Mathematical modeling of the stress-strain state of the knee joint model with aplasia of the cruciate ligaments and after restoration of the ligamentous apparatus

Abstract

Defects in the establishment and development of the cruciate ligaments are one of the main causes of the instability of the knee joint in congenital longitudinal defects of the development of the lower limbs. This pathology occurs with a frequency of 0.017 per 1000 newborns. The absence of cruciate ligaments leads to a change in the shape of the articular surfaces of the knee joint, and is formed due to hypoplasia of the femoral condyles, the absence of the intercondylar fossa of the femur, and the absence of the intercondylar elevation of the tibia. Purpose - to study the stressed-deformed state of the knee joint with aplasia of the cruciate ligaments before and after reconstructive interventions and to compare the obtained results with the norm. Materials and methods. A basic finite-element model of the lower limb was developed, which was supplemented with collateral and cruciate ligaments of the knee joint. On the basis of the basic model, a model with aplasia of the cruciate ligaments of the knee joint and a model reflecting the state of the knee joint after reconstructive surgery using the SUPER KNEE method according to D. Paley were developed. The model was tested under the influence of a vertical load in the position of bending the knee joint at an angle of 135. Results. The results of the mathematical modeling showed that the aplasia of the cruciate ligaments leads to an increase in the stress level, both in the bone elements of the model and in the elements of the ligamentous apparatus. Restoration of the ligamentous apparatus of the knee joint with artificial materials according to the SUPER KNEE method according to D. Paley allows to reduce the stress level in the bone elements of the model, while the stress in the femur is determined to be lower even compared to the normal model. Ligaments made of artificial material assume the main loads in the knee joint, and ensure an even load of mylar tape on both sides of the joint. The high level of stresses in mylar tape compared to normal ties is due to the higher modulus of elasticity of the material and its lower plasticity. Conclusions. Aplasia of the cruciate ligaments leads to an increase in the stress level, both in the bony elements of the model and in the elements of the ligamentous apparatus. Restoration of the ligamentous apparatus of the knee joint allows to reduce the stress level in the bony elements of the model with ligament aplasia, and brings the values closer to the parameters of the normal model. Tensions in the ligamentous apparatus of the knee joint after its restoration increase significantly, which is due to the mechanical properties of the artificial material that replaces the ligaments. The increased level of stress that occurs in the mylar tape indicates that it firmly holds the load arising in the joint. The research was carried out in accordance with the principles of the Helsinki Declaration. The study protocol was approved by the Local Ethics Committee of the participating institution. No conflict of interests was declared by the authors.