep; the study found that creep induced changes in trabecular separation and structural model index.23 Novitskaya et al. also found that the steady state creep rate was higher and the final creep strain was larger for samples with low bone volume fraction (BV/TV) (or apparent density).23 BV/TV or apparent density have been extensively employed to evaluate the time-independent stiffness of bone,11,14 which is then used in subject-specific models.33 Similar relationships between BV/TV and timedependent response will permit their application in computational simulations where modelling time-dependent behaviour is important e.g., implant loosening. These relationships need to be considered at multiple loads to incorporate any load-level dependence. Manda et al. conducted creep experiments at a single load level (corresponding to a small apparent strain of 2000 le) and reported the relationships between BV/TV and linear viscoelasticity for trabecular bone.19 Previous studies have shown that under static conditions (or very slow strain rates) the strain in trabecular bone increases non-linearly with applied loads.10,16,17,21 However, time dependent behaviour with changing load levels has received limited attention. A few previous studies have considered multiple load levels but different loads were applied to different specimens i.e., each specimen was subjected to a single load level.4,5,20 Bowman et al. found a strong power law relationship between the steady state creep rate and the applied stress level, but when they included apparent density into the relation, the fit did not improve, in fact the r2 value decreased.5 Also, Moore et al. related steady state creep rate to applied stress level, but this study also conducted cyclic loading tests on each sample at a single stress level.20 Multiple load levels were considered by one recent study in which a mathematical model for the recoverable (or elastic) strain18 with respect to load levels was developed; however, while this study alluded to BV/TV relationship with nonlinear viscoelasticity it did not develop it. In summary, previous studies have shown that under static loading trabecular bone has a non-linear stress–strain behaviour and its time-independent e (...truncated)


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Shuqiao Xie, Krishnagoud Manda, Robert J. Wallace, Francesc Levrero-Florencio, A. Hamish R. W. Simpson, Pankaj Pankaj. Time Dependent Behaviour of Trabecular Bone at Multiple Load Levels, Annals of Biomedical Engineering, 2017, pp. 1219-1226, Volume 45, Issue 5, DOI: 10.1007/s10439-017-1800-1