| Biomechanics is the application of mechanical engineering theory and practice to biological materials and systems. It has been widely studied and applied since the1960’s. It encompasses many disciplines including material science, mechanics, anatomy, physiology, computer science. It develops rapidly and emerges as an independent cross-discipline subject now. Among many branches of biomechanical research, its application in orthopedics is becoming more and more important because of urgent needs for accurate quantitative assessment in diagnosis, treatment and prevention of the common and frequently-occurring disease which are harmful to people’s health and the quality of life.There are two main methods used in biomechanical research:biomechanical testing and numerical simulation analysis. Biomechanical testing, in vitro, can directly obtain the information about the mechanical properties of measured object. The results and conclusions from the testing depend on test condition and method. Therefore, it only provides some heuristic guidelines in qualitative researches, but neglect the differences of individuals. Compared with biomechanical testing, Finite Element (FE) method, an important method of numerical simulation analysis, has many advantages: the cost of simulation is low, test finish without errors, non-invasive and non-destructive model can be repeatedly used and the complicated boundary condition can be added conveniently, etc. It is more important that FE method can built the complicated models of bone tissue of individuals, special in vivo, with very realistic geometry and material property. Thus, the analysis results can serve as references for clinical diagnosis, operation plan evaluation, plastic surgery, prosthetic design and manufacturing, etc.In1972, Brekelmans and Rybicki took the lead in the application of FE techniques in the biomechanical studies on vertebrae and femur. From then on, the technique came into widespread use which covered almost all human bones. The early efforts of the technology were limited in the analysis of two-dimensional linear problem with simplified loads and boundary conditions. The analysis results were far from the actual fact. With the development of computer technology and numerical analysis theory, there are many mature examples of FE application in complicated nonlinear and multi-medium coupling problems. It has been proved that the more accurate model get and more realistic conditions imposed, the more accurate results acquired. In existing commercial software, there is no better solution for the presence of face ambiguity for the complicated bone tissue model. Difficulties may arise when one attempts to generate the FE meshes from the geometrical model with face ambiguity. Thus, to build a frame which generates bone FE model effectively and accurately is still necessary. In clinic, the quantitative assessments about strength, stability, damage and fatigue life, are urgent needs for theoretical guidance. All those problems are involved with fracture and damage theory. The interfaces of bone-cement/bone, bone-cement/metal and bone/metal are weak links in replacement surgery. Fracture initiation and propagate may occur easily along weak interfaces. Thus, the weak interfaces are easy to induce postoperative complications such as prosthetic loosening, subsidence and rupture. Interface fracture mechanics can solve and explain the crack of the interfaces. However, honeycomb structure in human bone tissue, bubbles trapped in bone-cement and micro defects in prosthesis also contribute to the causes of postoperative complications. The occurrences of micro cracks and micro defects in bone tissue, bone-cement and prosthesis are inevitable, and the generation and distribution of them are at random. In FE modeling, micro cracks and micro defects are very hard to represent, thereby, bone, bone-cement and prosthesis are actually regarded as continuum media. Classical fracture mechanics take the model with crack as their research object. Numerical analysis method based on classical fracture mechanics seems incapable of solving the fracture problem of continuum media because the initial crack position and crack propagation direction are unknown. To explore a new method to determine crack position, estimate the fracture strength and fatigue life of continuum media has a very important practical significance. The coupling technology of cohesive zone model (CZM) and finite element has been widely used in the analysis of composite materials interface crack. This is beneficial attempt to introduce this technology for the assessment of interface damage and fracture in replacement surgery. Material damage is the gradual process of mechanical property deterioration. The concept of damage variable, which represents the change in material stiffness, is introduced to continuum mechanics. Cohesive elements are inserted into continuum media to represent potential crack paths. The separation of the upper and lower surfaces of cohesive element can be expressed as the discontinuous displacement during the deformation and fracture of continuum media. Additionally, it is desired to further implement the computer simulation of fatigue and fracture process based on strength deterioration theory.In view of the above, the main research contents and results in this paper are described as follows:(1) To establish a framework for precision bone FE modelConsidering that the face ambiguity of the model which generate by3D surface reconstruction using Marching Cube (MC) algorithm, is likely to lead to the difficult of mesh generation, a strategy is formulated:preprocessing of medical images for ROI (region of interest), stacking VOI (volume of interest) with ROI, smoothing the VOI for a closed surface domain of3D model. According to the characteristics of medical images, the voxels in medical image data can convert to the hexahedral meshes of FE bone model (voxel-based mesh model) directly by home-made program. The framework provides different mapping methods, such as centroid-based, node-based, grid-based, etc, and assigns inhomogeneous anisotropic properties for bone tissue. Due to little amount of the bone tissue with CT grey value～800Hu in human body, it is very hard to make suitable sample for testing material property. In the result, the material model represents a discontinuous leap. A smooth template is proposed to smooth the leap. Some researches show that the average method to group the material properties may overestimate or underestimate the material properties of bone. Thus, K-mean algorithm based on the volume of element is proposed to cluster the groups of material properties. Finally, the information about nodes, elements and material properties of model could be arranged automatically in accordance with different FE software packages. In contrast to the other commercial software, the framework avoids mesh generation bottleneck for complicated bone model, increases the mapping, smoothing, and clustering methods for the assignment of material properties, and also can describe the anisotropic property of bone tissue. The frame could be expanded to meet the users’ requirements.(2) Based on the above framework, two cases in orthopedic are analyzed.①Case one:To design custom prosthesis for patients with massive bone loss in proximal femur.In this case, a new concept of design based on investigating individual femur shape and femoral bone quality is proposed before custom prosthesis design. Then, the FE models including before and after the prosthesis replacement are built. The mesh models of femoral bone before and after the prosthesis replacement have the same structure. The technique of consistent meshes may make analysis results more comprehensive and objective. Two activities of daily living, normal walking and stair climbing, are simulated and muscle force is/is not simultaneously exerted. The change rate of strain energy is revised to replace stress shield signal to assess not only stress shield effect but fracture risk of bone tissue. Finally, an optimum scheme of custom prosthesis is determined after the comparison among simulation results.②Case two:To compare and evaluate two posterior atlantoaxial fixations including C1lateral mass to C2pedicle fixation (C1LM-C2P) and C1lateral mass to C2laminar fixation (C1LM-C2L).In this case, first analyze the anatomy structure of individual atlantoaxial and validate the feasible of C1LM-C2P and C1LM-C2L, then build fine FE models of C1LM-C2P and C1LM-C2L containing atlanto-odontoid and arthrodial. Seven loads to simulate different head postures:anterior-posterior (AP), translation (forward), extension, flexion, lateral bending (left/right), and torsion (left/right) are exerted for simulations. The FE analysis results are shown to be in good agreement with the published experimental data. To draw a conclusion is stating that C1LM-C2L is an alternative for some patients with congenital anomalies who are not suitable for other fixation treatment. It is worth to point out that the stability of C1LM-C2L is worse than the one of C1LM-C2P.(3) To analysis and assess the stability of cemented fixation for patients with massive bone loss in proximal femur using the technique of Cohesive Zone Model (CZM).In this research, shear strength and shear fracture toughness of cement/metal interface are measured by, respectively, sandwich shear and End Notched Flexure (ENF) testing. To avoid the measurements of the crack length during the crack growth, compliance calibration method is applied to determine the critical strain energy release (GIIC), a kind of fracture toughness, in ENF test. The coupling of CZM and FE method is employed to simulate the process of ENF test for the analytical solution of GIIC. The two solutions are compared with published experiment data. Furthermore, the stability of cemented fixation for patients with massive bone loss in proximal femur and the influences of the surfaces of prosthesis are investigated with the coupled method. The analysis results provide valuable insights into relevant clinical phenomena and quantitative guides to clinical therapy.(4) To investigate the fracture process and fracture property of bone-cement with the technique of coupling of cohesive element and FE.This research presents the different methods to set up potential crack paths corresponding to different load cases. A general method to set up potential crack paths is proposed. The model for fracture analysis based on this method could generate automatically by virtue of home-made program. The program is suitable for the tetrahedron element in commercial software ABAQUS. It can be expanded to other software. The uniaxial tensile test of bone-cement is taken as an example. The fracture process of this model is tracked. The results display the changes of stress field and damage field in the whole fracture process. The other focus of this study is to explore the influences of the numbers of potential crack path and crack morphology upon fracture mechanism and fracture property. That the findings agree well with other published experiment data validates the feasibility of application of the coupled method as mentioned above in solving the fracture problem of quasi-brittle or brittle material. In order to improve computational efficiency, components should be divided into two zones. One is the fracture risk zone. Fractures commonly occur in the zone and the model of the zone is built by the coupled method, whereas, another zone is only built by FE method.(5) To establish fatigue cumulative damage model with the technique of coupling of CZM and FE and to investigate the fatigue damage process of bone-cement.Based on strength degradation theory, the technique of coupling of CZM and FE is introduced in the analysis of fatigue cumulative damage. The tensile fatigue test of bone-cement is taken as an example. A new fatigue cumulative damage model with three stages is proposed. The three stages correspond to before crack initiation (I), fatigue crack initiation (II) and fatigue crack propagation (III). This research investigates the changes of material properties in damage evolution process. A program is written in Visual C language to control Abaqus solver for the analysis of fatigue damage evolution process. The mechanism of damage is investigated and fatigue life in different stages can be predicted under linear and logarithmic strength degradation modes. Compared with published experiment data, this research confirmed the feasibility of the coupled method in the application of fatigue damage and the validation of the fatigue cumulative damage model with three stages proposed in this study. |
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