Activity and Loading Influence the Predicted Bone Remodeling Around Cemented Hip Replacements

Alexander S. Dickinson Bioengineering Science Research Group. University of Southampton, Highfield, Southampton SÜ171BJ, UK e-maii: [email protected]

Periprosthetic bone remodeling is frequently observed after total hip teplacement. Reduced bone density increases the implant atid bone fracture risk, and a gross loss of botie detisity challenges fixation in subsequent revisioti surgery. Computational approaches allow bone remodeling to be predicted in agreement with the general clinical observations of proximal resorptiott and distal hypertrophy. However, these models do not reproduce other clinically observed bone density trends, including faster stabilizing mid-stem density losses, and loss-recovery trends around the distal stem. These may resemble trends in postoperative joint ¡oaditig and activity, during recovery attd rehabilitation, btit the established remodeling prediction approach is often used with identical pre- and postoperative load atid activity assumptions. Therefore, this study aimed to evaluate the influence of pre- to postoperative changes in activity and loading upon the predicted progression of remodeling. A strain-adaptive finite element model of a femur implanted with a cemented Charnley stem was generated, to predict 60 months of periprosthetic remodeling. A control set of model inptit data assumed identical pre- and postoperative loading and activity, and was cotnpared to the results obtained from another set of inputs with three varying activity and load profiles. These represented activity changes during rehabilitation for weak, intermediate and strong recoveries, and pre- to postoperative joint force changes due to hip center translation and the use of walking aids. Predicted temporal botie density change trends were analyzed, atid absolute bone density changes and the time to homeostasis were inspected, alongside virtual X-rays. The predicted periprosthetic botie density changes obtained using modified loading inputs demonstrated closer agreement with clinical measurements than the control. The modified inpttts also predicted the clitiically observed temporal density change trends, btit still under-estimated density loss during the first three postoperative months. This suggests that other mechanobiological factors have an infiuence, including the repair of surgical micro-fractures, thermal damage and vascular interruption. This study demonstrates the importance of aecoutiting for pre- to postoperative changes /n joittt loading and patient activity when predicting periprosthetic bone remodeling. The study's main weakness is the use of an individual patient model: computational expense is a ¡imitation of all previously reported iterative remodeling analysis studies. However, this model showed sufficient computatiotial ejficieticy for application in probabilistic analysis, and is an easily implemented modification of a well-established technique. [DOI: 10.1115/1.4026256] Keywords: FE analysis, total hip replacement, bone remodeling, activity, DXA

1 Introduction Periprosthetic bone remodeling is frequently observed in the proximal femur after total hip replacement (THR). Adaptive remodeling results from local changes in the mechano-biological environment, and can lead to significant changes in periprosthetic bone density. Clinical radiographie evidence indicates reduced bone mineral density (BMD) [ 1 ^ ] and cortex thickness [5,6] in the proximal bone, and increased BMD near the stem's tip. Quantitative measurement of BMD changes using dual energy X-ray absorptiometry (DXA) scanning indicates little net BMD change, but a redistribution of bone material towards the distal stem [1]. This is thought to indicate stress bypass, where the joint load follows the stiftest path through the stem distally to its tip, unloading Contributed by the Bioengineering Division of ASME for publication in the JOURNAL OF BIOHECHANICAL ENGINEERING. Manuscript received July 24. 2013; final manuscript received December 10. 2013; accepted manuscript posted December 16. 2013; published online March 24, 2014. Assoc. Editor; Tammy Donahue.

Journal of Biomechanical Engineering

the proximal bone. Reduced bone density increases the fracture risk of the bone and of the implant. The periprosthetic bone's stiffness decreases with BMD loss, so proximal résorption redistributes the stem's load transfer distally. This increases the bending stress in the stem and, potentially, the risk of fatigue failure. A gross loss of bone density will also present a greater challenge in achieving fixation in the event of revision surgery. A predictive bone adaptation model is a valuable preclinical analysis tool for implant development. Numerical modeling of macro-scale strain-adaptive bone remodeling within finite element (FE) analysis rnodels was developed and demonstrated for THR [7-10]. These phenomenological models have commonly been employed considering local pre- to postoperative changes in periprosthetic bone strain resulting from the presence of the implant only [11-17]. These models are capable of predicting patterns of BMD changes in agreement with the major clinically observed adaptations, proximal résorption and distal hypertrophy. However, in their reported use to date there are some limitations in their

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APRIL2014, Vol. 136 / 041008-1

capture of changes in other periprosthetic areas, and the temporal progression of remodeling observed clinically, discussed below. Attempts have been made to tune these models to fit predicted bone adaptations to clinical data, beginning with animal [8,9] and then human studies [14,18]. The most commonly applied approach of bone remodeling prediction with FE analysis was developed by HuLskes et al. [7]. The algorithm iteratively modifies the local density of the bone, by modifying the material properties of each element in response to its strain energy density S, compared to a reference level S^f Irom the intact bone. This process is implemented using Euler forwards integration to integrate incrementally the set of ordinary differential equations. Two remodeling parameters are used for tuning: the sfimulus threshold "s", and the rate constant "T". The stimulus threshold influences the predicted extent of remodeling, and the rate constant controls the time for homeostasis to be achieved. Typically, an appropriate stimulus threshold is selected which gives clinically representative BMD changes averaged across regions of bone by virtual DXA scan, in the zones defined by Gruen et al. [19]. A recent increase in published quantitative clinical DXA data indicates that these models, as implemented to date, have not reproduced the progression path of in vivo BMD changes in all cases. Local trends of BMD loss in the proximal-medial femur (Gruen zone 7) foUow an approximately exponential decay towards a homeostatic level, and this "loss" trend is reproduced by the described modeling method. However, a faster stabilizing BMD loss is observed clinically in neighboring regions (zones 2 and 6), and in other regions a "loss-recovery" trend is observed [3,20]: principally in zones 1, 3, 4, and 5. In zones 2 and 6, the loss trend dominates initially, and is followed by a recovery in some cases. The lossrecovery trend is also commonly observed in the bone supporting resurfacing hip replacements (RHR) [4,21-24], and around the rim of cementless acetabular cups [20]. To the author's knowledge, this loss-recovery trend has not been reproduced by published modeling studies to date, and will likely influence the predicted progression and homeostatic end point of bone adaptation. The loss-recovery trend has been measured distant from the implant [22], indicating that the local mechanical influence of the implant is not solely responsible for BMD changes. Load and activity factors would be expected to affect the progression of adaptive bone remodeling predicted using this technique, but are not commonly incorporated in modeling studies. First, step activity monitoring has indicated that hip replacement patients recover to a higher activity level than before surgery [25-27]. Second, many factors may influence the joint contact force in the operated hip, including external factors such as preand temporary postoperative use of a cane, and intemal factors such as the medialization of the joint center location. The aim of this study was to test the hypothesis that changes in pre- to postoperative activity and joint loading influence the progression of remodeling predicted by FE analysis, and are responsible in part for the clinically observed "loss-recovery" bone adaptation trend.

2

regions were retained in the partitioned model, to allow loading in analysis of the intact bone. The implanted bone model was imported into ANSYS 12 software (ANSYS Inc., Canonsburg, PA, USA) for FE meshing and analysis. A set of mapped second-order hexahedral meshes was created, and a verified mesh containing 36,520 elements and 108,902 nodes was selected using a convergence analysis. The implant stem and bone/cement meshes were congruent at their interface, which was modeled with a contact pair containing 1512 quadratic contact and target elements. This interface was bonded in the intact case and modeled with Coulomb friction in the implanted case, using a static coefficient of friction of 0.2 [28]. The implant elements were assigned a linear elastic material properties of Cobalt Chromium, Young's modulus E = 210GPa, Poisson ratio v = 0.3 (ASTM F-75). A 3-5 mm thick cement mantle/cement interdigitated bone zone was modeled surrounding the implant, with E = 2.1 GPa and ;/ = 0.3 [29]. The material properties of the bone were applied to the FE model with reference to the CTscan greyscale using Bonemat freeware (Rizzoli Institute, Bologna, Italy) as described in previous work [30]. Apparent density was related to the CT scan Hounsfield Units using a linear relationship, and fitting 100% dense bone in the diaphyseal cortex to 1.73 g/cc, and 0% dense bone in the medullary canal to 0 g/cc. Young's Modulus was related to apparent density using the relationship from Morgan et al. [31] for the proximal femur, E = 6850 p'*". To account for partial volume effects arising from CT-scan segmentation, the Young's modulus of each bone surface element (potentially containing a proportion of artificially low modulus material) was mapped from the nearest intemal neighboring element (containing entirely bone material with an appropriate modulus). The model was loaded quasi-statically to represent the peak load instant in a walking gait scenario [32], with a joint contact force and muscle forces from the hip abductors, tensor fascia latae and vastus lateralis (Fig. 1). 2.2 Model Outputs. The bone adaptation predicted by the model was evaluated quantitatively using virtual DXA measurements in the seven Gruen zones [19] (Fig. 2(a)) according to clinical protocols, without removal of cement [33]. Each Gruen zone's areal bone mineral density was extracted, and the percentage change compared to the immediately postoperative value was calculated. These virtual DXA data were compared to the most appropriate clinical DXA results available, for patients with Chamley stems [3] (n = 38, mean age 72 years, up to 2 years follow-up). To visualize the model predictions for qualitative Joint Contact Force

Methodology

2.1 Finite Element Model. An FE analysis model of a femur was produced from the CT scan of a 63 year-old male (height 1.77 m, mass 85 kg) with no known orthopaedic disease. The scan resolution was 0.781 mm, and slice width was 2 mm. The extemal cortex geometry was segmented using Amira software (Mercury Computer Systems Inc., Chelmsford, MA, USA). A solid NURBS model was created with SolidWorks 2012x64 CAD software (SolidWorks Corp., Concord, MA, USA). The model was partitioned using virtual cutting tools to incorporate a Charnley Roundback 40 THR stem (DePuy International, Leeds, UK) obtained from the Living Human Digital Library (LHDL). The stem was positioned centrally in the femoral canal as recommended in the surgical technique, using two orthogonal virtual X-rays of the bone (described below). Excised femoral head and neck bone 041008-2 / Vol. 136, APRIL 2014

istus Uteraiis Muscle Force

Fig. 1

FE meshes and loads for intact (a) and implanted (b) models

Transactions of the ASME

An appropriate remodeling rate constant value was obtained by running the bone remodeling algorithm until convergence of the predicted BMD changes was achieved in the seven zones, as noted in Sec. 3. 2.4 Study Design. First, four control cases were analyzed to find an appropriate stimulus threshold {s) value, tuning the model predictions to behavior reported in the clinical literature. The output measure tested was the final percentage BMD loss in Gruen zone 7 at homeostasis, which was compared to clinical DXA measurements. Second, the influence of changed activity and loading levels from the pre- to postoperative case was tested, by applying a normalized scaling factor to the remodeling stimulus signal level obtained from the quasi-static FE analysis described above; the model boundary conditions were unchanged. In the preoperative (baseline) case, the reference remodeling stimulus was scaled to incorporate the effect of Fig. 2 Gruen zones (GZ) defined for virtual DXA scan, in terms walking with a cane. The femur was thus assumed to be at of the stem shoulder-tip length (L) (a), and Sections defined for homeostasis prior to surgery. In the postoperative case, the internal inspection of BMD remodeling stimulus was scaled to incorporate the effect of short- and long-term changes in activity, and the effect of comparison to clinical observations, virtual X-rays were generated hip joint geometry changes on joint reaction force. Pedomefrom the adapted model [14,30], and the bone mineral density was ter and step activity monitor (SAM) studies suggest that acinspected on section plots at four distances along the stem's length tivity increases by 10% for elderiy THR patients [25], and (Fig. 2{b)). This was also necessary to account for the low resolu- up to 33% for younger THR and resurfacing patients tion offered by the DXA approach, which averages BMD changes [26,27], over the first 3 to 16 months postoperatively. Thereinto only seven regions of interest. fore, ultimate activity scaling factors "F^a" of 1.1 and 1.3 were applied for elderly and young patients, respectively. 2.3 Bone Adaptation Prediction. A strain adaptive bone Setting the preoperative activity to Fact = 1 indicated that the remodeling principle was incorporated into the quasi-static model as femur was at homeostasis before surgery. The joint loading proposed by Huiskes et al. [7,8] and described in previous work [30]. may be subject to a step change in contact force resulting This algorithm modified each element's density (p) and Young's from medialization of the joint center, and transient changes modulus (£) iteratively, with an adaptation rate proportional to the associated with favoring the nonoperated leg and the use of percentage change in strain energy density per unit volume (S) from a cane or walking frame. Therefore, a load scaling factor a reference level {Sj^f) in the intact bone. A surface area density func- "^Load" was applied to account for the pre- to postoperative tion a(p) [34] was applied which adjusts for the free surface available medialization of the joint center (load ratio 0.92) [36,37], for osteoclastic/osteoblastic activity as a function of porosity. Finally, and for walking with a cane (load ratio 0.60-0.78) [38,39] the bone atrophy rate was set at 3.5 times the hypertrophy rate [14], for a 1.5 month rehabilitation period (frehab)- These scale facbased on clinically observed remodeling [35]. tors were used to create suggested activity and load profiles This was incorporated in the established forward Euler integra- over the simulation time (Fig. 3) which demonstrate respection adaptive remodeling algorithm. Each element's density at the tively the changes in the number of gait cycles per day, and {n -\- l)th time increment with size Ai, was expressed by: in the magnitude of joint contact and abductor muscle force, over the years following surgery. This had the effect of simulating the influence of patient activity upon the frequency of the remodeling stimulus signal, and the effect of peak P„+l=Pn loading upon the signal's intensity. The activity factor.Fact was expressed by (1)

Fact = 0 . 1

when t 0.1 months (recovery)

(2)

giving an exponential recovery rate, for which C was a time constant (2.61 months ') such that 99% of the ultimate activity level was reached by 12 months. The loading factor Fioad was expressed by when Í < 0 months (preoperative)

Eiodd — f load.O I* load ^^ «^ load, I ^

•"load.o + -^

fload = fload, I

Journal of Biomechanical Engineering

o^^^±_ J

^i^gf, 0 < Í < 1.5 months (rehabilitation)

(3)

when Í > 1.5 months

APRIL2014, Vol. 136 / 041008-3

1.40 l.M 1.00

il

'I

0.60

I I 0.«

Z

0.20 0.00

6

9



J5

Veîrab

Postoperative Time (tj / months

Fig. 3 Example profiles of the activity and load level adjustment factors Fact and Fioadi used to scale the pre- and postoperative remodeling signals giving an assumed linear increase in loaded support on the operated limb until the patient walks unaided. The tested values for the activity and loading factors and rehabilitation time are included in Table 1. After the four control cases, three cases simulating changes in activity and load level were used to represent suggested effects of a poor, intermediate or strong postoperative recovery.

3

Results

The control models converged (less than 1% BMD change per Gruen zone between iterations) after 32 to 44 iterations. Clinical data suggests that a condition close to homeostasis is established after 2-3 years for both cemented [2,3,40] and cementless total hip replacements [20,41,42], with slight changes at 5-7 years. Therefore, the time constant (T) was fitted such that 90% of the BMD change in the most active Gruen Zone, 7, had completed at 2 years (Fig. 4). With the control test, the BMD profile fitted a "loss" trend in Gruen zones 1, 2, 6, and 7 from immediately after implantation. Homeostasis was achieved in zones 1 and 7, but changes were still progressive in zones 2 and 6 at 60 months. In all cases, the adaptation was more extensive when the threshold stimulus was lower (Table 2). In zone 4 a gradual BMD increase was predicted which did not stabilize at 60 months. In zone 5, the BMD was predicted

to change by less than 2%. Finally, in zone 3, BMD changes greater than 2% were predicted to begin around 12 months postoperatively, with the smaller tested threshold levels. These BMD changes were observable on virtual X-rays produced from the models (Fig. 5), and section plots (Fig. 6). In all cases, the model predicted a loss in cancellous BMD above the implant shoulder (GZl, Sec. 2), a loss in medial calcar thickness (GZ7, Sec. 1), and an increase in density distal to the implant tip (GZ4, Sec. 4). The medial cortical loss extended into GZs 5 and 6 (Section 2 and 3). Lateral cortex loss occurred in GZs 2 and 3 for the smaller threshold levels, but these changes appeared more focused than would be observed clinically, and initiated below the periosteum, indicating qualitatively that the higher threshold stimulus values were more realistic. Clinical DXA measurements for this implant type in the greatest changing (and most commonly reported) Gruen zone 7 have been reported to range from 7-20% [3,40,43,44], The BMD change after 60 months (Table 2) predicted by the control load and activity scenario was closest at -18.4% for the lowest tested threshold, .s = 75%. Clinical measurements indicate only small BMD changes after 24 postoperative months, which was consistent with the predictions obtained using this threshold value. More substantial cortex thickness changes may occur, but in a minority of patients [5]. On this evidence it was judged that a threshold retnodeling stimulus of 75% produced the most representative predictions for a majority of Chamley patients, so it was used to evaluate the effects of activity and load. When the remodeling algorithm loading inputs were modified in cases 5, 6 and 7, the model predicted the same "loss" trend in GZ7 as the control (Fig. 7). In zones 1, 2 and 6, again a BMD loss was predicted but it had stabilized by month 3, whereas the loss was slower but progressive with the control. In GZl, for a patient making a strong recovery (Case 7), BMD began to increase again after 6 months. More distally, in GZs 3, 4, and 5, a very slight loss (-0.43 to —1.1%) was predicted in the first three postoperative months, followed by a recovery. No substantial differences were visible between the virtual X-rays or section BMD plots for the modified loading/activity cases and the corresponding control. Quantitative analysis of the virtual DXA changes after 60 months (Table 2), however, indicated the effect of incorporating varying load and activity. In all zones except GZ4, homeostasis was reached between 24 and 60 months. In GZs 1, 2, and 6, the modified cases gave a greater early BMD loss than the control cases. In GZ7, incorporating an increase in postoperative activity produced a smaller BMD loss

Table 1 Modelled loading and activity factor cases Initial Case 1 2 3 4 5

Description Control 1 Control 2 Control 3 Control 4 Weak Recovery: Double Preop Cane Use, Single Postop Cane Use, Low Activity Increase

Transient

Final

.s/%

Pacl.O

Fload.O

trehab / mO.

Fact. I

Fload.I

75 70 65 60 75

1.00 1.00 1.00 1.00 1.00

1.00 1.00 1.00 1.00 0.60



LOO

— —

1.5

1.00 1.00 1.00 1.10

1.00 1.00 1.00 1.00 0.92 X 0.78



6

Intermediate Recovery: Single Preop Cane Use, No Postop Cane Use, Low Activity Increase

75

1.00

0.78

1.5

1.10

0.92

7

Strong Recovery: Single Preop Cane Use, No Postop Cane Use, High Activity Increase

75

1.00

0.78

1.5

1.30

0.92

041008-4 / Vol. 136, APRIL 2014

Transactions of the ASME

Fig. 4 Predicted percentage change in BiVID per Gruen zone for the four control loading scenarios of varying threshold remodeling stimulus (Cases 1-4), shown in comparison to representative clinical results. Shaded region represents 95% confidence interval [3]. Table 2 BMAD changes per Gruen zone for the seven simulated cases, predicted after 60 months Areal BMD at 60 Months , g/cm^ (% Change in paretitheses) GZl

GZ2

GZ3

GZ4

GZ5

GZ6

GZ7

Preoperative Case 1: Control, 75% Threshold Case 2: Control 70% Threshold Case 3: Control 65% Threshold Case 4: Control 60% Threshold Case 5: Weak Recovery Case 6: Intermediate Recovery Case 7: Strong Recovery

0.435 0.427 (-1.78) 0.422 (-2.99) 0.415 (-4.62) 0.406 (-6.59) 0.415 (-4.47) 0.418 (-3.82) 0.425 (-2.19)

1.294 1.248 (-3.62) 1.177 (-9.11) 1.043 (-19.39) 0.991 (-23.40) 1.244 (-3.88) 1.246 (-3.73) 1.257 (-2.88)

1.670 1.680 (-K0.64) 1.645 (-1.49) 1.534 (-8.14) 1.511 (-9.48) 1.681 (-1-0.65) 1.685 (-fO.91) 1.695 (-fl.52)

1.405 1.444 (+2.1%) 1.441 (-1-2.99) 1.457 (+3.67) 1.448 (-h3.03) 1.431 (-[-1.86) 1.448 (-^3.08) 1.473 (+4.86)

1.676 1.707 (+1.86) 1.708 (+1.92) 1.710 (+2.01) 1.706 (+1.80) 1.689 (+0.75) 1.693 (+1.00) 1.702 (+1.54)

1.552 1.524 (-1.84) 1.444 (-6.96) 1.252 (-19.34) 1.159 (-25.31) 1.438 (-7.37) 1.433 (-7.67) 1.451 (-6.49)

1.216 0.992 (-18.40) 0.907 (-25.43) 0.809 (-33.46) 0.759 (-37.58) 1.010 (-16.92) 1.033 (-15.05) 1.069 (-12.10)

Clinical Results [3] Change by 24 Months

(-H.91)

(-3.82)

(-0.86)

(-0.55)

(+2.66)

(-5.81)

(-13.00)

prediction than the control case. In GZ4, for a strotig recovery, the BMD increase was greater than for the control.

4

Discussion

Pedprosthetic bone remodeling was first observed in the 1960s [45] and is now a well-documented phenomenon [20, 4 1 ^ 4 , 46]. It has been the subject of recent clinical investigation for total hip replacement, both cemented and cementless [2,3,6], and for hip resurfacing [24]. Bone remodeling prediction is an important tool Journal of Biomechanical Engineering

for arthroplasty evaluation and development, to evaluate for example the probable influence of changes in implant geometry, material and fixation. The present study evaluated the effects of incorporating pre- to postoperative changes in joint loading and patient activity into strain adaptive FE analysis, for a cemented total hip replacement stem model. Suggested postoperative activity and loading profiles were applied to an adaptive FE model, based upon typical rehabilitation programs and measured pre- and postoperative activity changes, and compared to a control with identical pre- and postoperative activity and loading. APRIL2014, Vol. 136 / 041008-5

Case 1: Control 1,75% Threshold Remodelling Stimulus I Immediate Postop

24 Months Postop

60 Months Postop

Case 2: Control 2,70% Threshold Remodelling Stimulus

Immediate Postop

24 Months Postop

60 Months Postop

Case 4: Control 4,60% Threshold Remodelling Stimulus

Fig. 5 Virtual anterior-posterior X-rays showing changes in BMD throughout the bone for the four control loading scenarios with varying threshold remodeling stimulus (Cases 1-4). Shown immediately postoperatively, and after 24 and 60 months Qualitatively, the remodeling simulation input loads employed in this study all demonstrated the clinically observed trend of proximal stress shielding and résorption, followed by distal hypertrophy (Fig. 4 and Fig. 5). The progression of proximal résorption (GZs 7, 1 and 6) followed by distal hypertrophy (GZs 4 and 5), and subsequent mid-stem résorption (GZs 2 and then 3) agrees with the generally accepted theory that this retnodeling results from distal load redistribution. Quantitatively, the presented results showed that predicted periprosthetic BMD changes around the stem agreed more closely with clinical trends when changes in activity and loading were accounted for in the model input profile (Fig. 7, Table 2), supporting the hypothesis. Agreement was evaluated by comparing trends of BMD change over time predicted by the control and modified loading input cases, the time until homeostasis was reached, and the percentage change at homeostasis compared to preoperative levels. Considering temporal trends, the modified loading scenarios predicted loss trends in GZs 7, 6, 2, and 1, and loss-recovery trends in GZs 3, 4 and 5, and 1 in strongly recovering patients, representative of clinically reported DXA data trends and homeostatic changes [1,3,4,20,42,43]. The modified loading scenarios also predicted more representatively the faster achievement of homeostasis in mid-stem regions 2 and 6 than the more proximal zones 1 and 7. Furthermore, the model produced predictions that agreed with clinical trends of lower BMD loss for younger THR patients [40], for whom the increase in postoperative activity may be higher, and who may recover to unsupported gait. Considering absolute percentage BMD changes, surgical and patient variability precludes exact quantitative fitting for an individual model, but the model predictions were within the typically reported range of 041008-6 / Vol. 136, APRIL 2014

clinical radiographie measurements for the investigated implant type [3,43]. This limitation is discussed further below. Agreement between the models and clinical data was particularly close in the resorbing proximal-medial regions, but was weaker in the hypertrophie region around the distal stem. One limitation of the present model is that it is not capable of capturing extemal cortical hypertrophy, which may occur to some extent in GZs 3 and 5 [5], and which could explain the model's departure from predicted trends in these locations. In the present model which only permitted intemal hypertrophy, the BMD increase at the stem tip was focused largely in GZ4, where intemal densification could still occur after GZs 3 and 5 reached maximum theoretical density. Advanced adaptation models have been developed to include processes including bone ingrowth [18] and implant-bone interface gap healing [30], but in this cemented THR case these factors are unlikely to have a considerable effect. Cortical remodeling is one possible explanation for prediction inaccuracies around the stem tip, but may have limited effect especially in elderly patients. The model's distal fixation boundary condition may also adversely affect the validity of results owing to artificial stiffness, with increasing effect approaching the fixation. Efforts were made to minimize these effects by restraining the femur only at the distal metaphysis, to position boundary conditions remote from the study's region of interest and to permit the femur an appropriate degree of flexibility [47]. A measured decrease in bone mineral density by DXA in the early postoperative period is also necessarily a function of the remodeling process, irrespective of whether the final density is greater or lesser than the initial measurement. Osteoclastic résorption precedes the laying down of new remodeled bone by Transactions of the ASiUIE

24 Months Postop

60 Months Postop

Case 1: Control 1, 75% Threshold Remodelling Stimulus Immediate Postop

24 Months Postop

60 Months Postop

Case 3: Control 3, 65% Threshold Remodelling Stimulus

Immediate Postop

24 Months Postop

60 Months Postop

Case 2: Control 2, 70% Threshold Remodelling Stimulus Immediate Postop

24 Months Postop

60 Months Postop

Case 4: Control 4, 60% Threshold Remodelling Stimulus

Fig. 6 Bone Mineral Density shown on bone sections for the four control loading scenarios with varying threshold remodeling stimulus (Cases 1-4). Shown immediately postoperatively, and after 24 and 60 months. Black represents 0 g/cc, and white represents greater than 1.75 g/cc.

osteoclasts. This coupled remodeling transient can be quantified using biochemical markers of bone tumover that are predictive of the amount of bone loss observed [48]. The strain adaptive model used does not include prehypertrophic résorption, so there may be scope for further development of the algorithm. Determining clearly the regions of résorption and densification also justifies higher resolution interrogation of clinical BMD data than is achieved with current DXA techniques, into line with the full-field predictions offered by FE modeling. Increased spatial resolution of BMD changes would allow neighboring regions of densification and résorption to be discriminated, whereas with the present approach such changes could be lost through averaging within seven relatively large zones. This study supports the suggestion that strain adaptive effects account only partially for periprosthetic bone remodeling. Predicted postoperative BMD losses were under-estimated, in particular in the distal and lateral zones 1, and 3-5. This indicates that other factors are of particular importance during the immediately postoperative period. It is proposed that these regions will be subject to micro-damage from impaction, thermal damage from exoJournai of Biomechanical Engineering

thermic bone cement curing, abductor muscle weakness caused by the surgical approach, and some extent of postoperative vascular disruption. All these effects could cause additional résorption, and were not captured by this purely strain-comparative model. The under-estimated BMD loss in the first three postoperative months may also indicate that the modeled activity and loading profiles were over-estimates of the postoperative recovery rate. This is a third weakness of the present approach, which will affect all time points: its reliance upon suggested loading and activity profiles, for which clinical data is sparse, especially with high time resolution. With the available clinical data on actual rehabilitation versus recommended protocols, and in the face of variability in patient outcomes, it is not appropriate to define exact loading and activity profiles or to validate the model directly for any particular case. Therefore, a range of trends corresponding to weak and strong recoveries was proposed. These are argued to be representative; considering activity, step activity monitoring data for a range of patient ages and treatments was accounted for [25-27], and the approximate recovery trend was taken from clinical outcome scores [49]. Considering loading, Kim et al. [50] showed APRIL2014, Vol. 136 / 041008-7

Fig. 7 Predicted percentage change in BMD per Gruen zone for the control and three activity and load profile scenarios (Cases 1, 5, 6, and 7), with 75% threshold remodeling stimulus, shown in comparison to representative clinical results. Shaded region represents 95% confidence interval [3].

that in a representative patient group, 80% of patients walked with a cane or frame preoperatively, reducing to 0% postoperatively, and it is generally accepted that joint center medialization is a surgical goal to reduce the joint contact force. To evaluate the influence of the considered effects, a sensitivity analysis was conducted (presented and discussed in detail in the Appendix). This indicated that the model was most sensitive to the ultimate load and activity levels than the time taken to reach them, and these levels can be obtained reliably from clinical studies. While the study does not include precise patient specific loading and activity profiles, it demonstrates the importance of accounting for them, and supports recent work for single timepoint models which incorporate both population modeling of bone geometry and materials, and of load profiles [51]. The use of individual bone models (i.e., « = 1) is a common limitation to iterative, adaptive bone remodeling studies owing to computational expense. Practically, the present model which incorporated a mapped hexahedral mesh has sufficient computational efficiency to deliver within 16 hs a converged solution representing 60 months of follow-up, using a desktop computer. A similar approach has potential application for probabilistic analysis, incorporating multiple bone models, surgical positions, and stochastic loading. Finally, it is acknowledged that this model still uses a phenomenological representation of the bone remodeling process. More representative computational predictions may be achieved with mechanistic or multiscaled topographic optimization based models, in which there are on-going research efforts [52-55]. This study employed a cemented THR as its case study to limit the effects of mechanobiological processes that will compete with remodeling, such as bone ingrowth and damage healing, and demonstrates the continuing value of this simpler approach. The presented methodology address a gap in the scientific literature. 041008-8 / Vol. 136, APRIL 2014

and this study has demonstrated its potential to achieve more realistic predictions of periprosthetic bone remodeling, at very low additional computational expense or model complexity. This approach may benefit researchers in understanding the clinical failure modes of existing implant systems, and assist the development of novel prostheses. It is envisaged also that these methods could benefit the preclinical analysis of revision prostheses, by providing more representative initial condition bone models in which to evaluate their performance.

Acknowledgment The author would like to thank the University of Southampton's New Frontiers Fellowship scheme for funding this study, and Professor J. M. Wilkinson of the University of Sheffield for providing access to his group's DXA data, and his input into the interpretation of the results. There are no relevant disclosures or ethical issues associated with this work.

Appendix: Sensitivity Analysis A sensitivity analysis was conducted on the load and activity history, to evaluate the influence of the defined parameters on the predicted bone adaptation. A one-way sensitivity analysis was used, as the study aimed to investigate the relative influences of the input parameters, rather than uncertainty in their defined values, so parameter interactions were of limited interest. Three key parameters were selected for evaluation: the final postoperative activity (Fact.i "Act"), the recovery time constant (C "Time") and the final postoperative load (Fioaj i "Load"). Parameters were varied by -|-/—10% compared to nominal settings from Case 7, the strong recovery scenario. The sensitivity analysis output was the percentage BMD change over 60 months follow-up. The Transactions of the ASME

Variation in % Change in BMO -2.S0 -2.00 -1.50 -1.00 -O.SO O.£50 0.50 1.00

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Fig. 8 Tornado plot of model sensitivity to activity, time and load parameter perturbations upon each Gruen zone's %BMD change 60 months postoperatively parameters were ranked by their influence on each Gruen zone's result, and plotted on a tornado diagram indicating the model's sensitivity (Fig. 8). The sensitivity analysis results showed that the predicted bone adaptations were most sensitive to the final postoperative load level, then the final postoperative activity level, and then the recovery time constant. This was the case in 6 of the 7 Gruen zones. For all three parameters, an increase perturbation caused an increase in the predicted BMD change. These results indicate the direct relation between the loads applied and the trend of bone mass change, and demonstrate that most effort in applying this technique should be put into determining appropriate postoperative load and activity levels. The greatest uncertainty in the surveyed clinical data [25-27] related to the recovery time, owing to the practical limitations of patient data collection and the need to follow-up at discreet time points. However, these results indicate that the ultimate postoperative recovery level is of greater importance to the model, which is more reliably obtained from the literature.

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Activity and loading influence the predicted bone remodeling around cemented hip replacements.

Periprosthetic bone remodeling is frequently observed after total hip replacement. Reduced bone density increases the implant and bone fracture risk, ...
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