# In Silico Modeling the Impact of Cartilage Stiffness on Bone Tissue Stress
###### Abstract  
The knee joint is a complex biomechanical subsystem, modeling of which can reveal a deeper understanding of the processes occurring within it. The purpose of this study is to examine the stress alteration in bone based on mechanical properties of cartilage. To achieve this, a numerical model of the knee joint was developed and tested under different displacement values. The mechanical behavior of the model was represented by considering the hyperelastic properties of soft tissues, along with the verification of trabecular structure of bones, resulting in a more realistic mechanical depiction of the biological subsystem. The results showed that as the stiffness of the cartilage increased; the distribution of stresses in the bone became uneven; and stress concentrators dispersed over articular surface, while in the case of mild cartilage no stress concentrators were expressed. The proposed modeling approach allows the adaptation of patient-specific data in order to predict the outcomes of tissue diseases. The obtained results allow us to state that taking into account the non-linear properties of soft tissues is extremely important for assessing the stress state of the entire biological subsystem. The main difficulty, however, is the lack of data regarding the mechanical behavior of tissues in certain diseases. biomechanics; cartilage; femur; hyperelasticity; meniscus; numerical modeling; tibia; trabeculae +
Footnote †: journal: Medical  
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Despite their undeniable advantages, in silico methods present several challenges. Firstly, the development of geometrical models requires accurate processing of the joint's anatomical geometry, which demands appropriate software packages capable of reading medical images. Secondly, the problem formulation is another difficulty, as biological tissues generally behave as nonlinear elastic or hyperelastic bodies, requiring the use of more intricate mathematical techniques, and the material data should be well known. All of the mentioned points should be verified for sufficient investigation to be performed. Recent studies, for the most part, suggest using the finite element method for numerical modeling of the knee. A literature review has shown that the problems and research objectives that are addressed can be very diverse: authors [8] pronounced a numerical knee model for verifying the mechanical processes in knee joint in case of arthroplasty. The geometry of the model was obtained by processing DICOM data. The three-dimensional model contains femur, tibia, ligaments, and implants, although the bone components didn't reflect the trabecular structure; in addition, the ligaments were modeled as perfectly elastic bodies, so nonlinear behavior was not verified. The model proposed by [9] allowed the verification of the loads occurring in cases of flexion and was characterized by complex external geometry: it contained fibula and reflected the anatomical curvature of bone surfaces, though the trabecular structure of porous bone and the hyperelasticity of cartilages and ligaments were not verified too. Other authors [10] provided a shock wave of research on the knee joint affected with osteoarthritis. The porous material properties were taken into account, but at the same time, the representation of spongious bone was simplified, so the proposed model cannot accurately predict the interaction between cortical and trabecular bone. Some authors [11,12] provide numerical knee joint models with verification of nonlinear properties of soft tissues, although they assume the bone components to act as rigid bodies, so the elastic properties of femur and tibia remain uninvolved. The present study aims to investigate the stress changes of the bones which occur in cases of deterioration of cartilage. The numerical model of the knee joint containing components of femur, tibia, meniscus, and cartilage was developed. The trabecular structure of both femur and tibia was verified.