**6. Final discussion**

212 Injury and Skeletal Biomechanics

inflow in presence of the load.

zero which balances with the external pressure.

the behavior exhibited by the matrix to compressive loads.

*5.2.3. Oscillating loads response* 

environment. Then displacement occurs in response to stress and produces a reorganization of

**Figure 11.** 2D-tensile load response. a. *y* displacements. b. . Behavior of the fluid pressure *p* due to its

Figure 11b shows the behavior of the fluid pressure *p* for different time instants. It is observed that the fluid pressure is increased by small amounts in response to sustained tensile load. This action is due to the compensation of the tissue in response to deformation in elongation by the solid phase of the tissue that requires a redistribution of fluid into the tissue. However, it is evident that at the end of the tensile load time (approximately at t = 27s), the tissue can't undergo greater deformation in elongation and hence the fluid pressure also tends to stabilize at the inside thereof, causing a steady pressure maintained close to

Figure 12a corresponds to the displacement of the solid in the *y* axis at different time instants. It is noted that the displacements or deformations occur alternately; at the times 1, 3 and 5 (t = 0.67s, t = 27s = 6.57s respectively) the displacements are made positive, behavior similar to that observed during exposure to stress loads. Conversely, at the times 2, 4 and 6 (t = 3.37s, t = 16.5 s and t = 45s respectively) the displacements are negative, consistent with

Figure 12b shows the behavior of the fluid pressure *p*. Similar to what happened with the deformations of the solid phase, the pressure oscillation in response to cyclic loading imposed on the tissue is evident. Note that at times 1, 3 and 5 (t = 0.67s, t = 6.57syt = 27s respectively) the pressure tends to decrease due to the redistribution of fluid in response to perceived stress loads. Because the loads are not maintained, the tissue can't compensate with fluid inlet from the outside which is why the pressure is not increased. Thus, at times 2, 4 and 6 (t = 3.37s, t = 16.5 s and t = 45s respectively), the pressure tends to increase in

the fluid within the tissue, interfering with the variation in the pressure thereof.

There are several theories explaining the behavior of AC in the presence of load conditions, summarized in computational models that include the swelling process and the properties of the anisotropic structure of collagen. The most frequently used tests to determine the mechanical qualities of the AC are the confined compression, the unconfined compression, the indentation and the swelling tests (Wilson, et al., 2005), carried out using numerical approximation tools.

For purposes of meeting the stated objectives, we simulated a condition of confinement of the tissue that allows the flow at the bottom to restrict lateral and bottom movement. Conditions were similar to those reported in practical experiments as the papers presented by Ateshian et al., 1997; Frijns, 2000 and Wu et al., 1999; among others. The data obtained from the simulations confirm the theory of biphasic articular cartilage, first proposed by Mow et al., 1980; and supported by several authors as Haider et al., 2006; Wilson et al., 2005, Haider & Guilak , 2007; Meng et al., 2002; Wu et al., 1997, Terada et al., 1998, Donzelli et al., 1999 and Donzelli & Spilker, 1998; among others.

Results allow us to conclude that articular cartilage exhibits a displacement response of the solid component (matrix) and a variation in the pressure of fluid component due to the exit or entrance thereof, with decreases in pressure in response to compressive loads and increases at the same tensile loads. The displacement is caused by outflow of fluid in response to the maintained compressive load. However it is important to note that once the tissue reaches its maximum displacement, it behaves as a solid rather than as a poro-elastic material. From this point the fluid can't flow out of the tissue because the pressure is balanced with the external fluid begins to bear part of the load.

If this pressure is maintained for prolonged periods dehydration of the tissue may result and cause changes in normal behavior, making it temporarily or permanently more sensitive to injury. These findings support the conclusion that a load consistently maintained for long periods of time or an excessive load that exceeds the characteristics of the tissue once it has reached the maximum possible displacement, can make one more vulnerable to overuse injuries.

Mechanical Behavior of Articular Cartilage 215

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The data reported are the beginning of broader work in the study of cartilaginous tissues which can incorporate the cellular component differentially and cartilage's own biochemistry in the model. The results obtained motivate the efforts that currently seek to simulate the production and destruction of the matrix in the presence of mechanical loads, to simulate the restructuring of the same after an injury, to apply mathematical models in the study of cartilage growth and to study their behavior in vitro and in vivo. These lines of research aim to provide a solid foundation for the development of AC experiments *in vivo* and *in vitro* that expands the range of applications of numerical simulation techniques and techniques used in tissue engineering.
