(M-519) Quasilinear Viscoelastic Creep Model for Lumbar Soft Tissue Primary Creep Subject to Combined Loading

Introduction:: Development of lower back pain (LBP) may be linked to lumbar injury due to repeated combined flexion-compression loading such as that experienced by helicopter pilots and high-speed watercraft operators. The mechanical dynamic response of the lumbar spine is dependent on both time and loading history and can thus be characterized as viscoelastic. The viscoelastic properties of the lumbar spine under cyclic combined loading are presently undetermined. The porcine lumbar spine is a commonly-used in vitro experimental analog for the human lumbar spine due to similar anatomy and mechanical properties. Experimental response data from a porcine lumbar spinal unit loaded in repeated flexion-compression can be used to improve our understanding of viscoelastic lumbar spine biomechanics and develop injury prediction models.

Materials and Methods:: Ten porcine functional spinal units (FSU), consisting of two lumbar vertebrae and an intervertebral disc, were exposed to sinusoidal compression at 1 Hz and offset flexion using a biaxial test apparatus. FSUs were loaded until failure with maximum loads between 600N and 2300N, surrounded by an environmental chamber that approximated in vivo temperature and humidity. Distance between endplates and average endplate cross-sectional area were measured prior to the test from micro x-ray computed tomography (MicroCT) images. These values were used with force and displacement data to derive stress and strain for a primary creep model. Displacement data were filtered with an 8thorder phaseless low-pass Butterworth filter with a 0.1 Hz cutoff frequency to smooth data oscillations for slope assessment. The model assumed quasilinear viscoelasticity (QLV) with separable time-dependent (creep) and instantaneous elastic response. The creep response was estimated based on a generalized Kelvin-Voigt model with two time constants (τ1, τ2) and three associated creep coefficients (J1, J2, J∞), which represent the fraction in which each time constant contributes to the model’s overall response. The nonlinear instantaneous elastic response was modeled using Fung exponential form with two instantaneous elastic parameters (A, B). Values for each parameter were determined using an arbitrary time history integration of the history integral that minimized sum of squares error (SSE). Creep coefficients and time constants were iteratively optimized so that they were consistent across each test. Instantaneous elastic parameters were independently optimized for each test.


Results, Conclusions, and Discussions: Results:: Ten mechanical tests from six porcine lumbar spines were analyzed. The end of primary creep was characterized by an inflection in the displacement time history. Test durations used for modeling analysis averaged 300±224 seconds. The creep model for each test consistently had a good fit with experimental data (mean R2=0.996±0.003, mean SSE=0.0082±0.013) and creep profiles were qualitatively similar (Figure 1). Time constants were optimized to be τ1=42.5s and τ2=605s, and creep coefficients were optimized to be J1=0.210, J2=0.290, J∞=0.500. The average optimized instantaneous elastic constants were A=2.799±2.581 mm-1 and B=1.144±2.106 N.

Discussion:: Results from the creep model fit well with experimental data. The steady state creep coefficient J∞ dominates the model with a 50% contribution to the response, followed by the long strain-rate coefficient J2 with 29% contribution. The value of τ2 is longer than the duration of all but one of the tests which may indicate that creep could accurately be modeled for most of these tests using only one creep constant and associated time constants. A larger sample size with increased variation in time and stress values may help increase the versatility of this model. Another limitation of this study is that the inflection point determination is currently manual and subject to error. A computational algorithm to determine this inflection may more accurately represent primary creep behavior.

Conclusions:: This quasilinear viscoelastic creep model accurately fits strain values over time to experimental data with time and stress input. Thus, primary creep of the porcine lumbar spine under cyclic flexion-compression can be effectively represented by a generalized Kelvin-Voight quasilinear viscoelastic model. These results improve our understanding of the viscoelastic creep response of the lumbar spine and can be used to enable injury prediction modeling in future efforts.


Acknowledgements (Optional): This material is based upon work supported by the National Science Foundation under the Graduate Research Fellowship Program #2037785. The authors gratefully acknowledge the funding and collaboration from MTEC PRIME AWARD W81XWH-15-9-0001, subcontract MTEC-18-04-I-PREDICT-07.