FE analysis of stress and displacements occurring in the bony chain of leg

Abstract

Aims

The aim of this study was to assess how the stress shielding can influence the integrity and resistance of bones.

Methods

With this purpose a complete FE model of the human leg was realised. A load of 700 N has been applied at the top of pelvis and the feet, at the tip, was rigidly fixed.

Results

Obtained results reveal interesting consequences deriving by taking into account the complete bony chain.

Conclusion

A comparison among the literature data and our models can furnish a complete vision of the global spreading of the forces along the various bony components.

Introduction

The introduction of finite element analysis (FEA) into orthopaedic biomechanics allowed continuum structural analysis of bone and bone-implant composites of complicated shapes. However, besides having complicated shapes, musculoskeletal tissues are hierarchical composites with multiple structural levels that adapt to their mechanical environment. Mechanical adaptation influences the success of many orthopaedic treatments, especially total joint replacements. Recent advances in FEA applications have begun to address questions concerning the optimality of bone structure, the processes of bone remodelling, the mechanics of soft hydrated tissues, and the mechanics of tissues down to the micro structural and cell levels, but still have deeply difficulties to analysed complied skeletal chains involving different bony parts, because of the model size, and above all the boundary conditions to impose. Many different works in literature have investigated the single bony part such as femur, knee, tibia, or feet, fixing the base and loading with more or less detailed systems of forces. In this paper this question is faced by adopting a simplified model of the human leg, intended to assess how the stress shielding can influence the integrity and resistance of bones, if loaded with a vertical force of 700 N, and by comparing the obtained results with the ones present in literature. D.J. Rapperport¹ et al considered the pressure distributions across the articular surface for a resultant femoral load magnitude of 1.000 N angled of 40° medial of vertical obtaining an equivalent stress of 10 MPa on the hip joint. Breuckmann optical scanning and Metris laser scanning devices are used for scanning any object and producing a 3D form, while the CT device is used to visualize hard tissue of the human body. As a consequence of statistical evaluations, Breuckmann, CT and Metris models can be also compared with finite element analysis for the human upright stance position.² Montanini et al³ addresses the question of evaluating, by combining both experimental and numerical methods, the stress/strain distribution within a standardized composite femur. Two different loading conditions of the femur were considered. In the first one (LC-1) loads and boundary conditions exactly replicate those used in the experimental set-up: a rigid plate was modelled to transfer the axial load to the femoral head by imposing a vertical incremental displacement. In addition of providing information about the mechanical response of the implant/bone assembly under simplified yet physiological loads,⁴ LC-1 furnished a sound basis for the validation of the numerical model by direct comparison with in vitro testing. The effect of muscle action was then taken into account by considering a more complex loading case (LC-2). This load case has the same force resultant (980 N) as LC-1 but it considers the interdependence of muscles and joint forces as proposed by Bergmann et al,5, 6 who developed a simplified computer model of the physiological loading of the femur under walking activity by grouping functionally similar hip muscles. This load profile, which basically consists of four distinct muscle groups in addition to the hip joint force, is based on a validated musculoskeletal analysis and provides consistent torsion loading of the femur in addition to bending, loaded on the head with a force of 980 N. The human knee is the largest joint in the musculoskeletal system, which supports the body weight and facilitates locomotion. Gardiner and Weiss⁷ developed a finite element model of the MCL to study its 3D stress–strain behaviour under valgus loading. Gabriel et al⁸ determined ‘‘in situ’’ forces between the two bundles of the ACL with the knee subjected to anterior tibial and rotational loads. Hirokawa and Tsuruno⁹ developed a 3D model of the ACL that they used to study the strain and stress distributions in the ACL during knee flexion. Limbert et al¹⁰ proposed a 3D finite element model of the human ACL. This model was used to simulate clinical procedures such as the Lachman and drawer tests. In all these studies, the finite element model incorporated only one ligament without considering menisci and articular cartilages. Other authors analysed the distribution of contact pressures and compression stresses in menisci and articular cartilages, Bendjaballah et al¹¹ only considered a compressive load and modelled the ligaments as nonlinear springs. Pena et al¹² presented a 3D model of the knee considering the ligaments as isotropic. The results obtained in ligaments showed high stresses at full extension. This is essentially due to the large sagittal plane rotation of the femoral insertion of the ACL. This was also observed experimentally by Yamamoto et al¹³ that used photo elasticity to track the strains at the surface of the ACL. The anterior load produced a stress distribution in the MCL similar to a shear problem, with tension in the anterior–distal and posterior–proximal parts. Similar results were obtained by Hull et al¹⁴ in their work, were they measured the strain distribution in the MCL to determine the single and combined external loads most likely to cause injury. Due to the location of the tibial insertion of the PCL, during an anterior displacement of the knee, the tibia pushes the PCL and provokes bending. Different authors have used numerical techniques to analyse the distribution of contact pressures and compression stress in menisci and articular cartilage in the healthy knee joint14, 15 considered a compression load of 1300 N. The ankle mortise is composed of the distal articular surfaces of the tibia and fibula that are connected through a ligamentous complex known as the ankle syndesmosis. Together, these structures provide stability to the ankle joint. The distal tibio-fibular syndesmosis is composed of four ligaments: the anterior inferior tibio-fibular ligament (AITFL), the interosseous ligament, the posterior inferior tibio-fibular ligament (PITFL), and the posterior transverse tibio-fibular ligament. Proximally, the interosseous membrane joins the tibia and fibula. The fibres of the syndesmosis and interosseous membrane course inferolaterally and insert into the medial border of the fibula. These structures also maintain the integrity and stability of the ankle mortise and are important for balance loading of the foot through the fibula. Li and Anderson,¹⁶ carried on an FE analyses included several provisional loading steps (to bring the joint into a seated apposition as governed by the articular surfaces), followed by 13 steps spanning the stance phase of gait. Prevailing joint contact stresses following surgical fracture reduction were quantified in this study using patient specific contact finite element (FE) analysis. FE models were created for 11 ankle pairs from tibial plafond fracture patients. Both (reduced) fractured ankles and their intact contra laterals were modelled. A sequence of 13 loading instances was used to simulate the stance phase of gait. Contact stresses were summed across loadings in the simulation, weighted by resident time in the gait cycle. The maximum applied load was scaled to 320% body weight, rather than the normal 470% body weight. Information on the internal stresses/strains in the human foot and the pressure distribution at the plantar support interface under loadings useful in enhancing knowledge on the biomechanics of the ankle–foot complex. While techniques for plantar pressure measurements are well established, direct measurement of the internal stresses/strains is difficult. A three-dimensional (3D) finite element model of the human foot and ankle was developed by Cheunga, et al¹⁷ using the geometry of the foot skeleton and soft tissues, which were obtained from 3D reconstruction of MR images.