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The effect of storage time in saline solution on the material properties of cortical bone tissue
Accepted Manuscript The effect of storage time in saline solution on the material properties of cortical bone tissue
Guanjun Zhang, Xianpan Deng, Fengjiao Guan, Zhonghao Bai, Libo Cao, Haojie Mao PII: DOI: Reference:
S0268-0033(18)30390-5 doi:10.1016/j.clinbiomech.2018.06.003 JCLB 4546
To appear in:
Clinical Biomechanics
Received date: Accepted date:
21 July 2017 4 June 2018
Please cite this article as: Guanjun Zhang, Xianpan Deng, Fengjiao Guan, Zhonghao Bai, Libo Cao, Haojie Mao , The effect of storage time in saline solution on the material properties of cortical bone tissue. Jclb (2017), doi:10.1016/j.clinbiomech.2018.06.003
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ACCEPTED MANUSCRIPT The effect of storage time in saline solution on the material properties of cortical bone tissue
Guanjun Zhang1, Xianpan Deng1, Fengjiao Guan2, Zhonghao Bai1, Libo Cao1,
State Key Laboratory of Advanced Design and Manufacturing for Vehicle Body, Hunan University, Changsha, 410082, China
Science and Technology on Integrated Logistics Support Laboratory, National
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Haojie Mao3*
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University of Defense Technology, Changsha, 410073, China Department of Mechanical and Materials Engineering, Western University, London,
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ON N6A 5B9, Canada
Corresponding author: Haojie Mao
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Email: [email protected]
Abstract: 250 words Main text: 4807 words (Introduction till Acknowledgements)
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ACCEPTED MANUSCRIPT Abstract Background: The use of saline in preserving bone specimens may affect the mechanical properties of specimens. Yet, the reported effects varied and contradicted to each other, with a lack of investigating constitutive material parameters. Therefore,
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we quantified the effects of preservation time on the constitutive properties of cortical
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bone.
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Methods: We collected 120 specimens from the mid-diaphysis of six male bovine femora, which were assigned to five groups, including fresh-frozen for 60 days
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(-20℃), storage in saline for 3, 10, 36 and 60 days (25℃). All specimens underwent
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quasi-static three-point bending tests with a loading rate of 0.02 mm/s. Using the optimization method combined with specimen-specific finite element models, the
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Young's modulus, tangent modulus, yield stress, effective plastic strain, yield strain,
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ultimate stress, and toughness were calculated. Findings: Saline preservation resulted in a significant decrease of Young's modulus,
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yield stress, ultimate stress and pre-yield toughness (P < 0.001 for all four parameters),
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and a significant increase of effective plastic strain (P = 0.034). After 10 days of preservation, yield stress and pre-yield toughness decreased -14.9% and -21.4%, respectively, and they continued to decrease with longer preservation time. After 36 days of preservation, Young’s modulus and ultimate stress decreased -19.2% and -17.3%, respectively, and continued to decrease with longer preservation time. The effective plastic strain only decreased significantly after 60-day preservation (+33.7%, P = 0.011). Our data also showed changes of material properties collected after 3-day 2
ACCEPTED MANUSCRIPT saline preservation, while the low statistical power must be considered for this group. Interpretation: Saline preservation impacts on mechanical properties of cortical bone tissue and the effect is already observable after 3 days. When subjecting cortical bone to biomechanical tests at room temperature, saline preservation for 3 days or less is
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recommended.
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Keyword: cortical bone, saline preservation, material property, three-point bending,
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finite element optimization
1 Introduction
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Physiological saline, which has an osmotic pressure of human and animal plasma, is commonly used in physiology experiments and clinical treatments. In
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biomechanical experiments, specimens need to be washed with saline to clean the
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antiseptic solutions and to rehydrate the specimens before test
[1-6]
. Both fresh and
fresh-frozen bone specimens need saline to maintain cell viability and to thereby
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preserve their in vivo condition
[5, 7-11]
. Hence, saline is widely used in bone
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biomechanics tests and is applied throughout the entire process of specimen preparation and testing. There are several studies that reported the effect of saline preservation on bone property. In a study of the effects of formaldehyde fixation on the mechanical properties of bone, Currey et al. (1995)[4] found that preservation in saline for 3 days slightly increased (approximately 1%) the rigidity of machined bovine cortical bone specimens. On the other hand, Mcpherson et al. (1980)[12] showed that the rigidity of 3
ACCEPTED MANUSCRIPT machined fetal skull specimens preserved in saline was reduced by 4.4% compared with the value obtained from skull preserved in air, but the difference was not statistically significant. Kikugawa et al. (2007)[13] studied the fracture properties of bovine cortical bone with machined specimens stored for 7 or 30 days in saline and
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found that the fracture toughness of the specimens was decreased by 5% and 12%,
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respectively. On the contrary, Kuninori et al. (2009)[14] reported that fracture
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toughness of machined bovine cortical bone specimens increased slightly (about 2% 10% as estimated per authors’ Fig. 5) after being stored in saline for 30 days.
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Gustafson et al. (1996)[15] found that the Young's modulus of equine machined
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metacarpal cortical bone decreased significantly by 2.4% after 6 days of preservation in saline. However, after 10 days of preservation, the Young's modulus did not
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decrease significantly. Griffon et al(1995)[16] used the four point bending test to study
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energy absorption characteristics and ultimate displacement of canine rib, metacarpal and metatarsal bones after preservation in -20℃ saline solution for one year. Their
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results showed that energy absorbed at failure and ultimate displacement increased by
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25%~30% and 18%~24%, respectively. With variances and contradictions, the effects of saline preservation on bone material property remain to be further investigated. In addition, the literature studies mostly analyzed the effect of saline on properties such as bone stiffness, fracture toughness, energy absorption and ultimate displacement. However, there is a lack of data on constitutive material parameters (e.g., Young’s modulus, yield stress, ultimate stress, and ultimate strain). Furthermore, the testing methods and preservation time among labs are different, which added 4
ACCEPTED MANUSCRIPT difficulty for reaching definitive conclusions on the effect of saline preservation. In our own experience, we have previously maintained cortical bone specimens in saline for 58 days. Students used these specimens to practice testing methods as part of their training, and they observed that the Young’s modulus of these specimens were very
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different from the values reported in the literature for fresh specimens. With this
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experience and the awareness of differences in literature, Therefore, we deem it
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necessary to design a test to comprehensively quantify the effects of saline on the biomechanical properties of bone.
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Two methods are reported in the literature for determining the constitutive
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parameters of cortical bone in the three-point bending test. The first is the classical material parameter identification method based on beam theory and the second is the
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optimization method combined with specimen-specific finite element (FE) models.
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The former uses classic formulas of beam theory to obtain key material parameters of cortical bone based on experiment force-displacement curves
[17]
. This method has a
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high computational efficiency, but the yield stress and the parameters after yielding
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could be inaccurate[18]. The latter method adopts the specimen-specific FE model to accurately simulate specimens and use an optimization method to fit the test and simulation curves. This method provides appropriate constitutive parameters for characterizing the mechanical response of biological specimen[19-23], but has the limitation of being time-consuming and relatively computationally inefficient[24]. In studying the material properties of bone, even a small artificial effect on its material properties could change conclusions because variances among different 5
ACCEPTED MANUSCRIPT groups could be small. Therefore, in order to accurately assess the effects of saline on the material properties of cortical bone, machined cuboid bovine femoral cortical bone specimens, which have been frequently tested
[25-27]
, were harvested to carry out
quasi-static three-point bending tests. We further adopted a three-point bending test
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device that can be used to test extremely small specimens[19, 28] for characterizing
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region-specific properties. We designed a comprehensive study and preserved bone
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specimens at room temperature (25℃) for 3, 10, 36, and 60 days. We then calculated the constitutive parameters of cortical bone, including Young's modulus, yield stress,
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tangent modulus, and effective plastic strain, through the specimen-specific FE-based
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optimization method. Moreover, parameters such as yield strain, ultimate stress, and toughness including pre-yield toughness, post-yield toughness, and all toughness were
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2 Methods
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also analyzed.
2.1 Specimen extraction
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Due to the small size and crisp texture of cortical bone, its material properties are [29]
. Hence, we prepared cortical bone specimens
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heavily influenced by temperature
by low speed grinding to avoid quickly generating heat. Six fresh femora from the right legs of male bovines aged between 24 - 36 months were obtained from the slaughterhouse. After removing muscle tissue, CT examination (Philips Brilliance 64 CT Scanner, Philips Medical, Cleveland, Ohio) with a resolution of 512 × 512 and layer thickness of 0.625 mm was performed to ensure there were no bone defects that may affect bone mechanical properties. The middle sections (20 mm long) of the 6
ACCEPTED MANUSCRIPT femur diaphysis were obtained with a handsaw. Anterior (A), lateral (L), posterior (P), and medial (M) regions were marked, and 5 specimens from each region were harvested (Fig. 1, (a)). Sandpaper (Eagle #360) was used to shape the specimen into a cuboidal shape with dimensions of approximately 15 mm × 5 mm × 2 mm. A
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self-made miniature grinder was then used for low-speed fine grinding. The sand bar
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model was Congress EDM 1500, and the grinding line speed was below 20 mm/s. The
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final size of the specimens was 12 mm (L) × 2 mm (W) × 0.5 mm (T). In the process of cutting and grinding, 0.9% saline was applied continuously over the specimen.
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During preparation, specimens that were not yet processed or that were partially
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processed were wrapped in saline-soaked gauze and frozen at -20°C[11, 30, 31]. All of the specimens were prepared in vitro within 3 days, and the effect of this preparation
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process on the biomechanical response of the specimen was deemed as negligible
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without statistically significant changes [32, 33]. 2.2 Specimen grouping and preservation
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A total of 120 cortical bone specimens (6 femurs × 4 regions/femur × 5
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specimens/region) were prepared. To reduce the influence of sampling location on test results, the 5 specimens from the same anatomical region of one femur were assigned to 5 different groups, including a fresh-frozen group (F), saline preservation for 3 days (S3), 10 days (S10), 36 days (S36), and 60 days (S60). All specimens were harvested in the same time for mechanical test. Therefore, specimens in the S60 group were immediately immersed in normal saline, and the other specimens were stored at -20°C[11]. Each 0.9% saline-immersed specimen was placed in a glass tube (10 ml) 7
ACCEPTED MANUSCRIPT with a wood plug seal at room temperature 25°C[13]. After 24, 50 and 57 days, the specimens in the S36, S10 and S3 groups, respectively, were thawed at room temperature and then underwent the same saline preservation treatment as that for S60 group.
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2.3 Three-point bending test
[5, 12]
, and the saline-immersed specimens were washed with fresh
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saline for 2 hours
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The fresh-frozen specimens were thawed at room temperature (25°C) with 0.9%
0.9% saline at room temperature (25°C) for 2 hours. A micrometer (Mitutoyo103-137,
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graduation of 0.01 mm, accuracy of 0.002 mm, Japan) was used for accurate
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measurement of the two ends and the middle portion of the specimens along the length, width, and thickness (Fig. 1, (b)). The average values of the length, width and
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thickness were recorded for the construction of the FE model. The INSTRON 5985
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(Instron Corp., Norwood, MA, USA) material testing machine was used for quasi-static three-point bending test at a rate of 0.02 mm/s. The impact head and the
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supporting shaft are both metal cylinders with a diameter of 1 mm, and the axial span
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is 10 mm, as shown in Fig. 1, c. A miniature sealed stainless steel load cell with a capacity of 44.5 N (WMC-10-38, Interface, Inc., AZ, USA) was used to record the loading force. The displacement transducer of INSTRON systems was used to obtain the displacement history curves at the loading point. The obtained displacement history curve matches with the defined loading speed. TDAS-PRO (Diversified Technical System Inc., CA, USA) was used to collect the test data with a sampling frequency of 250 Hz. The failure load is defined as the maximum load
[34]
, and the 8
ACCEPTED MANUSCRIPT force-displacement curves before failure were used in this study. 2.4 Beam theory The stress-strain curves of loading point were derived from force-displacement curves in three-point bending tests using the beam theory as follows [17, 35]: 3𝐹𝐿
𝜎 = 2𝑊𝑇 2
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6𝑇𝛿 𝐿2
(2)
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𝜀=
(1)
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where σ and ε are the stress and strain, respectively; F is the loading force; L is the span between two supports; W and T are the average width and thickness of each
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specimen, respectively; δ is the specimen deflection at loading point.
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Using 25% of the ultimate stress as the window width [36], the stress-strain curve was fitted using a straight line within the window width. The maximum slope of the
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line was found by moving the window, which was defined as the Young's modulus of
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the specimen (EB, where B stands for beam). The point of zero strain was defined as the point where the straight line of stress-strain curve corresponding to Young's [37, 38]
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modulus crossed the zero-stress abscissa
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determined using the 0.2% strain offset method
. The yield stress (SIGYB) was
[17, 39]
. Effective failure strain (FSB)
was assumed as effective plastic strain at failure[28]. The tangent modulus (ETANB) was defined as 5% of Young’s modulus
[40, 41]
. These four parameters were
automatically calculated by the in-house codes developed using Matlab (Version R2017a, The MathWorks, MA, USA).
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ACCEPTED MANUSCRIPT 2.5 Specimen-Specific FE Optimization The specimen-specific FE models were automatically constructed by Matlab according to the length, the width/thickness of the specimens measured at both ends and middle locations. Each model consisted of eight layers of hexahedron elements in
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the thickness direction, based on our previous convergence study, for a total of 49,152
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elements. For cortical-bone specimens, the material was assumed to be an isotropic
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homogeneous material in FE models. The elastoplastic material model, LS-DYNA (LSTC, Livermore, CA) material #24, was used in this study. The Poisson’s ratio and [42, 43]
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density were set to 0.22 and 2000 kg/m3, respectively
. Young’s modulus (E),
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yield stress (SIGY), tangent modulus (ETAN), and effective plastic strain (FS) were constitutive parameters commonly used in bone FE models
[44, 45]
, and were therefore
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beam theory method [28].
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defined as design variables. The initial value of these design variables is calculated by
The material constitutive parameter optimization process is divided into three
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steps (Appendix A). In the first step, the objective function was defined as the
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root-mean-square errors between the elastic portion of simulated and experimental force-deformation curves of each specimen. Only the Young's modulus was defined as a design variable whose initial value was EB. Yield stress and tangent modulus were defined as constants, designated as SIGYB and ETANB, respectively. In the second step, the objective function was defined as the root-mean-square errors between the simulated and experimental force-deformation curves of each specimen. Yield stress and tangent modulus were defined as design variables, the initial values were SIGYB 10
ACCEPTED MANUSCRIPT and ETANB, respectively. The elastic modulus was set as a constant whose value was the optimum value obtained in the first step. In the first step and the second step of the optimization process, the failure of the material was not defined. In the third step, to test the displacement measurement accuracy of the testing machine the effective
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plastic strain was defined as the design variable, the Young’s modulus, yield stress,
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and tangent modulus were constants whose values were the optimum values obtained
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in the previous steps. LS-OPT 5.0 (LSTC, Livermore, CA) was used to optimize material constitutive parameters. Detailed optimization process was described in our
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previous article[28].
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The ultimate strength (UST) and yield strain (YS) were calculated based using the above four parameters (Eq. 3 and Eq. 4).
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UST = SIGY + FS × ETAN YS = SIGY/E
(3) (4)
The pre-yield toughness (PreT) was calculated as the area under the straight E
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line (Eq. 5), and the post-yield toughness (PostT) was calculated as the area under the
(Eq. 7).
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straight ETAN line (Eq. 6). The total toughness (T) was the sum of PreT and PostT
PreT = 0.5 × YS × SIGY
(5)
PostT = 0.5 × (SIGY + UST) × FS
(6)
T = PreT + PostT
(7)
2.6 Statistical method SPSS software (Version 21, IBM Corporation, Somers, NY, USA) was used to 11
ACCEPTED MANUSCRIPT analyze the test data. All constitutive parameters were verified to follow a normal distribution using the Shapiro-Wilk test (P > 0.05)[9, 17, 28]. The Levene method was used to test for homogeneous variance (P > 0.05). Constitutive parameters with normal distributions and homogeneous variance were further analyzed with one-way
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ANOVA, otherwise, non-parametric Kruskal-Wallis tests were used to determine
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whether the saline significantly affected the constitutive parameters of cortical bone.
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Multiple comparisons between groups were carried out for different constitutive parameters, so as to study how long-term saline preservation significantly impacts the
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constitutive parameters of cortical bone. The Tukey method was used for constitutive
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parameters in compliance with variance analysis conditions (normal distribution and homogeneous variance), and Dunnett's T3 method was used for that with
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non-parametric test conditions[46, 47]. A paired-sample t-test (for the between-group
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differences fitting the normal distribution) or Wilcoxon matched-pairs signed-ranks test (for the between-group differences not conforming to the normal distribution) was
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also performed between the fresh-frozen group and each saline-preserved group, and
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the corresponding power analysis was performed with G*Power software (Version 3.1.9.2, Universität Düsseldorf, German). Furthermore, Stata software (Version 14.1, StataCorp., College Station, TX, USA) was used to analyze the minimum detectable difference (MDD) with Power = 0.8. A significance level of 0.05 was introduced to test statistical significance.
3 Results The Young's modulus, yield stress, tangent modulus and effective plastic strain 12
ACCEPTED MANUSCRIPT were obtained using the optimization FE method. The yield strain, ultimate stress, pre-yield toughness, post-yield toughness, and total toughness were calculated using the above four parameters. A statistical description of these values is shown in Table 1. With increased preservation time, the Young’s modulus, yield stress, ultimate stress,
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and toughness (except for the S60 group) of the specimen gradually decreased, while
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the effective plastic strain gradually increased.
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The Young’s modulus (P < 0.001), yield stress (P < 0.001), effective plastic strain (P = 0.034), ultimate stress (P < 0.001), and pre-yield toughness (P < 0.001)
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were significantly different between the groups; the tangent modulus (P = 0.558),
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yield strain (P = 0.056), post-yield toughness (P = 0.299), and total toughness (P = 0.199) showed no statistically significant differences (Appendix B).
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The Tukey method and Dunnett's T3 method were used to perform multiple
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comparisons with results shown in Fig. 2. The Young's modulus of cortical bone gradually decreased with increased saline preservation time. Three days (P = 0.309)
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and 10 days (P = 0.961) preservation in saline did not significantly change the
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Young's modulus of cortical bone, but this metric significantly decreased by 19.2% (P < 0.001) and 23.6% (P < 0.001) after 36 and 60 days of preservation, respectively (Fig.2 (a)). The yield stress of cortical bone gradually decreased with increased saline preservation time. Three days of saline preservation did not significantly change (P = 0.408) the yield stress of cortical bone; however, 10, 36 and 60 days of preservation significantly decreased cortical bone yield stress by 14.9% (P = 0.008), 26.0% (P < 0.001) and 26.5% (P < 0.001), respectively (Fig.2 (c)). The ultimate stress of S36 13
ACCEPTED MANUSCRIPT group decreased significantly by 17.3% compared with that of fresh-frozen group (P < 0.001), and the S60 group decreased significantly by 20.3% (P < 0.001) (Fig.2 (f)). The preservation in saline for 3 days had no significant (P = 0.846) effect on pre-yield toughness of the specimens. However, the pre-yield toughness decreased significantly
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after 10 days (P = 0.003, -21.4%), 36 days (P < 0.001, -31.7%) and 60 days (P <
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0.001, -28.6%) of storage (Fig.2 (g)). Multiple comparisons showed no significant
toughness and total toughness between groups.
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difference in tangent modulus, yield strain, effective plastic strain, post-yield
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The results of the paired sample t-test showed that the Young’s modulus of S3
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group was lower than that of the fresh-frozen group with some significance (P = 0.041). However, the corresponding power analysis showed that the probability of
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making a type II error was about 45.6% (1-Power). Furthermore, the differences of
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Young’s modulus between the fresh-frozen group and the S3 group were less than MDD value (Table 1).
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Descriptive statistical analyses were performed for the material constitutive
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parameters of the fresh-frozen group according to the different source anatomical regions (Fig. 3). All of the constitutive parameters in the different anatomical regions were normally distributed, except for the effective plastic strain in the anterior region (P = 0.005) and the yield stress in the medial region (P = 0.048). Tests of variance homogeneity showed that the constitutive parameters in all four anatomical regions met this criterion. One-way ANOVA was performed for the Young's modulus and tangent modulus, and the Kruskal-Wallis test was performed for the yield stress and 14
ACCEPTED MANUSCRIPT effective plastic strain. The Young's modulus (P = 0.399), tangent modulus (P = 0.467) yield stress (P = 0.095), and effective plastic strain (P = 0.055) were not significantly different between the four anatomical regions.
4 Discussion
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Our data demonstrated that long-term saline preservation could decrease Young’s
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modulus (19.2% for 36-day preservation and 23.6% for 60-day preservation), yield
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stress (14.9% for 10-day preservation, 26.0% for 36-day preservation and 26.5% for
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60-day preservation), ultimate stress (17.3% for 36-day preservation and 20.3% for 60-day preservation) and pre-yield toughness (21.4% for 10-day preservation, 31.7%
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for 36-day preservation and 28.6% for 60-day preservation). Compared with other studies, our specimen-specific FE-based optimization method can eliminate the
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influence of geometric size on constitutive parameters, hence more accurately
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calculating Young's modulus, yield stress, and effective plastic strain responses of cortical bone [19, 28]. To the best of our knowledge, our study uniquely quantified how
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bone.
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saline preservation for 3, 10, 36, and 60 days affect constitutive parameters of cortical
The result of multiple comparisons using Dunnett’s T3 Test showed that the 3-day preservation did not significantly affect Young's modulus (P = 0.309). The paired-sample t-test indicated that preservation for three days, however, resulted in a decrease in Young's modulus with some significance (P = 0.041). The risk of concluding that there is no effect when there is one is high (1-Power = 45.6%). Furthermore, the difference between the mean values of the Young's moduli of S3 and 15
ACCEPTED MANUSCRIPT fresh-frozen groups was less than that MDD. Hence, we suggest that the statistical conclusion of the effect of 3-day saline preservation on Young’s modulus couldn’t be firmly drawn. Linde et al. (1993) reported that storage of male human tibial trabecular bone in saline for 1 day caused the Young's modulus to decrease by 10% (P < 0.05) [5],
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whereas 3 days of saline preservation for cortical bone resulted in no significant
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change (P = 0.309) in current study. The primary difference between Linde et al.’s and
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our experiments was the type of bone that was tested, suggesting that saline might more rapidly penetrate trabecular bone and thus has a greater impact on this bone type
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than on cortical bone. Gustafson et al. (1996)[15] showed that saline preservation of
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equine third metacarpal cortical bone for 6 days decreased the Young's modulus by 2.4% (P = 0.011); after 10 days, the Young's modulus was decreased by 2.7% (P =
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0.011). In our study, 10 days of saline preservation caused the Young's modulus of the
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bovine femoral cortical bone to decrease by 6.6%, although this effect was not significant (P = 0.961 from Dunnett’s T3 test and P = 0.303 from t-test). Our data
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showed that the Young's modulus of the S10 group did not change significantly with
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respect to the fresh-frozen group (P = 0.303). However, it should be noted that the variance of S10 group was large. And the difference (1.49 GPa) between the mean values of the Young's moduli of the fresh-frozen group and the S10 group is smaller than the MDD (1.89 GPa). Furthermore, the power analysis showed that the risk of concluding that there is no effect between fresh-frozen and S10 groups when there is one is very high (1-Power = 82.7%). Hence, we couldn’t firmly conclude that the effect of 10-day saline preservation on Young’s modulus was statistically not 16
ACCEPTED MANUSCRIPT significant. The same study by Gustafson et al.
[15]
showed that calcium ions can
dissolve small bone specimens (7.5 mm × 7.5 mm × 3 mm) in a saline bath at room temperature. In addition, Novitskaya et al. (2011) suggested that the Young’s modulus of bone decreases with reduced mineral volume fraction
[48]
, which is consistent with
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our results on the Young’s modulus.
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Levene’s test showed that five groups of specimens (fresh-frozen group and
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saline preservation groups) were significantly different in terms of yield stress (P < 0.001), suggesting that saline preservation significantly impacts cortical bone yield
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stress. Our Tukey analysis showed that, compared with the fresh-frozen group,
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cortical bone stored in saline for 3 days does not exhibit significantly different yield stress (P = 0.408: -7.7%). However, after 10, 36 and 60 days, the yield stress was
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significantly decreased by 14.9% (P = 0.008), 26.0% (P < 0.001) and 26.5% (P <
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0.001), respectively (Fig. 2). It is clear that the yield strength of cortical bone is decreased with increased preservation time in saline. No previous study has tested the
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effects of saline preservation effect on yield strength of cortical bone, but Kikugawa
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et al. (2007)[13] found that the fracture toughness of machined bovine cortical bone specimens decreased by 30% after normal saline preservation for 30 days. Yield stress and fracture toughness can, to a certain extent, reflect the resistance ability of cortical bone. At the same time, the toughness of specimens preserved with saline for 36 days decreased significantly by 15.6% (P = 0.006, paired-samples t test) in this paper. Therefore, it could be inferred from the results of this previous study that long-term preservation reduces the strength of cortical bone material, which is similar to the 17
ACCEPTED MANUSCRIPT results of the present study. The difference between the mean values of the yield stress of S3 and fresh-frozen groups were smaller than MDD, as well as the ultimate stress and tangent modulus. Hence, we couldn’t firmly conclude that the effects of 3-day saline preservation on these parameters were statistically not significant.
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The fresh-frozen bovine cortical bone was used as the control group in this study.
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This choice was based on a large number of studies that showed long-term freezing
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(at -20°C or below) up to 100 days does not significantly change the mechanical properties of bone and hence was commonly used
[5, 14, 49-51]
. The observed Young's
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modulus of bone in fresh-frozen group was 22.44 GPa (SD 2.34 GPa) in our study.
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This is in agreement with the work of Unger et al. (2010) (Mean 21.05 GPa, SD 1.39 GPa)[52] and Currey et al. (1995) (Mean 18.14 GPa, SD 0.47 GPa)[4]. Importantly,
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Unger et al.’s and Currey et al.’s data were also obtained using three-point bending
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tests (Fig. 5). In addition, our result of fresh-frozen group is in agreement with those of Abdel-Wahab et al. (2011)[31] (Mean 19.68 GPa, SD 3.46 GPa, tension) and Li et al.
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(2013)[9] (Mean 20.22 GPa, SD 3.12 GPa, tension; Mean 19.09 GPa, SD 2.84 GPa,
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compression), in which the Young’s modulus of bovine cortical bone specimens was obtained using tensile test and compression test methods. In our study, the yield stress of fresh-frozen specimens was 144.49 MPa (SD 19.71 MPa), which is comparable to the tensile (Mean 75.85 MPa, SD 13.98 MPa) and compression yield stresses (Mean 184.62 MPa, SD 22.51 MPa) [9]. This difference may be related to the experiment method. These results show that the adopted method can accurately obtain the constitutive parameters of the tested materials. 18
ACCEPTED MANUSCRIPT The Young's modulus was highest in fresh-frozen bone from the lateral region, followed by bone from the medial, posterior and anterior specimens However, the differences were not significantly different (P = 0.399). Abdel-Wahab et al. (2011)[31] studied these four anatomical regions using a tensile testing method, finding that the
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Young's modulus of axial specimens were highest in the anterior, followed by the
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medial, posterior and lateral specimens. Li et al. (2013)[9] showed similar results by
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stretching and compression tests. It should be noted that the study by Abdel-Wahab et al. (2011)[31] did not perform comparative statistical analyses; only the average values
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were compared. Li et al. (2013)[9] performed comparative statistical analyses and
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found that only differences between the opposite quadrants (i.e., anterior vs. posterior, lateral vs. medial) were consistently significant. The results of Abdel-Wahab et al.
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(2011) and Li et al. (2013) are derived from the compression and tensile tests,
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whereas the quasi-static three-point bending test method is adopted in this study. The different loading modes may be the cause of the different results between these
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studies[2, 53]. In addition, Abdel-Wahab et al. (2011) and Li et al. (2013) obtained the
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parameters based on an experimental curve and theoretical calculation method, whereas we used a method that employed specimen-specific FE model optimization. Therefore, different methods may contribute to the variation in results between the studies and more studies on region-specific material properties will help to better understand cortical bone. During preparation, specimens that were not yet processed were wrapped in saline-soaked gauze and frozen at -20°C. The specimen wrapping method used in this 19
ACCEPTED MANUSCRIPT paper prevents specimen dehydration and is used in a number of documents
[11, 30, 31]
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The prepared specimens were frozen, and then each group of specimens was thawed in sequence, followed by preservation in saline at room temperature. All samples were subjected to the three-point bending test at the same time. In the meantime, it has been
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reported that freezing at -20 ℃ does not change the biomechanical response of cortical
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bone [32, 33]. Therefore, the change of the biomechanical response of the sample can be
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neglected during the three-day sample preparation, and it can be assumed that all samples have the same starting point.
[48, 53]
and experience more contact with saline. There is
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higher degree of porosity
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The present study considered femoral cortical bone. Cancellous bones have a
likely a larger effect of saline preservation on cancellous bones than that of cortical
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bone. Therefore, caution should be used when applying the conclusions of this study
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to other types of bone. In this study, the effects of saline on cortical bone were studied at room temperature (25°C); the influence of other temperatures remains to be further
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studied. In addition, we analyzed the response of machined cortical bone specimens
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using a quasi-static three-point bending test. As the bone is a nonlinear material, strain rates can strongly influence the response of cortical bone mechanics. Therefore, studies on the effects of saline preservation on material properties of the cortical bone under different strain rates can help further understand the effect of saline preservation. Due to the lower sensitivity of the tangent modulus during optimization, the results on tangent modulus should be used with great care.
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ACCEPTED MANUSCRIPT 5 Conclusions Machined bovine cortical bone specimens were investigated in this study. The force-displacement curves were obtained through quasi-static three-point bending testing. Using the optimization FE method, we accurately calculated the Young's
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modulus, yield stress, tangent modulus, effective plastic strain, yield strain, ultimate
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stress and toughness of cortical bone specimens. ANOVA and nonparametric analyses
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showed that the Young's modulus, yield stress, ultimate stress and pre-yield toughness of cortical bone specimens significantly decreased with increased saline preservation
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time (P < 0.001). The effective plastic strain increased significantly with increasing
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preservation time (P = 0.034). Saline preservation for 10 days and longer (36 and 60 days) can significantly reduce the yield stress and pre-yield toughness of cortical bone,
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while preservation for 36 days and longer (60 days) can significantly reduce the
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Young's modulus and ultimate stress. Furthermore, saline preservation reduced Young's modulus, yield stress, and ultimate stress, and increased tangent modulus.
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The effect was already observable after 3 days. Therefore, it is ideal to control the
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preservation time of the specimen in saline less than 3 days to avoid deviations from the in vivo condition.
Conflict of interest There are no conflicts of interest.
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ACCEPTED MANUSCRIPT Acknowledgements This research was funded by the National Natural Science Foundation of China (51205118, 11402296), the Central University Basic Scientific Research Business Expenses Special Funds (No.531107040162), the Canada Research Chairs program,
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and the State Key Laboratory of Advanced Design and Manufacturing for Vehicle
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Body, Hunan University (51475002).
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Mechanics, 38 (2011) 209-297. [49] J.C. Goh, E.J. Ang, K. Bose, Effect of preservation medium on the mechanical properties of cat bones, Acta orthopaedica, 60 (1989) 465-467. [50] B. Kaye, D. Walsh, C. Randall, P. Hansma, The Effects of Freezing on the Mechanical Properties of Bone, Open Bone Journal, 67 (2012) 14-19. [51] A. Nazarian, B.J. Hermannsson, J. Muller, D. Zurakowski, B.D. Snyder, Effects of tissue preservation on murine bone mechanical properties, Journal of 28
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ACCEPTED MANUSCRIPT Figure Captions Fig. 1. Specimen preparation methods (a), illustration of specimen size measurements (b) and three-point bending test setup (c). Fig. 2. Comparative analysis of specimen constitutive parameters between
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fresh-frozen groups and saline-preserved groups. F: fresh, S3, S10, S36, S60:
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saline preservation for 3, 10, 36, and 60 days.
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Fig. 3. Boxplots of the constitutive parameters of fresh frozen specimens from four anatomic regions.
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Fig. 4 Comparison of the present results and those from the literature regarding the
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effects of saline preservation on the Young’s modulus (E). Fig. 5. Comparison of results in this study and those from the literature regarding the
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Fig. 1 Specimen preparation methods (a), illustration of specimen size measurements (b) and three-point bending test setup (c).
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Fig. 2 Comparative analysis of specimen constitutive parameters between fresh-frozen groups and saline-preserved groups. F: fresh, S3, S10, S36, S60: saline preservation for 3, 10, 36, and 60 days. *: Paired-sample t-test results. Pwr: Power analysis results based on paired-samples t-test or Wilcoxon matched-pairs signed-ranks test. 32
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Fig. 3 Boxplots of the constitutive parameters of fresh frozen specimens from four anatomic regions.
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Fig. 5 Comparison of results in this study and those from the literature regarding the Young's modulus and yield stress of longitudinal bovine bone specimens.
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ACCEPTED MANUSCRIPT Table Captions Table 1. The constitutive parameters (mean and SD) for the fresh-frozen group and other saline-preserved groups. E: Young's modulus, ETAN: tangent modulus, SIGY: yield stress, FS: effective plastic strain, YS: yield strain, UST: ultimate
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ACCEPTED MANUSCRIPT Table 1 The constitutive parameters (mean and SD) for the fresh-frozen group and other saline-preserved groups. E: Young's modulus, ETAN: tangent modulus, SIGY: yield stress, FS: effective plastic strain, YS: yield strain, UST: ultimate stress, PreT: pre-yield toughness, PostT: post-yield toughness, T: total
Group
MDD
Mean
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S10 Mean SD
S36 Mean SD
S60 Mean SD
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22.44 2.34 1.895 20.79 2.97 20.95 6.51 18.13 2.73 17.14 3.28 1.34 0.46 0.369 1.41 0.47 1.56 0.82 1.47 0.47 1.94 0.60 141.49 19.71 15.940 130.65 21.20 120.48 28.07 104.70 16.86 104.05 19.78 2.72 0.58 0.469 2.73 0.49 2.74 0.92 2.98 0.66 3.64 1.45 0.63 0.05 0.042 0.63 0.06 0.59 0.09 0.58 0.07 0.61 0.09 176.76 21.61 17.475 167.96 22.96 157.79 35.40 146.14 20.67 140.94 26.05 0.45 0.09 0.074 0.41 0.09 0.35 0.08 0.31 0.07 0.32 0.08 4.36 1.16 0.941 4.11 1.01 3.81 1.61 3.75 1.00 4.56 2.26 4.81 1.23 0.993 4.52 1.08 4.17 1.68 4.06 1.06 4.88 2.33
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E (GPa) ETAN (GPa) SIGY (MPa) FS (%) YS (%) UST (MPa) PreT (mJ/mm3) PostT (mJ/mm3) T (mJ/mm3)
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ACCEPTED MANUSCRIPT Appendix A Flowchart to determine the optimal material parameters of cortical bovine bone specimens. E: Young's modulus, ETAN: tangent modulus, SIGY: yield stress, FS: effective plastic strain, B: parameters derived from beam theory, Opt: parameters derived from specimen-specific
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finite element optimization method.
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ACCEPTED MANUSCRIPT Appendix B Summary of all statistical methods used in the study, main statistical significances, and which specific statistical method was used for certain finding. E: Young's modulus, ETAN: tangent modulus, SIGY: yield stress, FS: effective plastic strain, YS: yield strain, UST: ultimate stress,
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ACCEPTED MANUSCRIPT Highlights
Storage in saline solution affects the material properties of cortical bone tissue.
Saline storage significantly reduces the Young's modulus, yield/ultimate stress.
Saline storage significantly increases the effective plastic strain.
Such effects on mechanical properties are already observable after 3 days.
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Guanjun Zhang, Xianpan Deng, Fengjiao Guan, Zhonghao Bai, Libo Cao, Haojie Mao PII: DOI: Reference:
S0268-0033(18)30390-5 doi:10.1016/j.clinbiomech.2018.06.003 JCLB 4546
To appear in:
Clinical Biomechanics
Received date: Accepted date:
21 July 2017 4 June 2018
Please cite this article as: Guanjun Zhang, Xianpan Deng, Fengjiao Guan, Zhonghao Bai, Libo Cao, Haojie Mao , The effect of storage time in saline solution on the material properties of cortical bone tissue. Jclb (2017), doi:10.1016/j.clinbiomech.2018.06.003
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ACCEPTED MANUSCRIPT The effect of storage time in saline solution on the material properties of cortical bone tissue
Guanjun Zhang1, Xianpan Deng1, Fengjiao Guan2, Zhonghao Bai1, Libo Cao1,
State Key Laboratory of Advanced Design and Manufacturing for Vehicle Body, Hunan University, Changsha, 410082, China
Science and Technology on Integrated Logistics Support Laboratory, National
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2
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1
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Haojie Mao3*
3*
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University of Defense Technology, Changsha, 410073, China Department of Mechanical and Materials Engineering, Western University, London,
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ON N6A 5B9, Canada
Corresponding author: Haojie Mao
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Email: [email protected]
Abstract: 250 words Main text: 4807 words (Introduction till Acknowledgements)
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ACCEPTED MANUSCRIPT Abstract Background: The use of saline in preserving bone specimens may affect the mechanical properties of specimens. Yet, the reported effects varied and contradicted to each other, with a lack of investigating constitutive material parameters. Therefore,
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we quantified the effects of preservation time on the constitutive properties of cortical
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bone.
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Methods: We collected 120 specimens from the mid-diaphysis of six male bovine femora, which were assigned to five groups, including fresh-frozen for 60 days
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(-20℃), storage in saline for 3, 10, 36 and 60 days (25℃). All specimens underwent
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quasi-static three-point bending tests with a loading rate of 0.02 mm/s. Using the optimization method combined with specimen-specific finite element models, the
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Young's modulus, tangent modulus, yield stress, effective plastic strain, yield strain,
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ultimate stress, and toughness were calculated. Findings: Saline preservation resulted in a significant decrease of Young's modulus,
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yield stress, ultimate stress and pre-yield toughness (P < 0.001 for all four parameters),
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and a significant increase of effective plastic strain (P = 0.034). After 10 days of preservation, yield stress and pre-yield toughness decreased -14.9% and -21.4%, respectively, and they continued to decrease with longer preservation time. After 36 days of preservation, Young’s modulus and ultimate stress decreased -19.2% and -17.3%, respectively, and continued to decrease with longer preservation time. The effective plastic strain only decreased significantly after 60-day preservation (+33.7%, P = 0.011). Our data also showed changes of material properties collected after 3-day 2
ACCEPTED MANUSCRIPT saline preservation, while the low statistical power must be considered for this group. Interpretation: Saline preservation impacts on mechanical properties of cortical bone tissue and the effect is already observable after 3 days. When subjecting cortical bone to biomechanical tests at room temperature, saline preservation for 3 days or less is
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recommended.
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Keyword: cortical bone, saline preservation, material property, three-point bending,
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finite element optimization
1 Introduction
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Physiological saline, which has an osmotic pressure of human and animal plasma, is commonly used in physiology experiments and clinical treatments. In
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biomechanical experiments, specimens need to be washed with saline to clean the
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antiseptic solutions and to rehydrate the specimens before test
[1-6]
. Both fresh and
fresh-frozen bone specimens need saline to maintain cell viability and to thereby
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preserve their in vivo condition
[5, 7-11]
. Hence, saline is widely used in bone
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biomechanics tests and is applied throughout the entire process of specimen preparation and testing. There are several studies that reported the effect of saline preservation on bone property. In a study of the effects of formaldehyde fixation on the mechanical properties of bone, Currey et al. (1995)[4] found that preservation in saline for 3 days slightly increased (approximately 1%) the rigidity of machined bovine cortical bone specimens. On the other hand, Mcpherson et al. (1980)[12] showed that the rigidity of 3
ACCEPTED MANUSCRIPT machined fetal skull specimens preserved in saline was reduced by 4.4% compared with the value obtained from skull preserved in air, but the difference was not statistically significant. Kikugawa et al. (2007)[13] studied the fracture properties of bovine cortical bone with machined specimens stored for 7 or 30 days in saline and
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found that the fracture toughness of the specimens was decreased by 5% and 12%,
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respectively. On the contrary, Kuninori et al. (2009)[14] reported that fracture
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toughness of machined bovine cortical bone specimens increased slightly (about 2% 10% as estimated per authors’ Fig. 5) after being stored in saline for 30 days.
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Gustafson et al. (1996)[15] found that the Young's modulus of equine machined
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metacarpal cortical bone decreased significantly by 2.4% after 6 days of preservation in saline. However, after 10 days of preservation, the Young's modulus did not
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decrease significantly. Griffon et al(1995)[16] used the four point bending test to study
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energy absorption characteristics and ultimate displacement of canine rib, metacarpal and metatarsal bones after preservation in -20℃ saline solution for one year. Their
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results showed that energy absorbed at failure and ultimate displacement increased by
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25%~30% and 18%~24%, respectively. With variances and contradictions, the effects of saline preservation on bone material property remain to be further investigated. In addition, the literature studies mostly analyzed the effect of saline on properties such as bone stiffness, fracture toughness, energy absorption and ultimate displacement. However, there is a lack of data on constitutive material parameters (e.g., Young’s modulus, yield stress, ultimate stress, and ultimate strain). Furthermore, the testing methods and preservation time among labs are different, which added 4
ACCEPTED MANUSCRIPT difficulty for reaching definitive conclusions on the effect of saline preservation. In our own experience, we have previously maintained cortical bone specimens in saline for 58 days. Students used these specimens to practice testing methods as part of their training, and they observed that the Young’s modulus of these specimens were very
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different from the values reported in the literature for fresh specimens. With this
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experience and the awareness of differences in literature, Therefore, we deem it
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necessary to design a test to comprehensively quantify the effects of saline on the biomechanical properties of bone.
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Two methods are reported in the literature for determining the constitutive
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parameters of cortical bone in the three-point bending test. The first is the classical material parameter identification method based on beam theory and the second is the
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optimization method combined with specimen-specific finite element (FE) models.
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The former uses classic formulas of beam theory to obtain key material parameters of cortical bone based on experiment force-displacement curves
[17]
. This method has a
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high computational efficiency, but the yield stress and the parameters after yielding
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could be inaccurate[18]. The latter method adopts the specimen-specific FE model to accurately simulate specimens and use an optimization method to fit the test and simulation curves. This method provides appropriate constitutive parameters for characterizing the mechanical response of biological specimen[19-23], but has the limitation of being time-consuming and relatively computationally inefficient[24]. In studying the material properties of bone, even a small artificial effect on its material properties could change conclusions because variances among different 5
ACCEPTED MANUSCRIPT groups could be small. Therefore, in order to accurately assess the effects of saline on the material properties of cortical bone, machined cuboid bovine femoral cortical bone specimens, which have been frequently tested
[25-27]
, were harvested to carry out
quasi-static three-point bending tests. We further adopted a three-point bending test
PT
device that can be used to test extremely small specimens[19, 28] for characterizing
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region-specific properties. We designed a comprehensive study and preserved bone
SC
specimens at room temperature (25℃) for 3, 10, 36, and 60 days. We then calculated the constitutive parameters of cortical bone, including Young's modulus, yield stress,
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tangent modulus, and effective plastic strain, through the specimen-specific FE-based
MA
optimization method. Moreover, parameters such as yield strain, ultimate stress, and toughness including pre-yield toughness, post-yield toughness, and all toughness were
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2 Methods
D
also analyzed.
2.1 Specimen extraction
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Due to the small size and crisp texture of cortical bone, its material properties are [29]
. Hence, we prepared cortical bone specimens
AC
heavily influenced by temperature
by low speed grinding to avoid quickly generating heat. Six fresh femora from the right legs of male bovines aged between 24 - 36 months were obtained from the slaughterhouse. After removing muscle tissue, CT examination (Philips Brilliance 64 CT Scanner, Philips Medical, Cleveland, Ohio) with a resolution of 512 × 512 and layer thickness of 0.625 mm was performed to ensure there were no bone defects that may affect bone mechanical properties. The middle sections (20 mm long) of the 6
ACCEPTED MANUSCRIPT femur diaphysis were obtained with a handsaw. Anterior (A), lateral (L), posterior (P), and medial (M) regions were marked, and 5 specimens from each region were harvested (Fig. 1, (a)). Sandpaper (Eagle #360) was used to shape the specimen into a cuboidal shape with dimensions of approximately 15 mm × 5 mm × 2 mm. A
PT
self-made miniature grinder was then used for low-speed fine grinding. The sand bar
RI
model was Congress EDM 1500, and the grinding line speed was below 20 mm/s. The
SC
final size of the specimens was 12 mm (L) × 2 mm (W) × 0.5 mm (T). In the process of cutting and grinding, 0.9% saline was applied continuously over the specimen.
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During preparation, specimens that were not yet processed or that were partially
MA
processed were wrapped in saline-soaked gauze and frozen at -20°C[11, 30, 31]. All of the specimens were prepared in vitro within 3 days, and the effect of this preparation
D
process on the biomechanical response of the specimen was deemed as negligible
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without statistically significant changes [32, 33]. 2.2 Specimen grouping and preservation
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A total of 120 cortical bone specimens (6 femurs × 4 regions/femur × 5
AC
specimens/region) were prepared. To reduce the influence of sampling location on test results, the 5 specimens from the same anatomical region of one femur were assigned to 5 different groups, including a fresh-frozen group (F), saline preservation for 3 days (S3), 10 days (S10), 36 days (S36), and 60 days (S60). All specimens were harvested in the same time for mechanical test. Therefore, specimens in the S60 group were immediately immersed in normal saline, and the other specimens were stored at -20°C[11]. Each 0.9% saline-immersed specimen was placed in a glass tube (10 ml) 7
ACCEPTED MANUSCRIPT with a wood plug seal at room temperature 25°C[13]. After 24, 50 and 57 days, the specimens in the S36, S10 and S3 groups, respectively, were thawed at room temperature and then underwent the same saline preservation treatment as that for S60 group.
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2.3 Three-point bending test
[5, 12]
, and the saline-immersed specimens were washed with fresh
SC
saline for 2 hours
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The fresh-frozen specimens were thawed at room temperature (25°C) with 0.9%
0.9% saline at room temperature (25°C) for 2 hours. A micrometer (Mitutoyo103-137,
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graduation of 0.01 mm, accuracy of 0.002 mm, Japan) was used for accurate
MA
measurement of the two ends and the middle portion of the specimens along the length, width, and thickness (Fig. 1, (b)). The average values of the length, width and
D
thickness were recorded for the construction of the FE model. The INSTRON 5985
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(Instron Corp., Norwood, MA, USA) material testing machine was used for quasi-static three-point bending test at a rate of 0.02 mm/s. The impact head and the
CE
supporting shaft are both metal cylinders with a diameter of 1 mm, and the axial span
AC
is 10 mm, as shown in Fig. 1, c. A miniature sealed stainless steel load cell with a capacity of 44.5 N (WMC-10-38, Interface, Inc., AZ, USA) was used to record the loading force. The displacement transducer of INSTRON systems was used to obtain the displacement history curves at the loading point. The obtained displacement history curve matches with the defined loading speed. TDAS-PRO (Diversified Technical System Inc., CA, USA) was used to collect the test data with a sampling frequency of 250 Hz. The failure load is defined as the maximum load
[34]
, and the 8
ACCEPTED MANUSCRIPT force-displacement curves before failure were used in this study. 2.4 Beam theory The stress-strain curves of loading point were derived from force-displacement curves in three-point bending tests using the beam theory as follows [17, 35]: 3𝐹𝐿
𝜎 = 2𝑊𝑇 2
PT
6𝑇𝛿 𝐿2
(2)
RI
𝜀=
(1)
SC
where σ and ε are the stress and strain, respectively; F is the loading force; L is the span between two supports; W and T are the average width and thickness of each
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specimen, respectively; δ is the specimen deflection at loading point.
MA
Using 25% of the ultimate stress as the window width [36], the stress-strain curve was fitted using a straight line within the window width. The maximum slope of the
D
line was found by moving the window, which was defined as the Young's modulus of
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the specimen (EB, where B stands for beam). The point of zero strain was defined as the point where the straight line of stress-strain curve corresponding to Young's [37, 38]
CE
modulus crossed the zero-stress abscissa
AC
determined using the 0.2% strain offset method
. The yield stress (SIGYB) was
[17, 39]
. Effective failure strain (FSB)
was assumed as effective plastic strain at failure[28]. The tangent modulus (ETANB) was defined as 5% of Young’s modulus
[40, 41]
. These four parameters were
automatically calculated by the in-house codes developed using Matlab (Version R2017a, The MathWorks, MA, USA).
9
ACCEPTED MANUSCRIPT 2.5 Specimen-Specific FE Optimization The specimen-specific FE models were automatically constructed by Matlab according to the length, the width/thickness of the specimens measured at both ends and middle locations. Each model consisted of eight layers of hexahedron elements in
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the thickness direction, based on our previous convergence study, for a total of 49,152
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elements. For cortical-bone specimens, the material was assumed to be an isotropic
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homogeneous material in FE models. The elastoplastic material model, LS-DYNA (LSTC, Livermore, CA) material #24, was used in this study. The Poisson’s ratio and [42, 43]
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density were set to 0.22 and 2000 kg/m3, respectively
. Young’s modulus (E),
MA
yield stress (SIGY), tangent modulus (ETAN), and effective plastic strain (FS) were constitutive parameters commonly used in bone FE models
[44, 45]
, and were therefore
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beam theory method [28].
D
defined as design variables. The initial value of these design variables is calculated by
The material constitutive parameter optimization process is divided into three
CE
steps (Appendix A). In the first step, the objective function was defined as the
AC
root-mean-square errors between the elastic portion of simulated and experimental force-deformation curves of each specimen. Only the Young's modulus was defined as a design variable whose initial value was EB. Yield stress and tangent modulus were defined as constants, designated as SIGYB and ETANB, respectively. In the second step, the objective function was defined as the root-mean-square errors between the simulated and experimental force-deformation curves of each specimen. Yield stress and tangent modulus were defined as design variables, the initial values were SIGYB 10
ACCEPTED MANUSCRIPT and ETANB, respectively. The elastic modulus was set as a constant whose value was the optimum value obtained in the first step. In the first step and the second step of the optimization process, the failure of the material was not defined. In the third step, to test the displacement measurement accuracy of the testing machine the effective
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plastic strain was defined as the design variable, the Young’s modulus, yield stress,
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and tangent modulus were constants whose values were the optimum values obtained
SC
in the previous steps. LS-OPT 5.0 (LSTC, Livermore, CA) was used to optimize material constitutive parameters. Detailed optimization process was described in our
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previous article[28].
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The ultimate strength (UST) and yield strain (YS) were calculated based using the above four parameters (Eq. 3 and Eq. 4).
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D
UST = SIGY + FS × ETAN YS = SIGY/E
(3) (4)
The pre-yield toughness (PreT) was calculated as the area under the straight E
CE
line (Eq. 5), and the post-yield toughness (PostT) was calculated as the area under the
(Eq. 7).
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straight ETAN line (Eq. 6). The total toughness (T) was the sum of PreT and PostT
PreT = 0.5 × YS × SIGY
(5)
PostT = 0.5 × (SIGY + UST) × FS
(6)
T = PreT + PostT
(7)
2.6 Statistical method SPSS software (Version 21, IBM Corporation, Somers, NY, USA) was used to 11
ACCEPTED MANUSCRIPT analyze the test data. All constitutive parameters were verified to follow a normal distribution using the Shapiro-Wilk test (P > 0.05)[9, 17, 28]. The Levene method was used to test for homogeneous variance (P > 0.05). Constitutive parameters with normal distributions and homogeneous variance were further analyzed with one-way
PT
ANOVA, otherwise, non-parametric Kruskal-Wallis tests were used to determine
RI
whether the saline significantly affected the constitutive parameters of cortical bone.
SC
Multiple comparisons between groups were carried out for different constitutive parameters, so as to study how long-term saline preservation significantly impacts the
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constitutive parameters of cortical bone. The Tukey method was used for constitutive
MA
parameters in compliance with variance analysis conditions (normal distribution and homogeneous variance), and Dunnett's T3 method was used for that with
D
non-parametric test conditions[46, 47]. A paired-sample t-test (for the between-group
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differences fitting the normal distribution) or Wilcoxon matched-pairs signed-ranks test (for the between-group differences not conforming to the normal distribution) was
CE
also performed between the fresh-frozen group and each saline-preserved group, and
AC
the corresponding power analysis was performed with G*Power software (Version 3.1.9.2, Universität Düsseldorf, German). Furthermore, Stata software (Version 14.1, StataCorp., College Station, TX, USA) was used to analyze the minimum detectable difference (MDD) with Power = 0.8. A significance level of 0.05 was introduced to test statistical significance.
3 Results The Young's modulus, yield stress, tangent modulus and effective plastic strain 12
ACCEPTED MANUSCRIPT were obtained using the optimization FE method. The yield strain, ultimate stress, pre-yield toughness, post-yield toughness, and total toughness were calculated using the above four parameters. A statistical description of these values is shown in Table 1. With increased preservation time, the Young’s modulus, yield stress, ultimate stress,
PT
and toughness (except for the S60 group) of the specimen gradually decreased, while
RI
the effective plastic strain gradually increased.
SC
The Young’s modulus (P < 0.001), yield stress (P < 0.001), effective plastic strain (P = 0.034), ultimate stress (P < 0.001), and pre-yield toughness (P < 0.001)
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were significantly different between the groups; the tangent modulus (P = 0.558),
MA
yield strain (P = 0.056), post-yield toughness (P = 0.299), and total toughness (P = 0.199) showed no statistically significant differences (Appendix B).
D
The Tukey method and Dunnett's T3 method were used to perform multiple
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comparisons with results shown in Fig. 2. The Young's modulus of cortical bone gradually decreased with increased saline preservation time. Three days (P = 0.309)
CE
and 10 days (P = 0.961) preservation in saline did not significantly change the
AC
Young's modulus of cortical bone, but this metric significantly decreased by 19.2% (P < 0.001) and 23.6% (P < 0.001) after 36 and 60 days of preservation, respectively (Fig.2 (a)). The yield stress of cortical bone gradually decreased with increased saline preservation time. Three days of saline preservation did not significantly change (P = 0.408) the yield stress of cortical bone; however, 10, 36 and 60 days of preservation significantly decreased cortical bone yield stress by 14.9% (P = 0.008), 26.0% (P < 0.001) and 26.5% (P < 0.001), respectively (Fig.2 (c)). The ultimate stress of S36 13
ACCEPTED MANUSCRIPT group decreased significantly by 17.3% compared with that of fresh-frozen group (P < 0.001), and the S60 group decreased significantly by 20.3% (P < 0.001) (Fig.2 (f)). The preservation in saline for 3 days had no significant (P = 0.846) effect on pre-yield toughness of the specimens. However, the pre-yield toughness decreased significantly
PT
after 10 days (P = 0.003, -21.4%), 36 days (P < 0.001, -31.7%) and 60 days (P <
RI
0.001, -28.6%) of storage (Fig.2 (g)). Multiple comparisons showed no significant
toughness and total toughness between groups.
SC
difference in tangent modulus, yield strain, effective plastic strain, post-yield
NU
The results of the paired sample t-test showed that the Young’s modulus of S3
MA
group was lower than that of the fresh-frozen group with some significance (P = 0.041). However, the corresponding power analysis showed that the probability of
D
making a type II error was about 45.6% (1-Power). Furthermore, the differences of
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Young’s modulus between the fresh-frozen group and the S3 group were less than MDD value (Table 1).
CE
Descriptive statistical analyses were performed for the material constitutive
AC
parameters of the fresh-frozen group according to the different source anatomical regions (Fig. 3). All of the constitutive parameters in the different anatomical regions were normally distributed, except for the effective plastic strain in the anterior region (P = 0.005) and the yield stress in the medial region (P = 0.048). Tests of variance homogeneity showed that the constitutive parameters in all four anatomical regions met this criterion. One-way ANOVA was performed for the Young's modulus and tangent modulus, and the Kruskal-Wallis test was performed for the yield stress and 14
ACCEPTED MANUSCRIPT effective plastic strain. The Young's modulus (P = 0.399), tangent modulus (P = 0.467) yield stress (P = 0.095), and effective plastic strain (P = 0.055) were not significantly different between the four anatomical regions.
4 Discussion
PT
Our data demonstrated that long-term saline preservation could decrease Young’s
RI
modulus (19.2% for 36-day preservation and 23.6% for 60-day preservation), yield
SC
stress (14.9% for 10-day preservation, 26.0% for 36-day preservation and 26.5% for
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60-day preservation), ultimate stress (17.3% for 36-day preservation and 20.3% for 60-day preservation) and pre-yield toughness (21.4% for 10-day preservation, 31.7%
MA
for 36-day preservation and 28.6% for 60-day preservation). Compared with other studies, our specimen-specific FE-based optimization method can eliminate the
D
influence of geometric size on constitutive parameters, hence more accurately
PT E
calculating Young's modulus, yield stress, and effective plastic strain responses of cortical bone [19, 28]. To the best of our knowledge, our study uniquely quantified how
AC
bone.
CE
saline preservation for 3, 10, 36, and 60 days affect constitutive parameters of cortical
The result of multiple comparisons using Dunnett’s T3 Test showed that the 3-day preservation did not significantly affect Young's modulus (P = 0.309). The paired-sample t-test indicated that preservation for three days, however, resulted in a decrease in Young's modulus with some significance (P = 0.041). The risk of concluding that there is no effect when there is one is high (1-Power = 45.6%). Furthermore, the difference between the mean values of the Young's moduli of S3 and 15
ACCEPTED MANUSCRIPT fresh-frozen groups was less than that MDD. Hence, we suggest that the statistical conclusion of the effect of 3-day saline preservation on Young’s modulus couldn’t be firmly drawn. Linde et al. (1993) reported that storage of male human tibial trabecular bone in saline for 1 day caused the Young's modulus to decrease by 10% (P < 0.05) [5],
PT
whereas 3 days of saline preservation for cortical bone resulted in no significant
RI
change (P = 0.309) in current study. The primary difference between Linde et al.’s and
SC
our experiments was the type of bone that was tested, suggesting that saline might more rapidly penetrate trabecular bone and thus has a greater impact on this bone type
NU
than on cortical bone. Gustafson et al. (1996)[15] showed that saline preservation of
MA
equine third metacarpal cortical bone for 6 days decreased the Young's modulus by 2.4% (P = 0.011); after 10 days, the Young's modulus was decreased by 2.7% (P =
D
0.011). In our study, 10 days of saline preservation caused the Young's modulus of the
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bovine femoral cortical bone to decrease by 6.6%, although this effect was not significant (P = 0.961 from Dunnett’s T3 test and P = 0.303 from t-test). Our data
CE
showed that the Young's modulus of the S10 group did not change significantly with
AC
respect to the fresh-frozen group (P = 0.303). However, it should be noted that the variance of S10 group was large. And the difference (1.49 GPa) between the mean values of the Young's moduli of the fresh-frozen group and the S10 group is smaller than the MDD (1.89 GPa). Furthermore, the power analysis showed that the risk of concluding that there is no effect between fresh-frozen and S10 groups when there is one is very high (1-Power = 82.7%). Hence, we couldn’t firmly conclude that the effect of 10-day saline preservation on Young’s modulus was statistically not 16
ACCEPTED MANUSCRIPT significant. The same study by Gustafson et al.
[15]
showed that calcium ions can
dissolve small bone specimens (7.5 mm × 7.5 mm × 3 mm) in a saline bath at room temperature. In addition, Novitskaya et al. (2011) suggested that the Young’s modulus of bone decreases with reduced mineral volume fraction
[48]
, which is consistent with
PT
our results on the Young’s modulus.
RI
Levene’s test showed that five groups of specimens (fresh-frozen group and
SC
saline preservation groups) were significantly different in terms of yield stress (P < 0.001), suggesting that saline preservation significantly impacts cortical bone yield
NU
stress. Our Tukey analysis showed that, compared with the fresh-frozen group,
MA
cortical bone stored in saline for 3 days does not exhibit significantly different yield stress (P = 0.408: -7.7%). However, after 10, 36 and 60 days, the yield stress was
D
significantly decreased by 14.9% (P = 0.008), 26.0% (P < 0.001) and 26.5% (P <
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0.001), respectively (Fig. 2). It is clear that the yield strength of cortical bone is decreased with increased preservation time in saline. No previous study has tested the
CE
effects of saline preservation effect on yield strength of cortical bone, but Kikugawa
AC
et al. (2007)[13] found that the fracture toughness of machined bovine cortical bone specimens decreased by 30% after normal saline preservation for 30 days. Yield stress and fracture toughness can, to a certain extent, reflect the resistance ability of cortical bone. At the same time, the toughness of specimens preserved with saline for 36 days decreased significantly by 15.6% (P = 0.006, paired-samples t test) in this paper. Therefore, it could be inferred from the results of this previous study that long-term preservation reduces the strength of cortical bone material, which is similar to the 17
ACCEPTED MANUSCRIPT results of the present study. The difference between the mean values of the yield stress of S3 and fresh-frozen groups were smaller than MDD, as well as the ultimate stress and tangent modulus. Hence, we couldn’t firmly conclude that the effects of 3-day saline preservation on these parameters were statistically not significant.
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The fresh-frozen bovine cortical bone was used as the control group in this study.
RI
This choice was based on a large number of studies that showed long-term freezing
SC
(at -20°C or below) up to 100 days does not significantly change the mechanical properties of bone and hence was commonly used
[5, 14, 49-51]
. The observed Young's
NU
modulus of bone in fresh-frozen group was 22.44 GPa (SD 2.34 GPa) in our study.
MA
This is in agreement with the work of Unger et al. (2010) (Mean 21.05 GPa, SD 1.39 GPa)[52] and Currey et al. (1995) (Mean 18.14 GPa, SD 0.47 GPa)[4]. Importantly,
D
Unger et al.’s and Currey et al.’s data were also obtained using three-point bending
PT E
tests (Fig. 5). In addition, our result of fresh-frozen group is in agreement with those of Abdel-Wahab et al. (2011)[31] (Mean 19.68 GPa, SD 3.46 GPa, tension) and Li et al.
CE
(2013)[9] (Mean 20.22 GPa, SD 3.12 GPa, tension; Mean 19.09 GPa, SD 2.84 GPa,
AC
compression), in which the Young’s modulus of bovine cortical bone specimens was obtained using tensile test and compression test methods. In our study, the yield stress of fresh-frozen specimens was 144.49 MPa (SD 19.71 MPa), which is comparable to the tensile (Mean 75.85 MPa, SD 13.98 MPa) and compression yield stresses (Mean 184.62 MPa, SD 22.51 MPa) [9]. This difference may be related to the experiment method. These results show that the adopted method can accurately obtain the constitutive parameters of the tested materials. 18
ACCEPTED MANUSCRIPT The Young's modulus was highest in fresh-frozen bone from the lateral region, followed by bone from the medial, posterior and anterior specimens However, the differences were not significantly different (P = 0.399). Abdel-Wahab et al. (2011)[31] studied these four anatomical regions using a tensile testing method, finding that the
PT
Young's modulus of axial specimens were highest in the anterior, followed by the
RI
medial, posterior and lateral specimens. Li et al. (2013)[9] showed similar results by
SC
stretching and compression tests. It should be noted that the study by Abdel-Wahab et al. (2011)[31] did not perform comparative statistical analyses; only the average values
NU
were compared. Li et al. (2013)[9] performed comparative statistical analyses and
MA
found that only differences between the opposite quadrants (i.e., anterior vs. posterior, lateral vs. medial) were consistently significant. The results of Abdel-Wahab et al.
D
(2011) and Li et al. (2013) are derived from the compression and tensile tests,
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whereas the quasi-static three-point bending test method is adopted in this study. The different loading modes may be the cause of the different results between these
CE
studies[2, 53]. In addition, Abdel-Wahab et al. (2011) and Li et al. (2013) obtained the
AC
parameters based on an experimental curve and theoretical calculation method, whereas we used a method that employed specimen-specific FE model optimization. Therefore, different methods may contribute to the variation in results between the studies and more studies on region-specific material properties will help to better understand cortical bone. During preparation, specimens that were not yet processed were wrapped in saline-soaked gauze and frozen at -20°C. The specimen wrapping method used in this 19
ACCEPTED MANUSCRIPT paper prevents specimen dehydration and is used in a number of documents
[11, 30, 31]
.
The prepared specimens were frozen, and then each group of specimens was thawed in sequence, followed by preservation in saline at room temperature. All samples were subjected to the three-point bending test at the same time. In the meantime, it has been
PT
reported that freezing at -20 ℃ does not change the biomechanical response of cortical
RI
bone [32, 33]. Therefore, the change of the biomechanical response of the sample can be
SC
neglected during the three-day sample preparation, and it can be assumed that all samples have the same starting point.
[48, 53]
and experience more contact with saline. There is
MA
higher degree of porosity
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The present study considered femoral cortical bone. Cancellous bones have a
likely a larger effect of saline preservation on cancellous bones than that of cortical
D
bone. Therefore, caution should be used when applying the conclusions of this study
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to other types of bone. In this study, the effects of saline on cortical bone were studied at room temperature (25°C); the influence of other temperatures remains to be further
CE
studied. In addition, we analyzed the response of machined cortical bone specimens
AC
using a quasi-static three-point bending test. As the bone is a nonlinear material, strain rates can strongly influence the response of cortical bone mechanics. Therefore, studies on the effects of saline preservation on material properties of the cortical bone under different strain rates can help further understand the effect of saline preservation. Due to the lower sensitivity of the tangent modulus during optimization, the results on tangent modulus should be used with great care.
20
ACCEPTED MANUSCRIPT 5 Conclusions Machined bovine cortical bone specimens were investigated in this study. The force-displacement curves were obtained through quasi-static three-point bending testing. Using the optimization FE method, we accurately calculated the Young's
PT
modulus, yield stress, tangent modulus, effective plastic strain, yield strain, ultimate
RI
stress and toughness of cortical bone specimens. ANOVA and nonparametric analyses
SC
showed that the Young's modulus, yield stress, ultimate stress and pre-yield toughness of cortical bone specimens significantly decreased with increased saline preservation
NU
time (P < 0.001). The effective plastic strain increased significantly with increasing
MA
preservation time (P = 0.034). Saline preservation for 10 days and longer (36 and 60 days) can significantly reduce the yield stress and pre-yield toughness of cortical bone,
D
while preservation for 36 days and longer (60 days) can significantly reduce the
PT E
Young's modulus and ultimate stress. Furthermore, saline preservation reduced Young's modulus, yield stress, and ultimate stress, and increased tangent modulus.
CE
The effect was already observable after 3 days. Therefore, it is ideal to control the
AC
preservation time of the specimen in saline less than 3 days to avoid deviations from the in vivo condition.
Conflict of interest There are no conflicts of interest.
21
ACCEPTED MANUSCRIPT Acknowledgements This research was funded by the National Natural Science Foundation of China (51205118, 11402296), the Central University Basic Scientific Research Business Expenses Special Funds (No.531107040162), the Canada Research Chairs program,
PT
and the State Key Laboratory of Advanced Design and Manufacturing for Vehicle
SC
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Body, Hunan University (51475002).
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ACCEPTED MANUSCRIPT Figure Captions Fig. 1. Specimen preparation methods (a), illustration of specimen size measurements (b) and three-point bending test setup (c). Fig. 2. Comparative analysis of specimen constitutive parameters between
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Fig. 3. Boxplots of the constitutive parameters of fresh frozen specimens from four anatomic regions.
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Fig. 1 Specimen preparation methods (a), illustration of specimen size measurements (b) and three-point bending test setup (c).
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Fig. 2 Comparative analysis of specimen constitutive parameters between fresh-frozen groups and saline-preserved groups. F: fresh, S3, S10, S36, S60: saline preservation for 3, 10, 36, and 60 days. *: Paired-sample t-test results. Pwr: Power analysis results based on paired-samples t-test or Wilcoxon matched-pairs signed-ranks test. 32
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ACCEPTED MANUSCRIPT Table Captions Table 1. The constitutive parameters (mean and SD) for the fresh-frozen group and other saline-preserved groups. E: Young's modulus, ETAN: tangent modulus, SIGY: yield stress, FS: effective plastic strain, YS: yield strain, UST: ultimate
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ACCEPTED MANUSCRIPT Table 1 The constitutive parameters (mean and SD) for the fresh-frozen group and other saline-preserved groups. E: Young's modulus, ETAN: tangent modulus, SIGY: yield stress, FS: effective plastic strain, YS: yield strain, UST: ultimate stress, PreT: pre-yield toughness, PostT: post-yield toughness, T: total
Group
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S10 Mean SD
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22.44 2.34 1.895 20.79 2.97 20.95 6.51 18.13 2.73 17.14 3.28 1.34 0.46 0.369 1.41 0.47 1.56 0.82 1.47 0.47 1.94 0.60 141.49 19.71 15.940 130.65 21.20 120.48 28.07 104.70 16.86 104.05 19.78 2.72 0.58 0.469 2.73 0.49 2.74 0.92 2.98 0.66 3.64 1.45 0.63 0.05 0.042 0.63 0.06 0.59 0.09 0.58 0.07 0.61 0.09 176.76 21.61 17.475 167.96 22.96 157.79 35.40 146.14 20.67 140.94 26.05 0.45 0.09 0.074 0.41 0.09 0.35 0.08 0.31 0.07 0.32 0.08 4.36 1.16 0.941 4.11 1.01 3.81 1.61 3.75 1.00 4.56 2.26 4.81 1.23 0.993 4.52 1.08 4.17 1.68 4.06 1.06 4.88 2.33
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ACCEPTED MANUSCRIPT Appendix A Flowchart to determine the optimal material parameters of cortical bovine bone specimens. E: Young's modulus, ETAN: tangent modulus, SIGY: yield stress, FS: effective plastic strain, B: parameters derived from beam theory, Opt: parameters derived from specimen-specific
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ACCEPTED MANUSCRIPT Appendix B Summary of all statistical methods used in the study, main statistical significances, and which specific statistical method was used for certain finding. E: Young's modulus, ETAN: tangent modulus, SIGY: yield stress, FS: effective plastic strain, YS: yield strain, UST: ultimate stress,
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ACCEPTED MANUSCRIPT Highlights
Storage in saline solution affects the material properties of cortical bone tissue.
Saline storage significantly reduces the Young's modulus, yield/ultimate stress.
Saline storage significantly increases the effective plastic strain.
Such effects on mechanical properties are already observable after 3 days.
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