Analysis of compressive creep behavior of the vertebral unit subjected to a uniform axial loading using exact parametric solution equations of Kelvin-solid models—Part I. Human intervertebral joints

Burns, M.L.; Kaleps, Ints; Kazarian, Leon E.

doi:10.1016/0021-9290(84)90129-5

Cited by 63 publications

(27 citation statements)

References 8 publications

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“…The creep phenomenon has been more extensively studied in intervertebral joints. Burns, Kaleps, and Kazarian (Burns and Kaleps, 1980;Burns et al, 1984) analysed two-, three-, and four-parameter Kelvin-solid models based on experimental studies. Smeathers (1984) studied intervertebral joints with adjacent vertebral bodies under repetitive axial loading with 1 Hz frequency.…”

Section: Deformationmentioning

confidence: 99%

Material Properties of Cancellous Bone in Repetitive Axial Loading

Linde¹,

Hvid²,

Jensen³

1985

Engineering in Medicine

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Machined cancellous bone specimens from human cadaver knees were tested under repetitive nondestructive axial compression. Loads were applied up to 50 per cent of the ultimate strength of the specimens predicted from their mineral content measured by photon absorption technique. The stiffness increased greatly between the first two compressions, and thereafter asymptotically approached a constant level. There was a 44 per cent median increase in the modulus of elasticity from compression No. 1 to compression No. 10.Steady state was apparently reached after the fifth compression with intervals between compression cycles of not more than 2 minutes. The results were reproducible, and the precision of the modulus of elasticity determined by double measurement at compression No. 10 was E 9.8 per cent (95 per cent confidence limits). The modulus of elasticity at steady state determined as the mean of compressions 6-10 was found to be € & 5.6 per cent (95 per cent confidence limits). With both methods there was a strong linear correlation between the ultimate strength and the modulus of elasticity. The correlation coefficient was r = 0.95 (p < 0.005) and r = 0.99 (p < 0.001), respectively.

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Section: Deformationmentioning

confidence: 99%

Material Properties of Cancellous Bone in Repetitive Axial Loading

Linde¹,

Hvid²,

Jensen³

1985

Engineering in Medicine

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“…Our novel experiments were designed to minimize effects of bone or endplate deformation in the measurement of what we defined as the “effective modulus” of the entire disc. Based on experimental measures of whole-disc modulus by ourselves (< 50 MPa) and others (< 25 MPa; Burns et al, 1984; Keller et al, 1987; Li et al, 1995; O’Connell et al, 2007; Pollintine et al, 2010), it seems reasonable to assume conservatively that the effective modulus of human discs, in general, does not exceed about twice the observed highest value in this experiment, namely, about 100 MPa. Our finite element analysis demonstrated that variations of this disc effective modulus across our measured typical range, and variations of disc height, did not appreciably change the spatial distribution of stress in the vertebral body — most of the high-risk bone tissue was concentrated in the central trabecular bone and endplates of the vertebra, and not anteriorly as one might expect for forward-flexion loading.…”

Section: Discussionmentioning

confidence: 56%

Effective modulus of the human intervertebral disc and its effect on vertebral bone stress

Yang

Jekir

Davis

et al. 2016

Journal of Biomechanics

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The mechanism of vertebral wedge fractures remains unclear and may relate to typical variations in the mechanical behavior of the intervertebral disc. To gain insight, we tested 16 individual whole discs (between levels T8 and L5) from nine cadavers (mean ± SD: 66 ± 16 years), loaded in compression at different rates (0.05–20.0% strain/sec), to measure a homogenized “effective” linear elastic modulus of the entire disc. The measured effective modulus, and average disc height, were then input and varied parametrically in micro-CT-based finite element models (60-µm element size, up to 80 million elements each) of six T9 human vertebrae that were virtually loaded to 3° of moderate forward-flexion via a homogenized disc. Across all specimens and loading rates, the measured effective modulus of the disc ranged from 5.8 to 42.7 MPa and was significantly higher for higher rates of loading (p < 0.002); average disc height ranged from 2.9 to 9.3 mm. The parametric finite element analysis indicated that, as disc modulus increased and disc height decreased across these ranges, the vertebral bone stresses increased but their spatial distribution was largely unchanged: most of the highest stresses occurred in the central trabecular bone and endplates, and not anteriorly. Taken together with the literature, our findings suggest that the effective modulus of the human intervertebral disc should rarely exceed 100 MPa and that typical variations in disc effective modulus (and less so, height) minimally influence the spatial distribution but can appreciably influence the magnitude of stress within the vertebral body.

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“…The average time constant for four bovine coccygeal motion segments was: 2687 s [22]. For human lumbar and thoracic specimens a range of 1351±61728 s with a mean value of 6667 s has been reported [23]. Finally, unpublished data collected in preparation of this experiment suggest that trabecular orientation, distribution of trabecular density and strength are also highly comparable to human segments.…”

Section: Discussionmentioning

confidence: 62%

Stress distribution changes in bovine vertebrae just below the endplate after sustained loading

Dieën¹,

Kingma²,

Meijer³

et al. 2001

Clinical Biomechanics

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Objective. To describe the pattern of stress distribution in the vertebral body just behind the endplate, and to document its changes due to sustained loading.Methods. Twelve fresh bovine coccygeal motion segments were dissected and tested. Each specimen was axially loaded with a sustained compressive force of 50% of its estimated compressive strength. Before loading, after 1.5 h and after 3 h of loading, the distribution of the axial pressure under the bottom vertebra (i.e., just below its top endplate) was recorded at three force levels (25%, 37.5% and 50% of the estimated compressive strength), using pressure-sensitive ®lm.Results. Stress distribution over the endplate was found to be fairly uniform. At low compression forces, the stress was the highest centrally. With increased compression and after sustained compression the uniformity improved through a signi®cant redistribution of stress to the periphery. No stress peaks were found to occur after sustained loading.Conclusion. Stress peaks after sustained loading cannot explain the occurrence of endplate fractures in sustained cyclic compression in non-degenerated discs. Competing explanations, such as creep, and fatigue failure, would appear more likely candidates. RelevanceIt has been hypothesised that compression induced fractures of the lumbar vertebral endplate constitute an important etiological factor for low back pain. Competing theories exist on the fracture mechanism in sustained loading and these would have di erent implications with respect to prevention. The present study evaluated one of these theories. Ó

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Analysis of compressive creep behavior of the vertebral unit subjected to a uniform axial loading using exact parametric solution equations of Kelvin-solid models—Part I. Human intervertebral joints

Cited by 63 publications

References 8 publications

Material Properties of Cancellous Bone in Repetitive Axial Loading

Material Properties of Cancellous Bone in Repetitive Axial Loading

Effective modulus of the human intervertebral disc and its effect on vertebral bone stress

Stress distribution changes in bovine vertebrae just below the endplate after sustained loading

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