A description of spinal fatigue strength Gerd Huber a,n , Katrin Nagel a , Daniel M. Skrzypiec b , Anke Klein c , Klaus Püschel c , Michael M. Morlock a a Institute of Biomechanics, TUHH Hamburg University of Technology, Germany b Leeds Institute of Rheumatic and Musculoskeletal Medicine, University of Leeds, Leeds, UK c Dept. of Legal Medicine, University Medical Centre Hamburg-Eppendorf, Germany article info Article history: Accepted 28 January 2016 Keywords: Fatigue Functional spinal unit In vitro Wöhler S-N-curve abstract Understanding fatigue failure of the spine is important to establish dynamic loading limits for occupa- tional health and safety. In this study experimental data were combined with published data to develop a description of the predictive parameters for spinal fatigue failure. 41 lumbar functional spinal units (FSUs) from cadaveric spines (age 49.0 711.9 yr) where cyclically loaded. Three different levels of sinusoidal axial compression (0–3 kN, 0–2 kN or 1–3 kN) were applied for 300,000 cycles. Further, published data consisted of 70 thoracic and lumbar FSUs loaded in axial compression for 5000 cycles. Cyclic forces ranged from lower peaks (F min ) of 0.7–1 kN to upper peaks (F max ) of 1.2–7.1 kN. Based on Wöhler analysis, a fatigue model was developed accounting for three parameters: I) specimen-specific scaling based on the endplate area, II) specimen-specific strength dependency on age or bone mineral density, III) load-specific correction factors based on F max and F min . The most predictive model was achieved for a combination of F max , endplate area and bone mineral density; this model explained 61% of variation (p o0.001). A model including F max , endplate area and age explained only 28% of variation (p o0.001). Inclusion of a load-specific correction factor did not sig- nificantly improve model prediction of fatigue failure. This analysis presents the basis for the prediction of specimen-specific fatigue failure of the lumbar spine, provided the endplate area and bone mineral density can be derived. & 2016 Elsevier Ltd. All rights reserved. 1. Introduction The systematic approach for fatigue testing, introduced by August Wöhler in 1860, dramatically improved engineering of cyclically loa- ded systems. The empirical curves enable the prediction of the max- imum strength for a given number of consecutive loading cycles. The basic Wöhler approximation disregards extreme cases for either a few cycles of high load magnitude (close to the ultimate- strength), for low load magnitudes that could be applied indefinitely. Finite life fatigue strengths can be characterised by a pragmatic equation, describing the bearable stress (σ) by a power function based on the numbers of cycles (N), an exponent (κ) and two scaling con- stants (σ infinite life , N 0 ), with both sides of the equation dimensionless: σ σ inf inite lif e ¼ N N 0  κ ð1Þ If 0 logarithmic scales are used on both axes, the description of these so called S-N-curves (‘stresses’ vs. ‘number of cycles’) turns out to be linear (Basquin, 1910). Experimental data can thus be used to determine the slope (κ) and the combined constants. log 10 σ ð Þ¼ κ U log 10 N ð Þþ log 10 σ inf inite lif e    κ U log 10 N 0 ð Þ   ð2Þ The slope will be negative, since higher cycles to failure will decrease the failure stress. These graphs are based on a large number of individual measurements for a specific material or a specific structure and also for standardized loading – described by waveform, frequency and the applied force peaks (minimum and maximum, respectively). The relation of the two force peaks determines whether pure compression, pure tension or alternating loads are applied. Furthermore, loading with higher amplitudes might decrease the cycles to failure compared to loads with smaller amplitudes but the same maximum force. For the highly variable skeletal system such data is scarce. However, occupational health requires evidence-based guidance and limits to guarantee a safe working environment. Whole body vibrations (WBV) pose a particular problem because even Contents lists available at ScienceDirect journal homepage: www.elsevier.com/locate/jbiomech www.JBiomech.com Journal of Biomechanics http://dx.doi.org/10.1016/j.jbiomech.2016.01.041 0021-9290/& 2016 Elsevier Ltd. All rights reserved. n Correspondence to: Hamburg University of Technology, Biomechanics, Denickestraße 15 (K), 21073 Hamburg, Germany. Tel.: þ49 40 428 78 31 53; fax: þ49 40 428 78 29 96. E-mail address: g.huber@tuhh.de (G. Huber). Please cite this article as: Huber, G., et al., A description of spinal fatigue strength. Journal of Biomechanics (2016), http://dx.doi.org/ 10.1016/j.jbiomech.2016.01.041i Journal of Biomechanics ∎ (∎∎∎∎) ∎∎∎–∎∎∎