FE and experimental study on how the cortex material properties of synthetic femurs affect strain levels

Medical Engineering and Physics 46 (2017) 96–109

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FE and experimental study on how the cortex material properties of synthetic femurs affect strain levels Vitor M.M. Lopes a, Maria A. Neto a,∗, Ana M. Amaro a, Luis M. Roseiro b, M.F. Paulino a a

CEMMPRE, Center for Mechanical Engineering, Materials and Process, University of Coimbra, Rua Luís Reis Santos, 3030-788 Coimbra, Portugal Polytechnic Institute of Coimbra, Coimbra Institute of Engineering – Mechanical Engineering Department, Rua Pedro Nunes- Quinta da Nora, 3030-199, Coimbra, Portugal

b

a r t i c l e

i n f o

Article history: Received 24 January 2017 Revised 16 May 2017 Accepted 1 June 2017

Keywords: Synthetic femurs Strains Experimental Finite-element models Unhealthy femur

a b s t r a c t The primary aim of this work was to validate the “numerical” cortex material properties (transversely isotropic) of synthetic femurs and to evaluate how the strain level of the cancellous bone can be affected by the FE modeling of the material’s behavior. Sensitivity analysis was performed to find out if the parameters of the cortex material affect global strain results more than the Polyurethane (PU) foam used to simulate cancellous bone. Standard 4th generation composite femurs were made with 0.32 g/cm3 solid PU foam to model healthy cancellous bone, while 0.2 g/cm3 cellular PU was used to model unhealthy cancellous bone. Longitudinal and transversal Young’s moduli of cortical bone were defined according the manufacturer data, while shear modulus and Poisson’s ratios were defined from the literature. All femurs were instrumented with rosette strain gauges and loaded according to ISO7206 standards, simulating a one-legged stance. The experimental results were then compared with those from finite element analysis. When cortical bone was modelled as transversely isotropic, an overall FE/experimental error of 11% was obtained. However, with isotropic material the error rose to 20%. Strain field distributions predicted inside the two bone models were similar, but the strain state of a healthy cancellous bone was much more a compression state than that of unhealthy bone, the compression state decreased about 90%. Strain magnitudes show that average strain-levels of cancellous bone can be significantly affected by the properties of the cortical bone material and, therefore, simulations of femur-implanted systems must account for the composite behavior of the cortex, since small shear strains would develop near isotropic cancellous bone-implant interfaces. Moreover, the authors suggest that changing the volume fraction of glass fibers used to manufacture the cortical bone would allow a more realistic osteoporotic synthetic femurs to be produced. © 2017 IPEM. Published by Elsevier Ltd. All rights reserved.

1. Introduction Biomechanical experimentation and Finite Element (FE) computer simulation have been major tools for the biomechanical research community in the past few decades [1–3]. Nevertheless, the reliability of the computational results depends considerably on the accuracy of the material properties, boundary conditions and load applications [4]. Finite element models related to the definitions of bone material properties may be categorized into two groups: micro-finite element models and homogenized models [5]. Micro-finite (μFE) element material models are able to

∗

Corresponding author. E-mail addresses: [email protected] (V.M.M. Lopes), [email protected], [email protected] (M.A. Neto), [email protected] (A.M. Amaro), [email protected] (L.M. Roseiro), [email protected] (M.F. Paulino). http://dx.doi.org/10.1016/j.medengphy.2017.06.001 1350-4533/© 2017 IPEM. Published by Elsevier Ltd. All rights reserved.

capture trabecular and cortical bone morphology, while homogenized models assume that one finite element covers a larger bone region and has homogenized material. Generally, the μFE material models are proposed for identifying the metabolically relevant or the morphologic functional features of the trabecular bone, whereas homogenized models are used to derive the elastic properties of bone from its in vivo constituents and to predict the risk of fracture. Both in vivo models rely on imaging methods to measure the size and shape of bones, therefore, the limitations of imaging technology have a direct influence on the accuracy of a finite element model built upon it. Several studies based on micro and homogenized finite element material models have proved their ability to predict the reality of interest [6–12]. Despite the excellent quality of these results, they are subject-specific finite element studies and, because strain variability for cadaveric specimens can be larger than 100% [13], their use in tests specimens concerning the replacement of components would require a

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sample of several hundred specimens. Moreover, numerical models generated in this way consist of a very large number of elements, and this number can even be larger if replacing components is taken into account, requiring super computational techniques. Additionally, the low availability of donors and the large variability of human anthropometry and material properties, as well as storage requirements and high costs, have made synthetic bone an attractive alternative in the biomechanical community [14–16]. Despite the variety of synthetic bone materials available, fiberglass-reinforced with epoxy material and polyurethane (PU) foam simulating cortical and cancellous bone, respectively, have been used more extensively in orthopedic experiments. Standard 4th generation composite femurs (Sawbones, Pacific Research Laboratories, Inc., Vashon, WA, USA) are made with solid PU foam with a density of 0.32 g/cm3 to model good quality cancellous bone. Similarly, the 0.16 g/cm3 solid PU foam has been used to substitute osteoporotic human bones. O’ Neil and co-workers [17] have demonstrated that the 0.16 g/cm3 solid PU foam produces qualitatively similar force displacement curves for the DHS and the DHS Blade to those recorded within the osteoporotic cadaveric femoral heads. However, they recognized that no synthetic material can be considered as a definitive substitute for bone and suggest that more studies performed with synthetic bone are needed. Hence, no validated bone surrogate specimen exists to simulate weak bone, which makes the mechanical evaluation of implant performance in osteoporotic bone difficult at best [18]. Notwithstanding this, the use of composite femurs for studying hip fractures in the elderly population has been growing in the past decades. Many experimental studies using composite bones have provided the material properties [19–23], but many others do not supply any information [24–27], thereby limiting the applicability of their results to the development of computational models. Moreover, the material properties provided by the manufacturer [28] have typical values of transversely isotropic materials, but the information available lacks the material constants, namely shear modulus and Poisson’s ratios. The generality of the work published, related to finite element models of intact or implant bones, assumes that synthetic bones are isotropic with linear elastic properties. Additionally, Grassi et al. [29] states that the elastic transversely isotropic material properties provided by the manufacturer were used to validate finite element models of six composite femurs, but they have also not explicitly provided values for shear modulus and Poisson’s ratios. The primary aim of this work was to validate the “numerical” orthotropic (transversely isotropic) material properties of synthetic femurs, in order to compensate for the lack of material data, and develop and validate numerical models on the basis of experimental results. Moreover, a sensitivity analysis was performed to find out if the cortical material parameters affect the global strain results more than the PU foam used to simulate cancellous bone. Accordingly, the material parameter of the trabecular PU foam was changed to explore, simultaneously, the viability of using 0.20 g/cm3 cellular PU foam as an alternative material to simulate the global osteoporotic trabecular bone strength. 2. Material and methods Six 4th generation medium-sized composite femur bones (model#3403, Sawbones, Vashon, WA, USA) and a Digital/CAD geometry of composite femur with 16 mm medullar canal, core and cortex parts (model#3908, Sawbones, Vashon, WA, USA) [28] were used for the experimental study. All synthetic femurs have an outer layer of glass fiber reinforced by epoxy resin with an average density of 1.64 g/cm3 that simulates the human cortical bone. The inner layer of the three synthetic femurs is composed of a solid PU foam core with an average density of 0.32 g/cm3 , simu-

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lating adult human cancellous bone, whereas for the other three the inner layer is composed of a cellular PU foam core with an average density of 0.20 g/cm3 , simulating the material properties of unhealthy (UH) cancellous bone. The average values obtained for each group were used to establish a qualitative comparison with the FE results. However, due to the reduced number of samples per group, no statistical analysis was performed for the experimental data

2.1. Experimental measurements All the femurs were instrumented with four strain gauge rosettes from HBM® manufacturer (reference KRY8-3-45-350-3-3, Darmstadt, Germany; with three foils in constant measurement grids at 0°−45°−90°; resistance of 350 ± 0.35%; length of 3 mm and 0.9 mm) and one linear strain gauge also from HBM® manufacturer (reference LY18-6-350-3-3, Darmstadt, Germany; with one measurement grid foil in constantan, 350  of nominal resistance, 6 mm of grid length and temperature response match to plastic material). Strain gauges were glued on the femur at five anatomical locations. The exact position of each gauge was defined using a marking protocol: femurs were held in the load configuration by means of an aluminum block with the surfaces of the condyles imprinted and aligned with the desired loading angle, and the anatomical location of each strain gauge was marked using the information outlined in Fig. 1. Bone strains were measured from gauges placed on the posterior neck region (R1), on the posterior region close to the lesser trochanter (R2), on the posterior proximal diaphysis (R3), on the anterior region between the greater and lesser trochanters (R4) and on the medial diaphysis (LG). All strain gauges were connected to a data acquisition system PXI-1050 from National Instruments (NI Corporation, Austin, USA), which was connected to a PC to record the data by using LabView Software® (NI Corporation, Austin, USA). In order to evaluate and compare the strain levels of healthy and UH femurs, a single loading direction was chosen. Force direction was defined according the ISO7206 standard, which simulates the loading conditions occurring in the one-legged stance [30,31]. Muscle forces were not simulated, as experimental and finite element studies have indicated that they do not alter the stress distribution in the head-neck region [32–36]. Nevertheless, additional muscle forces can affect strain/stress levels in the vicinity of their attachment areas, especially the abductor muscle that can act as a counteractive force and, therefore, minimize the tensile stress along the superior part of femur neck and great trochanter [37,38] However, because this work is a comparative study between healthy and unhealthy femurs, it would be expected that muscle forces would lead to similar effects on both femurs. To ensure reproducibility, the femurs were fixed to the testing platform and consistently oriented by means of an aluminum block attached to the femoral condyles, holding the femoral shaft at 11° in adduction and 9° in flexion. This block was fixed to the platform of a Shimadzu AG-10 universal testing machine (Shimadzu Corporation, Kyoto, Japan), equipped with a 5 kN load cell and TRAPEZIUM software, and different levels of force were applied at a displacement rate of 2 mm/min. Forces were applied vertically to the femoral head using the machine actuator through an aluminumTeflon plate. The Teflon material was glued to the aluminum plate, thereby avoiding the transmission of horizontal forces. For all force magnitudes, the maximum force was held for 30 s, allowing a constant time for a repeatable amount of creep to take place. Each loading intensity was repeated three times on each specimen and, between repetitions, the specimen was allowed to recover for 10 min.

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Fig. 1. Femur with positions of strain gages: (a) anatomical positions using two orthogonal reference planes (left image is the femur posterior view and the right image is the femur anterior view); (b) Bone strains were measured from five gage glued on synthetic femurs.

2.2. Finite element modeling The loads and boundary conditions applied to the experimental femurs were replicated in the finite element modeling. The CAD femur (model#3908, Sawbones, Vashon, WA, USA) was aligned at 11° in adduction and 9° in flexion and condyles were subtracted to the CAD geometry of a 120 × 93 × 114mm3 aluminum block,

assuring that condyles were continuously connected to the aluminum block at approximately 94 mm of height. Afterwards, the FE model of both components, femur and block, was created and the three displacements (DOF) of the nodal points placed on the bottom surface of the aluminum block were fixed. Loads were applied vertically to the femoral head through the CAD geometry of an aluminum−teflon plate. Even though the teflon resin has

Table 1 Material properties for the cortical and cancellous parts of synthetic femurs. Material property

E1 [GPa] E2 [GPa] E3 [GPa] G12 [GPa] G13 [GPa] G23 [GPa]

υ 21 υ 31 υ 32

Density [g/cc] ∗ ∗∗

Cortical bone

Isotropic cancellous bone

Composite 1

composite 2

Isotropic [20]

Type 1 [27]

Type 2 [27]

10 [27] 10 [27] 16 [27] 3.97∗ 6.63 [40] 6.63 [40] 0.26 [27] 0.416 [39] 0.416 [39] 1.64

10 [27] 10 [27] 16 [27] 3.97∗ 3.85∗∗ 3.85∗∗ 0.26 0.30 0.30 1.64

16 16 16 6.35∗ 6.35∗ 6.35∗ 0.26 0.26 0.26 1.64

0.21 0.21 0.21 0.08∗ 0.08 0.08 0.3 0.3 0.3 0.32

0.0475 0.0475 0.0475 0.018∗ 0.018 0.018 0.3 0.3 0.3 0.2

This value was evaluated using (E1 /(2(1 + υ21 ) ) ), meaning that material has isotropy in plane x1 x2 . This values was evaluated using (E1 /(2(1 + υ31 ) ) ).

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low friction coefficient, the friction coefficient of 0.05 [39] was used to model the interface between plate and femoral head. Experimental femoral constraints were simulated assuming the material continuity between femur and aluminum block. Linear elastic isotropic and transversely isotropic material properties were applied, [20,28,40,41] Table 1. The principal axes of orthotropy were cylindrical with axial directions parallel to the anatomical axes of diaphysis and neck regions, respectively, [29,41]. The longitudinal and transversal Young’s modulus of composite cortical bone, with a density of 1.64 g/cm3 , were defined according the manufacturer’s data, while shear modulus and Poisson’s ratios were defined taking into account the relevant literature [40,42]. From table 1 it is possible to see that the material properties of the cortical bone represented by composites 1 and 2 differ only in shear modulus values. Sensitivity analysis was performed to find out if experimental and numerical strains show similar sensitivities to changes of cancellous material and to find out how the change of cortical material parameters affect numerical strains. The geometry of the numerical model was created in accordance with the geometry of the experimental setup and, afterwards, the femur was meshed with 4-noded unstructured regular tetrahedral elements, using an average element volume of 0.18mm3 [43]. The accuracy of this numerical model was verified previously by a mesh convergence study and by a comparison with the numerical solution obtained with 10-noded tetrahedral finite elements, for a mesh with the same number of elements [44]. The complete finite element mesh was built with 324,183 nodes and 1103,806 elements, simulations were obtained using the ADINA ® [45] standard solver. 2.3. Validation procedure The validation of the material properties presented in Table 1 involved the numerical and experimental comparison of femur strains as well as both vertical displacements in the aluminum−teflon plate. Nevertheless, because ADINA does not provide the in-plane principal strains at the surface rosettes, it was necessary to convert the global strains of the 3D-solid elements into surface strains. This transformation was guaranteed, in each one of the four rosettes, by the definition of a local coordinate system and by computing a strain transformation between the global system and each one of these coordinate systems [46]. Then, the in-plane principal strains were computed from the in-plane strains defined on each local coordinate system. During the mesh generation, special care was taken to assure that a node was coincident with the center of each rosette. However, since the majority of the rosettes were placed in a region of high-strain gradient, mean values of strains on 3 × 3mm2 local rectangular surfaces were used to average the principal strains on the rosette surfaces. The predicted principal strains were compared to the measured values using a linear regression. The goodness of prediction is expressed by the coefficient of linear regression R2 and by the slope. Ideally, we should find a perfectly linear relationship between the measurements and predictions (R2 = 1) with a unitary slope [47]. These metrics provide a global indication of the goodness of predictions, but for many conditions it is also important to know what is the local error associated with each single prediction. Thus, for each rosette and each bone type we also computed the peak error, and the root mean square error (RMSE). 3. Results 3.1. Experimental results Some nonlinearity was observed in the force-displacement curves for loads above 500 N, Fig. 2a) and b). Such nonlinearity

Fig. 2. Typical force-displacement curves for the two classes of cancellous bone: (a) healthy cancellous bone; (b) unhealthy cancellous bone. Force-strain curves for the healthy cancellous bone and a maximum load of 10 0 0 N: (c) First principal strain on rosettes R1, R2 and in the strain gage LG; (d) second principal strain on rosettes R3 and R4.

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V.M.M. Lopes et al. / Medical Engineering and Physics 46 (2017) 96–109 Table 2 The average and maximum errors, both defined as absolute and as a percentage of the measured value, in the two kind of femurs. Cancellous bone healthy

Unhealthy

R1

R2

R3

R4

LG

RMSE [microstrains] RMSE [%] Max. error [microstrains] Max. error [%]

9.54

18.59

18.83

47.2

21.6

4.71 10.42 (e2 ; 250 N) 10.42

7.85 39.03 (e1 ; 10 0 0 N) 12.63

3.24 19.07 (e2 ; 10 0 0 N) 5.33

9.26 115.65 (e2 ; 10 0 0 N) 16.71

4.18 29.43 (750 N) 5.07

RMSE [microstrains] RMSE [%] Max. error [microstrains] Max. error [%]

14.32

6.88

86.61

13.24

19.49

7.75 18.03 (e2 ; 10 0 0 N) 13.45

5.87 2.98 (e2 ; 250 N) 10.25

10.76 182.31 (e2 ; 10 0 0 N) 16.97

4.3 21.02 (e2 ; 500 N) 8.07

3.44 31.64 (750 N) 5.14

was also observed in the force-strain curves to the same levels of load, Fig. 2c and d. Healthy femurs showed lower vertical displacement than the UH femurs, the average displacement differences were 8.21% for the force of 750 N and 4.40% for the force of 10 0 0 N. The variation of vertical stiffness between healthy and UH cancellous bone was 1.5% for the force of 750 N and 5% for the force of 10 0 0 N. Nevertheless, no major differences were observed for 250 N and 500 N loads. The linearity between force and displacement, and between force and strain, was checked by the coefficient of determination (R2 ). The strain linearity on both kinds of cancellous bone for forces of 250 N and 500 N was always excellent, R2 ≥ 0.99. For loads higher than 500 N the coefficient of determination was only consistently R2 ≥ 0.99 on R3 and on LG, but in no case was it lower than 0.93. The repeatability of linearity was also excellent. In fact, only in the case of loading the UH femurs with the force of 10 0 0 N, did the repeatability of linearity in R1 and in the displacement show values of 1.34% and 1.12%, respectively, but in all the other cases it was always lower than 1%. All strain measurements were successfully performed and the repeatability between replicates under the same conditions was satisfactory. The variability or coefficient of variation, i.e. the ratio of the standard deviation to the mean, was generally lower than 5% of the magnitude measured Fig. 3 shows the average magnitude of the maximum (e1) and minimum (e2) principal strains for the four different loading intensities. Maximum values of the first principal strain were on gauges R1 and LG, while the maximum absolute values of the second principal strain were on gauges R3 and R4. The values of the first principal strain on strain gauges R1, R3 and R4 were higher on the UH femurs than on the healthy femurs. However, an inverse behavior was observed at gauge R2, which was placed close to the lesser trochanter. In fact, at R2, both principal strains had smaller absolute values in the UH femurs, whereas the values of axial deformation at gauge LG did not show noteworthy variations between both types of femurs, this may be related with a lack of cancellous bone in the region where the gauges were placed. 3.2. Comparison of FEM and experimental results The predicted principal strains correlated well with the experimental values for both the cancellous bone types, when composite material 1 was used. Linear regressions for this material are reported in Fig. 4 and, in both cases, the coefficient of determination is higher than 0.99. Nevertheless, the slope of the regression of the UH femurs is only of 0.9111, while for the healthy femurs it is of 0.9482. Moreover, the average RMS errors were of 6.71% in healthy femurs and of 7.56% in UH femurs. The maximum error was of 182.31 (μstrain) in the UH femur, which represent 16.97% of the second principal strain measured and occurred at gauge R3 for the load intensity of 10 0 0 N. The results of the average errors at each strain gauge are summarized in Table 2. The values predicted of

the first principal strain in the region of strain gauge R2 are higher for the UH femurs than for the healthy femurs. Nevertheless, because the strain distributions on the cortical bone of the healthy and UH femurs are quite similar, small misalignments of the measurements are suspected of being responsible for the major differences between predicted and experimental strains. Moreover, due to higher values of the sagittal displacement on UH femurs (see Fig. 7), it is natural to observe higher absolute values of the second principal strain at R2. The RMS errors of all principal strains were predicted using the three finite element material models and the results are compared in Fig. 5. Smaller values of RMSE are associated with the cortical bone modelled as composite 1, however, when the load changes from 250 to 10 0 0 N the RMS errors duplicates. All other material models, except the composite 2, show a similar RMSE behavior, i.e. the RMS error tends to increase with the load intensity. It is possible to conclude that the coupling between dissimilar normal stresses and normal strains (the well-known Poisson effect) has a higher relative importance for small forces than for higher forces, from the behavior of composite 2. Moreover, because the RMSE of R1 and R4 were those that contributed most to the RMSE variation of composite 2, it seems that the Poisson effect on the proximal femur bone is more relevant than that on the diaphysis. The sensitivity analysis results are presented in Fig. 6. All sensitivity values were evaluated by computing the ratios between the % change in the predicted (or measured) principal strains and the % change in the input parameter. In the case of the PU foam sensitivities the % of the input parameter variation was of −77.4%, according to the variation of Young’s modulus, whereas for the composite and isotropic materials the % of input parameter variations were of −42% and 27.9%, respectively. These input parameter variations were computed using shear modulus of composites and the average of Young’s and shear modulus variations of the isotropic material. Fig. 6 shows the average of sensitivities for all load cases on all gauges, the initials ES and NS are used to denote experimental and numerical sensitivities. In the case of a positive strain value and negative variations of input parameters, the negative sensitivity means that the strain value will increase with the decrease of the input parameter, whereas a positive sensitivity means the opposite. The results show that the numerical and experimental strain sensitivities for the PU foam material are almost coincident and that the PU foam type has the greatest impact on the resulting strains, especially on the maximum principal strain of R4 and on the minimum principal strains of R1 and R2. However, changing the material behavior also has a significant effect on the accuracy of the predicted strains. The predicted maximum vertical displacement correlated well with the experimental value, but all femoral experiments showed a significant posterior displacement, which was not measured. Nevertheless, it is possible to predict all the components of the

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Fig. 3. Magnitude of the maximum (e1 ) and minimum (e2 ) principal strains for the four different loading intensities on synthetic femurs made with healthy and unhealthy cancellous bones. The chart columns indicate the average and the standard deviation between three specimens.

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Fig. 4. Predicted and measured principal strains on both kinds of femurs: (a) femurs with healthy cancellous bone; (b) femurs with unhealthy cancellous bone.

Fig. 5. Average root mean square errors (RMSE) of all principal strains at different load intensities using different finite element materials models.

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Fig. 6. Experimental and numerical sensitivities of strain measurements to the cortical material parameters and to the PU foam used to simulate cancellous bone: (a) first principal strain sensitivities; second principal strain sensitivities.

displacement field from the FE results and, therefore, Fig. 7 shows the displacement field for both kinds of femurs, for one node located in the region of the fovea. The letters X, Y and Z are used to denote the displacements on the horizontal and vertical axes of the frontal plane and on the horizontal axis of sagittal plane (in the anterior to posterior direction), respectively. Initial “Mag” is used to denote the magnitude of the displacement field. These results show that the displacement in the frontal plane axes is similar, but the displacement along the sagittal axis is much higher than the displacement along axes of the frontal plane. The sagittal displacement, which is an indirect measure of the torsional stiffness of both femurs, is higher for the UH femur than for the healthy femur. Consequently, cancellous bone properties can be important to prevent buckling, due to the local elastic instability [48]. The variation of the vertical stiffness between the femurs with the healthy and the UH cancellous bone was of 5.5% for the force of 10 0 0 N. The distribution of the tensile and compressive strain fields for both the cancellous bones are presented in Fig. 8. These results were not directly validated, since no measurements were taken inside the bone, nevertheless it is reasonable to expect that the experimental strains on the surface will be influenced by the strain

field inside the bone. The histogram of the bone tissue level loading distribution represented by the three principal strains in the cancellous bone head, presented in Fig. 9a, show the differences between the healthy and the UH cancellous bones. The results of further analyses of the tissue strains in the cancellous bone concentrated on a rectangular prism volume of interest (VOI) located in the femoral nail and trochanteric line (the black rectangle drawn in Fig. 8b), are also presented in this figure. For the UH cancellous bone the distribution curve is wider, indicating that more fraction of tissue is under high strains than for the healthy bone. From the average values presented on Table 3, it is possible to conclude that the strain-state of the healthy cancellous bone is much more a compression state than that of the UH bone, as, on average, the compression state decreases by about 90%. Nevertheless, 25% of the compression loaded UH tissue shows strain values that are about 12.5% higher than those of a healthy bone, while 25% of the traction loaded UH tissue shows strain values that are only about 7% high, and the maximum value of the principal strain increase is about 27.7%. All these variations are much higher for the VOI, on average, the principal tissue-level strain in the healthy VOI was 16.2 μm/m and for the unhealthy VOI it was 75.5 μm/m, represent-

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Fig. 7. Displacement field of one node located in the region of the fovea of femoral head: X and Y denotes the displacement on the horizontal and vertical directions of frontal plane, respectively; Z denotes the displacement on the horizontal direction of sagittal plane. Table 3 Statistical description of the distributions found for head cancellous bone.

Principal strains [μm] Healthy composite Non-Healthyc Healthy isotropic VOI Healthy composite Non-healthy Maximum Shear [μm] Healthy composite Osteoporotic Healthy isotropic

Aver.

SD

Minimum

1st quartile

Median

3st quartile

Maximum

Skewness

Curtosis

−23.8 −2.2 −27.9

652.0 790.3 593.2

−10,459.2 −10,523.5 −8328.9

−426.6 −479.7 −388.2

−23.8 −19.9 −8.4

416.2 445.8 350.4

6499.5 8299.4 6527.6

−0.43 0.24 −0.29

7.94 6.77 6.96

16.2 75.5

854.8 1136.9

−4774.2 −5487.9

−480.9 −592.9

−112.9 −117.6

565.7 743.3

6260.9 8299.4

0.17 0.48

2.11 1.89

1282.5 1506.6 1167.0

752.7 996.5 673.0

89.6 91.9 76.5

864.3 940.3 790.2

1176.6 1294.3 1064.0

1454.2 1691.1 1334.1

14,181.2 14,082.4 14,266.6

2.72 2.20 2.69

16.10 7.91 16.76

ing an increase of 366.9%, the increase in the SED was about 33%. Fig. 9-b) shows the histograms of the tissue level loading distribution on the head of a healthy cancellous bone for both cortical bone types, i.e. FE simulated as isotropic or as composite materials. For the composite bone the distribution curve is also wider, thus more material is under higher strains than for the isotropic cortical bone. For the isotropic finite element model the 25% of cancellous bone under compression and traction shows smaller strain values of about 9% and 16%, respectively.

4. Discussion The aim of this study was to investigate the accuracy of finite element models in reproducing the mechanical behavior of healthy and unhealthy synthetic femurs. Nowadays, it is well accepted that the fourth-generation composite bones of the Pacific Research Laboratories Inc. have average stiffness and strains that are close to the corresponding values of natural bones [49]. For this reason, a great number of implants for fracture and/or of osteotomy fixation have been studied an analyzed experimentally using fourthgeneration composite bones [19,21,24,27,31,50–53]. However, some researchers have not explicitly provided the cancellous bone properties in their reports, thereby limiting the applicability of their results to the development of computational models. Moreover, to the authors’ knowledge, no study in the literature has experimentally and numerically assessed the effect of changing the density of

the synthetic cancellous bone on the biomechanics of whole synthetic bone. Nicayenzi et al. [54] experimentally evaluated the effect of synthetic cancellous bone density on the mechanical behavior of synthetic femurs, but the cancellous matrix was always formed with solid PU foam and no numerical evaluation was performed. Patel et al. [55] reported that solid PU foam of 0.32 g/cm3 density has values of Young’s modulus and yield strength similar to normal bone, whereas the classification of the 0.16 g/cm3 solid PU foam as healthy or as osteoporotic bone is difficult. Cellular PU foam with a density of 0.09 g/cm3 , studied by the same authors, proved to be weaker than the osteoporotic bone investigated by Li and Aspden [56], but the density of the cellular PU foam selected in this work is more than twice the value studied by Patel et al. and its Young’s modulus is even closer to the lower limit of the osteoporotic bone than the modulus of the 0.16 g/cm3 solid PU foam. So, even knowing that a true validation of an osteoporotic bone model implies that the material should be assessed in its similarity to true osteoporotic tissue [57], cellular and solid PU foams with densities of 0.2 g/cm3 and of 0.32 g/cm3 , respectively, were selected to gather qualitative information about the loadinglevel of unhealthy and healthy cancellous bones of synthetic femurs. From the results obtained, it is clear that there is a considerable difference in both the cancellous-tissue strains on the femoral head. The experimental results have shown that the largest tensile strains on the femurs were localized in the head-neck region (R1)

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Fig. 8. Predicted tensile strain distributions inside the femurs: (a) anterior view of healthy cancellous bone; (b) anterior view of UH cancellous bone; (c) posterior view of healthy cancellous bone; (d) posterior view of UH cancellous bone. Compressive strain distributions inside the femurs: (e) anterior view of healthy cancellous bone; (f) anterior view of UH cancellous bone; (g) posterior view of healthy cancellous bone; (h) posterior view of UH cancellous bone.

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and the largest compressive strains were localized at rosette R3, for both healthy and unhealthy femurs. These results agree with those reported by Cristofolini et al. [36,58] for the strain rosettes PN and A3, respectively. However, because the location of both rosettes is not coincident and the load direction is also different, a direct comparison of absolute values is not possible. Variations in vertical stiffness between the healthy and the UH cancellous bone were of 1.5% for the force of 750 N and of 5% for the force of 10 0 0 N. The sensibility of the vertical stiffness to the load intensity, between the healthy and the UH cancellous bone, was also reported in the work of Nicayenzi et al. [54]. They concluded that failure load, displacement, and deformation energy of synthetic femurs were highly dependent on the cancellous bone density. This behavior is also confirmed by the sensitivity results reported on Fig. 6, which show that the material properties of PU foam have the greatest impact on the resulting strains. Moreover, the results shown in Figs. 8, 9b and 9c indicate that, even with the same cancellous bone density, the average strain-level of the cancellous bone can be significantly affected by the material properties of the cortical bone. Hence, finite element simulations of femur-implanted systems using isotropic material properties for the cortical bone may influence the loosening of orthopedic implant, since small shear strains will develop near the cancellous bone-implant interfaces and, in these situations, the shear strain may be equal or even more relevant than the compressive strains [59]. In the case of loading the standard femurs with a load of 10 0 0 N, a variability of 12.5% was found in the first principal strain at rosette R4. In fact, for all the loads and for all the femurs, the largest coefficient of variation was consistently associated to R4. Through a detailed inspection, it was found that this rosette was placed in a region where the surface had a higher curvature and, therefore, is more prone to higher strain errors, due to small variations in the installation procedure [60]. Moreover, the strain magnitudes of R4 tended to decrease slightly between replicates, despite the 10 min recovery allowed between repetitions. The numerically predicted strains were highly correlated with the measured ones and the correlation coefficient was very high, when cortical bone was modelled as being of composite type 1, for both the cancellous bone models. The global strain accuracy was good, since both the root mean square and peak errors were low. Lower strain accuracy was found for the UH cancellous bone, where peak errors were higher at gauges R1 and R3. Numerically predicted strains on rosette R2 showed an inverse behavior compared to what was observed experimentally. In fact, both experimental principal strains had smaller absolute values at R2 in the UH femurs and the numerical study was not able to confirm these results, which could be attributed to small numerical/experimental misalignments of rosette R2 and to small changes in the surface geometry between the two types of femurs. Peak errors may be related with the differences in the numerical/experimental curvatures of the surfaces in those regions or even with misalignments between the numerical principal axes of orthotropy and the directions of fiber distribution on synthetic femurs. The RMS errors of all principal strains predicted by the other two finite element material models, i.e. isotropic and composite 2, showed that modeling the cortical bone with isotropic material properties led to higher errors. Combining this insight with the knowledge that the strain level of cancellous bone can be significantly affected by the material properties of cortical bone, it seems that the local behavior of femur-implanted systems can only be realistically improved if the composite behavior of cortical bone is numerically accounted for. In addition, the principal strain field distributions predicted inside the bone by the two numerical models were similar, but the UH femur showed higher levels of deformation, 27.7% on the maximum value of tensile strain and 2.7% on the maximum absolute value of compressive strain. Large compressive strains were devel-

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Fig. 9. Histograms of the distributions found for the head cancellous bone: (a) all three principal strains on healthy and unhealthy cancellous bones when cortical bone is numerically modelled as composite 1; (b) all three principal strains on healthy cancellous bone when cortical bone is numerically modelled as composite 1 and as isotropic; (c) maximum shear strains on healthy and unhealthy cancellous bones when cortical bone is numerically modelled as composite 1 and as isotropic.

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oped at the base of the femoral head in the inferior-medial region and between the greater and lesser trochanters. The largest tensile strains were developed at the base of the femoral neck in the superior-anterior region and, especially in the case of the UH femur, at the base of the great trochanter. The strain distribution in the UH femur was less favorable than that in the healthy femur, with higher fractions of the tissue (0.06% higher: 0.08% in unhealthy and 0.02% in healthy) loaded beyond 30 0 0 μm/m and a higher fraction of tissue-loaded with strains lower than 50 μm/m (9.95% in unhealthy and 9.81% in healthy). This behavior is in agreement with other results reported in the literature [57,61,62] that have reported a decrease in the mechanical stimuli associated with the bone morphology representative of osteoporosis. Rietbergen et al. [57] found that an osteoporotic human femur can have 0.045% of tissue loaded beyond 30 0 0 μm/m while 2.63% of the tissue is only loaded with strains lower than 50 μm/m, but because a different load and volume of interest (VOI) was used, these results are quantitatively different from ours. However, for the case of the VOI defined in this work, the fraction of the UH cancellous tissue loaded beyond 30 0 0 μm/m is about 8 times higher than in the case of the healthy cancellous bone (0.25% in unhealthy and 0.03% in healthy) and the fraction of the tissueloaded with strains lower than 50 μm/m is also about 1.4 higher (6.2% in unhealthy and 4.5% in healthy). Even though there are differences between this study and that of Rietbergen et al. [57], namely concerning the VOI and the load, it is worth noting that the fractions of cancellous tissue-loaded beyond 30 0 0 μm/m are of the same order, whereas those loaded below 50 μm/m are higher in this work. These results suggest that, in comparison with FE models, the μFE models will tend to decrease the fraction of cancellous tissue that is under low-loaded and increase the SD values, which may be due to the presence of small trabeculae and to the differences in the thicknesses of the cortical bone. Nevertheless, these results show that the selection of the density of the cancellous bone has a significant effect on the deformation level of the inside bone and it is quite clear that the contribution of the cancellous bone in maintaining the structural integrity of synthetic femur cannot be ignored [63], especially when synthetic femurs are used for studying implants and/or fixation devices in elderly people [16,22,64,65]. Despite knowing that both cortical and cancellous bones work in synergy to provide strength to the synthetic femur and that an osteoporotic human femur has a more reduced cortex thickness than healthy femur, the results reported within this work would have been even more pronounced if the unhealthy synthetic femur had a reduced cortex thickness. In fact, one of the limitations of this work is related with differences in morphologies between the unhealthy synthetic femur and that of an osteoporotic femur [66]. Cortical bone in the superior region is thinner than that in the inferior region of the femoral neck and, when compared with that of younger adults, the cortices in the elderly exhibit marked thinning in the superior region but are thicker in the inferior region [67]. However, the loss of cortical bone in the unhealthy femur was not accounted for, but because the main goal of this work was to investigate the relative structural contributions of the material properties of cancellous bone and the relative magnitude of strains between different loading intensities, we were interested in relative rather than absolute results. It is also noted that the material properties of the cortical bone on the unhealthy femurs were the same as those of a healthy synthetic femur. The changes in the material properties of cortical bone are mainly caused by the increase in porosity with age [68,69]. Nevertheless, several studies have indicated that the elastic modulus of cortical bone decreases only modestly with aging, while the strength and especially toughness decrease more substantially [70]. Hence, the assumption of standard material properties for the cortex bone in synthetic unhealthy bones has been

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widely used in the scientific community [18,71,72], together with the acceptance that the definition of the density of the PU foam is crucial to simulate the osteoporotic mechanical properties of long bones. However, the results reported here show that the average strain level of cancellous bone may be significantly affected by the material properties of cortical bone and, therefore, the authors suggest that changing the volume fraction of glass fibers used in the manufacture of cortical bone would make it possible produce a more realistic unhealthy synthetic femurs. The use of a plate to apply loads on the femur may also be questioned. In fact, this loading condition is far from the hip joint. Nevertheless, this procedure is in agreement with the ASTM F384 method that is designed to evaluate the strength properties of metallic angled orthopedic fracture fixation devices and is often used to evaluate the biomechanical properties of implanted and non-implanted orthopedic implants [31,73,74]. Moreover, the high flexibility of the teflon material ensures that the loads are well distributed over the contact area and that local strain concentrations are far from the measurement points. The findings of this work cannot be used to address issues concerning fractures of healthy and unhealthy synthetic femurs, but are suitable for use in the design optimization of prosthesis and fixation devices. Thus, even knowing that the research area of osteoporosis may be dominated by fracture issues [7,75,76], the in vitro or FE biomechanical models of fixation devices is also a research area that can provide information on load sharing, location of high strain concentrations, relative bone motion at the fracture sites and the global stability of fixation devices that may yield medical insights about the reliability of long-term implants [31,77,78]. Conflict of interest None declared Ethical approval Not required. Acknowledgments This research was co-financed by the Portuguese program COMPETE - Projeto QREN T.P.C. – Anca 30146, a new trochanteric plate of contention, and by PEst-C/EME/UI0285/2013 project. References [1] Shim V, Boheme J, Josten C, Anderson I. Use of polyurethan foam in orthopaedic biomechanical experimentation and stimulation, 2. InTech; 2012. pp 171–200 Chapter 9. [2] Juszczyk M, Schileo E, Martelli S, Cristofolini L, Viceconti M. A method to improve experimental validation of finite-element models of long bones. Strain 2010;46:242–51. [3] Emerson NJ, Offiah AC, Reilly GC, Carré MJ. Patient-specific finite element modelling and validation of porcine femora in torsion. Strain 2013;49:212–20. [4] Mengoni M, Sikora S, d’Otreppe V, Wilcox RK, Jones AC. In-Silico models of trabecular bone: a sensitivity analysis perspective. In: Geris L, Gomez-Cabrero D, editors. Uncertainty in biology: a computational modeling approach. cham. Springer International Publishing; 2016. p. 393–423. [5] Pahr DH, Zysset PK. Finite element-based mechanical assessment of bone quality on the basis of in vivo images. Current Osteoporos Rep 2016;14(6):374–85. [6] Luisier B, Dall’Ara E, Pahr DH. Orthotropic HR-pQCT-based FE models improve strength predictions for stance but not for side-way fall loading compared to isotropic QCT-based FE models of human femurs. J Mech Behav Biomed Mater 2014;32:287–99. [7] Dall’Ara E, Luisier B, Schmidt R, Kainberger F, Zysset P, Pahr D. A nonlinear QCT-based finite element model validation study for the human femur tested in two configurations in vitro. Bone 2013;52:27–38. [8] Keyak JH, Rossi SA, Jones KA, Skinner HB. Prediction of femoral fracture load using automated finite element modeling. J Biomech 1998;31:125–33. [9] Varga P, Baumbach S, Pahr D, Zysset PK. Validation of an anatomy specific finite element model of Colles’ fracture. J Biomech 2009;42:1726–31.

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