The risk of osteoporotic hip fractures may be reduced by augmenting susceptible femora with high- and low-viscosity cement. As the injection of excessive amounts of cement may result inthermal necrosis of bone tissue or even embolism, the minimum cement volume required to achieve a prede ﬁned level of augmentation should be determined. To this end, the present work introduces a novel eﬃcient generalized augmentation strategy combining a strain-based fracture criterion with experimental results of bone augmentation previously obtained. The proposedmethodology aims to estimate the fracture load improvement with two cement types (high- or low-viscosity). In total, 18 healthy and 17 osteoporotic ex vivo femora were numerically studied using the Finite Element Method and considering a typical lateral fall on the greater trochanter. In all cases, both a nonaugmented and an augmented state with injected bone cement were simulated. All augmented models of femora exhibited enhanced fracture loads regardless of the cement visc-osity used. Low viscosity cement showed a higher fracture load improvement than high-viscosity cement. Furthermore, augmentation of osteoporotic femora estimated a larger improvement in the fracture load (10.32 ± 3.22% with high-viscosity cement and 28.93 ± 7.04% with low-viscosity cement) with respect to healthy femora (9.41 ± 3.66% with high-viscosity cement and 25.19 ± 6.00% with low-viscosity cement). The results suggest that low-viscosity cement can be a powerful candidate for use in femoroplasty. Furthemore, the proposed methodology can beeﬃciently used for preoperative planning of bone augmentation surgery. 1. Introduction Osteoporotic proximal femur fractures are associated with high morbidity and mortality and dramatically decrease quality of life [1–3]. The high rate of occurrence of these injuries, which is continually increasing, puts a substantial load on the healthcare system [4]. Thus, there is a critical need for preventive actions that can help reduce fracture risk. Various treatments have been proposed for increasing bone mass and decreasing fracture incidence. A potential near-term pre- ventive measure for osteoporotic hip fractures is femoroplasty-augmentation of the mechanical properties of the proximal femur using polymethylmethacrylate (PMMA) bone cement, hereafter referred to as cement [5–8]. Reinforcement is achieved by means of percutaneous cement injection to prevent progressive deformity or collapse and to alleviate disabling pain [9]. Cement has been https://doi.org/10.1016/j.engfracmech.2019.106647 Received 10 November 2018; Received in revised form 25 June 2019; Accepted 27 August 2019⁎Corresponding author at: Mechanical Engineering, University of Zaragoza, Ed. Betancourt-Campus Río Ebro, C/María de Luna, 50018 Zaragoza, Spain. E-mail address: angeles@unizar.es (M.A. Pérez).Engineering Fracture Mechanics xxx (xxxx) xxxx 0013-7944/ © 2019 Elsevier Ltd. All rights reserved. Please cite this article as: S.J. Ramos-Infante and M.A. Pérez, Engineering Fracture Mechanics, https://doi.org/10.1016/j.engfracmech.2019.106647 widely used in implant ﬁxation and bone augmentation [8,10,11] due to its mechanical properties. The suitability of this material explains why most femoral augmentation studies use commercial cement as the reinforcing agent [5,6,8,12 –16]. However, cement presents certain disadvantages, such as a high polymerization temperature, toxicity, embolism and insu ﬃcient osseointegration [17,18] . Therefore, there are considerable risks involved in femoral augmentation when using large amounts of cement, including: bone necrosis due to high temperatures, risk of cement leakage into the blood vessels or development of regions of stress con- centration. To this end, computational studies have been conducted to determine the optimum amount of cement and injection locations to minimize the aforementioned possible side e ﬀects [19–21]. First-generation femoroplasty approaches have resulted in signiﬁcant improvements in both fracture load (40 –80%) and energy (150 –190%) compared with the nonaugmented contralateral side using large cement volumes up to 40 –50 ml [5,7,8] . However, an elevated risk of biological impairment due to heat, toxicity, pressure, leakage or blockage of blood support associated with the large cement volume has been recognized. Therefore, in second-generation femoroplasty studies, the amount of cement was decreased to 8 –15 ml [6,12 –14]and optimization methods were pro- posed [15,19,20,22] . The biomechanical advantages varied considerably both in terms of fracture force (0 –35%) and energy (0–160%). As a result, augmentation of the bone should be performed by employing a limited amount of strategically placed cement. Computational ﬁnite element (FE) analysis is a useful method for studying the mechanical characteristics of hip fracture. FE analysis was previously recognized as a noninvasive tool to estimate fracture load [23–27]or the risk for a speci ﬁc fracture type [23–29]. Computer tomography (CT)-based nonlinear FE analysis, which incorporates three-dimensional geometry and bone density distribution, has been used to estimate fracture load of the proximal femur with reasonable accuracy for given boundary conditions [23,30 –32]. In[23,30] a stance loading con ﬁguration, which may not adequately elucidate the failure mechanisms behind the clinical os- teoporotic hip fractures that typically occur in sideways falls. Few previous FE studies have estimated the experimental fracture load in a con ﬁguration that simulates a fall to the side [24–26,33] . However, a limited number of models of femora and linear FE analyses were used in these studies. The generation of an accurate FE model using linear analysis and strain-based criteria with a larger samplesize for a sideways fall con ﬁguration is therefore required [34–39]. Thus, it seems advisable to implement strain-based criteria in FE models of bone for the prediction of fracture risk. Given the high volume of published computational studies, it is clear that results from numerical simulations depend on a variety of factors such as the bone morphology, the degree of osteoporosis, the imposed boundary conditions and the material properties ofthe augmented bone [40,41] . The bone geometry, the degree of osteoporosis and the respective material properties are often obtained from a CT scan [21–24,42] . Similarly, the most commonly used boundary conditions in experimental and computational studies of femoroplasty replicate a lateral fall on the greater trochanter [5,6,13 –15]. In a recent paper [43], we described our approach to computer-assisted planning of femoroplasty to optimize cement volume and placement. In summary, we showed that by introducing 4 ml of high- and low-viscosity cement (substantially less than the 10 –50 ml volumes used in previous experimental studies [5,7,8,15,20] ) into open-cell structures with di ﬀerent porosities resembling di ﬀerent trabecular bone structures, it was possible to improve the Young's modulus. Thus, computational and experimental di ﬀerences between high- and low-viscosity cement were shown under the same loading conditions. The purpose of the current study is to computationally augment healthy and osteoporotic models of femora according to an eﬃcient generalized augmentation strategy by which we control the cement volume and its injection location. We hypothesize that the resulting cement augmentation (with high- and low-viscosity cement) will increase the Young's modulus of the femur comparedwith nonaugmented controls, as was observed in a previous study with open-cell structures [43]. We also hypothesize that the experimentally measured augmented parameters of interest will not be signi ﬁcantly di ﬀerent from those of model predictions; moreover, these results will be obtained using smaller cement volumes than previously reported for signi ﬁcant augmentation. To our knowledge, no other report has been published on the comparison between high- and low-viscosity cement for osteoporotic femoraaugmentation. 2. Materials and methods This study consisted of two parts. The ﬁrst part concerns a linear strain-based criteria that were utilized to predict the ideal reinforcement zones and fracture risks of the proximal femur under loads from a sideways fall on the greater trochanter. The second part concerns a new e ﬃcient generalized augmentation strategy based on the minimum density and the total volume of the failure zone. This data was used to virtually augment thirty- ﬁve models of femora (healthy and osteoporotic). The volume of the cement cloud varied among models of femora according to the di ﬀerent failure areas achieved after FE simulations. Thus, changes in the biomechanical properties and fracture risk of the augmented bones (with high- and low-viscosity cement) were evaluated by means ofa linear strain-based criteria and compared sample-wise to the nonaugmented state. 2.1. Linear strain-based fracture simulation2.1.1. Study sample Eighteen healthy femora (female/male: 7/11, age: mean 44.5 ± 28.5 years, left: 18) and seventeen osteoporotic femora (female/ male: 6/11, age: mean 70.5 ± 14.5 years, left: 17) were previously collected and scanned using a CT system (Brilliance 64, Philips Healthcare, Netherlands) with the following settings: tube current: 257 mA, voltage: 120 KV, slice thickness: 0.65 mm, spacing between slices: 2 mm and pixel spacing: 0.234 mm. The healthy femora were obtained from the Hospital Quirón (Valencia, Spain), and the osteoporotic femora, from the Hospital Universitario y Politécnico La Fe (Valencia, Spain). Both healthy and osteoporoticS.J. Ramos-Infante and M.A. Pérez Engineering Fracture Mechanics xxx (xxxx) xxxx 2 femora were retrospectively extracted from the Picture Archiving and Communications Systems (PACS). T-score data of the osteo- porotic femora was not available, but all 17 cases were diagnosed and received treatment as osteoporotic cases. 2.1.2. Model development The scanned images were reconstructed using a semiautomatic reconstruction (MIMICS, Materialise NV; Leuven, Belgium) to obtain a 3D solid bone model. The mesh was generated using tetrahedral elements (C3D4) comprising 105304 ± 27480 elements for the healthy femora and 110481 ± 32720 elements for the osteoporotic femora. Inhomogeneous isotropic bone properties were mapped from the CT images to the mesh (MIMICS, Materialise NV; Leuven, Belgium). Normally, CT calibration phantom is used to obtain the radiological density ( ρQCT). However, in the present paper, as no scanner calibration was available for the used ﬁles, each Hounsﬁ eld unit (HU) was converted to radiological density ( ρQCT) using information from the images and the literature [20]. In more detail, Eq. (1)was used to convert HUs to radiological density for the healthy tissue: =+ ρhealthy HU ( ) 0.209 0.001086·QCT (1) Eq.(2)was used to convert HU to radiological density for the osteoporotic tissue: =+ ρosteoporotic HU ( ) 0.1712 0.0007058·QCT (2) The bone mineral density (BMD) of an osteoporotic femur is approximately 65% of the BMD of a healthy femur [44]. This relation was considered to obtain Eq. (2)from Eq. (1). For material heterogeneity, an average grey value of all of the voxels inside an element was calculated in Mimics (MIMICS, Materialise NV; Leuven, Belgium). The bone equivalent density (ash density, ρash) was then deﬁ ned by assuming a linear relationship by which the density is proportional to the attenuation ( ρash=ρQCT)[3]. Apparent density was found using [45]: =+ρ ρ1.79 0.0119app ash (3) where ρashand ρappare the ash and apparent densities in gr/cm3, respectively. Finally, the elastic modulus for each element (in MPa) was calculated using the following equations [19] for femoral neck specimens [46]: ==E ρν 10500· ; 0.32 cortical ash2.29(4) ==E ρν 6850· ; 0.2 trabecular ash1.49(5) 2.1.3. Fall loading con ﬁguration The examined load case was that of a lateral fall onto the greater trochanter. To this end, the distal femur and the great trochanter were fully constrained [47]. The total applied force was uniformly distributed over the medial nodes of the femoral head, while the force direction was tilted 15° in the frontal plane, as seen in Fig. 1. Fig. 1. Boundary and loading conditions of the fall con ﬁguration: vertical load on the femoral head toward the ﬂoor with the femoral shaft slanted by 30° and internally rotated 15° relative to the ﬂoor.S.J. Ramos-Infante and M.A. Pérez Engineering Fracture Mechanics xxx (xxxx) xxxx 3 2.1.4. Fracture load prediction of nonaugmented subject-speci ﬁc models A linear strain-based criteria were utilized to predict the ideal reinforcement zones and fracture risks of the proximal femur under loads from a sideways fall. To compute the fracture load under the fall con ﬁguration, a maximum principal strain criterion, including asymmetry in the tensile/compressive limit values, was selected. This criterion incorporates many of the fundamental bone elastic limit characteristics reported in the literature and can be easily implemented [46]. In each element of the FE mesh, e minand e maxwere assigned as follows: >= =If ε then eε εelse eε ε0 max limTmax limC111 (6) >= =If ε then eε εelse eε ε0 min limTmin limC333 (7) where εlimT= 0.0073 and εlimC= 0.0104 [36]. Thus, the fracture risk (RF) was evaluated as RF = max(|e max|,|e min|). If the element RF exceeded the value of unity, its volume was added to the volume of the failed elements. We increased the load (10 N) until the total volume of the failed elements reached 2% of the total volume of the specimen ( Fig. 2) [48,49] . The value of 2% was arbitrarily selected according to the literature because it is not known what percentage of bone tissue actually exceeds the yield strain when bone fractures occur [48]. To determine whether another value would yield a signi ﬁcantly diﬀerent estimation of the bone failure load, the fracture load was also calculated under the assumption that fracture occurs when 1%, 2% or 3% of the bone tissue exceeds the yield strain. Therefore, the instant of fracture was de ﬁned by assessing the volume of the failed elements, in line with previous studies [3,47] . No degradation of the material properties of the failed elements was considered. The algorithm was implemented as a user-de ﬁned material (UMAT) subroutine in Abaqus v6.14 (Dassault Systèmes Simulia Corp., Suresnes Frances) and run in a computational cluster of 224 cores with 576 GB of RAM. 2.2. Local bone augmentation strategy The optimum volume of cement and its distribution within the femur was computed for each model following the next approach. In a previous paper [43], a discrete particle model for cement in ﬁltration within open cell structures resembling trabecular bone was developed. Brie ﬂy, this particle model allowed us to predict the improvement in the Young's modulus depending on the bone density, cement viscosity and injected cement volume. The computational approach was experimentally validated. Data generated in [43] consisted in cement volume injected, average density of the open-cell structures, and improvement of the Young's modulus between augmented and nonaugmented open-cell structures using two cement types (high- and low-viscosity cements). Thus, usingprevious data [43] and the Curve Fitting Toolbox of Matlab (Matlab r2017a, The Mathworks Inc., Natick, USA), a power law to predict local femur strength improvement was proposed (Eq. (8)andFig. 3). =+ + + + + +I F P P TV P MD P TV P TV MD P TV P MD TV. . (%) 00 ( 10· ) ( 01· ) ( 20· ) ( 11· · ) ( 30· ) ( 21· · )23 2(8) where I.F. is the improvement factor (in %), TV is the total accumulated volume of the failed elements or total volume of cement injected (in cm3), MD is the minimum density associated with this femoral area or the average density of the open-cell structures Fig. 2. Workﬂow of the linear strain-based criteria for the prediction of the fracture load.S.J. Ramos-Infante and M.A. Pérez Engineering Fracture Mechanics xxx (xxxx) xxxx 4 resembling trabecular bone [43] (in g/cm3) and P00, P10, P01, P20, P11, P30 and P21 are the coe ﬃcients associated with the cement viscosity ( Table 1). The I.F. is a ratio that allows us to to estimate the Young's modulus improvement after cement injection. Once the fracture load for each nonaugmented femur specimen was obtained, we were able to determine the minimum density (MD) associated with this failed area and the total accumulated volume (TV) of the failed elements, which will be considered equivalent to the cement volume injected. Then, the local I.F. of the Young's modulus was obtained using Eq. (9). Later, once we obtain the local I.F., the Young ’s modulus (in MPa) of the failed elements was changed to that of augmented trabecular elements using the following equation: =⎛ ⎝+⎛ ⎝⎞⎠⎞ ⎠= EIFρν 1.. 100·6850· ; 0. 3trabecularIF ash1.49 (9) Finally, the fracture load was calculated using the maximum principal strain criterion ( Section 2.1.4 ) and compared with non- augmented cases. 3. Results 3.1. Local bone augmentation Table 2 shows the TV, MD and the corresponding improvement factor (I.F.) related to the type of cement injected (high- and low- Fig. 3. Interpolation surfaces for (a) high- and (b) low-viscosity cement in open-cell structures. Table 1 Calculated coe ﬃcients for each cement. High-viscosity cement Low-viscosity cement P00 −2.474 P00 6.571 P10 4.784 P10 69.77 P01 13.68 P01 77.8 P20 3.609 P20 18.52 P11 −8.348 P11 −268.6 P30 −0.1458 P30 −4.224 P21 −4.49 P21 24.49 R-squared 0.9921 R-squared 0.9978S.J. Ramos-Infante and M.A. Pérez Engineering Fracture Mechanics xxx (xxxx) xxxx 5 viscosity cement) obtained for the study sample. Important di ﬀerences between cement viscosities can be easily observed for similar total volumes of the healthy and osteoporotic models of femora. 3.2. Subject-speci ﬁc fracture load prediction All augmented models of femora exhibited increased fracture-relevant properties of the femora compared with the nonaugmented state. As discussed in Section 2.1 35 models of femora were assessed (18 healthy models of femora and 17 osteoporotic models of femora). Fig. 4 shows the mean fracture loads for all simulations from this study. For the nonaugmented state, the mean fracture load was 5078.33 ± 1356.59 N for the healthy subjects and 2437.65 ± 758.91 N for the osteoporotic bone model. For a given cement volume (TV), the relative increase depended on the nonaugmented properties –MD and cement viscosity (high and low) ( Table 2). Augmentation with approximately 3 ml of high-viscosity cement resulted in a 9.41 ± 3.66% increase in fracture load in healthyfemora (5622.78 ± 1557.45 N) and 10.32 ± 3.22% increase in osteoporotic femora (2728.24 ± 863.98 N). Similarly, augmen- tation with approximately 3 ml of low-viscosity cement resulted in a 25.19 ± 6.00% increase in fracture load in healthy femora (6800.00 ± 1827.92 N) and a 28.93 ± 7.04% increase in osteoporotic femora (3478.00 ± 1189.43 N). Regarding the fracture load improvements for the di ﬀerent ratios considered (the volume of failed elements with respect to the local volume of the femur), Table 3 shows that the di ﬀerence between RATIO 1 and RATIO 2 is considerably greater than the di ﬀerence between RATIO 2 and RATIO 3. These di ﬀerences could also be observed in Fig. 5, in which the failed femur area is similar in Fig. 5b and c. All detailed fracture load values for each healthy and osteoporotic subject in nonaugemented and augmented simulations are provided in the supplementary material. 4. Discussion Augmentation of an osteoporotic femur using cement to prevent or reduce the risk of fracture has been suggested as an alternative preventive treatment [50]. The results of the current study support our original hypothesis that femoroplasty improves the me- chanical properties of the femur compared with nonaugmented controls ( Fig. 4). A few recent studies have reported attempts to restore the mechanical strength of models of femora using a relatively small amount of in ﬁltrated cement with limited or no success [6,12,51,52] . A successful planning framework should include a module for predicting the cement inﬁ ltration inside trabecular bone. The majority of fragility fractures occur at trabecular-dominant bone sites. Indeed, the trabecular bone plays important roles in loadtransmission and energy absorption in major joints. Indeed, most proximal femur fractures initiate at the femoral neck superior cortex under compression, followed by damage of the inferior cortex under tension [53,54] . Reinforcing this region may help delay the superior cortex collapse and increase the overall strength of the proximal femur toTable 2 Calculated TV, MD and I.F. for the healthy and osteoporotic bone models (SD, standard deviation). Parameter Healthy bone model (Mean ± SD) Osteoporotic bone model (Mean ± SD) TV (cm3) 3.36 ± 0.75 3.03 ± 0.62 MD (g/cm3) 0.14 ± 0.06 0.08 ± 0.03 I.F. high viscosity (%) 40.66 ± 14.61 37.48 ± 11.25 I.F. low viscosity (%) 202.13 ± 46.28 224.08 ± 30.03 0100020003000400050006000700080009000 NONAUGMENTED FRACTURE LOADAUGMENTED FRACTURE LOAD/HIGH VISCOSITYAUGMENTED FRACTURE LOAD/LOW VISCOSITYFRACTURE LOAD (N)Healthy femora Osteoporotic femora Fig. 4. Calculated fracture loads for the healthy and osteoporotic bone model for the nonaugmented and augmented states (high- and low-viscosity cement). Bars indicated standard deviation values.S.J. Ramos-Infante and M.A. Pérez Engineering Fracture Mechanics xxx (xxxx) xxxx 6 protect against injury during sideways falls. In a recent work [43], a discrete particle model for cement in ﬁltration within open cell structures was developed. As discussed in Section 2.2 , this particle model allowed us to build a generalized local bone augmentation strategy to control cement volume and its injection placement in healthy and osteoporotic models of femora. The goal of the present work was to quantify and compare the di ﬀerences between high- and low-viscosity cement for osteo- porotic bone augmentation at the macroscopic level. Indeed, the main novelty of the current work was that our hypothesis to build the model was based on previous studies [43,55] in which computational approaches were experimentally validated. Thus, as a multiscale problem, thirty- ﬁve models of femora were augmented based on the developed model to computationally quantify the fracture load improvement when high- and low-viscosity cement was injected. We performed a control set of validation tests using nonaugmented healthy and osteoporotic models of femora. Thus, fracture loads were 53.41% lower in the osteoporotic models of femora, similar to the values reported in the literature [56]. Some signi ﬁcant diﬀerences can be observed in comparing the method presented in the aforementioned articles with the method presented in this study. First, as the generation of an accurate FE model using a linear analysis and strain-based criteria with a larger sample size for asideways fall con ﬁguration was required [34–39], the method presented uses principal strain values as the failure criterion. Although the goal of this work was not to set any optimization volume for bone augmentation, the results suggest that by injecting approximately 3 ml of high- and low-viscosity cement, the inherent mechanical properties of healthy and osteoporotic femora are improved. Additionally, a Young ’s modulus improvement factor based on the total volume generated by the failed elements of nonaugmented controls and the minimum local density allowed us to predict the improvement in mechanical properties that could beachieved in the failed area, such as the femoral neck. In [19] was applied a constant load and scaled the strains assuming linearity. In fact, their BESO methodology terminated when there was a 100% increase in the predicted yield load of the osteoporotic femurmodel. In [20] was established a target load 15% higher than the yield load of the healthy femur. In [21] was used di ﬀerent sizes of cement cylinders within the trabecular bone domain and quanti ﬁed the mechanical improvement. In our particular case, the target loads and hypotheses established in the literature were integrated to develop a power model. Two cement viscosities were used in this work. The results of our FE analyses suggested that low-viscosity cement led to a better improvement in the Young's modulus and fracture loads of the proximal femora in sideways falls on the greater trochanter than the high-viscosity cement ( Fig. 4). This fact was experimentally observed in our previous work [43]. The material distribution was highly similar to the results obtained in the literature [15,19 –21](Fig. 5). Our model showed that approximately 3 ml of high-viscosity cement resulted in increased fracture loads ranging from 9.41% (healthy models of femora) to 10.32% (osteoporotic models of femora). Similarly, approximately 3 ml of low-viscosity cement resulted in increased fracture loads ranging from 25.19% (healthy models of femora) to 28.93% (osteoporotic models of femora). These observations were also con ﬁrmed by the sensitivity analysis (Table 3), in which, regardless of the amount of cement injected, both cement types resulted in increased fracture loads for non- augmented states. The impact of augmentation of healthy femora was lower than osteoporotic femora. This fact was experimentally demonstrated in [43] where open-cell structures with high porosity fraction showed a considerable increase in Young ’s modulus. As shown in Table 2, the minimum density values were similar in healthy and osteoporotic models of femora. The main reason for this similarity is that no calibration phantom was obtained. The density calibration phantom provides a basis for HU conversion to density values [23,57,58] . As discussed in the literature, one inherent problem in bone augmentation research is the fact that osteoporoticTable 3 Results of the sensitivity analysis: fracture load improvement (%) (mean ± SD). Parameter RATIO 1 RATIO 2 RATIO 3 Augmented (healthy/high viscosity) 3.09 ± 1.46 9.41 ± 3.66 16.16 ± 5.42 Augmented (healthy/low viscosity) 16.45 ± 3.24 25.19 ± 6.00 23.70 ± 10.61 Augmented (osteoporotic/high viscosity) 3.14 ± 1.33 10.32 ± 3.22 18.26 ± 4.69 Augmented (osteoporotic/low viscosity) 17.10 ± 4.81 28.93 ± 7.04 32.65 ± 10.19 Fig. 5. Failed femur volume (red area) for an augmented osteoporotic femur specimen for (a) RATIO 1, (b) RATIO 2 and (c) RATIO 3 (transversal section). (For interpretation of the