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Correlation between signalment and the biphasic hyperelastic mechanical properties of equine articular cartilage
Biotribology 7 (2016) 31–37
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Correlation between signalment and the biphasic hyperelastic mechanical properties of equine articular cartilage Hyeon Lee a,⁎, William D. Campbell a, Margaret E. Canning b, Kelcie M. Theis b, Hannah Y. Ennis b, Robert L. Jackson a, James C. Wright b, R. Reid Hanson b a b
Department of Mechanical Engineering, Samuel Ginn College of Engineering, Auburn University, Auburn, AL 36849, United States Department of Clinical Sciences, College of Veterinary Medicine, Auburn University, Auburn, AL 36849, United States
a r t i c l e
i n f o
Article history: Received 8 April 2016 Received in revised form 23 June 2016 Accepted 30 July 2016 Available online 01 August 2016 Keywords: Equine articular cartilage Signalment Hyperelasticity Correlation
a b s t r a c t The correlation between mechanical properties from the equine articular cartilage and signalment was investigated. Fresh articular cartilage of fetlock, carpus, and stifle were harvested from 12 deceased horses with information on the breed, age, sex, and weight within 4 h of euthanasia for measurements. Seven indentation tests at different normalized displacements of 10, 20, 30, 35, 40, 45, and 50% of the cartilage thickness were performed with a spherical probe indenting at 0.1 mm/s velocity. The solid matrix of the cartilage was found to follow a hyper-elastic material behavior defined by Ogden; the solid phase aggregate modulus (Ea), hyperelastic material constant (α), and fluid load fraction (F′) of the cartilage were characterized. The characterized material properties were statistically analyzed using a mixed model ANOVA and Scheffe's test to check the correlation between the properties and signalment variables (breed, age, sex, and weight). There were correlations between both the solid phase aggregate modulus and age (p b 0.0392) and weight (p b 0.0375). The fluid load fraction also correlated with both age (p b 0.0146) and weight (p b 0.0003). Breed and sex were not statistically significant variables affecting the variation of theses material properties. No statistically significant correlations between the hyperelastic material constant and the signalment variables were observed. © 2016 Elsevier Ltd. All rights reserved.
1. Introduction Articular cartilage has been extensively researched to understand its characteristics in order to better design more durable and comfortable artificial joints. In addition, the rates of primary and revision hip and knee arthroplasties have increased from 1993 to 2010 as the aging of the population has accelerated [1–3]. There has also been a significant effort to find how biological factors affect the behavior of the articular cartilage [4–8]. For instance, Kempson performed tensile testing on the cartilage surfaces from humans (the femoral head, the talus of the ankle, and the femoral condyle of the knee) to characterize the effects of age [9,10]. The work demonstrated that tensile properties of the cartilage reduce with aging. However, no research has demonstrated systematic correlations between the various signalment parameters (e.g. age, weight, etc.) and the material properties of the articular cartilage. It seems to be important to understand the correlations because signalment parameters are linked with physical, physiological, and chemical factors that could systematically affect the change of cartilage performance, more specifically the mechanical properties [11–13]. This is because understanding how different parameters affect the cartilage ⁎ Corresponding author at: Department of Mechanical Engineering, Virginia Polytechnic Institute and State University, Blacksburg, VA 24061, United States. E-mail address: [email protected] (H. Lee).
http://dx.doi.org/10.1016/j.biotri.2016.07.001 2352-5738/© 2016 Elsevier Ltd. All rights reserved.
properties can help in precise analysis of the articular cartilage and joint functions for proper repairing, healing and creating of artificial replacement cartilage [14,15]. Therefore, mechanical measurements were implemented on equine articular cartilage to find the correlation between the signalment variables (breed, age, sex, and weight) and the material properties of fresh equine articular cartilage. Collagen in the cartilage serves as the basic framework around which other components are settled, as shown in Fig. 1. In addition, the collagen network plays a major role among the solid components of the matrix in supporting external loads. It counteracts the compressive and shear stresses generated by the external loads. The collagen fibrils are submerged in a gel of glycosaminoglycan (GAGs) and water. Since the ability of the cartilage matrix to retain synovial fluid decreases with age, the cartilage gets dehydrated [16]. Eventually, the dehydrated cartilage causes poor lubrication in the joint, triggering an inflammatory cascade and eventual degenerative changes to the articular cartilage. Hence, it was hypothesized that older articular cartilage tends to be less stiff. The indentation test is probably the most popular method used to obtain the mechanical properties for biomaterials [17–19]. This test has been refined to determine the mechanical properties of metallic materials such as the elastic modulus and hardness [20,21]. The indentation test is also employed in biomechanical applications [17–19] because special specimen preparation is not required, the test can be
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2. Anatomical background The basic anatomical background to understand equine joints was previously described [26,27]. Three different equine joints were studied: Fetlock, Carpus, and Stifle. Unlike the previous work, however, only the proximal radial carpal bone was harvested from the carpus. The proximal radial carpal bone is part of radiocarpal joint that is composed of the distal radius proximally and the proximal radial carpal bone distally. The radiocarpal joint is considered to be a hinge joint type (Fig. 2). Also, the medial aspect of the bone was investigated because most of the weight bearing and movement occur on the medial side of the carpus [37–39]. The proximal radial carpal bone is called the carpus for simplicity in this work. The radiocarpal joint shows a range of sliding and rolling motion of 90 to 100 degrees under various loading when a horse is standing, walking, and running [37–39]. Fig. 1. Organization of the articular cartilage matrix components.
3. Materials and methods 3.1. Material acquisition
performed on the intact sample tissue on the bone, and the sample is not destroyed due to the test [22]. For these reasons, the indentation test was employed to characterize the mechanical properties of the equine articular cartilage in this study. Various tip sizes and shapes of the indenters influence the determined properties, and should factor in when using the indentation test [23,24]. Specifically, the research showed that the elastic modulus of cartilage increases as the tip size of the indenter decreases [23,24]. Therefore, it is crucial to select an indenter with the proper geometry for the aims of the measurement. For instance, if a large indenter indents a concave cartilage surface, the indenter could not reach the targeted spot on the middle of the surface without touching taller parts of the sample. As another example, the use of a flat-ended indenter can result in imperfect contact between the indenter and the convex cartilage surface if the targeted peak-flat area of the cartilage surface is not as wide as the size of indenter diameter. A flat indenter also causes a stress concentration at the sharp edges of contact. Hence, a spherical indenter was employed in this work to prevent this issue. Bonnevie et al.'s work [25] was also referred to extensively to design the experimental procedures. The equine model was chosen because it provides a close approximation for human pre-clinical studies as described previously [26,27]. There are more studies that demonstrate the effectiveness of employing the equine model for human pre-clinical studies [28–30]. Based on the idea that the articular cartilage consists of the cartilage matrix and synovial fluid, Mow and his coworkers established the biphasic theory; it is both a basic and popular theory to explain the cartilage system [7,31,32]. According to the biphasic theory, cartilage is divided into two principal phases: a solid and fluid phase. The solid phase is the mesh which consists predominantly of collagens with the tangled proteoglycans. The fluid phase consists of the interstitial fluid which is mainly synovial fluid flowing through the solid phase. The mechanical properties of cartilage are characterized by this multiphasic nature based on the assumption that the cartilage matrix behaves linear elastically, is isotropic and homogeneous. This study was implemented based on this concept of the biphasic theory. Tests on plug or cylindrical samples are advantageous because ideally a uniform stress distribution will result in the cartilage. In our work, however, the cartilage surface surrounding the test location was left untouched, while many researchers have used plugs for testing [25, 33–35]. This is because the cartilage can be damaged and its properties may vary from cartilage in situ by extracting a plug from the cartilage. Anderson et al. showed the importance of extreme care in sample preparation because they observed that the articular cartilage surface is damaged by simply wiping it with a latex glove [36]. In the current work, operators did not touch the surfaces on which the measurements were performed.
Fetlock, carpal, and stifle joints were harvested from 12 deceased horses. The horses were humanely euthanized for reasons unrelated to the study. They had no history of lameness or joint surgery. From these horses, 11, 10, and 10 fresh articular cartilage surfaces were collected from the fetlock, carpus, and stifle, respectively. The information on breed, age, sex, and weight of the horses was collected as well (see Table 1). Sample populations were well distributed in each variable (breed, age, sex, and weight) as shown in Fig. 3. The 12 horses are classified into three groups depending on their ages: young, middle, and old. Horses younger than 5 years are classified as young, those in the range of 6 and 15 years as middle aged, and those older than 15 years are considered to be old. For weight, horses are classified as light (lighter than 300 kg), medium (in the rage of 300 and 500 kg), and heavy (heavier than 500 kg) groups. All articular cartilage surfaces with any damage by injury or operator error during dissection were filtered from the test samples. The joints from the same horse were surgically obtained from the Thomson Bishop Sparks State Diagnostic Laboratory within 4 h of euthanasia. After the necropsy, the joints were transported to the Auburn University Tribology Laboratory located 5 min away on campus for measurement. The joints were dissected to obtain the articular cartilage surfaces as soon as they arrived at the Tribology Laboratory. Only one of the right and
Fig. 2. The radiocarpal joint of the carpus (left) and the proximal radial carpal bone articular cartilage surface from the joint (right, the red dash line indicates the proximal radial carpal bone). (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)
H. Lee et al. / Biotribology 7 (2016) 31–37
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left joint sets were randomly chosen and used for measurement immediately after the dissection. After approximately 3 min of exposure to air during dissection, all cartilage samples were preserved in saline solution for testing. The osteochondral samples were harvested by dissection of the surrounding and associated structures and sized for measurement by a band saw. Following this, the cartilage left untouched until testing due to the reasons described in the introduction (i.e. plugs were not extracted from the surface). After testing was completed, all samples were labeled, frozen in saline, and stored.
cartilage: 10%, 20%, 30%, 35%, 40%, 45%, and 50%. The normalized displacement is essentially the average strain applied to the cartilage. The normalized displacements are calculated by the indentation depth relative to the cartilage thickness. A maximum indentation depth of 0.0861 mm was set for the cartilage from the fetlock and carpus, while 0.2147 mm was set for the cartilage from the stifle to apply 10% normalized displacement to the samples. This is based on our group's previous thickness measurement result that the articular cartilage thicknesses of the cartilage on the fetlock, carpus, and stifle were 0.8606 mm, 0.8685 mm, and 2.1466 mm, respectively [26]. Since the cartilage thickness of the fetlock and carpus were nearly identical, the indentation depth for the cartilage of the fetlock was applied to the carpus equivalently. The indentation depths at each normalized displacement are displayed in Table 2. Indentation was implemented with a velocity of 0.1 mm/s providing a constant strain rate of approximately 0.116/s. Each indentation measurement procedure followed exactly the same methodology used in Bonnevie et al.'s work except indenting velocity and depth [25]. The indenter maintained its position at the designated indentation depth for 600 s in order to reach equilibrium (i.e. the liquid is squeezed out and the force becomes practically constant). All the steps of each measurement were identical except that different indentation depths were employed. All measurements were performed on the same spot on the center of the weight bearing area. Force, indentation depth, and time were recorded during the entire duration of each experiment.
3.2. Experimental design
4. Analysis
A Bruker UMT-3 Tribometer was used to perform the indentation test to measure the mechanical properties of the articular cartilage. The UMT-3 is a versatile modular machine that measures the vertical displacement of the indenter into the cartilage at a resolution of 1 μm. It is equipped with a high-sensitivity force sensor (1 mN of resolution). A spherical indenter of physiologically relevant size is employed because it makes a relatively controlled contact with the cartilage surface in contrast to flat ended indenters as discussed in the introduction. An indenter with a 10 mm diameter was used to better simulate in-vivo opposing articular cartilage contact as shown in Fig. 4. An indentation test on a sample consisted of seven measurements with different normalized displacement was performed to the articular
Initially the authors attempted to fit a biphasic model with a linear elastic solid to the measured results, but the model could not properly describe the observed cartilage behavior. Therefore, a biphasic model with a hyperelastic solid was chosen for use with the cartilage matrix. A single-term Ogden hyperelastic model showed the best fit of the experimental data among various tested hyperelastic indentation models from Lin et al.'s work [40]. To illuminate the difference between these two behaviors beyond the Hertzian regime (i.e. the difference between a linear elastic and a hyperelastic model), the Ogden hyperelastic model in spherical indentation was compared to the Hertz model widely used in contact mechanics [41] in Fig. 5. The Ogden model boosts dramatically as displacement increases, while the Hertz model increases relatively
Table 1 Information on breed, age, sex, and weight of each horse from which the articular cartilage surfaces were harvested. No.
Breed
Age (years)
Sex
Weight (kg)
1 2 3 4 5 6 7 8 9 10 11 12
Arabian American Paint Horse Hanoverian Belgian Draft Thoroughbred Arabian Thoroughbred AQH AQH Warmblood × Connemara AQH Thoroughbred
15 12 1 9 10 23 15 24 11 3 months 3 months 16
Mare Gelding Stallion Gelding Gelding Gelding Mare Gelding Gelding Filly Filly Gelding
382 544 270 567 525 453 544 590 431 225 227 442
Fig. 3. Sample population in each variable of (a) breed, (b) age, (c) sex, and (d) weight. Numbers below the bars indicate the number of horses.
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H. Lee et al. / Biotribology 7 (2016) 31–37
Fig. 4. Schematic of the experimental setup.
linearly with a gradual slope. The difference between the two models surely vary with different material property values, but Fig. 5 merely shows how the inclusion of hyperelastic properties will create a different force to displacement behavior from the linear elastic Hertz contact model. Cartilage might behave more like a hyperelastic solid in our measurements because of the relatively large strains causing the fibers to compress together. The hyperelastic properties also could arise from the substrate effect (the bone below the cartilage). However, we believe that this is physiologically representative of the deformations in actual articular joints. The aggregate modulus of the solid phase (Es), the hyperelastic material constant (α), and fluid load fraction (F′) of the equine articular cartilage were determined at end of the relaxation step using a solution for the contact of a sphere consisting of Ogden hyperelastic material [40] as follows: F¼
α Bπa2 a−2 −1 aα−1 1−0:2 − 1−0:2 α R R
ð1aÞ
B¼
40E0 40 ¼ Es 9πð1−v2 Þ 9π
ð1bÞ
Es ¼ a¼
E0 ð1−v2 Þ
ð1cÞ
pffiffiffiffiffiffi Rδ
ð1dÞ
where F is applied load, a is the contact radius, R is the radius of the indenter, E0 is Elastic Modulus at zero strain, ν is Poisson's ratio, and δ is the indentation depth. Poisson's ratio is not characterized separately because it is incorporated into the aggregate modulus. It was theoretically verified that the larger curvature of the articular cartilage surface barely affects the characterization of the mechanical properties using elliptical contact case [41] between the spherical indenter and the curved surface of the cartilage (around 4% difference at most). Hence, the effect of the curvature of
Table 2 Applied indentation depth and duration during the indentation step at each normalized displacement. Normalized displacement
10% 20% 30% 35% 40% 45% 50%
Indentation depth (mm)
Duration (s)
Fetlock & Carpus
Stifle
Fetlock & Carpus
Stifle
0.0861 0.1721 0.2582 0.3012 0.3442 0.3873 0.4303
0.2147 0.4294 0.6441 0.7515 0.8588 0.9962 1.0735
0.861 1.721 2.582 3.012 3.442 3.873 4.303
2.147 4.294 6.441 7.515 8.588 9.962 10.735
Fig. 5. Comparison between the Ogden hyperelastic model and Hertzian contact in spherical contact where R = 5 mm, E0 = 1 MPa, ν = 0.4, δ = 0.8 mm and α = −50.
the articular cartilage surface was neglected because it is also difficult to measure. The contact radius, a, was defined following Hertz's contact model (Eq. (1d)). The extrapolated force versus time curve from the equilibration step allowed us to determine the force at equilibrium. The equilibrium was defined as the state with an assumption of infinite time in the relaxation step of the measurement at each normalized displacement using an extrapolation, as shown in Fig. 6 (b). Measurements were taken for a relatively long period of time (600 s) to allow the equilibrium to be approximate [25]. It was assumed that the force on the articular cartilage at equilibrium is supported by only the solid cartilage matrix without the support of the synovial fluid in the articular cartilage. All of the synovial fluid was considered to have been completely expelled from the cartilage. Hence, the load support by the solid cartilage matrix was defined as the residual force after the equilibrium was reached after an infinite amount of time. This allowed us to theoretically determine the force purely supported by the matrix, even if the articular cartilage did not reach the perfect equilibrium state during the equilibration step in the experiment. After seven equilibrium forces were collected, the hyperelastic contact model was fitted to the seven data points (Eqs. (1a)–(1d)). The solid phase aggregate modulus (Es) and the hyperelastic material constant (α) of the cartilage matrix itself were acquired from the fitted curve. Fluid load fraction (F′) was characterized by employing the definition from Bonnevie et al.'s work [25] as follows: F0 ¼
F− F s F
ð2Þ
where Fs is the supported force by the cartilage matrix. The fluid load fraction is a ratio of the force supported by the synovial fluid (the fluid phase in the biphasic model) to the total applied force. Since the solid (matrix) force was determined from the relaxation curve as described previously, the fluid force is merely the difference between the total force and the solid force. Hence, the fluid load fraction was characterized without direct measurement of the fluid force. Here is an example of determination of the solid phase aggregate modulus (Es), hyperelastic material constant (α), and fluid load fraction (F′) on a sample. From the indentation tests on an articular cartilage surface of the stifle, the indentation curves were obtained as shown in Fig. 6 (a). In the relaxation step of the measurement at each normalized displacement, equilibrium was acquired using an extrapolation. The equilibrium force was defined as the force when the time is set to infinite, as shown in Fig. 6 (b). The equilibrium force was assumed as the solid phase force as mentioned earlier. The solid phase forces were determined at each normalized displacement in the same manner. Seven solid phase forces from measurements were displayed as data points as shown in Fig. 6 (c). The hyperelastic contact model (Eq. 1) was fit
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line in Fig. 6 (a). From the fit hyperelastic contact equation, the solid phase aggregate modulus (Es) and the hyperelastic material constant (α) of the articular cartilage surface were characterized. The fluid load fraction (F′) at each normalized displacement was defined as the ratio of the difference between the maximum force and the solid phase force to the maximum force using Eq. (2) at each normalized displacement.
5. Results
Fig. 6. Example measurement of the solid phase aggregate modulus (Es), hyperelastic material constant (α), and fluid load fraction (F′) on an articular cartilage of the stifle: (a) force versus indentation depth curve at every normalized displacement, (b) force versus time curve at 50% normalized displacement, and (c) fit curve to seven solid phase forces data employing Ogden hyperelastic model.
to the data points. Note again that the linear elastic Hertz contact solution did not fit the data well, but the hyperelastic model appears to fit the data very well. The fit curve in Fig. 6 (c) is equivalent to a dashed
The results of testing in the three different joints for each horse are displayed in Table 3. Correlations between the material properties and signalment variables were studied (Table 4). The material properties were statistically analyzed using mixed model ANOVA. Scheffe's test was used to compare the material properties of the articular cartilage in the three different joints. The solid phase aggregate modulus does not statistically correlate with breed and sex, but it shows significant correlations with weight (p b 0.0375) and age (p b 0.0392). Significant correlations between the fluid load fraction, and both breed and sex, are also not observed, while there are highly significant correlations between the fluid load fraction and both weight (p b 0.0003) and age (p b 0.0146). The hyperelastic material constant does not show a significant statistical correlation with any of the signalment variables. The Ogden hyperelastic model showed excellent agreement with the force-displacement curves through the measurements (average R2 N 0.9684). It demonstrates that the hyperelastic model could be the best to explain the behavior of the articular cartilage. The results suggest that the solid phase aggregate modulus of the equine articular cartilage varies depending on the weight and age of a horse. The fluid load fraction of the equine articular cartilage also varies depending on the weight and age of a horse. Hence, one can conclude that the articular cartilage functions differently depending on weight and age. The relations between the mechanical properties and signalment variables were plotted on Fig. 7. It appears that the solid phase aggregate modulus and fluid load fraction tend to decrease as weight and age increase, though the trends cannot be clearly detected in each graph. In Fig. 7, the fluid load fraction is clearly more correlated to weight and age than the solid phase aggregate modulus, which agrees with the statistical results in Table 4. The hyperelastic material properties (solid phase aggregate and fluid load fraction) showed a trend of decreasing with age, which agrees that the tensile properties reducing with age as mentioned in earlier literature [9,10]. It appears that the hyperelastic properties also decrease as weight increases. As shown in Fig. 8, it appears that the weight and age of horses may loosely correlate with each other, but this is probably mostly due to the inclusion of young immature horses.
Table 3 The characterized mechanical properties in different joints for each horse. No.
1 2 3 4 5 6 7 8 9 10 11 12 Ave
Lateral Fetlock
Medial Fetlock
Carpus
Stifle
Es
α
F′
Es
α
F′
Es
α
F′
Es
α
F′
0.001 1.158 – 0.484 0.426 0.083 1.248 0.573 0.961 – 0.212 0.544 0.632
−187.0 −74.44 – −64.22 −70.55 −35.68 −34.92 −54.32 −53.25 – −45.45 −50.13 −67.00
0.711 0.675 – 0.730 0.764 0.670 0.742 0.761 0.715 – 0.835 0.671 0.727
0.815 – 1.382 0.451 0.559 0.092 1.417 1.300 0.432 1.221 0.231 0.851 0.796
−57.08 – −45.53 −82.69 −63.33 −27.80 −41.23 −32.47 −47.95 −34.02 −84.91 −56.70 −52.16
0.689 – 0.835 0.762 0.676 0.694 0.784 0.745 0.721 0.852 0.774 0.679 0.747
0.547 2.453 1.146 0.268 – 0.244 0.370 – 3.679 1.101 0.012 0.821 0.910
−58.83 14.43 1.653 −60.11 – −14.72 −71.34 −289.9 −25.62 −28.44 −120.9 −50.13 −41.40
0.685 0.662 0.823 0.759 – 0.553 0.543 – 0.590 0.843 0.793 0.616 0.686
0.050 0.682 0.074 0.143 – – 0.410 0.022 0.108 0.023 0.248 0.007 0.177
−65.74 −31.06 −64.97 −59.13 – – −42.87 −71.94 −51.63 −78.15 −44.65 −85.59 −59.57
0.593 0.567 0.739 0.698 – – 0.664 0.578 0.669 0.761 0.777 0.335 0.638
Es: solid phase aggregate modulus (MPa), F′: fluid load fraction, α: hyperelastic material constant, –: no data obtained.
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Table 4 Correlations between each material property and each variable.
Es F′
α
Weight
Age
Breed
Sex
Significant (p b 0.0375) Highly significant (p b 0.0003) ×
Significant (p b 0.0392) Highly significant (p b 0.0146) ×
×
×
×
×
×
×
Es: solid phase aggregate modulus, F′: fluid load fraction, α: hyperelastic material constant, ×: indicator of no statistically significant association.
6. Discussion and conclusions
Es (MPa)
According to the study, to find correlations between the mechanical properties of equine articular cartilage (Es, α, F′) and the signalment variables (breed, age, sex, and weight), breed and sex were not significantly influential variables on the variation of any of the material properties, while the solid phase aggregate modulus showed a statistically significant correlation with age and weight. The fluid load fraction also displayed a significant correlation with age and weight. There was no significant correlation between the hyperelastic material constant and any of the signalment variables. It was also found that weight impacts much more on the variation of the mechanical properties than age. All phenomena of the articular cartilage through the measurements were successfully characterized by one closed form model (the Ogden hyperelastic model) as proposed previously in the Analysis section [40]. The observed hyperelasticity of the articular cartilage might not be due solely to the cartilage behavior itself, but also the substrate effect [40,41]. It appears that the normalized displacements up to 50% in articular cartilage are nondestructive because the repeated forcedisplacement curves of the same cartilage surface followed on nearly the same line. The authors are unaware of any previous reports on the systematic influence of the age or weight on the elastic behavior of mammalian articular cartilage. However, similar work correlating the collagen fiber arrangement between different species was found. Kääb et al. compared the collagen fiber arrangement of the articular cartilage of the medial tibial plateau from human, cow, pig, dog, sheep, rabbit and rat joints [42]. They found that the maximum thickness of the articular cartilage increased as weight increased and were therefore correlated (the heavier animal was, the thicker articular cartilage was). It illustrated that weight can affect the variation of the mechanical properties of the articular cartilage because the properties can vary due to a variation of the cartilage thickness. The lubricating performance of cartilage is also
4
4
2
2
0 200
F
dependent on its thickness. Hence, it seems reasonable that the material properties also correlate to the weight. In this work, it was verified that material properties are dependent on age and weight. This work showed that cartilage properties might be influenced due to age and subsequent degradation over time. A higher weight might also cause the cartilage to degrade or change more over time, however, the cartilage could also adapt to higher weights to maintain functionality. The findings in this work could be useful for proper repairing, healing and designing biomimetic artificial articular cartilage. For instance, the repairing process of cartilage varies depending on the individual. This is because the degradation rate of the articular cartilage varies by individual, and aging is one of reasons for the variation of the degradation rate; aging accelerates the degradation rate [10,43,44]. The age of each person, therefore, affects the repairing process for their cartilage [45,46]. As another example, the articular cartilage healing time of a heavier person should be significantly different from one with lighter weight. This is because the material properties directly associated with the performance of the articular cartilage vary with weight, and the time for the cartilage recover to healthy condition would vary. On the other hand, sex and breed are not correlated with the mechanical properties of articular cartilage. This means sex and breed should not be considered for any processes of repairing, healing, or designing artificial articular cartilage. Being aware of the absence of correlation between mechanical properties and specific parameters such as sex and breed in this study, therefore, would help in saving time and resources in research as well as treatment. Especially in veterinary medicine, which deals with various breeds, there should be no need for veterinarians to be concerned about variation of treatment depending on breed, allowing them to focus fully on improvement of general care methodologies. It could also contribute to improving the assessment system of articular cartilage; considering the two influential signalment parameters would lead to more advanced evaluation of the cartilage degeneration and regeneration or repair of tissue to identify
300
400
500
600
0 0
1
1
0.5
0.5
0 200
300
400
Weight (kg)
500
600
0 0
10
20
30
10
20
30
Age (Years)
Fig. 7. Relations between weight and the solid phase aggregate modulus as well as fluid load fraction were displayed (left). Also, relations between age and the solid phase aggregate modulus as well as fluid load fraction were displayed (right). All solid phase aggregate moduli and fluid load fraction values measured on different joints were plotted.
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700
Weight (kg)
600 500 400 300 200 100 0
5
10 15 Age (years)
20
25
Fig. 8. Relation between weight and age of the horses.
the cartilage health more accurately for proper treatments or diagnosis [47–49]. Awareness of the expected mechanical properties of healthy articular cartilage, considering the correlations described in this work, could help avoid misinterpretations of the healing process or the degradation process followed by diagnosis with incorrectly expected cartilage performance directly related to the mechanical properties. Acknowledgements The authors gratefully acknowledge the financial support of the Auburn University Intramural Grant Program, the Auburn University Undergraduate Research Fellowship Program, and the Merial-NIH Veterinary Scholar Program. References [1] H. Bang, Y.-l. Chiu, S.G. Memtsoudis, L.A. Mandl, A.G. Della Valle, A.I. Mushlin, et al., Total hip and total knee arthroplasties: trends and disparities revisited, Am. J. Orthop. 39 (2010) E95–102. [2] E.S. Fisher, J. Bell, I. Tomek, A. Esty, D. Goodman, K. Bronner, Trends and regional variation in hip, knee, and shoulder replacement, Dartmouth Atlas Surgery Report, The Dartmouth Institute for Health Policy and Clinical Practice, Hanover, NH, 2010. [3] S.M. Kurtz, K.L. Ong, E. Lau, K.J. Bozic, Impact of the economic downturn on total joint replacement demand in the United States, The Journal of Bone & Joint Surgery 96 (2014) 624–630. [4] M.D. Buschmann, J. Soulhat, A. Shirazi-Adl, J.S. Jurvelin, E.B. Hunziker, Confined compression of articular cartilage: linearity in ramp and sinusoidal tests and the importance of interdigitation and incomplete confinement, J. Biomech. 31 (1997) 171–178. [5] K.M. Clements, A.P. Hollander, M. Sharif, M.A. Adams, Cyclic loading can denature type II collagen in articular cartilage, Connect. Tissue Res. 45 (2004) 174–180. [6] L. Li, M. Buschmann, A. Shirazi-Adl, Fibril stiffening accounts for strain-dependent stiffness of articular cartilage in unconfined compression, Transactions of the Orthopaedic Research Society 26 (2001) 425. [7] V. Mow, Biphasic creep and stress relaxation of articular cartilage in compression, J. Biomech. Eng. 102 (1980) 73–84. [8] L. Røhl, F. Linde, A. Odgaard, I. Hvid, Simultaneous measurement of stiffness and energy absorptive properties of articular cartilage and subchondral trabecular bone, Proceedings of the Institution of Mechanical Engineers, Part H: Journal of Engineering in Medicine 211 (1997) 257–264. [9] G. Kempson, Relationship between the tensile properties of articular cartilage from the human knee and age, Ann. Rheum. Dis. 41 (1982) 508–511. [10] G.E. Kempson, Age-related changes in the tensile properties of human articular cartilage: a comparative study between the femoral head of the hip joint and the talus of the ankle joint, Biochimica et Biophysica Acta (BBA)-General Subjects 1075 (1991) 223–230. [11] R. Karvonen, W. Negendank, R. Teitge, A. Reed, P. Miller, F. Fernandez-Madrid, Factors affecting articular cartilage thickness in osteoarthritis and aging, J. Rheumatol. 21 (1994) 1310–1318. [12] C. Novelli, J. Costa, R. Souza, Effects of aging and physical activity on articular cartilage: a literature review, Braz. J. Morphol. Sci 29 (2012) 1–17. [13] E.L. Radin, D.A. Swann, I.L. Paul, P.J. Mcgrath, Factors influencing articular cartilage wear in vitro, Arthritis & Rheumatism 25 (1982) 974–980. [14] F.M. Hall, G. Wyshak, Thickness of articular cartilage in the normal knee, J. Bone Joint Surg. Am. 62 (1980) 408–413. [15] I. Otterness, M.-P. Le Graverand, F. Eckstein, Allometric relationships between knee cartilage volume, thickness, surface area and body dimensions, Osteoarthr. Cartil. 16 (2008) 34–40.
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[16] D. Frisbie, Synovial joint biology and pathobiology, in: J.A. Auer, J.A. Stick (Eds.), Equine Surgery, third ed.Elsevier, Saunders, St. Louis, Mo 2006, pp. 1036–1055. [17] R.C. Appleyard, M.V. Swain, S. Khanna, G.A. Murrell, The accuracy and reliability of a novel handheld dynamic indentation probe for analysing articular cartilage, Phys. Med. Biol. 46 (2001) 541–550. [18] J. Huyghe, J. Janssen, Quadriphasic mechanics of swelling incompressible porous media, Int. J. Eng. Sci. 35 (1997) 793–802. [19] E. Poiré, Advanced Surface Mechanical Testing of Materials for Medical Applications, 2009. [20] W.C. Oliver, G.M. Pharr, Improved technique for determining hardness and elastic modulus using load and displacement sensing indentation experiments, J. Mater. Res. 7 (1992) 1564–1583. [21] G. Pharr, W. Oliver, F. Brotzen, On the generality of the relationship among contact stiffness, contact area, and elastic modulus during indentation, J. Mater. Res. 7 (1992) 613–617. [22] X. Lu, V. Mow, Biomechanics of articular cartilage and determination of material properties, Medicine + Science in Sports + Exercise 40 (2008) 193–199. [23] H. Jin, J.L. Lewis, Determination of Poisson's ratio of articular cartilage by indentation using different-sized indenters, J. Biomech. Eng. 126 (2004) 138–145. [24] N.K. Simha, H. Jin, M.L. Hall, S. Chiravarambath, J.L. Lewis, Effect of indenter size on elastic modulus of cartilage measured by indentation, J. Biomech. Eng. 129 (2007) 767–775. [25] E.D. Bonnevie, V.J. Baro, L. Wang, D.L. Burris, Fluid load support during localized indentation of cartilage with a spherical probe, J. Biomech. 45 (Apr 2012) 1036–1041. [26] H. Lee, W.G. Kirkland, R.N. Whitmore, K.M. Theis, H.E. Young, A.J. Richardson, et al., Comparison of equine articular cartilage thickness in various joints, Connect. Tissue Res. 55 (2014) 339–347. [27] H. Lee, K.M. Theis, R.L. Jackson, R.R. Hanson, Equine articular cartilage stiffness determination using indentation, J. Tribol. 137 (2015) 011201. [28] D. Frisbie, M. Cross, C. McIlwraith, A comparative study of articular cartilage thickness in the stifle of animal species used in human pre-clinical studies compared to articular cartilage thickness in the human knee, Vet. Comp. Orthop. Traumatol. 19 (2006) 142–146. [29] J. Malda, K. Benders, T. Klein, J. de Grauw, M. Kik, D. Hutmacher, et al., Comparative study of depth-dependent characteristics of equine and human osteochondral tissue from the medial and lateral femoral condyles, Osteoarthritis and cartilage 20 (2012) 1147–1151. [30] C.W. McIlwraith, L.A. Fortier, D.D. Frisbie, A.J. Nixon, Equine models of articular cartilage repair, Cartilage 2 (2011) 317–326. [31] A. Mak, W. Lai, V. Mow, Biphasic indentation of articular cartilage—I. Theoretical analysis, J. Biomech. 20 (1987) 703–714. [32] V. Mow, M. Gibbs, W. Lai, W. Zhu, K. Athanasiou, Biphasic indentation of articular cartilage—II. A numerical algorithm and an experimental study, J. Biomech. 22 (1989) 853–861. [33] M.R. DiSilvestro, J.-K.F. Suh, A cross-validation of the biphasic poroviscoelastic model of articular cartilage in unconfined compression, indentation, and confined compression, J. Biomech. 34 (2001) 519–525. [34] Y. Merkher, S. Sivan, I. Etsion, A. Maroudas, G. Halperin, A. Yosef, in: Parma (Ed.), A rational friction test using a human cartilage on-cartilage arrangement, 2006. [35] G. Verberne, Y. Merkher, G. Halperin, A. Maroudas, I. Etsion, Techniques for assessment of wear between human cartilage surfaces, Wear 266 (2009) 1216–1223. [36] R. Sayles, T. Thomas, J. Anderson, I. Haslock, A. Unsworth, Measurement of the surface microgeometry of articular cartilage, J. Biomech. 12 (1979) 257–267. [37] J.F. Burn, B. Portus, C. Brockington, The effect of speed and gradient on hyperextension of the equine carpus, Vet. J. 171 (2006) 169–171. [38] H. Clayton, D. Sha, J. Stick, D. Mullineaux, Three-dimensional carpal kinematics of trotting horses, Equine Vet. J. 36 (2004) 671–676. [39] K.M. Dyce, W.O. Sack, C.J.G. Wensing, Textbook of Veterinary Anatomy, Saunders, 2009. [40] D. Lin, D. Shreiber, E. Dimitriadis, F. Horkay, Spherical indentation of soft matter beyond the Hertzian regime: numerical and experimental validation of hyperelastic models, Biomechanics and Modeling in Mechanobiology 8 (2009) 345–358 2009/ 10/01. [41] K.L. Johnson, K.L. Johnson, Contact Mechanics, Cambridge University Press, 1987. [42] M. Kääb, I. Ap Gwynn, H. Nötzli, Collagen fibre arrangement in the tibial plateau articular cartilage of man and other mammalian species, J. Anat. 193 (1998) 23–34. [43] P.J. Roughley, R. White, Age-related changes in the structure of the proteoglycan subunits from human articular cartilage, J. Biol. Chem. 255 (1980) 217–224. [44] R. Sztrolovics, M. Alini, P.J. Roughley, Aggrecan degradation in human intervertebral disc and articular cartilage, Biochem. J. 326 (1997) 235–241. [45] B. Johnstone, J.U. Yoo, Autologous mesenchymal progenitor cells in articular cartilage repair, Clin. Orthop. Relat. Res. 367 (1999) S156–S162. [46] J.A. Martin, J.A. Buckwalter, The role of chondrocyte senescence in the pathogenesis of osteoarthritis and in limiting cartilage repair, J. Bone Joint Surg. Am. 85 (2003) 106–110. [47] A.I. Caplan, M. Elyaderani, Y. Mochizuki, S. Wakitani, V.M. Goldberg, Overview: principles of cartilage repair and regeneration, Clin. Orthop. Relat. Res. 342 (1997) 254–269. [48] E. Hunziker, Articular cartilage repair: basic science and clinical progress. A review of the current status and prospects, Osteoarthr. Cartil. 10 (2002) 432–463. [49] M. Brittberg, C.S. Winalski, Evaluation of cartilage injuries and repair, The Journal of Bone & Joint Surgery 85 (2003) 58–69.
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Biotribology journal homepage: http://www.elsevier.com/locate/biotri
Correlation between signalment and the biphasic hyperelastic mechanical properties of equine articular cartilage Hyeon Lee a,⁎, William D. Campbell a, Margaret E. Canning b, Kelcie M. Theis b, Hannah Y. Ennis b, Robert L. Jackson a, James C. Wright b, R. Reid Hanson b a b
Department of Mechanical Engineering, Samuel Ginn College of Engineering, Auburn University, Auburn, AL 36849, United States Department of Clinical Sciences, College of Veterinary Medicine, Auburn University, Auburn, AL 36849, United States
a r t i c l e
i n f o
Article history: Received 8 April 2016 Received in revised form 23 June 2016 Accepted 30 July 2016 Available online 01 August 2016 Keywords: Equine articular cartilage Signalment Hyperelasticity Correlation
a b s t r a c t The correlation between mechanical properties from the equine articular cartilage and signalment was investigated. Fresh articular cartilage of fetlock, carpus, and stifle were harvested from 12 deceased horses with information on the breed, age, sex, and weight within 4 h of euthanasia for measurements. Seven indentation tests at different normalized displacements of 10, 20, 30, 35, 40, 45, and 50% of the cartilage thickness were performed with a spherical probe indenting at 0.1 mm/s velocity. The solid matrix of the cartilage was found to follow a hyper-elastic material behavior defined by Ogden; the solid phase aggregate modulus (Ea), hyperelastic material constant (α), and fluid load fraction (F′) of the cartilage were characterized. The characterized material properties were statistically analyzed using a mixed model ANOVA and Scheffe's test to check the correlation between the properties and signalment variables (breed, age, sex, and weight). There were correlations between both the solid phase aggregate modulus and age (p b 0.0392) and weight (p b 0.0375). The fluid load fraction also correlated with both age (p b 0.0146) and weight (p b 0.0003). Breed and sex were not statistically significant variables affecting the variation of theses material properties. No statistically significant correlations between the hyperelastic material constant and the signalment variables were observed. © 2016 Elsevier Ltd. All rights reserved.
1. Introduction Articular cartilage has been extensively researched to understand its characteristics in order to better design more durable and comfortable artificial joints. In addition, the rates of primary and revision hip and knee arthroplasties have increased from 1993 to 2010 as the aging of the population has accelerated [1–3]. There has also been a significant effort to find how biological factors affect the behavior of the articular cartilage [4–8]. For instance, Kempson performed tensile testing on the cartilage surfaces from humans (the femoral head, the talus of the ankle, and the femoral condyle of the knee) to characterize the effects of age [9,10]. The work demonstrated that tensile properties of the cartilage reduce with aging. However, no research has demonstrated systematic correlations between the various signalment parameters (e.g. age, weight, etc.) and the material properties of the articular cartilage. It seems to be important to understand the correlations because signalment parameters are linked with physical, physiological, and chemical factors that could systematically affect the change of cartilage performance, more specifically the mechanical properties [11–13]. This is because understanding how different parameters affect the cartilage ⁎ Corresponding author at: Department of Mechanical Engineering, Virginia Polytechnic Institute and State University, Blacksburg, VA 24061, United States. E-mail address: [email protected] (H. Lee).
http://dx.doi.org/10.1016/j.biotri.2016.07.001 2352-5738/© 2016 Elsevier Ltd. All rights reserved.
properties can help in precise analysis of the articular cartilage and joint functions for proper repairing, healing and creating of artificial replacement cartilage [14,15]. Therefore, mechanical measurements were implemented on equine articular cartilage to find the correlation between the signalment variables (breed, age, sex, and weight) and the material properties of fresh equine articular cartilage. Collagen in the cartilage serves as the basic framework around which other components are settled, as shown in Fig. 1. In addition, the collagen network plays a major role among the solid components of the matrix in supporting external loads. It counteracts the compressive and shear stresses generated by the external loads. The collagen fibrils are submerged in a gel of glycosaminoglycan (GAGs) and water. Since the ability of the cartilage matrix to retain synovial fluid decreases with age, the cartilage gets dehydrated [16]. Eventually, the dehydrated cartilage causes poor lubrication in the joint, triggering an inflammatory cascade and eventual degenerative changes to the articular cartilage. Hence, it was hypothesized that older articular cartilage tends to be less stiff. The indentation test is probably the most popular method used to obtain the mechanical properties for biomaterials [17–19]. This test has been refined to determine the mechanical properties of metallic materials such as the elastic modulus and hardness [20,21]. The indentation test is also employed in biomechanical applications [17–19] because special specimen preparation is not required, the test can be
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2. Anatomical background The basic anatomical background to understand equine joints was previously described [26,27]. Three different equine joints were studied: Fetlock, Carpus, and Stifle. Unlike the previous work, however, only the proximal radial carpal bone was harvested from the carpus. The proximal radial carpal bone is part of radiocarpal joint that is composed of the distal radius proximally and the proximal radial carpal bone distally. The radiocarpal joint is considered to be a hinge joint type (Fig. 2). Also, the medial aspect of the bone was investigated because most of the weight bearing and movement occur on the medial side of the carpus [37–39]. The proximal radial carpal bone is called the carpus for simplicity in this work. The radiocarpal joint shows a range of sliding and rolling motion of 90 to 100 degrees under various loading when a horse is standing, walking, and running [37–39]. Fig. 1. Organization of the articular cartilage matrix components.
3. Materials and methods 3.1. Material acquisition
performed on the intact sample tissue on the bone, and the sample is not destroyed due to the test [22]. For these reasons, the indentation test was employed to characterize the mechanical properties of the equine articular cartilage in this study. Various tip sizes and shapes of the indenters influence the determined properties, and should factor in when using the indentation test [23,24]. Specifically, the research showed that the elastic modulus of cartilage increases as the tip size of the indenter decreases [23,24]. Therefore, it is crucial to select an indenter with the proper geometry for the aims of the measurement. For instance, if a large indenter indents a concave cartilage surface, the indenter could not reach the targeted spot on the middle of the surface without touching taller parts of the sample. As another example, the use of a flat-ended indenter can result in imperfect contact between the indenter and the convex cartilage surface if the targeted peak-flat area of the cartilage surface is not as wide as the size of indenter diameter. A flat indenter also causes a stress concentration at the sharp edges of contact. Hence, a spherical indenter was employed in this work to prevent this issue. Bonnevie et al.'s work [25] was also referred to extensively to design the experimental procedures. The equine model was chosen because it provides a close approximation for human pre-clinical studies as described previously [26,27]. There are more studies that demonstrate the effectiveness of employing the equine model for human pre-clinical studies [28–30]. Based on the idea that the articular cartilage consists of the cartilage matrix and synovial fluid, Mow and his coworkers established the biphasic theory; it is both a basic and popular theory to explain the cartilage system [7,31,32]. According to the biphasic theory, cartilage is divided into two principal phases: a solid and fluid phase. The solid phase is the mesh which consists predominantly of collagens with the tangled proteoglycans. The fluid phase consists of the interstitial fluid which is mainly synovial fluid flowing through the solid phase. The mechanical properties of cartilage are characterized by this multiphasic nature based on the assumption that the cartilage matrix behaves linear elastically, is isotropic and homogeneous. This study was implemented based on this concept of the biphasic theory. Tests on plug or cylindrical samples are advantageous because ideally a uniform stress distribution will result in the cartilage. In our work, however, the cartilage surface surrounding the test location was left untouched, while many researchers have used plugs for testing [25, 33–35]. This is because the cartilage can be damaged and its properties may vary from cartilage in situ by extracting a plug from the cartilage. Anderson et al. showed the importance of extreme care in sample preparation because they observed that the articular cartilage surface is damaged by simply wiping it with a latex glove [36]. In the current work, operators did not touch the surfaces on which the measurements were performed.
Fetlock, carpal, and stifle joints were harvested from 12 deceased horses. The horses were humanely euthanized for reasons unrelated to the study. They had no history of lameness or joint surgery. From these horses, 11, 10, and 10 fresh articular cartilage surfaces were collected from the fetlock, carpus, and stifle, respectively. The information on breed, age, sex, and weight of the horses was collected as well (see Table 1). Sample populations were well distributed in each variable (breed, age, sex, and weight) as shown in Fig. 3. The 12 horses are classified into three groups depending on their ages: young, middle, and old. Horses younger than 5 years are classified as young, those in the range of 6 and 15 years as middle aged, and those older than 15 years are considered to be old. For weight, horses are classified as light (lighter than 300 kg), medium (in the rage of 300 and 500 kg), and heavy (heavier than 500 kg) groups. All articular cartilage surfaces with any damage by injury or operator error during dissection were filtered from the test samples. The joints from the same horse were surgically obtained from the Thomson Bishop Sparks State Diagnostic Laboratory within 4 h of euthanasia. After the necropsy, the joints were transported to the Auburn University Tribology Laboratory located 5 min away on campus for measurement. The joints were dissected to obtain the articular cartilage surfaces as soon as they arrived at the Tribology Laboratory. Only one of the right and
Fig. 2. The radiocarpal joint of the carpus (left) and the proximal radial carpal bone articular cartilage surface from the joint (right, the red dash line indicates the proximal radial carpal bone). (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)
H. Lee et al. / Biotribology 7 (2016) 31–37
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left joint sets were randomly chosen and used for measurement immediately after the dissection. After approximately 3 min of exposure to air during dissection, all cartilage samples were preserved in saline solution for testing. The osteochondral samples were harvested by dissection of the surrounding and associated structures and sized for measurement by a band saw. Following this, the cartilage left untouched until testing due to the reasons described in the introduction (i.e. plugs were not extracted from the surface). After testing was completed, all samples were labeled, frozen in saline, and stored.
cartilage: 10%, 20%, 30%, 35%, 40%, 45%, and 50%. The normalized displacement is essentially the average strain applied to the cartilage. The normalized displacements are calculated by the indentation depth relative to the cartilage thickness. A maximum indentation depth of 0.0861 mm was set for the cartilage from the fetlock and carpus, while 0.2147 mm was set for the cartilage from the stifle to apply 10% normalized displacement to the samples. This is based on our group's previous thickness measurement result that the articular cartilage thicknesses of the cartilage on the fetlock, carpus, and stifle were 0.8606 mm, 0.8685 mm, and 2.1466 mm, respectively [26]. Since the cartilage thickness of the fetlock and carpus were nearly identical, the indentation depth for the cartilage of the fetlock was applied to the carpus equivalently. The indentation depths at each normalized displacement are displayed in Table 2. Indentation was implemented with a velocity of 0.1 mm/s providing a constant strain rate of approximately 0.116/s. Each indentation measurement procedure followed exactly the same methodology used in Bonnevie et al.'s work except indenting velocity and depth [25]. The indenter maintained its position at the designated indentation depth for 600 s in order to reach equilibrium (i.e. the liquid is squeezed out and the force becomes practically constant). All the steps of each measurement were identical except that different indentation depths were employed. All measurements were performed on the same spot on the center of the weight bearing area. Force, indentation depth, and time were recorded during the entire duration of each experiment.
3.2. Experimental design
4. Analysis
A Bruker UMT-3 Tribometer was used to perform the indentation test to measure the mechanical properties of the articular cartilage. The UMT-3 is a versatile modular machine that measures the vertical displacement of the indenter into the cartilage at a resolution of 1 μm. It is equipped with a high-sensitivity force sensor (1 mN of resolution). A spherical indenter of physiologically relevant size is employed because it makes a relatively controlled contact with the cartilage surface in contrast to flat ended indenters as discussed in the introduction. An indenter with a 10 mm diameter was used to better simulate in-vivo opposing articular cartilage contact as shown in Fig. 4. An indentation test on a sample consisted of seven measurements with different normalized displacement was performed to the articular
Initially the authors attempted to fit a biphasic model with a linear elastic solid to the measured results, but the model could not properly describe the observed cartilage behavior. Therefore, a biphasic model with a hyperelastic solid was chosen for use with the cartilage matrix. A single-term Ogden hyperelastic model showed the best fit of the experimental data among various tested hyperelastic indentation models from Lin et al.'s work [40]. To illuminate the difference between these two behaviors beyond the Hertzian regime (i.e. the difference between a linear elastic and a hyperelastic model), the Ogden hyperelastic model in spherical indentation was compared to the Hertz model widely used in contact mechanics [41] in Fig. 5. The Ogden model boosts dramatically as displacement increases, while the Hertz model increases relatively
Table 1 Information on breed, age, sex, and weight of each horse from which the articular cartilage surfaces were harvested. No.
Breed
Age (years)
Sex
Weight (kg)
1 2 3 4 5 6 7 8 9 10 11 12
Arabian American Paint Horse Hanoverian Belgian Draft Thoroughbred Arabian Thoroughbred AQH AQH Warmblood × Connemara AQH Thoroughbred
15 12 1 9 10 23 15 24 11 3 months 3 months 16
Mare Gelding Stallion Gelding Gelding Gelding Mare Gelding Gelding Filly Filly Gelding
382 544 270 567 525 453 544 590 431 225 227 442
Fig. 3. Sample population in each variable of (a) breed, (b) age, (c) sex, and (d) weight. Numbers below the bars indicate the number of horses.
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H. Lee et al. / Biotribology 7 (2016) 31–37
Fig. 4. Schematic of the experimental setup.
linearly with a gradual slope. The difference between the two models surely vary with different material property values, but Fig. 5 merely shows how the inclusion of hyperelastic properties will create a different force to displacement behavior from the linear elastic Hertz contact model. Cartilage might behave more like a hyperelastic solid in our measurements because of the relatively large strains causing the fibers to compress together. The hyperelastic properties also could arise from the substrate effect (the bone below the cartilage). However, we believe that this is physiologically representative of the deformations in actual articular joints. The aggregate modulus of the solid phase (Es), the hyperelastic material constant (α), and fluid load fraction (F′) of the equine articular cartilage were determined at end of the relaxation step using a solution for the contact of a sphere consisting of Ogden hyperelastic material [40] as follows: F¼
α Bπa2 a−2 −1 aα−1 1−0:2 − 1−0:2 α R R
ð1aÞ
B¼
40E0 40 ¼ Es 9πð1−v2 Þ 9π
ð1bÞ
Es ¼ a¼
E0 ð1−v2 Þ
ð1cÞ
pffiffiffiffiffiffi Rδ
ð1dÞ
where F is applied load, a is the contact radius, R is the radius of the indenter, E0 is Elastic Modulus at zero strain, ν is Poisson's ratio, and δ is the indentation depth. Poisson's ratio is not characterized separately because it is incorporated into the aggregate modulus. It was theoretically verified that the larger curvature of the articular cartilage surface barely affects the characterization of the mechanical properties using elliptical contact case [41] between the spherical indenter and the curved surface of the cartilage (around 4% difference at most). Hence, the effect of the curvature of
Table 2 Applied indentation depth and duration during the indentation step at each normalized displacement. Normalized displacement
10% 20% 30% 35% 40% 45% 50%
Indentation depth (mm)
Duration (s)
Fetlock & Carpus
Stifle
Fetlock & Carpus
Stifle
0.0861 0.1721 0.2582 0.3012 0.3442 0.3873 0.4303
0.2147 0.4294 0.6441 0.7515 0.8588 0.9962 1.0735
0.861 1.721 2.582 3.012 3.442 3.873 4.303
2.147 4.294 6.441 7.515 8.588 9.962 10.735
Fig. 5. Comparison between the Ogden hyperelastic model and Hertzian contact in spherical contact where R = 5 mm, E0 = 1 MPa, ν = 0.4, δ = 0.8 mm and α = −50.
the articular cartilage surface was neglected because it is also difficult to measure. The contact radius, a, was defined following Hertz's contact model (Eq. (1d)). The extrapolated force versus time curve from the equilibration step allowed us to determine the force at equilibrium. The equilibrium was defined as the state with an assumption of infinite time in the relaxation step of the measurement at each normalized displacement using an extrapolation, as shown in Fig. 6 (b). Measurements were taken for a relatively long period of time (600 s) to allow the equilibrium to be approximate [25]. It was assumed that the force on the articular cartilage at equilibrium is supported by only the solid cartilage matrix without the support of the synovial fluid in the articular cartilage. All of the synovial fluid was considered to have been completely expelled from the cartilage. Hence, the load support by the solid cartilage matrix was defined as the residual force after the equilibrium was reached after an infinite amount of time. This allowed us to theoretically determine the force purely supported by the matrix, even if the articular cartilage did not reach the perfect equilibrium state during the equilibration step in the experiment. After seven equilibrium forces were collected, the hyperelastic contact model was fitted to the seven data points (Eqs. (1a)–(1d)). The solid phase aggregate modulus (Es) and the hyperelastic material constant (α) of the cartilage matrix itself were acquired from the fitted curve. Fluid load fraction (F′) was characterized by employing the definition from Bonnevie et al.'s work [25] as follows: F0 ¼
F− F s F
ð2Þ
where Fs is the supported force by the cartilage matrix. The fluid load fraction is a ratio of the force supported by the synovial fluid (the fluid phase in the biphasic model) to the total applied force. Since the solid (matrix) force was determined from the relaxation curve as described previously, the fluid force is merely the difference between the total force and the solid force. Hence, the fluid load fraction was characterized without direct measurement of the fluid force. Here is an example of determination of the solid phase aggregate modulus (Es), hyperelastic material constant (α), and fluid load fraction (F′) on a sample. From the indentation tests on an articular cartilage surface of the stifle, the indentation curves were obtained as shown in Fig. 6 (a). In the relaxation step of the measurement at each normalized displacement, equilibrium was acquired using an extrapolation. The equilibrium force was defined as the force when the time is set to infinite, as shown in Fig. 6 (b). The equilibrium force was assumed as the solid phase force as mentioned earlier. The solid phase forces were determined at each normalized displacement in the same manner. Seven solid phase forces from measurements were displayed as data points as shown in Fig. 6 (c). The hyperelastic contact model (Eq. 1) was fit
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line in Fig. 6 (a). From the fit hyperelastic contact equation, the solid phase aggregate modulus (Es) and the hyperelastic material constant (α) of the articular cartilage surface were characterized. The fluid load fraction (F′) at each normalized displacement was defined as the ratio of the difference between the maximum force and the solid phase force to the maximum force using Eq. (2) at each normalized displacement.
5. Results
Fig. 6. Example measurement of the solid phase aggregate modulus (Es), hyperelastic material constant (α), and fluid load fraction (F′) on an articular cartilage of the stifle: (a) force versus indentation depth curve at every normalized displacement, (b) force versus time curve at 50% normalized displacement, and (c) fit curve to seven solid phase forces data employing Ogden hyperelastic model.
to the data points. Note again that the linear elastic Hertz contact solution did not fit the data well, but the hyperelastic model appears to fit the data very well. The fit curve in Fig. 6 (c) is equivalent to a dashed
The results of testing in the three different joints for each horse are displayed in Table 3. Correlations between the material properties and signalment variables were studied (Table 4). The material properties were statistically analyzed using mixed model ANOVA. Scheffe's test was used to compare the material properties of the articular cartilage in the three different joints. The solid phase aggregate modulus does not statistically correlate with breed and sex, but it shows significant correlations with weight (p b 0.0375) and age (p b 0.0392). Significant correlations between the fluid load fraction, and both breed and sex, are also not observed, while there are highly significant correlations between the fluid load fraction and both weight (p b 0.0003) and age (p b 0.0146). The hyperelastic material constant does not show a significant statistical correlation with any of the signalment variables. The Ogden hyperelastic model showed excellent agreement with the force-displacement curves through the measurements (average R2 N 0.9684). It demonstrates that the hyperelastic model could be the best to explain the behavior of the articular cartilage. The results suggest that the solid phase aggregate modulus of the equine articular cartilage varies depending on the weight and age of a horse. The fluid load fraction of the equine articular cartilage also varies depending on the weight and age of a horse. Hence, one can conclude that the articular cartilage functions differently depending on weight and age. The relations between the mechanical properties and signalment variables were plotted on Fig. 7. It appears that the solid phase aggregate modulus and fluid load fraction tend to decrease as weight and age increase, though the trends cannot be clearly detected in each graph. In Fig. 7, the fluid load fraction is clearly more correlated to weight and age than the solid phase aggregate modulus, which agrees with the statistical results in Table 4. The hyperelastic material properties (solid phase aggregate and fluid load fraction) showed a trend of decreasing with age, which agrees that the tensile properties reducing with age as mentioned in earlier literature [9,10]. It appears that the hyperelastic properties also decrease as weight increases. As shown in Fig. 8, it appears that the weight and age of horses may loosely correlate with each other, but this is probably mostly due to the inclusion of young immature horses.
Table 3 The characterized mechanical properties in different joints for each horse. No.
1 2 3 4 5 6 7 8 9 10 11 12 Ave
Lateral Fetlock
Medial Fetlock
Carpus
Stifle
Es
α
F′
Es
α
F′
Es
α
F′
Es
α
F′
0.001 1.158 – 0.484 0.426 0.083 1.248 0.573 0.961 – 0.212 0.544 0.632
−187.0 −74.44 – −64.22 −70.55 −35.68 −34.92 −54.32 −53.25 – −45.45 −50.13 −67.00
0.711 0.675 – 0.730 0.764 0.670 0.742 0.761 0.715 – 0.835 0.671 0.727
0.815 – 1.382 0.451 0.559 0.092 1.417 1.300 0.432 1.221 0.231 0.851 0.796
−57.08 – −45.53 −82.69 −63.33 −27.80 −41.23 −32.47 −47.95 −34.02 −84.91 −56.70 −52.16
0.689 – 0.835 0.762 0.676 0.694 0.784 0.745 0.721 0.852 0.774 0.679 0.747
0.547 2.453 1.146 0.268 – 0.244 0.370 – 3.679 1.101 0.012 0.821 0.910
−58.83 14.43 1.653 −60.11 – −14.72 −71.34 −289.9 −25.62 −28.44 −120.9 −50.13 −41.40
0.685 0.662 0.823 0.759 – 0.553 0.543 – 0.590 0.843 0.793 0.616 0.686
0.050 0.682 0.074 0.143 – – 0.410 0.022 0.108 0.023 0.248 0.007 0.177
−65.74 −31.06 −64.97 −59.13 – – −42.87 −71.94 −51.63 −78.15 −44.65 −85.59 −59.57
0.593 0.567 0.739 0.698 – – 0.664 0.578 0.669 0.761 0.777 0.335 0.638
Es: solid phase aggregate modulus (MPa), F′: fluid load fraction, α: hyperelastic material constant, –: no data obtained.
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H. Lee et al. / Biotribology 7 (2016) 31–37
Table 4 Correlations between each material property and each variable.
Es F′
α
Weight
Age
Breed
Sex
Significant (p b 0.0375) Highly significant (p b 0.0003) ×
Significant (p b 0.0392) Highly significant (p b 0.0146) ×
×
×
×
×
×
×
Es: solid phase aggregate modulus, F′: fluid load fraction, α: hyperelastic material constant, ×: indicator of no statistically significant association.
6. Discussion and conclusions
Es (MPa)
According to the study, to find correlations between the mechanical properties of equine articular cartilage (Es, α, F′) and the signalment variables (breed, age, sex, and weight), breed and sex were not significantly influential variables on the variation of any of the material properties, while the solid phase aggregate modulus showed a statistically significant correlation with age and weight. The fluid load fraction also displayed a significant correlation with age and weight. There was no significant correlation between the hyperelastic material constant and any of the signalment variables. It was also found that weight impacts much more on the variation of the mechanical properties than age. All phenomena of the articular cartilage through the measurements were successfully characterized by one closed form model (the Ogden hyperelastic model) as proposed previously in the Analysis section [40]. The observed hyperelasticity of the articular cartilage might not be due solely to the cartilage behavior itself, but also the substrate effect [40,41]. It appears that the normalized displacements up to 50% in articular cartilage are nondestructive because the repeated forcedisplacement curves of the same cartilage surface followed on nearly the same line. The authors are unaware of any previous reports on the systematic influence of the age or weight on the elastic behavior of mammalian articular cartilage. However, similar work correlating the collagen fiber arrangement between different species was found. Kääb et al. compared the collagen fiber arrangement of the articular cartilage of the medial tibial plateau from human, cow, pig, dog, sheep, rabbit and rat joints [42]. They found that the maximum thickness of the articular cartilage increased as weight increased and were therefore correlated (the heavier animal was, the thicker articular cartilage was). It illustrated that weight can affect the variation of the mechanical properties of the articular cartilage because the properties can vary due to a variation of the cartilage thickness. The lubricating performance of cartilage is also
4
4
2
2
0 200
F
dependent on its thickness. Hence, it seems reasonable that the material properties also correlate to the weight. In this work, it was verified that material properties are dependent on age and weight. This work showed that cartilage properties might be influenced due to age and subsequent degradation over time. A higher weight might also cause the cartilage to degrade or change more over time, however, the cartilage could also adapt to higher weights to maintain functionality. The findings in this work could be useful for proper repairing, healing and designing biomimetic artificial articular cartilage. For instance, the repairing process of cartilage varies depending on the individual. This is because the degradation rate of the articular cartilage varies by individual, and aging is one of reasons for the variation of the degradation rate; aging accelerates the degradation rate [10,43,44]. The age of each person, therefore, affects the repairing process for their cartilage [45,46]. As another example, the articular cartilage healing time of a heavier person should be significantly different from one with lighter weight. This is because the material properties directly associated with the performance of the articular cartilage vary with weight, and the time for the cartilage recover to healthy condition would vary. On the other hand, sex and breed are not correlated with the mechanical properties of articular cartilage. This means sex and breed should not be considered for any processes of repairing, healing, or designing artificial articular cartilage. Being aware of the absence of correlation between mechanical properties and specific parameters such as sex and breed in this study, therefore, would help in saving time and resources in research as well as treatment. Especially in veterinary medicine, which deals with various breeds, there should be no need for veterinarians to be concerned about variation of treatment depending on breed, allowing them to focus fully on improvement of general care methodologies. It could also contribute to improving the assessment system of articular cartilage; considering the two influential signalment parameters would lead to more advanced evaluation of the cartilage degeneration and regeneration or repair of tissue to identify
300
400
500
600
0 0
1
1
0.5
0.5
0 200
300
400
Weight (kg)
500
600
0 0
10
20
30
10
20
30
Age (Years)
Fig. 7. Relations between weight and the solid phase aggregate modulus as well as fluid load fraction were displayed (left). Also, relations between age and the solid phase aggregate modulus as well as fluid load fraction were displayed (right). All solid phase aggregate moduli and fluid load fraction values measured on different joints were plotted.
H. Lee et al. / Biotribology 7 (2016) 31–37
700
Weight (kg)
600 500 400 300 200 100 0
5
10 15 Age (years)
20
25
Fig. 8. Relation between weight and age of the horses.
the cartilage health more accurately for proper treatments or diagnosis [47–49]. Awareness of the expected mechanical properties of healthy articular cartilage, considering the correlations described in this work, could help avoid misinterpretations of the healing process or the degradation process followed by diagnosis with incorrectly expected cartilage performance directly related to the mechanical properties. Acknowledgements The authors gratefully acknowledge the financial support of the Auburn University Intramural Grant Program, the Auburn University Undergraduate Research Fellowship Program, and the Merial-NIH Veterinary Scholar Program. References [1] H. Bang, Y.-l. Chiu, S.G. Memtsoudis, L.A. Mandl, A.G. Della Valle, A.I. Mushlin, et al., Total hip and total knee arthroplasties: trends and disparities revisited, Am. J. Orthop. 39 (2010) E95–102. [2] E.S. Fisher, J. Bell, I. Tomek, A. Esty, D. Goodman, K. Bronner, Trends and regional variation in hip, knee, and shoulder replacement, Dartmouth Atlas Surgery Report, The Dartmouth Institute for Health Policy and Clinical Practice, Hanover, NH, 2010. [3] S.M. Kurtz, K.L. Ong, E. Lau, K.J. Bozic, Impact of the economic downturn on total joint replacement demand in the United States, The Journal of Bone & Joint Surgery 96 (2014) 624–630. [4] M.D. Buschmann, J. Soulhat, A. Shirazi-Adl, J.S. Jurvelin, E.B. Hunziker, Confined compression of articular cartilage: linearity in ramp and sinusoidal tests and the importance of interdigitation and incomplete confinement, J. Biomech. 31 (1997) 171–178. [5] K.M. Clements, A.P. Hollander, M. Sharif, M.A. Adams, Cyclic loading can denature type II collagen in articular cartilage, Connect. Tissue Res. 45 (2004) 174–180. [6] L. Li, M. Buschmann, A. Shirazi-Adl, Fibril stiffening accounts for strain-dependent stiffness of articular cartilage in unconfined compression, Transactions of the Orthopaedic Research Society 26 (2001) 425. [7] V. Mow, Biphasic creep and stress relaxation of articular cartilage in compression, J. Biomech. Eng. 102 (1980) 73–84. [8] L. Røhl, F. Linde, A. Odgaard, I. Hvid, Simultaneous measurement of stiffness and energy absorptive properties of articular cartilage and subchondral trabecular bone, Proceedings of the Institution of Mechanical Engineers, Part H: Journal of Engineering in Medicine 211 (1997) 257–264. [9] G. Kempson, Relationship between the tensile properties of articular cartilage from the human knee and age, Ann. Rheum. Dis. 41 (1982) 508–511. [10] G.E. Kempson, Age-related changes in the tensile properties of human articular cartilage: a comparative study between the femoral head of the hip joint and the talus of the ankle joint, Biochimica et Biophysica Acta (BBA)-General Subjects 1075 (1991) 223–230. [11] R. Karvonen, W. Negendank, R. Teitge, A. Reed, P. Miller, F. Fernandez-Madrid, Factors affecting articular cartilage thickness in osteoarthritis and aging, J. Rheumatol. 21 (1994) 1310–1318. [12] C. Novelli, J. Costa, R. Souza, Effects of aging and physical activity on articular cartilage: a literature review, Braz. J. Morphol. Sci 29 (2012) 1–17. [13] E.L. Radin, D.A. Swann, I.L. Paul, P.J. Mcgrath, Factors influencing articular cartilage wear in vitro, Arthritis & Rheumatism 25 (1982) 974–980. [14] F.M. Hall, G. Wyshak, Thickness of articular cartilage in the normal knee, J. Bone Joint Surg. Am. 62 (1980) 408–413. [15] I. Otterness, M.-P. Le Graverand, F. Eckstein, Allometric relationships between knee cartilage volume, thickness, surface area and body dimensions, Osteoarthr. Cartil. 16 (2008) 34–40.
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