Cancellous bone and PMMA cement interfacial fracture properties evaluation using heaviside digital image correlation/wedge splitting test method

Keywords:

• Cancellous bone
• PMMA cement
• specific fracture energy
• digital image correlation
• wedge splitting test

1. Introduction

Balloon Kyphoplasty is a minimally invasive surgery, which has acquired great importance recently for treating compressive bone fractures by balloon inflation and PMMA cement injection (Achatz et al. 2017). The PMMA cement is subjected to challenging body environment once it is injected into the cancellous bone. The PMMA and porous cancellous bone interface experiences complex in vivo 3 D loading which causes compressive and fracture configuration. Many researchers have worked intensively on the mechanical analysis of the bone and PMMA cement. However, works reported on mechanical analysis of bone and PMMA cement interface were limited and none when it comes to fracture analysis.

Therefore, the work reported here focusses mainly on understanding and evaluating the fracture properties (specific fracture energy (G_f) of the cancellous bone, PMMA cement and Bone/PMMA interface using a recently developed integrated methodology (wedge splitting test (WST) and Heaviside based digital image correlation (H-DIC)) (Bokam.P et al., 2020).

2. Methods

2.1. Materials

Three groups of specimens (4 samples per each group) were prepared for present study as shown in Figure 1. (a) cancellous bone extracted from bovine shinbone; (b) PMMA (Kyphon^® Xpede™ Bone Cement) prepared by mixing the powder (Methylmethacrylate-styrene-copolymer 69.1% w/w, Barium sulfate 30%w/w) and liquid (Methylmethacrylate (monomer) 99.4% w/w). (c) cancellous bone extracted from proximal epiphysis region (bovine shine bone) is placed in a mold and in the other half of the mold, the PMMA cement is poured and let it cure. The bonded (Cancellous bone + PMMA) sample was then removed and machined to prepare wedge-splitting samples.

Figure 1. Top: Speckle pattern on WST specimen for (a) cancellous bone, (b) PMMA cement, (c) PMMA + bone interface sample.

2.2. Method

The principle of the wedge splitting method and specimen shapes considered similar as described by E.K. Tschegg 1986. The wedge unit transforms the vertical load (F_v) from the compression test machine (under displacement control) into a higher magnitude of the horizontal force (F_h). This horizontal force F_h (Equation 1(1) $$F_h=\frac{F_v}{2tan(\alpha )}\cdot \frac{1-\mu \cdot tan(\alpha )}{1+\mu \cdot cot(\alpha )}\approx {1.37}^{°}\cdot F_v$$(1) ) leads to the crack initiation at the notch allowing the crack propagating through the specimen. (1) $$F_h=\frac{F_v}{2tan(\alpha )}\cdot \frac{1-\mu \cdot tan(\alpha )}{1+\mu \cdot cot(\alpha )}\approx {1.37}^{°}\cdot F_v$$(1) where F_v is the vertical load applied by the test machine, 2α is the wedge angle (here α = 15 degrees) and µ is the coefficient of friction for the roller bearing.

The entire experimentation was carried in the presence of two CMOS camera (1280 × 1024 pixels with a video acquisition frequency of 0.5 Hz) which are used to record images for the optical full field measurements using Heaviside Digital Image Correlation (H-DIC) method (Valle et al. 2015) to retrieve the crack opening displacement and corresponding crack length. The recorded images were analyzed using Digital Image Correlation H-DIC (Valery et al. 2015) to retrieve the crack opening displacement (COD) and the corresponding crack length.

From the principle of WST, to evaluate the specific fracture energy (G_f) required to open a crack of unit area, the total dissipated energy calculated from load –COD curve was divided with the fractured area (Equation 2(2) $$G_f=\frac{1}{A}\underset{\delta }{\overset{\delta \mathit{max}}{\int }}F\left(\delta \right)d\delta \mathrm{ }$$(2) ). (2) $$G_f=\frac{1}{A}\underset{\delta }{\overset{\delta \mathit{max}}{\int }}F\left(\delta \right)d\delta \mathrm{ }$$(2) where ‘A’ is the ligament area, δ is the COD, and F is the splitting force (two times (F_h)).

The ligament area (A) is obtained by multiplying the crack length (L) by the thickness of the sample. The values of the crack length (L) and COD (δ) were obtained from the H-DIC analysis as shown in Figure 2 (top)).

Figure 2. Top: Von mises equivalent strain maps with crack propagation for (a) cancellous bone, (b) PMMA cement, (c) PMMA-bone samples obtained using the H-DIC. Bottom: Load-COD curves obtained for the three groups of samples.

3. Results and discussion

Figure 2 shows the von mises equivalent strain maps and Load- COD curves obtained from the 2D H-DIC analysis of the images which are recorded during the test.

The maximum force (F_max) at which the crack initiated for the three groups are 99 ± 15 N, 308 ± 12 N, and 22 ± 4 N, respectively. From the load-COD curves for the cancellous bone and PMMA + bone interface samples, we observe variation in the F_max. This can be directly linked to the porosity of the cancellous bone. In addition, the presence of large pores near the crack tip will lower the values of the F_max. The specific fracture energy (G_f) values for the three groups of samples are reported in the Table 1.

Table 1. Specific fracture energy (G_f) values obtained using WST and H-DIC.

Material	Reference	Gf (N/mm)
Bovine	Present study	1.08 ± 0.11
	Tschegg et al. 2012	3.32 ± 1.17
PMMA	Present study	1.71 ± 0.175
	Merta et al. 2017	1.75–1.95
Bone + PMMA	Present study	0.20 ± 0.06

The evaluated values are compared with available literature for cancellous bone and PMMA cement specimens. In addition, the study presents the first results of specific fracture energy values for the PMMA + bone interface samples. However, we observe the obtained values for the samples are lower compared to the PMMA cement. This can be due to the variation of porosity in the cancellous bone and the weak bonding between the cancellous bone and PMMA cement.

4. Conclusions

The present findings contribute the first reports on the specific fracture energy (G_f) values of cancellous bone and PMMA cement interface. The bonding between the cancellous bone and PMMA cement gives an idea to the interfacial fractures between bone and PMMA cement and to understand the re-fracture complications that arouse post kyphoplasty operation.