MODELING OF VISCOELASTIC BEHAVIOR OF RABBIT NUCLEUS PULPOSUS TISSUE IN TORSIONAL CREEP

*Agosti, C D; *Bell, K M; *Plazek, D J; *Larson, J; *Kang, J D; **Gilbertson, L G; +*Smolinski, P

+University of Pittsburgh, Pittsburgh, PA smolinski@engr.pitt.edu

INTRODUCTION

A rabbit model is currently in use providing a repeatable platform of intervertebral disc degeneration (IDD) for the study of molecular therapy treatments.1 MRI, x-ray, histology, and gene expression are typical experimental outcome measures for the rabbit model of IDD.2 Another property for comparing the efficacy of treatments is biomechanical function and the viscoleastic behavior of tissue is a measure of this.

Relaxation testing comprises the majority of available viscoelastic data on disc tissue.3 However, the necessity for creep testing which measures changes in strain with time at a constant applied stress has been suggested,.4,5 Recently, rabbit nucleus pulposus (NP) tissue was successfully described in torsional creep at low stresses using the Andrade creep model.6 In the current study, data from torsional creep testing of healthy rabbit NP tissue was used to compare the Andrade creep model to other common creep models. METHODS

Experimentation: Lumbar spines (n = 5) were freshly harvested from healthy, female New Zealand White rabbits and frozen at –20 ºC (approved by University of Pittsburgh IACUC). The spines were individually thawed for testing and the L5-6 intervertebral disc was sectioned via a full transverse cut though the annulus. The nucleus pulposus tissue was excised and mounted between the cone and plate of an AR1000 Rheometer (TA Instruments, New Castle, DE). Torsional creep experiments were performed at 25 ºC, consisting of the application of a 6 Pa shear stress for 1000 s, followed by a zero stress recovery period of 1000 s.

Analysis: An analysis was performed to determine if the Andrade, Nutting, logarithmic, or exponential creep models could successfully predict creep behavior beyond the data range used to fit the model parameters. Creep model equations and parameter definitions are provided in Table 1.

Compliance versus time experiemental data was imported into Matlab (The MathWorks Inc., Natick, MA). Parameters for the Andrade, Nutting, logarithmic, and exponential creep models were obtained by fitting each equation to data between 10 s and 300 s using nonlinear least squares regression. The remaining 700 s of data were computed using each creep equation and compared to the experimental results.

Table 1. Creep model equations and parameter definitions.

RESULTS From the analysis it was determined that the Andrade and Nutting

exponential creep models best fit the NP creep data in the 10 s to 300 s interval (Figure 1). For each of the five specimens studied, the Andrade creep model provided a better extrapolation of the data than the Nutting model while the logarithmic and exponential gave a poor fit (Figure 2). While the Nutting model is capable of providing a strong fit to the data within the fitting data range (a more accurate fit than the Andrade model), it is less effective in extrapolating or predicting data beyond the

fitting range. In this context, the Andrade model provides the best fit of all the models compared to the experimental data via the extrapolation computation.

Figure 1. Sum of the squares error for the Andrade and Nutting model fit to the experiment data for 5 specimens over the interval 10s <t< 300s.

Figure 2. Experimental creep compliance data plotted versus time. The Andrade model closely fits data in the extrapolation range (t > 300 s). DISCUSSION

The Andrade creep model is widely accepted in describing the viscoelastic creep behavior of numerous materials.8 This study has shown that of commonly used creep models, the Andrade creep model best predicts the viscoelastic behavior of healthy rabbit nucleus pulposus tissue.

The application of this model to degenerated rabbit NP tissue is expected to result in altered Andrade parameters – thus providing quantifiable, functional benchmarks of success for molecular therapy approaches to the treatment of IDD. REFERENCES [1] Shimer, Trans ORS 0183, 2005. [2] Sobajima, Spine, 2005; 30: 15. [3] Iatridis, Spine, 1996; 21: 1174. [4] Plazek, Meth. Exp. Phys., v16C, AP, 1980. [5] Provenzano, Ann Biomed Eng, 2001; 29:10. [6] Agosti, Trans ORS 1224, 2006. [7] Findley, Crp Rlx Nonlin Visc Matls, 1976. [8] Plazek, J Colloid Sci, 1961; 16: 101. ACKNOWLEDGEMENTS

The support of the Albert B. Ferguson, Jr. MD Orthopaedic Fund of The Pittsburgh Foundation is gratefully acknowledged. ** The Cleveland Clinic, Cleveland, OH

Andrade creep model: J(t) = J 0+βt1/3+t/η Nutting creep model: J(t) = J 0+βtn+t/η Logarithmic creep model: J(t) = J 0+Blog(t)+t/η Exponential creep model: J(t) = J 0+C(1-e-dt)+t/η J(t) = creep compliance J0 = intercept compliance η = viscosity β = Andrade or Nutting slope t = time n = power of time

B is the creep slope plotted as linear compliance vs. Log(time) C and d are general characterizing parameters.7

←EXP LOG→

DATA & ANDRADE NUTTING

53rd Annual Meeting of the Orthopaedic Research Society

Poster No: 1035