Numerical Investigation of Braided Structure Potential as a Cast for Femur Shaft Fracture

Abstract

Femur fractures are repaired using orthopedic implants involving external and internal fixators. Meanwhile, tubular braided structures have not been considered for bone-shaft fracture repair, despite their potential in use as orthopedic casts. This study investigates potential of using bi-axial braided structures as casts for femur diaphysis fracture under bending loads. The braided structure model was developed using a python script while a hollow femur bone shaft was created in a 3D interface using FE Analysis methods in ABAQUS (v17) from a femur bone model rendered using MIMICS from femur bone CT scan. Numerical methods were used to investigate the change in bone shape eccentricity due to bending loads in-terms of load carrying capacity, bone curvature, bending resistance and stresses in the bone shaft. The results portrayed influence of the braided structure in ensuring the stresses due to the bending load are distributed evenly on the femur shaft surface.

1. Introduction

Human Femur bone is a natural composite material consisting of a cellular component and an extra cellular component. It consists of the cortical bone and the trabecular bone [1]. The femur bone’s cortical bone is the primary load carrying material. This is attributed to the presence of osteon density and fraction of osteonal structures within the cortical bone layer of the femur structure [2]. It has also been shown that tissue strength in the cortical region is superior compared to other sections of the femur bone [3]. In the course of femur use during motion the cortical bone is loaded mostly by bending moments, resulting in a high percentage of tensile strain. Even though cortical shell and the trabecular matrix contribute substantially to the strength of the peripheral skeleton [4], the cortical bone has also been attributed with supporting most of the loads on the human skeleton. The toughness of femur bone also known as energy to failure, which is the bones property associated to its capability to absorb energy during failure has been linked to the risk of fracture in the bones. Nevertheless, even though the bone structure is susceptible to rupture, there is evidence that the living tissue material within its micro-structure is capable of self-repair [5]. This special property can be exploited during repair of femur bones.

Conventionally, fracture in femur’s cortical bone has been done using metal plates [6]. This repair technique using plates is normally associated with stress shielding that may lead to resorption and osteoporosis [7] due to insufficient physiological loading on the bone [8]. which eventually can cause bone refractures when the plate is removed especially in fracture in diaphyseal region [9].

An attempt of replacing the conventional bone repair techniques have been done by using braided [8, 9] and knitted [10] composite casts to repair bone fractures. The results from the use of the braided structures were associated with reduction in stress concentrations in the fractured ends of the bone than a plate. It was also reported that The tubular cast has been shown to be a promising fixation method for healing broken bones [8]. This could be linked to the fact that braided structures used as bone casts have demonstrated better ability for distributing stress [11].

The use of Finite Element (FE) modeling has been effective in the analysis of bone mechanics [12]. Further, FE approaches have been used in predicting modes of bone failure under stance and fall configurations [13] and also in the analysis of the composite reinforcement of femur bone using composite casts [8].

In this paper, we propose a braided structure with enough rigidity to reinforce the bone at fracture site. The braided structure potentially offers support and enough stiffness to the bone around the site of fracture. This study applies numerical and analytical techniques to demonstrate feasibility of using tubular braided structures in reinforcing fractured femur bones under single stance conditions.

2. Design of braided reinforcement structure

The reinforcement consists of a braided structure and fixators at both ends of the structure. The design of the braided structure was done by modeling a circular coordinate of a helical path in a three-dimensional space in both clockwise and counter-clockwise directions. The general coordinates of the helical yarn path in the clockwise and anticlockwise direction as (Figure 1):

Figure 1.

Illustration of the geometry of the yarn path on a tubular braided structure.

Clockwise direction:

$${\mathrm{X}}_{\mathrm{i}}=\left[{\mathrm{r}}_{\mathrm{o}}+\mathrm{r}\left(\mathrm{\theta }\right)\right]cos\left[-\mathrm{\theta }-\left(\mathrm{i}-1\right)\mathrm{\beta }\right],\mathrm{i}=1,2,\cdots \mathrm{n}$$E1

$${\mathrm{Y}}_{\mathrm{i}}=\left[{\mathrm{r}}_{\mathrm{o}}+\mathrm{r}\left(\mathrm{\theta }\right)\right]sin\left[-\mathrm{\theta }-\left(\mathrm{i}-1\right)\mathrm{\beta }\right],\mathrm{i}=1,2,\cdots \mathrm{n}$$E2

$${\mathrm{Z}}_{\mathrm{i}}={\mathrm{r}}_{\mathrm{o}}\text{tanαθ},\mathrm{i}=1,2,\cdots \mathrm{n}$$E3

where:

$${\mathrm{r}}_{\mathrm{o}}=\frac{2\text{pcos}\propto }{\mathrm{\beta }}$$E4

$$\mathrm{r}\left(\mathrm{\theta }\right)=\frac{a}{2}sin\left(\frac{2\mathrm{\pi }}{\mathrm{\beta }}\mathrm{\theta }+\frac{3\mathrm{\pi }}{2}\right)$$E5

Anti-clockwise direction:

$${\mathrm{X}}_{\mathrm{i}}=\left[{\mathrm{r}}_{\mathrm{o}}+\mathrm{r}\left(\mathrm{\theta }\right)\right]cos\left[\mathrm{\theta }+\left(\mathrm{i}-1\right)\mathrm{\beta }\right],\mathrm{i}=1,2,\cdots \mathrm{n}$$E6

$${\mathrm{Y}}_{\mathrm{i}}=\left[{\mathrm{r}}_{\mathrm{o}}+\mathrm{r}\left(\mathrm{\theta }\right)\right]sin\left[\mathrm{\theta }+\left(\mathrm{i}-1\right)\mathrm{\beta }\right],\mathrm{i}=1,2,\cdots \mathrm{n}$$E7

$${\mathrm{Z}}_{\mathrm{i}}={\mathrm{r}}_{\mathrm{o}}\text{tanαθ},\mathrm{i}=1,2,\cdots \mathrm{n}$$E8

In which the values of r_o are the same as Eq. (4) and r(θ) can be evaluated as: where:

$${\mathrm{r}}_{\mathrm{o}}=\frac{2\text{pcos}\propto }{\mathrm{\beta }}$$E9

$$\mathrm{r}\left(\mathrm{\theta }\right)=\frac{a}{2}sin\left(\frac{2\mathrm{\pi }}{\mathrm{\beta }}\mathrm{\theta }+\frac{\mathrm{\pi }}{2}\right)$$E10

The generic designs of braided fabrics can be modeled by formulating the coordinates for the yarn path by imputing the values of the parameters r_o and r(θ) into Eqs. (6)–(8) to (9)–(11). In the case of a diamond braided fabric, the parameters can be evaluated as follows:

Clockwise direction:

$${\mathrm{r}}_{\mathrm{o}}=\frac{\left(2\mathrm{p}+{\mathrm{p}}^{\prime }\right)cos\propto }{\mathrm{\beta }}$$E11

$$\mathrm{r}\left(\mathrm{\theta }\right)=\left\{\begin{array}{cc}\frac{-a}{2}& 0<\mathrm{\theta }<\frac{{\mathrm{k}}_1\mathrm{\beta }}{2},\\ \frac{a}{2sin\left(\frac{2\mathrm{\pi }}{\mathrm{\beta }}\mathrm{\theta }+\frac{3\mathrm{\pi }}{2}\right)}& \frac{{\mathrm{k}}_1\mathrm{\beta }}{2}<\mathrm{\theta }<\frac{\left({\mathrm{k}}_1+1\right)\mathrm{\beta }}{2},\\ \frac{-a}{2}& 0<\mathrm{\theta }<\frac{{\mathrm{k}}_1\mathrm{\beta }}{2},\\ \frac{a}{2sin\left(\frac{2\mathrm{\pi }}{\mathrm{\beta }}\mathrm{\theta }+\frac{3\mathrm{\pi }}{2}\right)}& \frac{{\mathrm{k}}_1\mathrm{\beta }}{2}<\mathrm{\theta }<\frac{\left({\mathrm{k}}_1+1\right)\mathrm{\beta }}{2},\end{array}\right.$$E12

Anti-clockwise direction:

the value for r_o can be evaluated using Eq. (11), then,

$$\mathrm{r}\left(\mathrm{\theta }\right)=\left\{\begin{array}{cc}\frac{-a}{2}& 0<\mathrm{\theta }<\frac{{\mathrm{k}}_1\mathrm{\beta }}{2},\\ \frac{a}{2sin\left(\frac{2\mathrm{\pi }}{\mathrm{\beta }}\mathrm{\theta }+\frac{3\mathrm{\pi }}{2}\right)}& \frac{{\mathrm{k}}_1\mathrm{\beta }}{2}<\mathrm{\theta }<\frac{\left({\mathrm{k}}_1+1\right)\mathrm{\beta }}{2},\\ \frac{-a}{2}& 0<\mathrm{\theta }<\frac{{\mathrm{k}}_1\mathrm{\beta }}{2},\\ \frac{a}{2sin\left(\frac{2\mathrm{\pi }}{\mathrm{\beta }}\mathrm{\theta }+\frac{3\mathrm{\pi }}{2}\right)}& \frac{{\mathrm{k}}_1\mathrm{\beta }}{2}<\mathrm{\theta }<\frac{\left({\mathrm{k}}_1+1\right)\mathrm{\beta }}{2},\end{array}\right.$$E13

3. Materials and methods

The study involves 3D CAD developed human femur bone. Quasi-Static structural analysis was carried out using ABAQUS17 to determine the load, stress, and deformation criterion of the bone with fracture before, during and after repair with a braided structure. The model of the braided structure was developed using a python script using the parameters illustrated in Figure 2.

Figure 2.

Illustration of the geometry of braided structure.

A force of 800 N was applied to induce bone displacement to simulate two configurations of single stance conditions of a human femur: (SC1, θ = 120 and SC2, θ = 90) as shown in Figure 3.

Figure 3.

Models of the femur bone structure showing: (a) single stance configuration (SC1 θ = 120); (b) position of the femur fracture at the bone shaft; and (c) ingle stance configuration (SC2 θ = 90).

The profile of the femur mid-shaft was isolated inform of a surface using the commercial software paraview and then the center-line of the shaft surface traced in VMTK after-which a MATLAB algorithm was used to develop a crimper model for deploying the circular braided structure onto the oblique cut-femur bone as shown in Figure 4 in ABAQUS CAE.

Figure 4.

Illustration of the numerical models for deployment of the braided structure onto the cut-femur model.

The 3D model of the braided structure was developed using a python script, an input file generated and imported into ABAQUS17. The assembly of the bone and braided structure and quasi-static structural analysis was carried out in ABAQUS17. The material properties assigned for the cortical bone are as shown in Table 1. The femur bone was modeled as a linear elastic material to reduce computation time and complexity of the analysis [15].

SI units	Material properties
Young’s modulus	17 GPa
Density	2 gcm^−3
Poisson’s ratio	0.30
Tensile strength	130 MPa

Table 1.

Material properties of cortical bone [14].

Quasi-Static structural analysis was carried out for both the models of the single stance configurations (SC1, θ = 120 and SC2, θ = 90). The lower end of the femur bone was fixed to mimic the normal human stance condition in all the analysis. Force applied was 800 N and was applied on femoral head at 120 and 90. The total load in the femur von Misses stress and total deformation in Z axis were evaluated for an intact femur, then for a fracture femur and eventually for a reinforced femur.

4. Validation

The Finite Element (FE) models adopted in this study were validated using data from previous research [16] as shown in Figure 5. The data shows close correlation between our model data and experimental data of femur bone analysis. The data was then used in the analysis of fall and stance configuration for the femur bone used in this study.

Figure 5.

Validation results for 3D femur model.

5. Results and discussions

The results from the numerical simulation of a single stance configurations (SC1 and SC2) for a human intact femur bone were plotted as shown in Figure 6a for load against displacement. It was established from the results that in an intact femur the load due to SC1 will be more than that in a SC2 type of stance configuration. The results further show that the intact bone during SC1 stance could withstand more stress than in the SC2 stance as shown in Figure 6b.

Figure 6.

(a) The illustration of load against displacement for human femur fall and single stance configuration for an intact bone structure; and (b) the illustration of stress against displacement for human femur fall and single stance configuration for an intact bone structure.

A fracture was then introduced to the intact femur. The force of 800 N was then applied to simulate a single stance configuration. The results of numerical simulation were plotted as shown in Figure 7a for load against displacement. It was established from the results that in a fractured femur the load due to SC1 stance will be more than that in an SC2 configuration. The results further show that the fractured bone during SC1 stance could withstand more stress than in the SC2 configuration as shown in Figure 7b.

Figure 7.

(a) The illustration of load against displacement for human femur fall and single stance configuration for a fractured bone structure; and (b) the illustration of stress against displacement for human femur fall and single stance configuration for a fractured bone structure.

The model of the fractured femur was then reinforced using a tubular braided structure. To simulate fixators on the braided structures tie-constraints in ABAQUS were introduced at the ends of the the braided structure. An 800 N was then applied to simulate a single stance and fall configurations. The results of numerical simulation were plotted as shown in Figure 8a for load against displacement. It was established from the results that in the reinforced femur the load due to SC1 stance was more than that in an SC2 configuration. The results further show that the reinforced bone during SC1 could withstand more stress than in the SC2 configuration as shown in Figure 8b.

Figure 8.

(a) The illustration of load against displacement for human femur fall and single stance configuration for a braid-reinforced femur bone structure; and (b) the illustration of stress against displacement for human femur fall and single stance configuration for a braid-reinforced femur bone structure.

The deformation of the femur bone was analyzed for the SC1 conditions because it had higher mechanical properties than the SC2 stance as shown in the results. The deformation results established as shown in Figure 9 that in an intact femur there was an increase in bone deformation with yielding stress. This was illustrated by the contour plots for the von Misses stress on the surface of the femur bone.

Figure 9.

Contour plots for the deformation of the model of the intact femur bone under stance configuration.

The deformation in the fractured femur shown in Figure 10 shows that the femur bone deformation would be higher than that of the intact femur, there was also evidence of the bone yielding at lower stress levels portrayed by the levels of von Misses stress contour plots.

Figure 10.

Contour plots for the deformation of the model of the fractured femur bone under stance configuration.

The reinforced femur structure (Figure 11) however, illustrated lower deformations as compared to both the intact femur model and the fractured femur model.

Figure 11.

Contour plots for the deformation of the model of the braid-reinforced femur bone under stance configuration.

The results predicted in simulation models shows a trend where the load values were higher than the values in the fall configuration, these results were consistent with the findings elsewhere [17] where the fracture load in a stance configuration recorded higher loads than in a fall configuration of the femur bone. The results further established that even though the force applied to the femur was able to deform the bone to some extent, the reinforced bone structure was able to withstand the loads better. This was illustrated by the small deflection and minimum yield stress in the reinforced femur. This is further supported by the large deflection in the femur bone with the obliquecut, when the cut was reinforced using the braided structure the deflection decreased.

6. Quasi-static analysis

The simulation results shows that the models were not affected by viscous energies as portrayed in Figure 12.

Figure 12.

The illustration of quasi-static energy analysis for the simulations for (a) intact femur bone structure; (b) fractured femur bone structure; and (c) reinforced human femur bone structure.

7. Conclusion

The reinforced fractured femur portrayed improved strength and stability which could be attributed to the braided structure. There was also evidence from deformation results that showed that when reinforced the fractured femur, deformed less. Further, the use of finite element methods was found to be appropriate in the study of the feasibility of reinforcing fractured femur with braided structure.

Acknowledgments

The support from Stellenbosch Institute for Advanced Study (STIAS), University of Stellenbosch is appreciated.