compressive behaviour of bovine cancellous bone and bone ... · web viewfigure 1. the two finite...
TRANSCRIPT
Stress Shielding in Bone of a Bone-Cement Interface
Qing-Hang Zhang1, Andrew Cossey1,2, Jie Tong1,*
1Mechanical Behaviour of Materials Laboratory
School of Engineering,
University of Portsmouth, UK
2Spires Portsmouth Hospital, UK
For correspondence:
Prof. Jie Tong, Ph.D.
Mechanical Behaviour of Materials Laboratory
Department of Mechanical and Design Engineering
University of Portsmouth
Portsmouth PO1 3DJ
UK
Tel: 0044-9284-2326
Fax: 0044-9284-2351
Email: [email protected]
1
2
3
4
5
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
1
ABSTRACT
Cementation is one of the main fixation methods used in joint replacement
surgeries such as Total Knee Replacement (TKR). This work was prompted by a
recent retrieval study [1, 2], which shows losses up to 75% of the bone stock at the
bone-cement interface ten years post TKR. It aims to examine the effects of
cementation on the stress shielding of the interfacing bone, when the influence of an
implant is removed.
A micromechanics finite element study of a generic bone-cement interface is
presented here, where bone elements in the partially and the fully interdigitated
regions were evaluated under selected load cases. The results revealed significant
stress shielding effect in the bone of all bone-cement interface regions, particularly in
fully interdigitated region. This finding may be useful in the studies of implant fixation
and other related orthopedic treatment strategies.
Keywords: bone-cement interface, stress shielding, bone resorption, finite element
analysis.
2
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
2
3
1. Introduction
Bone cement, or polymethylmethacrylate (PMMA), is widely used to anchor
joint replacement prostheses to host bone. It acts as a grout, adapting the surface
irregularities of the surrounding bone tissue to the surface of the inserted prosthesis.
Pressurising cement during insertion improves cement penetration into the
cancellous bone interstices, enabling a better mechanical interdigitation thought
critical for long-term durability. Despite of new joint replacement strategies
introduced, the use of PMMA bone cement in TKR remains one of the most popular
procedures, representing 84.3% of the annual total TKRs performed in England and
Wales [3].
Aseptic loosening is a major failure mechanism in joint replacement, and has
been partially attributed to stress shielding of the bone due to the presence of a
metal prosthesis [4][3]. Although periprosthetic bone density change around a metal
knee implant has been known to occur [5-7], it is only recently that evidence came to
light on bone resorption in the bone-cement interdigitated region in cemented TKR.
Miller et al [1, 2] presented a postmortem retrieval study, where 75% of bone loss
was found at the bone-cement interface in metal-backed tibial components within 10
years of in vivo service, with extensive bony resorption at the periphery of the tibial
trays. This finding has significant implications on the long-term prognosis of this type
of fixation method, as excessive bone resorption will lead to increased micro-motion
and eventual implant loosening.
It is well known that when stiff metal implants are used to replace native
bones, stress shielding in the surrounding bones will occur, regardless of the fixation
3
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
4
5
methods. The question we seek to answer is if bone cement, when interdigitated
with the bone, would have an effect of stress shielding on the bone? Our previous
work [8, 9] seems to suggest that when trabecular bone is interdigitated with cement,
the main damage occurred in the bone whilst the stress level in the bone-cement
interdigitated region is relatively low. In the present study, we hypothesize that the
loss of bone stock may be attributed to the stress shielding caused by cement, in
addition to that by the implant.
2. Material and Methods
A micro-finite element (FE) model of a typical bovine bone-cement interface
sample from our previous study [9], of which the BV/TV of the bone is 0.15, was
used for the current work. A detailed description of specimen preparation, FE mesh
generation and validation of the model was given elsewhere [9], but for
completeness a summary is given here: Images of the bone-cement interface
specimen from µCT were imported into Avizo 6.3 (Visualization Sciences Group,
Mérignac, France), in which the bone and the cement structures were reconstructed,
meshed and imported into Abaqus (6.12) (Dassault Systemes, USA) to assemble a
bone-cement interface model (model BC), which consists 2,506,235 tetrahedral
elements and 571,756 nodes (Figure 1a). The dimension of the model is
9mm×8mm×4.4mm, and the maximum depth of cement penetration is 5.2mm. In
addition, the cement was removed from the model BC to form model BB for
comparison purposes (Figure 1b).
The trabecular bone tissue was modelled as an elastic–plastic material, with
an asymmetric yield strain of 0.6% in tension and 1% in compression [10]. The
elastic modulus, Poisson's ratio and post-yield tangent modulus were assumed to be
4
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
6
7
15GPa, 0.3 and 750MPa, respectively [10]. A similar asymmetrical elastic to perfect
plastic constitutive law was also used for the cement, where the elastic modulus,
Poisson's ratio, yield stress under tension and yield stress under compression were
assumed to be 3GPa, 0.33, 30MPa, and 70MPa, respectively [11, 12]. The
interaction between the contact surface of the bone and the cement was modelled as
surface-to-surface finite sliding contact with a friction coefficient of 0.4 [9].
A compressive load of 88N (Load 1) was applied to the top surface of model
BC and model BB, and the stress distributions in the two models are compared.
Load 1 was chosen to be close to the upper bound of stresses experienced during
routine activities in a normal proximal tibia [13]. Two additional loading conditions,
Load 2 (70.4N) and Load 3 (35.2N), representing 80% and 40% of Load 1,
respectively, were also applied to model BC. These two load cases were chosen to
simulate the reduced stresses experienced in the bone due to the presence of an
implant with a relatively low (Load 2) and high (Load 3) stiffness [14]. Under all
loading conditions, the bottom surfaces of the models were fully constrained.
To assess the effects of stress shielding quantitatively, the bone was divided
roughly into 8 layers, representing bone (Layers 1 to 3), partially interdigitated region
(Layers 4 and 5), where only partial cement penetration occurred; and fully
interdigitated region (Layers 6 to 8), where full cement penetration occurred to form a
bone-cement composite structure. A height of approximately 1mm was chosen for
each layer, and the grey represents cement (Figure 2).
A number of parameters [13-15] have been used to evaluate the effect of
stress shielding in bones. A strain energy density criterion [16] was chosen in this
work as it has been successfully used as a stimulus in bone remodelling [13, 17]. An
5
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
8
9
effective strain energy density in each bone layer may be obtained by averaging the
strain energy of all the elements in that layer:
j=1-8 (1)where SED is the strain energy density, Vi is the volume of element i, n is the total
number of elements within the layer; and j is the number of layers. The difference
between the SEDs of each bone layer from model BB (under Load 1) and model BC
(under Load 1, 2, 3) were calculated and the percentage reduction of SED was used
to measure the effect of stress shielding in bone across the bone-cement interface
for the three load cases k = 1, 2 and 3:
k=1, 2, 3(2)
3. Results
The strain energy density distributions in the eight bone layers under Load 1
are shown in Figure 3 for model BC and model BB. The load was distributed
throughout the entire bone structure in model BB and the bone struts deformed most
evenly. For model BC, however, the load applied from the top surface of bone was
mainly transferred to the cement thus the lower part of the bone interdigitating with
the cement is off-loaded with low stain energy (in blue). It is clear that the load is
effectively distributed throughout the bone structure in model BB, whilst much
6
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
10
11
reduced SED experienced in the bone in the bone-cement interdigitated region in
model BC, indicating stress shielding of bone as a result of cementation. Stress
shielding may be observed from Layer 4 onwards in model BC, where progressively
increased stress shielding in bone is evident. The percentage reductions in SED of
all layers of bone in model BC, as calculated by Equation (2), are shown in Figure 5,
where significant reductions in SED in all bone layers are evident. Under Load 1, the
reduction of SED in Layers 1 to 3 of bone are 3.4%, 11.2% and 27.5%, respectively,
as opposed to above 95% when the bone is fully interdigitated with the cement
(Layers 6 to 8). These results clearly indicate the role of cement in stress shielding
of bone.
4. Discussion
Proximal tibial bone resorption due to stress-shielding post TKR has been a
clinical concern. The loss of bone stock hence bone–prosthesis support can have
direct detrimental effects on long-term fixation stability leading to aseptic loosening
[6, 16]. To date, stress shielding has been attributed to the large difference in the
stiffness between the tibial component and the surrounding bone, although this may
be further compounded by factors such as loading conditions, implant materials,
component designs and cementation techniques [13, 14, 17, 18]. Previous studies
are based on continuum FE models where detailed interaction between the bone
and the cement in cemented replacements could not be assessed. The present
micromechanics study is the first attempt at investigating the role of cement in stress
shielding of bone across the bone-cement interface. The predicted micro-mechanical
behaviour of the trabecular bone-cement model (model BC) under compressive
loading have been validated by comparing the apparent stress-displacement curve
7
136
137
138
139
140
141
142
143
144
145
146
147
148
149
150
151
152
153
154
155
156
157
158
159
12
13
and local deformation with those obtained experimentally of the same specimen [8,
9]. The present results reveal that the reduction in SED of bone in a bone-cement
interface composite is common, particularly so within the fully interdigitated region.
Even under an idealised situation where no stress shielding due to implant is
experienced by the periprosthetic bone, the SED reduction in the fully interdigitated
bone region can be above 95% due to the presence of cement alone. Under the
simulated stress shielding situations due to a metal-backed tibial component, the
SED reduction of bone in the fully interdigitated region is predicted to be nearly
100% (Load 3), suggesting stress shielding due to both cement interlocking and
implant. According to Huiskes et al [16], a 75% reduction in SED in the bone would
trigger bone resorption [13, 17]. The current simulation results are well above this
threshold, hence bone resorption in bone-cement interdigitated region would seem
inevitable, regardless the implant types that would give rise to stress shielding (Load
2 and Load 3).
In the studies of Miller et al. [1, 2], the initial mould shape of PMMA cement
was used to estimate the amount of interdigitated bone at the time of implantation
and the loss following in vivo service. Their results show that after 10 years service,
less than 10% of the cement mould shape was still filled with bone, and the
remaining bone was mainly in the partially interdigitated region. Several possible
mechanisms have been suggested to explain this, including osteolysis, fluid induced
trabecular lysis, demineralization of viable trabeculae due to low pH environment and
monomer toxicity and thermal necrosis attributed to heat polymerization. The present
results seem to suggest that, in addition to the above, the impact of stress shielding
due to cementation should not be overlooked. Consistent with previous studies [1, 9],
our study supports some limit on the depth of cement penetration. It seems that in 8
160
161
162
163
164
165
166
167
168
169
170
171
172
173
174
175
176
177
178
179
180
181
182
183
18414
15
fully-interdigitated region the bone is off-loaded almost completely hence the bone-
cement composite behaves as cement with many “pores”, resulting in an “inferior”
performance to that of bulk cement [19].
There are limitations of this short study: Only one case of bovine trabecular
bone-cement interface was considered, hence the effects of bone morphology,
structure size, boundary conditions on stress shielding cannot be assessed.
Considering mainly trabecular bone and compressive load condition were
considered here, the results might be more relevant to the bones in knee and
acetabulum. Although cement application and curing were consistently done
according to surgical procedures, exothermic reaction during polymerization was not
simulated. Bone cement, with an elastic modulus about 2 to 3 GPa, is significantly
less stiff than most metallic implants, hence a preferred method for fixation. But the
global mechanical properties of cement are still higher than those of cancellous
bones, which are highly site-dependent but generally below 1 GPa [20]. This
represents a significant challenge for joint fixation and other related clinical
procedures such as vertebralplasty or dental implant fixation.
Conflict of interest statement
There is no conflict of interest to declare.
Ethical Approval
Not applicable.
9
185
186
187
188
189
190
191
192
193
194
195
196
197
198
199
200
201
202
203
204
205
206
207
16
17
REFERENCES
[1] Miller MA, Goodheart JR, Izant TH, Rimnac CM, Cleary RJ, Mann KA. 2014.
Loss of cement-bone interlock in retrieved tibial components from total knee
arthroplasties. Clin Orthop Relat Res. 472(1), 304-13.
[2] Miller MA, Terbush MJ, Goodheart JR, Izant TH, Mann KA. 2014. Increased
initial cement-bone interlock correlates with reduced total knee arthroplasty micro-
motion following in vivo service. J Biomech. 47(10), 2460-6.
[3] 12th Annual report, National Joint Registry, 2015.
[4] Sundfeldt M, Carlsson LV, Johansson CB, Thomsen P, Gretzer C. 2006.
Aseptic loosening, not only a question of wear: a review of different theories. Acta
Orthop. 77(2):177-97.
[5] Abu-Rajab RB, Watson WS, Walker B, Roberts J, Gallacher SJ, Meek RM.
2006. Peri-prosthetic bone mineral density after total knee arthroplasty. Cemented
versus cementless fixation. J Bone Joint Surg Br. 88(5), 606-13.
[6] Lonner JH, Klotz M, Levitz C, Lotke PA. 2001. Changes in bone density after
cemented total knee arthroplasty: influence of stem design. J Arthroplasty. 16(1),
107-11.
[7] Soininvaara TA, Miettinen HJ, Jurvelin JS, Suomalainen OT, Alhava EM,
Kröger HP. 2004. Periprosthetic femoral bone loss after total knee arthroplasty: 1-
year follow-up study of 69 patients. Knee. 11(4), 297-302.
[8] Tozzi G, Zhang QH, Tong J. 2012. 3D real-time micromechanical
compressive behaviour of bone-cement interface: experimental and finite element
studies. J. Biomech. 45, 356-363.
10
208
209
210
211
212
213
214
215
216
217
218
219
220
221
222
223
224
225
226
227
228
229
230
18
19
[9] Zhang QH, Tozzi G, Tong J, 2014. Micromechanical damage of trabecular
bone-cement interface under selected loading conditions: a finite element study.
Comput Methods Biomech Biomed Engin. 17(3), 230-8.
[10] Niebur GL, Feldstein MJ, Yuen JC, Chen TJ, Keaveny TM, 2000. High-
resolution finite element models with tissue strength asymmetry accurately predict
failure of trabecular bone. J. Biomech. 33, 1575-1583.
[11] Kuehn KD, Ege W, Gopp U. 2005. Acrylic bone cements: mechanical and
physical properties. Orthop Clin North Am. 36, 29-39.
[12] Kurtz SM, Villarraga ML, Zhao K, Edidin AA. 2005. Static and fatigue
mechanical behavior of bone cement with elevated barium sulfate content for
treatment of vertebral compression fractures. Biomaterials. 26, 3699-3712.
[13] Cawley DT, Kelly N, Simpkin A, Shannon FJ, McGarry JP. 2012. Full and
surface tibial cementation in total knee arthroplasty: a biomechanical investigation of
stress distribution and remodeling in the tibia. Clin Biomech (Bristol, Avon). 27(4),
390-7.
[14] Au AG, James Raso V, Liggins AB, Amirfazli A. 2007. Contribution of loading
conditions and material properties to stress shielding near the tibial component of
total knee replacements. J Biomech. 40(6), 1410-6.
[15] Bryan R, Nair PB, Taylor M. 2012. Influence of femur size and morphology on
load transfer in the resurfaced femoral head: A large scale, multi-subject finite
element study. J Biomech. 45(11):1952-8.
[16] Huiskes R, Weinans H, van Rietbergen B. 1992. The relationship between
stress shielding and bone resorption around total hip stems and the effects of flexible
materials. Clin Orthop Relat Res. 274, 124-34.
11
231
232
233
234
235
236
237
238
239
240
241
242
243
244
245
246
247
248
249
250
251
252
253
254
20
21
[17] Chong DY, Hansen UN, van der Venne R, Verdonschot N, Amis AA. 2011.
The influence of tibial component fixation techniques on resorption of supporting
bone stock after total knee replacement. J Biomech. 44(5), 948-54.
[18] Scott CE, Biant LC. 2012. The role of the design of tibial components and
stems in knee replacement. J Bone Joint Surg Br. 94(8), 1009-15.
[19] Race A, Mann KA, Edidin AA. 2007. Mechanics of bone/PMMA composite
structures: an in vitro study of human vertebrae. J Biomech. 40(5):1002-10.
[20] Morgan EF, Bayraktar HH, Keaveny TM. 2003. Trabecular bone modulus-
density relationships depend on anatomic site. J Biomech. 36(7):897-904.
12
255
256
257
258
259
260
261
262
263
264
265
266
267
268
269
270
271
272
273
274
275
276
277
278
27922
23
Figure Captions
Figure 1. The two finite element models used for the present study. (a) A typical bone-cement
interface sample (model BC, with a dimension of 9.0mm×8.0mm×4.4mm); (b) the same
model as (a) but with the cement removed (model BB, with a dimension of
7.6mm×8.0mm×4.4mm). Red – bone; Blue - cement.
Figure 2. A column (7.6mm×8.0mm×4.4mm) of the eight bone layers defined for the
comparison of the strain energy density (SED) between model BC and model BB. Layers 1 to
3 (a height of 2.9mm) contain bone only; Layers 4 and 5 (a height of 1.9mm) are partially
interdigitated with cement whilst Layers 6 to 8 (a height of 2.8mm) are fully interdigitated
with cement. The central part of the cement is also included for illustration purposes.
Figure 3. A comparison of SED distribution in the eight bone layers from model BC and
model BB under Load 1.
Figure 4. The percentage reduction of effective stain energy density of the eight layers from
model BC under the three loading conditions compared with that from model BB under Load
1. Load 2 and Load 3 were used to simulate the idealised off-load conditions due to the
presence of an implant with low (Load 2) and high (Load 3) stiffness.
13
280
281
282
283
284
285
286
287
288
289
290
291
292
293
294
295
296
297
298
24
25
Figures
(a) (b)
Figure 1
Layer 1
Bone
Layer 2
Layer 3
Layer 4 Partially
InterdigitatedLayer 5
Layer 6
Fully
Interdigitated
Layer 7
Layer 8
Figure 2.
14
299
300
301
302
303
304
305
306
307
26
27
model BC model BB
Layer1
Layer2
Layer3
Layer4
Layer5
Layer6
Layer7
Layer8
Figure 3.
15
308
309
310
311
312
313
314
315
28
29
Figure 4.
16
316
317
318
319
30
31