# In Silico Modeling the Impact of Cartilage Stiffness on Bone Tissue Stress
## 3 Numerical Results and Discussion
with the mechanical properties of the model components, since the locations of the stress concentrators are close to the location of the applied load. For this reason, for a more detailed analysis of the stress state of the model, it is necessary to study other plots, as well as section-views of the finite element model. They are presented below.  
The finite element model section-view for the bone components is shown in Figure 7. We can observe an increase in stress values on the posterior side of both bones; however, it should be noted that this distribution is related to the geometry of the bones and the loading pattern. Firstly, the tibia and femur are not strictly collinear to each other; for this reason, the displacement that is applied to the upper surface of femur causes an external moment, due to which the model is subjected not only in compression, but also undergoes bending. As a result, we get stress concentrators at the fixed base of the model, as well as in the tubular section of femur. It must be admitted that changes in the stress state in these areas are not the direct object of our study, but, at the same time, changes in stress values in these locations allow us to conclude that the properties of the meniscus affect the load distribution not only in the case of compression but also in the case of bending.  
Figure 6: Von Mises stress plots in case of walking. General view of the model: (**a**) With mild cartilage stiffness; (**b**) With moderate cartilage stiffness; (**c**) With severe cartilage stiffness.  
Figure 7: [PERSON] stress plots on cortical bone section view in case of walking: (**a**) With mild cartilage stiffness; (**b**) With moderate cartilage stiffness; (**c**) With severe cartilage stiffness.  
For this study, the stress in the area of the articular surfaces is of much greater interest. Plots of the stress are shown in Figure 8. It should be noted that Figure 8 depicts exactly the articular surfaces of the bone, while cartilage and soft tissues are hidden.  
As can be seen from Figure 8a, in the case of cartilage with mild stiffness, there are no stress concentrators on the articular surfaces. The zones of increased stress are not clearly expressed, and basically the model shows a uniform distribution of stresses. In the case of moderate cartilage stiffness (Figure 8b), the zones of increased stress are more clearly expressed; in addition, their area is noticeably larger. For the model with severe cartilage (Figure 8c), stress concentrators are identified in four locations (two for tibia and two for femur). However, compared to the model shown in Figure 8b, the area of the high stress remains approximately the same.  
The stress plots of the trabecular tissue are shown in Figure 9. As can be seen from the plots presented, as the cartilage stiffness increases, not only do the values of the stresses themselves change, but also their distribution changes. With mild cartilage, the zones of increased stress values are more likely to be located outside, while with an increase in stiffness, stress concentrators spread deeper and cover both vertical and horizontal trabeculae. The values of the maximum stresses on the trabeculae themselves turned out to be lower than the stresses on the cortical bone: 9.6 MPa for mild stiffness cartilage, 11.2 MPa for moderate stiffness cartilage, and 12.9 MPa for severe stiffness cartilage.