Compressive behaviour of bovine cancellous bone and bone ...



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

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.

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 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.

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 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 effective strain energy density in each bone layer may be obtained by averaging the strain energy of all the elements in that layer:

[pic] 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:

[pic] k=1, 2, 3 (2)

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 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.

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 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 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.

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.

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.

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.

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.

Figures

[pic] [pic]

a) (b)

Figure 1

|Layer 1 |[pic] | |

| | | |

| | |Bone |

|Layer 2 | | |

|Layer 3 | | |

|Layer 4 | |Partially Interdigitated|

|Layer 5 | | |

|Layer 6 | | |

| | |Fully Interdigitated |

|Layer 7 | | |

|Layer 8 | | |

| | | |

Figure 2.

| | |model BC |model BB |

|Layer1 | |[pic] |[pic] |

| | | | |

| |[pic] | | |

|Layer2 | |[pic] |[pic] |

|Layer3 | |[pic] |[pic] |

|Layer4 | |[pic] |[pic] |

|Layer5 | |[pic] |[pic] |

|Layer6 | |[pic] |[pic] |

|Layer7 | |[pic] |[pic] |

|Layer8 | |[pic] |[pic] |

Figure 3.

[pic]

Figure 4.

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