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Journal of Biomechanics 39 (2006) 1153–1157

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Short communication

The effects of refreezing on the viscoelastic and tensileproperties of ligaments

Daniel K. Moon, Savio L-Y. Woo�, Yoshiyuki Takakura, Mary T. Gabriel,Steven D. Abramowitch

Musculoskeletal Research Center, Department of Bioengineering, University of Pittsburgh, 405 Center for Bioengineering,

300 Technology Drive, Pittsburgh, PA 15219, USA

Accepted 14 February 2005

www.JBiomech.com

Abstract

Biomechanical testing protocols for ligaments can be extensive and span two or more days. During this time, a specimen may have

to undergo more than one cycle of freezing and thawing. Thus, the objective of this study was to evaluate the effects of refreezing on

the viscoelastic and tensile properties of ligaments. The femur-medial collateral ligament-tibia complexes (FMTC) from six pairs of

rabbit knees were used for this study. Following sacrifice, one leg in each pair was assigned to the fresh group and the FMTC was

immediately dissected and prepared for testing. The contralateral knees were fresh-frozen at �20 1C for 3 weeks, thawed, dissected

and then refrozen for one additional week before being tested as the refrozen group. The cross-sectional area and shape of the

medial collateral ligament (MCL) was measured using a laser micrometer system. Stress relaxation and cyclic stress-relaxation tests

in uniaxial tension were performed followed by a load to failure test. When the viscoelastic behavior of the MCL was described by

the quasi-linear viscoelastic (QLV) theory, no statistically significant differences could be detected for the five constants (A, B, C, t1;and t2) between the fresh and refrozen groups (pX0:07) based on our sample size. In addition, the structural properties of the

FMTCs and the mechanical properties of the MCLs were also found to be similar between the two groups (pX0:68). These resultssuggest that careful refreezing of the specimens had little or no effect on the biomechanical properties measured.

r 2005 Elsevier Ltd. All rights reserved.

Keywords: Refreezing; Medical collateral ligament; Mechanical properties; Viscoelastic properties

1. Introduction

Fresh frozen soft tissues are normally used forbiomechanics research. However, as experimental pro-tocols for biomechanical evaluation are becoming morecomplex and time-consuming, specimens may requireextra periods of frozen storage before the experiment iscompleted (Shoemaker and Markolf, 1982). Althoughone period of frozen storage on ligaments has beenshown to have relatively little effect on the biomecha-nical properties of ligaments (Viidik and Lewin, 1966;

e front matter r 2005 Elsevier Ltd. All rights reserved.

iomech.2005.02.012

ing author. Tel.: +1412 648 2000;

2001.

ess: ddecenzo@pitt.edu (S.L-Y. Woo).

Noyes and Grood, 1976; Dorlot et al., 1980; Barad etal., 1982; Nikolaou et al., 1986; Woo et al., 1986) andtendons (Matthews and Ellis, 1968; Leitschuh et al.,1996; Clavert et al., 2001), it is unclear if refreezing willsignificantly affect these properties.

Therefore, the objective of this study was to evaluatethe effects of refreezing on ligaments, specifically on theviscoelastic and structural properties of the femur-medial collateral ligament-tibia complex (FMTC), aswell as the mechanical properties of the medial collateralligament (MCL) midsubstance in comparison to freshspecimens. In addition, the preparation used for therefrozen specimen was a regimen designed to mimic thelaboratory setting where a frozen/thawed ligament maybe completely exposed during dissection and testing

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1.5A C E

F

gati

on (

mm

)

D.K. Moon et al. / Journal of Biomechanics 39 (2006) 1153–11571154

before it is refrozen. Since one cycle of freezing andthawing was previously found to affect the area ofhysteresis in the previous study (Woo et al., 1986), amore robust viscoelastic analysis was performed in thisstudy.

B D

0.5

Elo

n

Time (not drawn to scale)

0

Fig. 1. Schematic of the tensile testing protocol: (A) 2N preload and

preconditioning for 10 cycles, (B) 1 h recovery, (C) static stress-

relaxation test for 25min, (D) 1 h recovery, (E) cyclic stress-relaxation

test for 30 cycles, and (F) load to failure test.

2. Materials and methods

Six pairs of knees from skeletally mature female NewZealand white rabbits (body mass ¼ 5.070.5 kg) wereused. All animal procedures were done in compliancewith the National Institutes of Health guidelines foranimal care and the Institutional Animal Care and UseCommittee (IACUC). One knee in each pair wasassigned to the fresh group. These specimens weredissected down to the FMTC and prepared for testingimmediately after sacrifice. Knees in the refrozen groupwere wrapped in saline soaked gauze and then sealed inplastic bags and fresh frozen at �20 1C for 3 weeks(Woo et al., 1986). Afterwards, they were thawed toroom temperature before being dissected and preparedfor testing in a manner identical to the fresh group. Theywere then wrapped in saline soaked gauze, sealed inplastic bags, and refrozen at �20 1C for one more week.After this second period, the specimens were thawed toroom temperature and tested.

For testing, each specimen was prepared in a manneras described by previous studies done at our researchcenter (Weiss et al., 1991; Musahl et al., 2004). Thecross-sectional area and shape of the MCL wasmeasured using the laser micrometer system (Lee andWoo, 1988; Woo et al., 1990). Four reflective markers(2mm diameter) were glued on the insertion sites andthe midsubstance with cyanoacrylate for strain tracking(VP110, Motion AnalysisTM, Santa Rosa, CA). TheFMTC was then fixed to a materials testing system(Model 4502; InstronTM, Canton, MA) in a 37 1C salinebath. Please refer to the referenced manuscripts forpictures and more details on the experimental setup(Weiss et al., 1991; Musahl et al., 2004).

The specimen was equilibrated in the bath for 30minbefore a preload of 2N was applied and the gauge lengthwas reset. This was followed by preconditioning between0 and 1.5mm of elongation for 10 cycles; 1 h recovery; astatic stress-relaxation test whereby it was elongated to1.5mm and held for a period of 25min; 1 h recovery; acyclic stress-relaxation test whereby it was subjected to30 cycles of elongation between 0.5 and 1.5mm ofelongation, and a load to failure test (Fig. 1). All testswere conducted at an elongation rate of 10mm/min,which corresponded to a strain rate of 0.4570.08%/s.

To more completely describe the viscoelastic beha-vior, the quasi-linear viscoelastic (QLV) theory wasutilized in conjunction with experimental results fromstatic stress-relaxation tests (Fung, 1972; Woo et al.,

1981; Abramowitch and Woo, 2004; Abramowitch etal., 2004). The loading and relaxation data weresimultaneously curve-fit to obtain constants A, B, C,t1; and t2 using a methodology described by Abramo-witch and Woo (2004). To validate the application of thetheory to the MCL for the strain level utilized in thisstudy, predictions of a different experiment, i.e. thecyclic stress-relaxation test, were made on the basis ofthe obtained constants (Woo et al., 1981).

In analyzing the data obtained from the load tofailure tests, the slope of the linear region from the1–2mm elongation interval of the load–elongation curvewas used to calculate stiffness. The slope of the linearregion from the 3–5% strain interval of the stress–straincurve was used to calculate tangent modulus.

For statistical analysis, the normality of differences inthe biomechanical properties obtained was analyzedusing a one sample Kolmogorov–Smirnov test. Only thedifference in the initial slope of the elastic response (AB)between groups was found to be not normally dis-tributed. Therefore, a Wilcoxon signed rank test wasused to compare groups for this value. Paired t-testswere used to compare all other properties obtained. Thesignificance level was set at po0:05 for all tests. The b-values for each comparison were then calculated using apower analysis for the sample size tested.

3. Results

No differences in the gross appearance of the tissuescould be discerned as all specimens appeared shiny,white, and opaque, with well-defined edges. In addition,no significant differences were detected in the cross-sectional areas between the fresh group ð4:0� 0:6mm2Þ

and the refrozen group ð4:1� 0:6mm2; p ¼ 0:66; b ¼0:92Þ:

The peak strains for the static stress-relaxation testwere 4.270.3% and 4.171.1% with peak stresses of28.575.2 and 28.076.9MPa, respectively, for the freshand refrozen groups. At 25min, the total amount ofstress relaxation was found to be 17.274.2% and

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Table 1

Constants describing the instantaneous elastic response and reduced relaxation function for the fresh and refrozen groups

Fresh (n ¼ 6) Refrozen (n ¼ 6) p b

Constants describing instantaneous elastic response

A 12.772.5 20.2711.5 0.13 0.68

B 29.271.8 25.577.8 0.31 0.85

AB 371778 448796 0.12 0.69

Constants describing reduced relaxation function

C 0.04270.012 0.04270.005 0.84 0.95

t1 (s) 0.3570.02 0.3270.01 0.07 0.47

t2 (s) 4627116 4947175 0.74 0.94

Data expressed as mean7S.D. The p-values and b-values for each comparison have also been reported.

05

10152025303540

0 5 10 15 20 25 30Cycle Number

Str

ess

(MP

a)

Fresh (Experimental)Fresh (Analytical)

0

510

15

20

2530

35

40

0 5 10 15 20 25 30Cycle Number

Stre

ss (M

Pa)

Frozen (Experimental)Frozen (Analytical)

(a)

(b)

Fig. 2. Average peak stresses of the theoretically predicted values

versus the average experimentally measured values for (a) fresh MCLs

and (b) refrozen MCLs, respectively. Data expressed as mean7S.D.

05050

100100

150150200200

250250300300

350350400400

450450

0 2 5ElongaElongation (on (mm)

Loa

dL

oad

( (N)

FreFreshReRefrozozenen

1 3 4 6(a)

0

2020

4040

6060

8080

100100

120120

0 5 1010 1515Strain (%)Strain (%)

Str

Stre

ss ( (

MP

aP

a)

FreshFresh

RefrozenRefrozen

(b)

Fig. 3. Representative (a) load–elongation curves and (b) stress–strain

curves for paired specimens.

D.K. Moon et al. / Journal of Biomechanics 39 (2006) 1153–1157 1155

17.372.2%, respectively (p ¼ 0:96; b ¼ 0:95). For thecyclic stress-relaxation tests, the peak stress decreased by9.473.4% and 9.172.3%, respectively, after 30 cyclesof elongation (p ¼ 0:76; b ¼ 0:95). Curve fits of thestatic stress relaxation data using the QLV theoryrevealed an R2 value of 0.99 or higher for all specimens.No significant differences were found for constantsdescribing the instantaneous elastic response, A

(p ¼ 0:13; b ¼ 0:68) and B (p ¼ 0:31; b ¼ 0:85), as wellas their product, AB (p ¼ 0:12; b ¼ 0:69). In addition,no significant differences were found for the constantsdescribing the MCLs’ relaxation response, C ðp ¼

0:84; b ¼ 0:95Þ; t1 ðp ¼ 0:07; b ¼ 0:47Þ and t2 ðp ¼0:74; b ¼ 0:94; Table 1). In terms of validation, the

theory predicted the initial peak stresses of the cyclicstress-relaxation test most accurately, but less so with anincreasing number of cycles. However, the close agree-ment confirms the validity of the five constants at thestrain level utilized in this study (Fig. 2).

The load–elongation curves and stress–strain curvesobtained for both groups were similar in appearance toeach other (Fig. 3). Refreezing did not induce anysignificant differences in the structural properties of theFMTC (pX0:79; Table 2). In addition, no significantdifferences were found in the mechanical properties ofthe MCL (pX0:68; Table 2).

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Table 2

Structural properties of the femur-medial collateral ligament-tibia complex (FMTC) and mechanical properties of the medial collateral ligament

(MCL) for the fresh and refrozen groups

Fresh (n ¼ 6) Refrozen (n ¼ 6) p b

Structural properties of the FMTC

Stiffness (N/mm) 106.575.9 107.7711.2 0.79 0.94

Ultimate load (N) 331.0781.8 336.7750.1 0.83 0.95

Elongation at failure (mm) 4.270.9 4.370.8 0.81 0.95

Energy absorbed (Nmm) 703.87270.1 697.27264.9 0.96 0.95

Mechanical properties of the MCL

Tangent modulus (MPa) 1107.27126.3 1056.27207.9 0.68 0.94

Ultimate tensile strength (MPa) 84.4722.2 83.2716.0 0.83 0.95

Ultimate strain (%) 10.672.8 11.174.1 0.74 0.94

Strain energy density (MPa) 4.6272.35 4.5872.53 0.97 0.94

Data expressed as mean7S.D. The p-values and b-values for each comparison have also been reported.

D.K. Moon et al. / Journal of Biomechanics 39 (2006) 1153–11571156

4. Discussion

In this study, the effects of refreezing on theviscoelastic and structural properties of the FMTC inaddition to the mechanical properties of the MCL wereevaluated. This study is uniquely different from theprevious studies looking at the effects of freezing (Viidikand Lewin, 1966; Noyes and Grood, 1976; Dorlot et al.,1980; Barad et al., 1982; Nikolaou et al., 1986; Woo etal., 1986), in that the specimen was frozen and thawedtwice. Further, the ligament was dissected and exposedbefore being rewrapped in saline soaked gauze forrefreezing to mimic possible experimental conditions. Inaddition, a more robust analysis of the viscoelasticproperties by modeling the stress relaxation behavior ofthe tissue using the QLV theory was also done(Abramowitch and Woo, 2004; Abramowitch et al.,2004).

Using these methodologies, no statistically signi-ficant differences could be detected in any of themeasured biomechanical properties with refreezingbased on our sample size. Thus, it can be concludedthat the effects of refreezing on these properties arerelatively small and not detectable using currentmethodologies. These findings also add to thoseprevious data which showed that minimal or no changein tensile properties could be found after careful freezing(Viidik and Lewin, 1966; Noyes and Grood, 1976;Dorlot et al., 1980; Barad et al., 1982; Nikolaou et al.,1986; Woo et al., 1986). However, differences in severalconstants of the QLV theory (A, AB) approachedsignificance, which supports a previous finding by ourresearch center regarding the area of hysteresis (Woo etal., 1986). Although t1 also approached significance, themagnitude of the difference between groups was0.03370.035 s. Thus, even if this difference was foundto be significant, one would have to question therelevance.

Therefore, it can be recommended for complexbiomechanical testing protocols requiring several days,that the specimen be refrozen with caution while keepingthe specimen moist when it is not in use. However, if thepurpose is to do sensitive viscoelastic analyses, the use offresh specimens should be considered. Future studies arealso suggested in order to determine the effects of morethan two cycles of freezing and thawing before theseconclusions are applied to studies that require more thantwo cycles.

Acknowledgment

The authors acknowledge the financial supportprovided by the National Institute of Health GrantAR41820.

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