In situ biomechanical properties of normal and diabetic nerves: An efficient quasi-linear viscoelastic approach Rung-Jian Chen a , Chou-Ching K. Lin b , Ming-Shaung Ju a,n a Department of Mechanical Engineering, National Cheng Kung University, 1 Ta-Hsueh Road, Tainan 701, Taiwan, ROC b Department of Neurology, National Cheng Kung University Hospital, Tainan, Taiwan, ROC article info Article history: Accepted 7 December 2009 Keywords: Quasi-linear viscoelastic model Biomechanics Nerve Diabetes abstract Biomechanical properties of nerves were investigated using the quasi-linear viscoelastic model. An improved parameter estimation technique based on fast convolution was developed and tested in sciatic nerves of normal and diabetic rats. In situ dynamic compression response of sciatic nerves was obtained by a modified custom-designed compression system. Six normal and five diabetic neuropathic Wistar rats were used. The model derived from the high strain rate (0.1 s 1 ) data could predict the responses of lower strain rates (0.05 and 0.01 s 1 ) satisfactorily. The computation time was cut down 49.0% by using the newly developed technique without increasing the root-mean-square error. The percentage of stress relaxation of the diabetic and normal rats, calculated directly from the experimental data, was not significantly different (51.03 71.96% vs. 55.97 75.89%, respectively; p =0.247). After model fitting, compared with the QLV parameters of normal nerves, the smaller parameter C for diabetic nerves (0.27 70.06 vs. 0.20 70.02, p o 0.05) indicated that diabetic nerves had a smaller amplitude of viscous response (stress relaxation). The larger parameter t 2 of diabetic nerves (199 7153 s vs. 519 7337 s, p o0.05) implied that diabetic nerves needed a longer relaxation period to reach equilibrium. & 2009 Elsevier Ltd. All rights reserved. 1. Introduction Pathological changes of human diabetic nerves have been investigated by several researchers (Giannini and Dyck, 1994, 1995). Reske-Nielsen and Lundbæk, 1968 noted that diabetes affected particularly the sciatic nerve and its branches in the lower limbs. Dyck and Giannini (1996) demonstrated the pathological changes including loss of myelinated and unmyeli- nated fibers, axonal degeneration, regeneration clusters, and segmental demyelination with remyelination in the sural nerve. Malik et al. (1993) noted a significant increase in the endoneurial basement membrane area and endothelial cell area in the nerves of diabetic patients. The above studies focused on the histological and structural changes of nerves while mechanical properties of diabetic nerves were another important facet to provide detailed information for pathologic mechanism. Understanding the biomechanical proper- ties of the affected nerves will help develop strategies to improve the repair and regeneration process (Wall et al., 1991) and facilitate the interpretation of structural findings. Increased endoneurial fluid pressure has been measured in the galactose- induced diabetes model and may contribute to permanent nerve damage (Myers and Powell, 1984). Layton et al. (2004b) conducted a uniaxial testing on both normal and diabetic sciatic nerves and detected a small difference in the elasticity between the two groups. They also proposed a collagen fibril model to illustrate the effect of collagen glycation on the mechanical behavior of peripheral nerves (Layton and Sastry, 2004a). These studies, however, concentrated more on the longitudinal mechan- ical properties of nerves with limited discussion on the differ- ences of viscoelastic properties between diabetic and normal nerves. A transverse viscoelastic model will provide different aspect of the effects of disease on the mechanical behavior of nerves. To better compare the viscoelastic biomechanical proper- ties of nerves in normal and pathological conditions, we proposed to use Fung’s quasi-linear viscoelastic model (QLV) (Fung et al., 1972), a model commonly used to characterize soft biological tissues (Carew et al., 1999; Kwan et al., 1992; Myers et al., 1991; Provenzano et al., 2001; Puso and Weiss, 1998; Sauren et al., 1983; Woo et al., 1981; 1980). Under a step strain, the QLV model separates the stress response into an instantaneous nonlinear elastic response and a reduced relaxation function. Since a step strain input is not achievable in practical experiments, a fast strain rate input approach is usually adopted, although the relaxation that occurs during the ramp phase is often neglected (Dortmans et al., 1984; ARTICLE IN PRESS Contents lists available at ScienceDirect journal homepage: www.elsevier.com/locate/jbiomech www.JBiomech.com Journal of Biomechanics 0021-9290/$ - see front matter & 2009 Elsevier Ltd. All rights reserved. doi:10.1016/j.jbiomech.2009.12.002 n Corresponding author. Tel.: + 886 6 2751636; fax: + 886 6 2352973. E-mail address: msju@mail.ncku.edu.tw (M.-S. Ju). Journal of Biomechanics 43 (2010) 1118–1124