A realistic 3D human femur bone was modeled and finite element analysis was performed using ABAQUS with different material models. Mechanical analysis of biomaterials is performed with the concepts of continuum mechanics. Mechanical analysis of hard tissues (such as bone) can be analyzed with the help of linear/nonlinear elasticity theories.
The computational analysis of soft tissue can be performed using finite strain theory and computer simulations. Computational biomechanics is the application of engineering computational tools, such as the Finite element method, to study the mechanics of biological systems. These computational models and simulations can be used to predict the relationship between different parameters.
Different computational models can be used to design more relevant experiments, reducing the time and cost of experiments. Mechanical modeling using finite element analysis has been a hot topic for several years and is used to interpret the experimental observation of the behavior of various biological systems. In medicine, the finite element method has become a great alternative to in vivo surgical assessment in recent years.
Biomechanical research can be used to investigate forces in the musculoskeletal system, such as
Finite Element Analysis
It is the longest and strongest bone in the human body, extending from the hip to the knee. The condyles are the attachment points to the tibia, which is a lower leg bone. The patellar surface is the groove where the bone attaches to the patella, or kneecap.
Bone matrix consists of collagen fibers and organic ground substance, mainly hydroxyapatite formed from calcium salts. One is the cortical or compact bone and the other is the cancellous or spongy bone. When loaded, the collagen fibers align along the length of the shaft and the bone becomes stiffer.
Femur bone is mostly under compression and the properties are better in the direction of the longitudinal axis. The human femur can withstand forces of 1,800 to even 2,500 pounds, so it does not break easily.
Osteoporosis
Bone tissue is anisotropic in nature, indicating that the bone behavior will change according to the direction of the applied load. On a macroscale, bone can be considered as an assembly formed from osteons, trabeculae and body fluids [7]. The entire femur bone is considered a single unit with a hollow cylindrical cavity within it.
The results show that femur strength is highly variable in different areas of the bone. Yousif et al presented their study on biomechanical analysis of femur bone during normal walking and standing [10]. These material coefficients accurately define the hyperelastic behavior of the developed rubber material and can be used in various load simulations.
The model can be created using either MRI or CT scanned images. A bounding box was created with length, width and thickness as 0.4, 0.4 and 0.06 respectively to match the model dimensions with the actual femur bone. With the help of 'Surface View' module both the cortical and cancellous surface can be seen as shown below.
In the 'Surface Editor' module, the surface can be refined by specifying the distance between the nodes. The biggest advantage of using AMIRA for generating geometric models is that the surface model can be converted to a solid model by generating tetrahedral elements within the defined boundaries of the surfaces. This can be done by saving the tetra-generated file in the '.inp' format and importing it directly into the ABAQUS as a model.
In the label, the surface model can be converted into a solid model with tetrahedral elements by using the 'Tetra Gen' module. In ABAQUS, the orphan mesh model can be edited and the element type can be changed to a 10-node tetrahedron for analysis. Before the 'Tetra Gen' is generated, the surface model must be assessed to meet the criteria below.
After quality control, 'Tetra Gen' can be applied and the solid model can be generated. From the '.grid' module, after tetra gen, the model can be saved in '.inp' file format which can be directly imported into ABAQUS.
Loading and Boundary Conditions
Isotropic Linear Elasticity
Bone is hyperelastic and anisotropic in nature, indicating that the mechanical properties are dependent on orientation. This section deals with the mechanical analysis of bone by assuming it as a linear isotropic elastic material. The strain energy formulation in elasticity theory shows that it is necessary for the stiffness matrix to be symmetric and thus there are only 21 independent elastic constants in the most general case, i.e. anisotropic elasticity.
To define isotropic linear elasticity, the symmetry of the stiffness matrix is reduced to two independent elastic constants.
Orthotropic Linear Elasticity
Mesh Optimization
Simulation results using ABAQUS: Linear Isotropic
After defining the material model and the optimized mesh size, the next step was to analyze the model using ABAQUS. The meshed bone model has been imported into ABAQUS and the material properties, as shown in Table 5.1 below, were defined in the properties module for cortical and cancellous sections individually. In the load module, the compressive load was defined along the Y direction (assumed longitudinal axis) of the bone model on the sphere area and a magnitude of 1700N was given.
In the boundary condition module, the bottom surface of the model was given a fixed boundary (by constraining all translational and rotational motions). The areas with the greatest tension are located in the neck and the upper part of the shaft area. In the neck region, the applied load is transverse to the loading direction, which acts as a bending load and creates high compressive stress in the lower neck and high tensile stress in the upper neck region with a value of 0.465 GPa.
The regions of highest stress are located in the neck region of the cancellous bone. In the neck region the applied load is transverse to the loading direction, acts as a bending load, which creates high compressive stress in the lower part of the neck and high tensile stress in the upper region of the neck with a value of 0.057 GPa .
Simulation results using ABAQUS: Orthotropic
In the neck region, the applied load is transverse to the loading direction which acts as a bending load and creates high compressive stress in the lower neck and high tensile stress in the upper neck region. The maximum principal stress distribution in the cancellous portion of the bone model is shown in figure 5.7 above. In the neck region, the applied load is transverse to the loading direction, acting as a bending load, creating high compressive stress in the lower neck and high tensile stress in the upper neck region.
In the first case, linear isotropic elastic behavior is assumed for both bone sections with different material constants. The 1700N load is the maximum load applied to the femur by the hip joint in the gait cycle of a 75 kg male during walking. In the cortical section, the maximum stress of 0.465 GPa appeared in the neck region.
This is because, in the neck region, even in the shaft section, the applied load would create a bending couple and this causes high compressive stresses in the lower neck and high tensile stresses in the upper neck region. In the second case, the orthotropic behavior for both the cortical and the cancellous sections and adopted. The behavior of the bone model was studied under the same physiological conditions as in the first case.
The orthotropic assumption brings the analysis a step closer, if not completely, to the actual anisotropic behavior of bone. There is a significant decrease in the maximum stress value for the cortical section, because the orthotropic properties show a large difference in directions 1 and 2 (perpendicular to the longitudinal axis). The maximum principal stress value of the cancellous section was 0.087 GPa, located only in the neck region.
Here there is an increase in the maximum voltage value compared to the first case. And the orthotropic behavior of the cortical bone transfers more load to the cancellous section there by generating more stress in the cancellous neck region. If we observe the femur of a human, the cancellous section is widely distributed and the cortical section is thinner in the neck region and being the weak part of the bone, it is vulnerable to fracture.
Osteoporosis
Implant material models
Department of Mechanical and Engineering, University of Illinois at Urbana-Champaign, Urbana, IL 61801, USA. A new microscale constitutive model of human trabecular bone based on a depth sensing technique.
![Table 5.1 The properties for linear isotropic elastic analysis [10]](https://thumb-ap.123doks.com/thumbv2/azpdfnet/10473719.0/29.918.168.756.354.525/table-5-properties-linear-isotropic-elastic-analysis-10.webp)
