The mechanical effects of different levels of cement penetration at the cement-bone interface

Abstract

The mechanical effects of varying the depth of cement penetration in the cement-bone interface were investigated using finite element analysis (FEA) and validated using companion experimental data. Two FEA models of the cement-bone interface were created from micro-computed tomography data and the penetration of cement into the bone was varied over six levels each. The FEA models, consisting of the interdigitated cement-bone constructs with friction between cement and bone, were loaded to failure in tension and in shear. The cement and bone elements had provision for crack formation due to excessive stress. The interfacial strength showed a strong relationship with the average interdigitation (r(2)=0.97 and r(2)=0.93 in tension and shear, respectively). Also, the interface strength was strongly related with the contact area (r(2)=0.98 and r(2)=0.95 in tension and shear, respectively). The FEA results compared favorably to the stiffness-strength relationships determined experimentally. Overall, the cement-bone interface was 2.5 times stronger in shear than in tension and 1.15 times stiffer in tension than in shear, independent of the average interdigitation. More cracks occurred in the cement than in the bone, independent of the average interdigitation, consistent with the experimental results. In addition, more cracks were generated in shear than in tension. In conclusion, achieving and maintaining maximal infiltration of cement into the bone to obtain large interdigitation and contact area is key to optimizing the interfacial strength.

Figure 1

Two finite element models were generated from micro-CT scans of the cement-bone interface. These two specimens were sectioned from total hip reconstructions, which were prepared using third generation cementing techniques using PMMA in a laboratory setting. From the initial FE-model of Specimen 1 (top), five other models were generated, each with a different penetration levels (the normal distance with respect to the transverse plane between the top of the bulk of the cement and the bottom of the bone). This resulted in six models of specimen 1 with penetration levels of 0.2, 0.6, 1.0, 1.4, 1.8 and 2.2mm. Same process was done for specimen 2 (bottom), resulting in levels of 0.2, 0.5, 0.8, 1.1, 1.4 and 1.7mm. The figures on the right are section views of the specimens for each penetration level.

Figure 2

A grid (12×6; 0.65mm spacing (Miller et al., 2009)) was constructed on the micro-CT scans and projected vertically through the image sets (a). For each vertical grid line and cement penetration level, the local cement penetration depth was measured (b), resulting in different distributions of interdigitation (c). The average of the 72 local interdigitation measurements was used as a measure of cement penetration depth.

Figure 3

The stress-displacement curve of a cement-bone specimen. The strength was defined as the maximum applied load divided by the nominal cross sectional area of the cement-bone interface. The initial stiffness was determined by a least-squares fit through the stress versus displacement response for applied stress levels less than 50% of the strength (Mann et al., 1997). All cement-bone specimens were characterized by a linear slope followed by yielding till the strength was reached.

Figure 4

Approach used to estimate the contact area between cement and bone (Mann et al., 2008). The micro-CT scan (a) represented the gaps and initial contact between the bone and cement. Subsequently, the micro-CT scan was segmented into two 3D objects (b): cement (grey) and bone (white). Next, the 3D cement object was dilated by two voxels (24μm) (c). The Boolean intersection between the dilated cement and bone object was calculated (d). This volume was subsequently divided by the amount of cement dilation (24μm), resulting in an estimation of the contact area between cement and bone.

Figure 5

Strong linear relationships existed between (a) the tensile strength and average interdigitation (r²=0.97) as well as between (b) shear strength and average interdigitation (r²=0.93). For specimen 2, there was a jump in strength with a small increase in the average interdigitation. The relationship between strength and contact area were also strong in tension (c) and shear (d) (r²=0.98 and r²=0.95, respectively. Note the different scales of the tensile and shear results.

Figure 6

a. The bone-cement interface was 2.5 times stronger in shear than in tension, independent of the penetration depth of the cement (r²=0.98). b. The bone-cement interface was 1.15 times stiffer in tension than in shear, independent of the penetration depth of the cement (r²=0.97).

Figure 7

Strength-stiffness relationships for tensile and shear loading. Lab-prepared specimens were loaded to failure in tension (Mann et al., 2008) and shear, while the post-mortem retrievals were loaded to failure only in tension (Miller et al., 2009). For the strength-stiffness relation in tension (a.), it is noted that even the higher penetrated models of specimen 2 have a strength-stiffness relation that corresponds with post-mortem interfaces. Like the strength-stiffness relation in tension, the strength-stiffness relation in shear compared satisfactorily with the experimental findings (b.).

Figure 8

a. Crack volume of the cement and bone for specimen 1 and 2 when the specimen’s strength was reached in tension. b. Crack volume of the cement and bone for specimen 1 and 2 when the specimen’s strength was reached in shear.

Figure 9

Crack patterns for a cross-section of specimen 1 loaded in tension when the apparent strength was reached. Although the figure only shows one specific cross-section of the interface, it can be seen that the cement in the 1.4mm penetration level envelops several bony spurs which increases the average interdigitation and subsequently the apparent strength (Figure 4a–b). In shear, cracks generally at the same locations, but progressed in a different direction compared to the ‘tensile cracks’. For all penetration levels and loading directions, all cracks were in the interdigitated area of the cement-bone interface and did not progress into the bulk of the bone or cement.