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: jie.tong@port.ac.uk

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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.

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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

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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

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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

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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

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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

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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

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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.

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REFERENCES

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Loss of cement-bone interlock in retrieved tibial components from total knee

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initial cement-bone interlock correlates with reduced total knee arthroplasty micro-

motion following in vivo service. J Biomech. 47(10), 2460-6.

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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.

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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.

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model BC model BB

Layer1

Layer2

Layer3

Layer4

Layer5

Layer6

Layer7

Layer8

Figure 3.

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Figure 4.

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