J. Biomedical Science and Engineering, 2010, 3, 124-137 doi:10.4236/jbise.2010.32018 Published Online February 2010 (http://www.SciRP.org/journal/jbise/ JBiSE ). Published Online February 2010 in SciRes. http://www.scirp.org/journal/jbise Effect of deformation rate on the mechanical properties of arteries Jorge O. Virues Delgadillo 1 , Sebastien Delorme 2 , Vincent Mora 2 , Robert DiRaddo 2 , Savvas G. Hatzikiriakos 1 1 Department of Chemical & Biological Engineering, UBC, Vancouver, BC, Canada 2 Industrial Materials Institute, National Research Council of Canada, Boucherville, QC, Canada Email: hatzikir@interchange.ubc.ca ; Sebastien.Delorme@imi.cnrc-nrc.gc.ca Received 27 June 2008; revised 18 December 2009; accepted 20 December 2009. ABSTRACT Pig aorta samples were tested uniaxially and equi- biaxially at deformation rates from 10 to 200 %/s. Under uniaxial and biaxial testing, loading forces were reduced up to 20% when the deformation rate was increased from 10 to 200 %/s, which is the opp- osite to the behaviour seen in other biological tissues. A rate-dependent isotropic hyperelastic constitutive equation, derived from the Mooney-Rivlin model, was fitted to the experimental results (e.g. aorta specimens) using an inverse finite element technique. In the proposed model, one of the material par- ameters is a linear function of the deformation rate. The inverse relationship between stiffness and defo- rmation rate raises doubts on the hypothesized rel- ationship between intramural stress, arterial injury, and restenosis. Keywords: Mechanical Properties; Artery; Uniaxial & Biaxial Testing; Deformation Rate; Viscoelasticity; Constitutive Model 1. INTRODUCTION The knowledge of the viscoelastic properties is impor- tant to predict the biomechanical behaviour of soft tis- sues. To model their viscoelastic behaviour, first one performs appropriate mechanical tests to characterize de- formation-rate effects, and then one selects a constitutive equation capable of representing those effects. Material parameter estimation is fundamental for posterior simu- lation of soft tissue at boundary conditions not selected in the experimental protocol. The effect of deformation rate on the mechanical properties of soft biological tissues has been investigated, in particular for ligaments [1-7], tendons [4,7-9], spines [10-13], bones [14-17], liver [18], heart valves [19,20] and myocardium [21,22]. Most biological tissues stiffen with increasing deformation rate [4,7,9,11-13, 17]. This time-dependent behavior has been described by viscoe- lastic constitutive models [6,22-26]. However, it was recently demonstrated that some biological tissues, such as liver, myocardium and skin, soften with increasing deformation rate [18,22]. Deformation rate effects of arteries, in particular thoracic aorta, were not included in previous studies. Overstretch injury to the arterial wall during an an- gioplasty or stenting procedure has been shown to be correlated to the incidence of restenosis, i.e. in-growing tissue re-blocking the artery lumen [26,27]. Based on the hypothesis that lower deformation rate results in lower intramural stresses, slow balloon inflation has been pro- posed as a means to minimize vascular injury and reduce restenosis incidence [28]. Early studies did not conclude there was any difference in restenosis rates between conventional and slow balloon inflation [28-30], while some observed better immediate results [31,32]. In more recent studies, significantly lower restenosis rates were clinically observed with slow balloon inflation [33,34]. Slow stent deployment has also been proposed as a means to minimize arterial injury [35]. Finite element simulation of angioplasty and stenting can be used to optimize angioplasty procedure parame- ters, such as inflation pressure [36-40]. Optimization of inflation pressure rate requires accurate constitutive mo- deling of artery behavior including the effect of defor- mation rate. Numerous experimental studies have been performed to characterize the mechanical behaviour of arteries in vitro [41-44]. However, only a single defor- mation rate was used. The objective of this study is thus to measure and model the effect of deformation rate on the tensile be- havior of the arteries (e.g. pig aortas). In other words, the intention of this paper is to investigate experimentally the dependence of uniaxial and biaxial extensional str- etching of arterial wall on the deformation-rate, and consequently to modeling the experimental data by me- ans of an appropriate constitutive equation.