The Anisotropic Compressive Properties of Patellar
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Abstract
In this study, we examine the transverse and longitudinal compressive mechanical behavior of the rabbit patellartendon. The anisotropic compressive properties are of interest, because compression occurs where the tendon attaches to bone and where the tendon wraps around bone leading to the development of fibro-cartilaginous matrices. We quantified the time dependent viscoelastic and anisotropic behavior of the tendon under compression. For both orientations, sections of patellartendon were drawn from mature male white New Zealand rabbits in preparation for testing. The tendons were sequentially compressed to 40% strain at strain rates of 0.1, 1 and 10% strain(s) using a computer-controlled stepper motor driven device under physiological conditions. Following monotonic loading, the tendons were subjected to stress relaxation. The tendon equilibrium compressive modulus was quantified to be 19.49 ± 11.46 kPa for the transverse direction and 1.11 ± 0.57 kPa for the longitudinal direction. The compressive modulus at applied strain rates of 0.1, 1 and 10% strain(s) in the transverse orientation were 13.48 ± 2.31, 18.24 ± 4.58 and 20.90 ± 8.60 kPa, respectively. The compressive modulus at applied strain rates of 0.1, 1 and 10% strain/s in the longitudinal orientation were 0.19±0.11, 1.27±1.38 and 3.26±3.49 kPa, respectively.The modulus values were almost significantly different for the examination of the effect of orientation on the equilibriu mmodulus (p = 0.054). Monotonic loading of the tendon showed visual differences of the strain rate dependency; however, no significant difference was shown in the statistical analysis of the effect of strain rate on compressive modulus. The statistic analysis of the effect of orientation on compressive modulus showed a significant difference. The difference shown in the orientation analysis validated the anisotropic nature of the tendon. [1]
Methods
Eight skeletally mature white New Zealand male rabbits were euthanized as part of a separate and unrelated IACUC approved protocol. The rabbits weighed between 3 and 4 kg. In preparation for the unconfined compression testing, the tendons were thawed and allowed to equilibrate for 30 min in 0.9% saline solution. Nine replicates of tendons were compressed transverse to the fiber direction, and nine replicates were compressed longitudinal to the fiber direction. This study considered two methods of compression testing, one in a transverse orientation and the other in the longitudinal orientation (Fig. 1). Compression was performed with an impermeable platen. All samples were subjected to unconfined compressive loads. The dish containing the PBS was 5 inches in diameter. Therefore, fluid was free to flow from the tendon in the direction transverse to the loading direction. Permeable platens are often used in studies of confined compression so that the fluid flow could be monitored in a uniaxial direction to prevent elevated stress values.
Transverse compression
In the transverse orientation, nine 6 mm diameter circular samples were removed from the proximal and distal ends of the tendon using a dermal punch. Three samples were tested at strain rates of 0.001/s, three were tested at 0.01/s, and three tested at 0.1/s. The 6 mm pieces were individually compressed with a 30 mm diameter platen. Hence, the area of interest related to engineering strain for transverse compression was 28.3 mm2. Specimens were placed in the center of a stainless steel dish filled with saline solution to prevent dehydration.
Longitudinal compression
Portions of the tendon were extracted from the whole tendon using a rectangular steel punch with parallel blades and compressive loads applied with a 30 mm diameter platen along the fiber direction. Nine sections were harvested for longitudinal compression testing. Three samples were tested at strain rates of 0.001/s, three were tested at 0.01/s, and three tested at 0.1/s. The tendon sections harvested for longitudinal compression were bonded to a stainless steel cylindrical dish filled with saline solution and compression was applied along the fiber direction. The cross-sectional area of the specimens was calculated using NIH image J digital imaging program. The average area of the rectangular specimens used in the longitudinal orientation was 37 mm2.
Compression apparatus
A Mach-1TM (Biosyntech Inc., Canada) micromechanical testing machine was used to apply compression for each orientation. The Mach-1TM system consisted of a vertical load frame, an actuator, a motion controller, a load cell and a load cell amplifier. Testing was performed in a controlled environmental chamber at 37◦C with 5% carbon dioxide gas, and the protocols were constant for both setups.
Thickness measurement
A modified indentation technique was used to measure the thickness of the whole tendon prior to the sample extraction. Soft tissues such as tendons are pliable and the use of pressure to measure the thickness, regardless of however small, could deform the tissue in an undesirable way and compromise the actual measurement. In this technique, the whole tendon was placed on a flat surface and a circular platen was driven to meet the flat surface at a rate of 0.5 mm/s to a maximum of 2 g of load. This location was noted as zero. The platen was then lifted and driven to meet the top of the tendon. From the recorded ordinates, the thickness of the whole tendon was calculated. This was done by using the difference between the ordinates recorded with and without tendon sandwiched between the indenter and flat surface. The purpose of this task was to obtain initial specimen thickness for future computation of engineering strains.
Compression protocol
A 10 kg load cell was used to test the tendon specimens. The tendon was equilibrated in saline for 30 min before commencing tests. Stress relaxation tests began with the ramp amplitude being 10% of the thickness of the specimen and ramp velocity being approximately 50% of the ramp amplitude with 5–7 ramps per specimen. The equilibrium compressive modulus was calculated by analyzing stresses in the small strain region of four samples per orientation. The load was removed and the tissue left to rest and recover for 30 min before initiating the monotonic loading of the specimen. Monotonic loading was applied at 0.001/s, 0.01/s and 0.1/s, respectively, up to 40% strain, and the stress–strain responses were plotted. Thirty minutes of recovery time were allowed between the three different loading rates. The compressive modulus was computed in the small strain regions of the monotonic loading curves.
Statistical analysis
Paired samples t-tests were used to analyze the effect of orientation on the equilibrium modulus of the tissue, the effect of orientation on the compressive modulus (monotonic loading), and the effects of strain-rate on the compressive modulus. Significance was defined as p < 0.05.
Results
Both the transverse and longitudinal orientations showed strain rate differences under 0.001/s, 0.01/s and 0.1/s. Just as in tension [20] the compression stress–strain responses were nonlinear; however, unlike tension; the nonlinearity was more concave in compression. Anisotropy was also evident at each strain rate, with the transverse orientation having higher stress values than the longitudinal orientation.
Statistical analysis
The evaluation of the effect of orientation on the equilibrium modulus showed no significant difference between the longitudinal and transverse orientations (p > 0.05). The comparison of the means for the effect of orientation on the compressive modulus showed a significant difference for both orientations (p < 0.05). However, the effect of strain rate on the compressive modulus did not show a significant difference. Table 1 lists the modulus for the equilibrium compressive modulus ± standard deviation for both orientations. Table 2 lists the compressive modulus values ± standard deviation of the mean for both orientations.
Transverse compression
The tendon responses from the monotonic loading rates in the transverse orientation of 0.001/s, 0.01/s and 0.1/s illustrated the rate dependence of soft viscoelastic tissues. The rate of 0.001/s had lower stresses for a given strain, with greater stresses at the rate of 0.01/s, and the greatest stresses at a rate of 0.1/s. At each strain rate, the transverse modulus was greater than that of the longitudinal modulus, with large significant differences shown based on orientation. The average equilibrium modulus value in the transverse orientation was between the transverse modulus at 1 and 10%/s. Therefore, this shows that the tissue reached equilibrium at a rate greater than 1% of compression per second. Figure 2 is characteristic of the overall stress–strain response of transverse bulk compression.
Longitudinal compression
The tendon responses from the monotonic loading rates in the longitudinal orientation of 0.001/s, 0.01/s and 0.1/s illustrated the rate dependence of soft viscoelastic tissues. However, the magnitude of the stresses was typically lower than the transverse direction. Clearly, as the strain rate increased, the stress increased. The equilibrium modulus in the longitudinal orientation was between the longitudinal modulus at 0.1 and 1%/s. Therefore, this shows that the tissue reached equilibrium at a rate less than 1% of compression per second. Figure 3 is characteristic of the overall stress–strain response of transverse bulk compression.
Compressive anisotropy
The stress–strain responses of the transverse and longitudinal orientations display the material anisotropy in the tendon (Figs 4–6). This test of significance confirms the directional dependence of the material response of a rabbit patellar tendon to applied compression. Although a significant difference in modulus was not shown based on strain rate, greater magnitudes of anisotropy were shown at the higher strain rates.
