The articular cartilage is an important part of the human bone joints, which plays critical roles in reducing vibration and bone protection in daily activities of the human body. Studies suggested that the articular cartilage has a quite complex composition and specific material properties like nonlinearity and viscoelasty [
The articular cartilage can rarely be repaired if damaged; due to the absence of blood vessel, this usually results in osteoarthritis. Therefore, the study on mechanical properties of cartilage with the defect has started drawing attention in the scientific literature. Repeated load deformation can cause fatigue wear, which alters the mechanical properties of the cartilage. Generally, the greater the surface roughness, the faster the wear is. Delamination damage is the major form of damage for a cartilage under a friction load [
The distribution mode of collagen fibers in the cartilage plays a key role in the mechanical properties of cartilage. Based on the distribution and arrangement mode of the collagen fibers, the articular cartilage can be roughly divided into three layers [
Previous studies have focused on the analysis of the mechanical properties of intact cartilage; however, various degrees of articular cartilage damages can be observed even in the early stage of osteoarthritis [
Fresh knee joint cartilage of the distal femoral end was obtained from a 6-month-old pig. Cartilage slices (length = 8 mm; height = 18 mm; thickness = 3 mm) were cut along the normal direction of the cartilage surface. The defect of cartilage was made of machine tools. The thickness of the circle blade was 0.5 mm, and the circle blade rotated with the main axis. The sample of the cartilage was fixed on the knife rest. The depth of notch was controlled by the feed of knife rest, and the feed precision is 0.1 mm. Notches with a width of 0.5 mm and a varying depth were prepared (Figure
(a) A tested cartilage sample; (b) the picture of making defects.
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(a) Schematic diagram of the experimental apparatus; (b) the practicality of the experimental apparatus.
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The image acquisition system mainly consisted of a charge-coupled device (CCD) camera, which helped us obtain images with a 1376 × 1035 resolution. Images were then analyzed and postprocessed by an image processing software, producing data about the displacement and strain of the mark points of cartilage samples.
The cartilage samples were fixed on the fixture clamp of the portal frame and then placed in a saline tank. After that, saline was heated to 37°C so as to reduce the experimental errors. The indenter rolled onto the surface of the cartilage sample 50 times back and forth, with a compression quantity of 0.1 mm and a rolling velocity set as 1 mm/s, 2 mm/s, 4 mm/s, and 6 mm/s, respectively. Images were acquired continuously by the CCD camera with 2 frames/s frequency (Figure
Images acquired by the CDD camera. From (a) to (d) represented image acquisition sequence.
In order to facilitate the analysis of stress and strains near the notch, regions near the notch were divided by uniformed grid partition. The interval between two longitudinal lines was set at 0.125 mm. The selected horizontal lines were located 5%, 25%, 45%, 65%, and 85% away from the cartilage surface (Figure
The position of the grid and the grid partition of the different notch depths. (a) Notch depth was 0.2 mm; (b) notch depth was 0.5 mm; and (c) notch depth was 0.7 mm.
The iron oxide nanoparticles as mark points and pixels were embedded on the side surface of the sample before the experiments. The speckle image of the sample including mark points in its load-free state was first acquired and used as the reference image. The continuous and instantaneous speckle images including the mark points were also obtained at the different stages of loading. The images in random half cycle that the roller rolled above the sample from the left to the right were selected from all the acquired images. Using the computer to identify the mark points and pixels, the displacements of mark points and pixels were calculated by comparing the coordinates of current pixel images with reference image. And then, the strain values were obtained according to the relationship between the displacement and strain.
Figure
Comparison of the strain curves between intact and defective cartilages. (a) The strain curves at the A3 point; (b) the strain curves at the D3 point.
In this part, strain values were measured at each observation point around the notch with different depths under a compression quantity of 0.1 mm and a rolling velocity of 4 mm/s (Figure
The strain values measured at the observation points around the notches. (a) Notch depth was 0.2 mm; (b) notch depth was 0.5 mm; and (c) notch depth was 0.7 mm.
The strain curves measured at different points across the different notch depths. (a) Equivalent strain measured at point A3; (b) equivalent strain measured at point C3; and (c) equivalent strain measured at point D3.
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Figure
Variation trend curves of strain measured for dangerous points at different rolling velocities. (a) Equivalent strain measured at point A3; (b) equivalent strain measured at point C3; and (c) equivalent strain measured at point D3.
For point C3, a single distinct peak could be found for the equivalent strain. Peak values presented an increasing trend and then a reduction with the increase in the rolling velocity. A maximum value of 0.16 was observed at a rolling velocity of 4 mm/s, which was 1.5 times of the value recorded at 2 mm/s.
In contrast, the case was rather complicated for point D3. There were two peaks with in half rolling period, and the peak frequency appeared enlarged with the increase in the rolling velocity. The first peak was located in the same position across the different rolling velocities, that is, when the indenter was right above the D3 point, while the second peak was located differently and decreased at velocities of 2 mm/s and 4 mm/s. When rolling at a velocity of 6 mm/s, the second peak increased to 0.12.
In this paper, we used the noncontact digital image correlation (DIC) technique to focus on the mechanical responses of cartilage with different defect depths under rolling load. As the distribution and content of the major components varied with defect depth, fibers inside the cartilage can be divided into three parts: superficial, middle, and deep layers (accounts for 5%, 45%, and 50% of the cartilage thickness, resp.). Collagen fibers in the superficial layer distribute densely and parallel with the articular surface, which has maximum moisture content and for which deformation can easily occur under normal stress. Collagen fibers in the middle layer are irregularly arranged with large interspaces and crisscross at a certain angle with joint surface, which has less moisture content and deforms slowly under normal stress. The deep layer fibers are nearly perpendicular to the articular surface and have the lowest water content and the smallest deformation under normal stress [
As can be seen from Figure
When notch is shallow, the maximum equivalent strain appeared at the bottom corner of the notch; with the increase of notch depth, the strain value rose quickly because the supporting structure became loose. Figure
The positive and negative strain variations at points C3 and D3 existed in our study. These points were located in the vicinity of 50% of the cartilage height, which may be the interface between the middle and the deep layers. The distribution of cartilage fibers may vary in this position, resulting in different strain change rules compared with other points. This result indicated that fiber distribution has an important influence on the mechanical properties of cartilage [
Compared with the other points of the location, the points near the superficial layer showed different responses to the defect depth (Figure
The rolling velocity has a certain impact on the cartilage strain. It was reported that the friction coefficient increased first then became lower with the increase in the rolling velocity [
The main problem is that the experimental model of defect cartilage was a plane model using digital correlation technology to investigate mechanical properties of defect cartilage. The difference between experimental model and the cartilage model in vivo is that the confining pressure conditions could not be considered. However, the authors think that it is possible to obtain the confining pressure condition of the experimental model by using the method both numerical simulation and experiment. The displacement field and stress strain field of the model of integral cartilage and femur could be obtained by using the numerical simulation method, then the plane model of the experiment was taken into account from the integral numerical model, and the boundary condition was applied to the cutting surface of the plane model base on the results of the integral cartilage and femur. Modified boundary conditions decreased the error between the strains of the experiment and strains of the numerical simulation. The confining pressure conditions could be obtained by the numerical simulation. The confining pressure conditions could be used to conduct the experimental defect cartilage model.
In addition, the analyzed images were from the random half cycle in this paper. Due to the viscoelastic properties of the cartilage, its strain is correlative with rolling number, which could result in experimental errors. As a result of the limitation of cartilage samples taken from the position, the experimental samples from different pig femoral cartilages could also cause error. The physical load of the knee joint involves rolling, sliding, and a combination of rolling and sliding. This paper focused on the defect cartilage subjected to single load such as rolling, and the research work will be carried out in the future to understand the mechanical properties of the defect cartilage under other loads.
In this paper, we used a noncontact DIC technique to measure the displacement and the strain fields near the notch of a defected cartilage under rolling load. Based on our study, we can conclude that the cartilage damage may increase the strain values and strain peak frequency around the defect. The shear strain, which serves as the main factor causing cartilage destruction, increased with the increase in the defect depth. The cartilage would be destructed firstly at the bottom corner of the defect, and when the defect reached the certain depth, it might be destroyed along the interface between the middle and deep layers. The rolling velocity showed a significant effect on the superficial and middle layers. The equivalent strain increased first and then decreased with the increase in the rolling velocity. Changes were not obvious in the deep layer except for the rising strain peak frequency. The special structure of the cartilage exhibited a self-protective function against destruction, which may slow down this destruction process. Our results can provide a basis for the clinical treatment of osteoarthritis and cartilage repair. It is also of great significance for the mechanical analysis of artificial cartilage.
The authors declared that they have no conflicts of interest to this work.
The project was supported by the National Natural Science Foundation of China (no. 11402171 and no. 11672208) and was partly supported by the National Natural Science Key Foundation of China (no. 11432016).