Computational and experimental investigation on the effect of failure stress in a femur bone

Abstract

The recent trends in numerical methods and computational techniques in the field of biomechanics facilitate to solve complex problems encountered in the assessment of the strength and reliability of structures and implants. In the present investigation, a Finite Element Analysis (FEA) analysis of Femur bone structure implant is done, to determine the relationships among the quantities that characterise the failure stresses. The fracture behavior of human bone during the action of unexpected cause of accidents is analyzed by the related works and numerical analysis on the model of particular bone is performed under various loading and boundary conditions. Stress fracture occurs predominantly in the weight-bearing bones of the lower leg and foot, with fewer incidents in the femur, pelvis, and lumbar spine. The combination of advanced numerical tools with the capacity of modern computers resulted in the creation of limitless possibilities towards the allowable stress and strain analysis in bone structures. The novel FEA method presented in this article can be used to identify the biomechanical phenomena occurring in femur bone structures as well as to validate the experimental results in the course of implants. It also enables the fast rehabilitation of fractured bone and shapes them optimally by taking into account of the limit tensile or compressive strengths exerted.

Keywords

Biomechanics FEA femur bone photoelasticity ANSYS

1. Introduction

The femur bone is a most proximal bone of leg in vertebrates that capable of walking and jumping. In human anatomy, the femur is the longest and largest bone however it is muscular for compressive loads only. The femur is responsible to bear the major percentage of body weight during standard force bearing activities. Its length is about 26% of the total height of a body, which is a ratio used in anthropology since it offers a reasonable estimate of the height of person. The structure of femur is long, slender and almost cylindrical in nature, where the straight part of the femur is known as the femoral shaft [1]. If any breaking occurs anywhere along the length of bone, it is called as femoral shaft failure. The bone spatial structure is a major complexity in the course of detailed analysis to observe the mechanical properties. The varying cross section of a long bone with a curvature makes the standard stress-strain studies unreliable using a typical Instron-type machine. In fact, simple numerical figures corresponding to the maximum strain a bone can withstand would influence the fracture at an early stage because of the unreliable stress distribution data. In addition, the dynamic analysis of Femur implants should replicate the real time results to ensure the strength and stiffness characteristics of biomaterials [2].

Photoelasticity is an attractive approach to capture the picture of stress distribution even around abrupt discontinuities in a material. Though, it is a tool for determining the critical stress points in irregular geometries, Photoelastic studies of actual bone are relatively inadequate in the literature. Further, most of the available references deal with teeth and mouth clip implants that are obvious relevance to orthodontics. On the other hand, computational design and simulation has witnessed incredible advancements in the last few decades, because of the availability of powerful FEA packages and several remarkable attempts to understand the biomechanics problems by the computing tools. At the free boundary of a two-dimensional (2-D) body critical stresses occur frequently and hence photoelasticity techniques are useful for determining stress distributions. However, at points in the interior part of 2-D specimens, individual values corresponding to the principal stresses cannot be attained directly through the optical patterns without using supplementary data or by employing numerical methods. In the case of porous structural analysis, the most apposite scaffold configuration will be used to attain the 3D shapes with the help of FEA analysis [3]. The outcome of the stress distribution in the scaffold configuration helps to identify the bio compatible metallic materials for the injured portions.

Accordingly, in the present work FEA approach is used towards the characterization of the behaviour of human femur by using FEM simulations. It is intended to have better understanding about the key parameters to be considered for the fracture investigation of a real long bone [4]. The photo elastic approach is used to validate the computational solutions particularly to identify the regions of higher stress concentrations. Although, FEM has been utilized successfully in recent years for many biomechanical applications, including topological optimization of prosthesis, its use for understanding the mechanical properties of the bone itself has been more limited. FEA based investigation on the evaluation of frequency variations versus depth bone crack is an emerging field as a measure of rehabilitation of fractured bone [5]. A simple validation is also carried out using photoelastic technique to understand the critical stress distribution behaviour at the required nodes [6]. It helps to enhance the clinical performance of Femur implants through the selection of efficient biomaterials for other orthopaedic applications as well. The different sections of a Femur bone are illustrated in Fig. 1.

Figure 1.

Different sections of a Femur bone.

1.1 Simulation modelling in bioengineering

In the case of 2-D stress fields, the isochromatic fringes are loci of points of constant maximum shear stress in the plane of the specimen. By the simple counting of fringes and multiplying their number of order by a calibration constant, the maximum principal stress difference throughout the specimen can be computed. In FEA, on free boundaries and at any other point where the stress field is uniaxial, the maximum shear stress is equal to one-half of the non-zero principal stress (i.e., 1.5). The stress distribution and deformation patterns are extremely important because of the following reasons:

•
Worldwide, lifetime risk for osteoporotic fractures in women is 30–50%. In men risk is about 15–30% [1].
•
Osteoporosis is often called as the “silent disease” because bone loss occurs without any symptoms. In numerous cases, the first “symptom” is a broken bone [1].
•
Broken bones can be associated with a further deterioration in health.
•
Major contribution to the fracture toughness of a bone is intrinsic toughening mechanism that promotes “plasticity” through which micron-scale cracks occur.

1.2 Femur failure

Biomechanical analysis is an interdisciplinary branch which combines biology and Mechanical engineering to realize the behaviour of biological materials. Femur fractures are the important subject of investigation in orthopaedic trauma because they are the strongest and heaviest bones in a human body. Normally, injury occurs to a healthy femur because of high energy phenomena such as sporting activities, motor vehicle accident and adventure actions. If a diaphyseal fracture of a femur bone occurs, then prosthetic device such as bone plates are placed across the fracture line on the lateral femur surface with bicortical screws [7]. These plainly shaped bone plates with various material properties are used to enhance the biomechanical functions as required. In the course of computational investigation, Femur bone with horizontal and oblique loads at the cortical zone is modelled to determine the fracture characteristics using FEA. Stress fracture is a type of biomechanical failure of bones caused by repetitive skeletal loads during intense physical training. It is a kind of fatigue fracture and the FEA findings of such Femur failures are widely used to identify the best suitable material for the implant.

1.3 Types of femoral shaft fractures

Based on the forces acting on the Femur and the nature of incidents, Femur fractures are classified as follows [8];

•
The location of fracture.
•
The pattern of fracture.
•
Whether the skin and muscle above the bone is torn by the injury.

Two example femoral shaft fractures are illustrated in Fig. 2. The most common types of femoral shaft fractures can be listed as follows:

•
Transverse fracture.
•
Oblique fracture.
•
Spiral fracture.
•
Comminuted fracture.
•
Open fracture.

Figure 2.
Femoral shaft fractures.

2. Related work

Horta et al. studied the behaviour of human Femur by Finite Element simulations along with Photoelastic analysis that aims to have better understanding of key parameters related to the fracture of a real long bone. Further, it was emphasized that the FEA simulations should include the possible changes in cross section at different boundary conditions of the epiphysis of femoral human bones to achieve better agreement with Clinical studies [9]. Kubicek and Florian did the stress strain analysis of a normal tibio-femoral joint in its basic position and the system was loaded by displacement. Here, the force representing the load within the knee joint area has been determined by ANSYS direct 3D numerical simulation [10]. The combination of experimental methods with high capacity modern computers resulted in the creation of tools for stress and strain analysis in orthopaedics biomechanics by immeasurable possibilities [11]. A 3D graphical modelling method for human Femur bone was presented by Popa et al through Computer Aided Design (CAD) parametric software which permits to define models with high degree of difficulty. Here, the virtual Femur can be prepared for any FEA to perform kinematical and dynamic simulations [12].

FEA is widely used to describe the Mechanical behaviour of bones and a typical Biomechanical stress analysis of a human Femur using ANSYS was presented by Kumar et al. Here, the stress and strain distribution is determined through two loading cases as follows: i) Hip joint reaction force alone, ii) hip joint reaction force with all other muscle forces. The results obtained from this study can be used to determine the stress at which the fracture occurs in a Femur and it also helps to decide the thickness and the type of material required to repair the fractured bone [13]. Similarly, Huang et al. examined the fundamental dynamic characteristics of both the solid and hollow Femur through experimental and numerical methods. Reverse engineering is applied to obtain the outer geometry of synthesis Femur. The drawing process of excavation in the Femur canal is built up to approximate real human hollow Femur situation. The natural frequencies, stresses, strains, and displacements are obtained by applying a 1000 N force and then compared between the solid and hollow femur where the promising results are matched with the physical rules [14]. Gomide (1996) studied the human bones through Photoelasticity techniques to obtain the distribution of stresses in some critical points of the human body. It is concluded that the utility of Photoelastic studies is extensive for determining stress distribution in the Femur bones [15].

Yousif and Aziz did the Biomechanical analysis of a human Femur bone during normal walking and standing up such that the data associated with the hip contact forces during one cycle has been investigated. The results of the analysis are supportive for an orthopaedic surgeon to understand the Biomechanical behaviour of the Femur bone to perform surgeries and bone prosthesis. The obtained stress distributions are useful for determining the strength, material selection, fixation and friction of implants [17]. Das and Sarangi investigated the stress distribution at the fractured site of the Femur as the system is subjected to torsional and compressive loadings along with different curing phases. Here, three different materials were selected for fabricating bone plate and screws. Then, FE analysis was done using the assembled models and it is observed that the torsion loads have major effect on the resultant stress to fix the bone plate system [18]. Heyland et al. stated that a proper understanding of mechanical Boundary Condition (BC) is mandatory to compute the Biomechanical characteristics of a Femur. Any modifications in the BC may lead to different strain distributions that would influence the mode of deflection under the action of loads [19]. From the related works, it has been concluded that the stress and deformation distribution varies with applied BC. Further, the maximum stresses and minimum deformations are located at the restraint end of Femur which indicates typical behaviour of cantilever beam structure in a bone.

2.1 Inference from literature survey

•
Femur is the longest and strongest bone in our body and the most common case of femoral shaft fracture caused by motor cycle crash [8, 14].
•
From the experiments, it is observed that the knee is more likely to be injured than any other joint in the body because of displacements and the stress distribution.
•
To predict the forces acting at the screw/rod junction, FEA methods are highly feasible due to the transmission of much greater bending moment.
•
A smaller femoral neck-shaft angle is a key risk factor for the unstable tension type of fracture [19].

3. Materials and methods

In the present work, a Femur bone is assumed from the right leg which is subjected to an impact in middle of the shaft by an accident or any external force. The hard outer layer of bones is composed of cortical bone also called compact bone. Cortical refers to the outer (cortex) layer. The hard outer layer provides smooth, solid appearance, and accounts for 80% of the total bone mass of an adult human skeleton. The failure stress investigation is focused towards the Cortical bone in the present article because of its role on the stress bearing at various circumstances. Figure 3 shows a typical failure of femoral shaft that is caused by an accident of a Motorcycle. Here, the external force on shaft causes the crack and the victim is treated with flat rod and nail by an orthopedic. Hence, to determine the stresses, stress intensity and deflection in a reliable manner, the femoral shaft should be investigated with horizontal loads and femoral head with vertical load cases respectively.

3.1 Bone types and material properties

Bone is a typical example for natural composite material and its properties differ from section to section [20]. Primarily, bone is a matrix material and bone tissue is relatively hard and lightweight in nature. Its matrix portion is made up of composite materials by incorporating the inorganic mineral calcium phosphate in the chemical arrangement termed as calcium hydroxyl apatite and collagen. Bone is formed by the solidification matrix material around entrapped cells. However, in the present study the behaviour of human Femur bone has been assumed as orthotropic, and homogeneous. The values of Young’s modulus for the Femur model have been determined according to the empirical relationship that correlates the density of the bone as listed in Table 1.

Table 1
Femur bone properties [16]

S.No	Parameter	Cortical bone
1.	Density(g/cm ${}^{3}$ )	2.0208
2.	Modulus of Elasticity (MPa)	$E_{1}=$ 6982.9
		$E_{2}=$ 6982.9
		$E_{3}=$ 18155
3.	Poisson’s ratio	$\upsilon_{12}=$ 0.4
		$\upsilon_{23}=$ 0.25
		$\upsilon_{31}=$ 0.25
4.	Shear modulus (GPa)	$G_{12}=$ 4.69
		$G_{23}=$ 5.61
		$G_{31}=$ 7.68

Figure 3.

Scan report of a sample fracture in a Femur bone.

4. Modeling of bone structure

The knee joint is an essential for the human locomotion system that includes bones, ligaments, and cartilages. It is tricky to realize the Biomechanical properties and fractural type of Femur because of the knee joint. Primarily, a typical Femur structure consists of compact bone, sponge bone, medullary cavity, yellow marrow, periosteum, and articular cartilage.

Figure 4.

Actual illustration and measurement of Femur bone [16].

Typically, the average length of an adult Femur is about 48 cm and diameter at the mid-shaft is about 2.84 cm. The geometric parameters of Femur are measured through X-ray photograph and it has the ability to sustain up to 30 times of the weight of an adult. The length of Femur medullary cavity of male and female are 33.51 $\pm$ 0.63 cm and 33.13 $\pm$ 0.64 cm respectively. Figure 4 shows an actual illustration of Femur bone with the angle of bending measurement at the mid-section.

4.1 Computational dimensions of bone

Image-based scans are generally used for preparing the Femur model to conduct the FEM based investigations. Hence, few orthopedic fracture reports have been reviewed to develop the computational model. The computational modeling of Femur bone is done by Solidworks software based on the orthopedic reports.

Figure 5.

Different sections in modelling a). 40, b). 190, c). 300, d). 420.

Initially, five reference planes are defined (0, 40, 190, 300 and 420) in which the measurements are made with respect to the correspondent planes on real model by the command Insert/Plane [12]. The first section is defined and sketched in plane 40 as presented Fig. 5a. Similarly, in planes 190, 300 and 420 the sections are defined as presented Fig. 5b–d respectively. Later, the defined sections were united into a single shape by the command Insert/Base/Loft options. The Fillet command was applied for different edges and surfaces to obtain the final version of computational model (virtual Femur) for FEA.

Figure 6.

Cross sectional view and dimensions of femoral shaft (in mm).

Figure 6 illustrates the various dimensions of Femur considered during the modelling process. That dimensions shown in Fig. 6 are related in proportion with the cross section values. The modelling of shaft with different planes is performed with wireframe technique to view the path of edges. Once the vertex of each plane is joined, the femur shaft modelling is completed at the head end.

5. Fea analysis of bone structure

In the recent years, FEA has been widely used to describe the Biomechanical behaviour of human bones. By applying the suitable assumptions and physical principles, the characteristics of bone structures can be studied through simulations with high reliability. Mainly, the force vector acting on a femoral head depends on the external forces acting on the limb and the internal forces are primarily generated by muscle contraction. Asymmetrical geometry, intricate microstructure of biological tissues and loading conditions are the specific problems encountered while the FEA methodology is applied for Biomechanics applications. Firstly, the 3D model of Femur bone is developed as similar to the one presented in Fig. 4 with the assumption that the dimensions are equivalent to a healthy adult individual.

5.1 Mesh preparation

Meshing is a process of dividing a complex domain into finite number of parts and it is an essential step involved in FEA. Here, an optimized mesh has been developed for the Femur model as illustrated in Fig. 7 using ANSYS Workbench meshing tools. Appropriate pre-processor settings and values have been executed to employ smaller elements on proximities and curvatures of the model. The present investigation uses the material model of the bones, cartilage, meniscus and ligaments as anisotropic, linearly elastic continuum based on the data observed from the literatures. The total number of tetrahedral elements used for the Femur model is about 18,144 and the number of nodes is 29,871. Previously, mesh dependency check has been exercised to analyse the magnitude of stress variation with mesh size [13]. The regions of higher stress concentration are tailored with more nodes to capture the nonlinear stress fields with optimal accuracy. Further, the element type assumed as PIPE 16 that is a uniaxial element with tension-compression, torsion and bending capabilities. PIPE 16 element has six Degrees of Freedom (DoF) at the two reference nodes.

Figure 7.

Meshed view of the Femur model.

5.2 Boundary condition

The FEA analysis is done for the two different cases with appropriate boundary condition. Firstly, the cortical bone is subjected to a straight down vertical force about 3 KN while the substructure end is arrested for all DoF (Example: falling from altitudes or vertical object collision). This force magnitude has been assigned based on the assumption that the load bearing capacity is 10 times of body heaviness in a single side (30 kg for a healthy adult). In the second case, the external load (1000 N) is applied perpendicular to the axis of femur shaft while the top and bottom ends are arrested (Example: Motorcycle racing or any other vehicle impact). In both the cases, the loads are assumed as momentary strikes and the duration of impact is one second.

5.3 Results for cortical bone under straight down load

Firstly, the computational simulations are done for the cortical bone with straight down load and the boundary conditions are displayed in Fig. 8a. For the vertical instant load applied on the Femur head of cortical bone, the maximum dislocation obtained is 9.932 mm. Here, approximately half of the length of Femur is not subjected to any deformation whereas the remaining half portion undergoes large displacements that indicate a fatal fracture zone in Fig. 8b. Similarly, the equivalent stress distribution in the Femur because of the vertical load of 3000 N is highlighted in Fig. 8c. Since, the knee joint of cortical bone is fixed comminute fracture occurs beneath the head at the maximum stress level reaches about 123.59 MPa. The stress intensity is also high at the bottom neck of Femur head and it reaches the minimum value at base that refers lateral condyle on femur as illustrated in Fig. 8d. Though, the failure stresses are comparatively higher for the Femur, the impact loads have the potential to initiate the fracture and dislocations at the joints. Hence, the diaphysis region is highly vulnerable to facture in the course of inclination exists for any kind of impact loads. The stress concentration factor is a key parameter to assess the region of fracture and it can be visualized perfectly through photoelastic technique.

Figure 8.

Results for cortical bone under straight down load case.

5.4 Results in cortical bone under external impact load

In the second case, the cortical bone is subjected to an external impact load with the prescribed boundary conditions as shown in Fig. 9a. Here, the top and bottom ends are fixed and it acts as a simply supported beam with a point impact load of 1000 N at the mid-span. In the course of lateral impact loading, it is well known that a micro crack could induce severe fracture and the bone material possess meagre fracture toughness. The maximum deformation occurs in the middle of shaft as highlighted in Fig. 9b and the value is about 0.0724 mm. The stress concentration is also high at the middle of Femur but interestingly it is observed that the neck region experiences more stress intensity as compared to the midpoint (Fig. 9c and d). The reduction in the cross sectional area and the fixed support reaction are the crucial reasons behind the higher stress concentrations at the neck regions.

Figure 9.

Results for cortical bone under external impact load.

6. Photoelastic analysis

Experimental stress analysis is a great approach to conclude the reliability of FEA results and it has extensive applications in the field of Biomechanics. For complex geometries with different loading conditions, photoelasticity offers point-by-point stress and strain information with high order of accuracy [16, 21]. The 3D photoelastic investigation is done in the present work to capture the regions of high stress intensity in the Femur. The results show that the Femur bone has the potential to withstand straight down loads (about 5 times of adult weight) as compared to the external impact loads. If a small deformation exists in Femur shaft, it leads to micro level fracture initiation and subsequently it causes the pain [22]. The strain magnitudes may be changed based on various boundary conditions and stiffness of the bone structures. The photoelastic method helps to avoid the analysis of fresh or dry human bones and it offers quite promising results to validate the numerical analysis.

6.1 3D model of femur

The 3D model of Femur bone is prepared using Acrylic material with maximum similarity except the curvature at the Knee joint. A wax pattern of Femur is developed by moulding technique with the 1:6 ratio scaled dimensions as shown in Fig. 6. This scaling is necessary to fix the model in the testing environment of a circular Polariscope. A wax sheet is shaped based on the scale ratio and a cavity shape is created using Plaster of Paris as presented in Fig. 10a. In the next step, Acrylic powder is filled inside the cavity and it is heated for several seconds. The plasters in Femur model are removed after cooling and the edges are polished to produce better transparency. The 3D model of Femur bone created by moulding technique is shown in Fig. 10b.

Figure 10.

Fabricated 3D model of Femur bone.

Figure 11.

Photoelastic bench apparatus (circular Polariscope).

6.2 Isochromatic fringes from circular Polariscope

The photoelastic bench apparatus (circular Polariscope) that is used for capturing the isochromatic fringes is displayed in Fig. 11. In the plane polariscope, angles and phase difference are the key factors to compute the light intensity. In addition to this, isochromatics and isoclinics emerge concurrently in plane polariscope that makes the fringe understanding task as complex one. Hence, circular polariscope arrangement is used in this experimental analysis to remove the isoclinics for capturing the isochromatics precisely [23]. The principal stress difference should be constant to justify that the captured fringes are isochromatic in nature [11]. The direction of principal stress distribution can be specified as Isoclinics because it is simply the loci of all principal directions.

Figure 12.

Isochromatic fringes in the 3D model observed at various loading points.

Figure 13.

Isochromatic fringes in 3D model observed using white light.

Figure 14.

Isochromatic fringes in 3D model observed using monochromatic light.

The isochromatic fringes are captured at different loading conditions and positions of the Femur bone to analyse the variation of stress intensity around the epiphyseal plate. Figure 12 shows the fringes that are captured at different loading conditions on the Femur neck and head. As the 5 kg load is applied on the Femur neck, the epiphyseal line experiences significant amount of residual stresses because of the remote loading point as highlighted in Fig. 12a. It is further intensified in proportion to the incremental applied loads (Fig. 12b) and growing around the cartilage plates. The region of high stress intensity on Femur head is observed for the similar loading conditions shown in Fig. 12c and d. From the isochromatic fringes, the quantitative stress intensity analysis is done and a linear variation of stress intensity factor ( $\sigma$ ) is observed in the range of $\sigma=$ 0.3 to $\sigma=$ 2.11.

Figure 13 shows the isochromatic fringes that are captured under the application of straight down load about 500 N (scaled for the model size). The illumination of white light offers the colour fringes and then the quantitative stress analysis is performed. The region of high stress intensity on Femur bone is observed by the isochromatic fringes because its intensity is invariant with respect to the Polariser or Analyser. For validating the quantitative stress analysis done by FEA tools, region of high stress intensity is observed through expanded view as shown in Fig. 12b. The lines of constant colour are obtained through circular polariscope and it is related to the stress concentration factor to identify the load distribution in the Femur.

The black fringes are observed with Photoelastic method when the monochromatic light source is enabled. Figure 14 shows the loading point of Femur head that is subjected to a monochromatic light source with isochromatic fringes corresponding to the light field. It is observed that the region of maximum stress intensity is exactly matched while the Figs 8 and 14 are compared. However, the input load magnitudes are different and the light field is obtained by rotating the analyser to 90 ${}^{\circ}$ . The dense fringes presented in Fig. 14b represent the higher stress concentration which is essential to identify the impact strength of Femur [24].

The stress concentration around the epiphyseal prostheses probably induces the femoral neck failures in the course of minimal impacts. At different loading conditions (Figs 12 and 13), it is observed that the localized stresses around the point of contact hasten the stress concentrations across anterior surface. Hence, under various loading conditions the treatments like epiphyseal replacement or stress shielding should elucidate the stress concentrations around anterior and posterior surfaces. The photoelastic method is a simple approach to determine the stress distribution in a Femur bone. In the present work, the FEA investigation is validated through photoelastic experiment and these results can be easily correlated to actual bone implants. However, to attain quantitative results few additional calculations are required by including the optical parameters and different loading conditions.

7. Conclusions

The determination of the stress concentration factor is essential to perform any kind of bone implants. The benefit of photoelastic method is that the stress distribution can be visualized to identify the weak sections of the bone. It helps to minimize the post surgical problems caused by the frozen stresses around the Femur neck or head. Since, there is no specific law exist for bone modelling in FEA, often the mechanical environment would not be matched with biological responses. Hence, the cortical patterns are modelled with extra care to obtain maximum reliability in the FEA results. The mechanical environment of Femur requires density based simulation and hence the trabecular portion was treated with special elements in the course of FEA analysis. The Mechanobiological interactions can be treated well by understanding the direction of internal stresses of Femur around proximal epiphysis at various loading circumstances which includes horizontal as well as vertical impacts. The maximum stress concentration about 2.11 is obtained at the Femur neck because of the geometrical changes between the femur ball and shaft. In the practice of bone implants, it is mandatory to ensure the exact radius of bone shaft and ball to have the stress concentration as minimum as possible. Hence, the determination of stress intensity and direction of principal stress by means of experiments and/or computational methods is essential prior to the bone implants to attain optimal benefits.

Footnotes

Conflict of interest

None to report.

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