Finite element analysis of 6 large PMMA skull reconstructions: A multi-criteria evaluation approach

RESEARCH ARTICLE Finite element analysis of 6 large PMMA skull reconstructions: A multi-criteria evaluation approach Angela Ridwan-Pramana 1,2 , Petr Marcia ´n 3 *, Libor Bora ´k 3 , Nathaniel Narra 4 , Tymour Forouzanfar 1 , Jan Wolff 1 1Department of Oral and Maxillofacial Surgery/Oral Pathology and 3D Innovationlab, VU University Medical Center, Amsterdam, The Netherlands, 2Department of Maxillofacial Prosthodontics, Center for Special Care in Dentistry, Amsterdam, The Netherlands, 3Institute of Solid Mechanics, Mechatronics and Biomechanics, Faculty of Mechanical Engineering, Brno University of Technology, Brno, Czech Republic, 4BioMediTech Institute, Faculty of Biomedical Sciences and Engineering, Tampere University of Technology, Tampere, Finland *[email protected] Abstract In this study 6 pre-operative designs for PMMA based reconstructions of cranial defects were evaluated for their mechanical robustness using finite element modeling. Clinical experience and engineering principles were employed to create multiple plan options, which were subsequently computationally analyzed for mechanically relevant parameters under 50N loads: stress, strain and deformation in various components of the assembly. The factors assessed were: defect size, location and shape. The major variable in the cranioplasty assembly design was the arrangement of the fixation plates. An additional study variable introduced was the location of the 50N load within the implant area. It was found that in smaller defects, it was simpler to design a symmetric distribution of plates and under limited variability in load location it was possible to design an optimal for expected loads. However, for very large defects with complex shapes, the variability in the load locations introduces complications to the intuitive design of the optimal assembly. The study shows that it can be beneficial to incorporate multi design computational analyses to decide upon the most optimal plan for a clinical case. Introduction Bone defects due to trauma or tumors are common in craniomaxillofacial (CMF) surgery. The reconstruction, hence cranioplasty, of such defects still remains a challenge. Cranioplasty primarily offers mechanical protection and subsequently seeks to restore the appearance of the patients. To date, the two most commonly used implant materials are polyetheretherketone (PEEK) and polymethylmethacrylate (PMMA). Furthermore, patient specific 3D printed titanium implants are being sporadically used [1]. Overall, PEEK and PMMA have similar properties. Both are biologically inert and maintain biomechanical properties similar to those found in bone [2]. PEEK is a synthetic material that has advantages in cranial-repair surgery, PLOS ONE | https://doi.org/10.1371/journal.pone.0179325 June 13, 2017 1 / 16 a1111111111 a1111111111 a1111111111 a1111111111 a1111111111 OPEN ACCESS Citation: Ridwan-Pramana A, Marcia ´n P, Bora ´k L, Narra N, Forouzanfar T, Wolff J (2017) Finite element analysis of 6 large PMMA skull reconstructions: A multi-criteria evaluation approach. PLoS ONE 12(6): e0179325. https://doi. org/10.1371/journal.pone.0179325 Editor: Jose Manuel Garcia Aznar, University of Zaragoza, SPAIN Received: November 11, 2016 Accepted: May 26, 2017 Published: June 13, 2017 Copyright: ©2017 Ridwan-Pramana et al. This is an open access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited. Data Availability Statement: All relevant data are within the paper and its supporting information files except for raw result images that are available from: https://figshare.com/projects/FEA_study_of_ 6_skull_implant_cases/20981. Funding: The research was supported by the Czech Science Foundation: Grant No. GA16-08944S. Competing interests: The authors have declared that no competing interests exist. including strength, stiffness, durability, and inertness. PMMA on the other hand is easy to use, readily available and most importantly, biocompatible [3]. An advantage of PMMA is that it can be molded intra-operatively. Moreover PMMA is a relatively low cost option [4] with an extensive track record dating back to the 1940s. Currently, cranioplasty treatment planning involves several steps. It starts with 3D tomographic imaging of the defect site, followed by computer modeling of the corresponding implant. After the implant is fabricated, the surgery is performed. During the surgery, the performing surgeon decides upon the fixation devices required and their subsequent arrangement based on his/her clinical experience and any peculiarities of the case. In craniofacial surgery, stable fixation of bone is a prerequisite to achieving good results [5]. However, in spite of the best efforts, failures do occur due to a variety of factors [6]. Post operative infections are a major cause of reconstruction failures [7]. Such failures often occur due to tissue dehiscences commonly caused by a lack of a protective “watertight” soft tissue closure. Furthermore a reduced angiogenesis due to postoperative implant movement can jeopardize wound healing and tissue repair. Mechanical stability of cranial implants is pivotal for local vascularization and angiogenesis during bone regeneration. In an in-vivo study by Lienau et al [8], it was shown that smaller inter-fragmentary movements led to the formation of a greater number of vessels within the callus, particularly in areas close to the periosteum. While, larger movements increased inter-fragmentary shear and reduced vascularisation during early bone healing. Reduced angiogenesis due to postoperative implant movement can jeopardize wound healing and tissue repair, and can subsequently lead to complications after reconstructive surgery. Besides biological factors, several design factors influence the quality and stability of the implant assembly; to name a few, shape, fixation device arrangement and osteotomy geometry [9]. Another important aspect to take into account when designing an implant is its load-bearing capacity. It is evident that the outcome of cranial reconstruction is markedly influenced by a wide range of factors, in addition to the surgeons skills and experience. In the case of large defects, the surgeons experience becomes especially critical and yet may not be sufficient to give enough consideration to the numerous variables that may contribute to the long term success. The surgeon may design multiple treatment options for a particular case, but the best option may not be intuitively apparent. In such cases, it may be beneficial to have a quantitative assessment of these options based on established bio-mechanical paradigms. In this regard, numerical simulations have become an important method in biomechanics field since they allow to estimate the load-bearing capacity of the design without the need of making a prototype and performing a mechanical test [10]. With increasing incorporation of technology and investment in computational infrastructure at clinical institutions, it is reasonable to pursue the most optimal treatment option for customized skull reconstructions. The feasibility and availability of medical grade rapid fabrication further enhances the prospects for a composite planning approach. This study analyses 6 clinical cases in terms of skull defect size, incident load locations and fixation device arrangement. With increasing size and/or shape complexity of the defect, the possible combinations of fixation arrangement and loading grows and consequently the number of options for the implant assembly increases significantly. A metric to evaluate these options in terms of relative performance of relevant biomechanical parameters in components (stress, strain etc.), is presented in this study. Materials and methods Construction of computational models The computational models constructed in this study represent a system of 4 components: PMMA implant, skull and plates with screws (fixation devices). For each of the 6 clinical cases Evaluation of treatment design options for PMMA based skull reconstructions: FEA study of 6 cases PLOS ONE | https://doi.org/10.1371/journal.pone.0179325 June 13, 2017 2 / 16 a generic model of skull was used. The generic model was reconstructed from a CT dataset obtained from clinical Case 2. The CT image volume consisted of 264 cross-sectional slices with pixel dimensions of 0.7 ×0.7 mm and slice thickness of 1.0 mm. This case was the most suitable for simulating all examined defects of Cases 1 through 6. The CT dataset was imported into an image processing software (STL Model Creator [11,12]) programmed by the authors in a numerical computing environment (Matlab 2010, MathWorks, Natick, MA, USA) to construct the 3D polygonal stereolitography (STL) model of the skull. The segmentation of the skull bone as one homogeneous compartment was performed through greyscale thresholding of the CT images. The PMMA implants were individually designed based on the defect shape for each patient. The curvature of the implant was decided upon by assuming the patient’s skull to be symmetrical along its mid-sagittal plane. This facilitated the replication of the missing bone fragment from a mirrored volume of the contra-lateral side of the skull. PMMA implant and skull were modeled in 3D in SolidWorks (Dassault Systems, Ve ´lizy-Villacoublay, France). The 3D geometries of the individual components were assembled in Ansys 17.2 (Swanson Analysis Systems Inc., Houston, PA, USA) and finite element meshes were subsequently constructed. All volumes were discretized using a higher-order, 3-D hexahedral, 10-node element type (SOLID187). In a typical surgical procedure, fixation devices (plates and screws) are used to affix PMMA implants to the skull. A thorough investigation of mechanical competence of an assembly would consequently require the fixation device to be included in the model. To avoid increasing the complexity of the model, the fixation devices were modeled implicitly by adding an equivalent stiffness to the global FE stiffness matrix of the skull and PMMA plate. The equivalent stiffness was applied by using an element type with undefined geometry but with specified additional stiffness coefficients in a matrix form (MATRIX27). The stiffness coefficients were calculated in a previous study [9] and are listed in Table 1. All interfaces between components were connected using elements representing 3 dimensional contact and sliding between the target surfaces and a deformable contact surface (TARGE160 and CONTA174). A conservative friction coefficient of 0 was used for all contact pairs. All participating volumes were modeled using linear, homogeneous, and elastic material type and a corresponding Young’s moduli and Poisson’s ratios were used as listed in Table 2. The values listed are not specific to the particular components used in the reconstruction. They are instead representative values for the material taken from literature. The model of the implant assembly is evaluated under loading conditions reflecting a scenario where the head of the patient rests on a hard surface. The point of contact is modelled to be incident over a small area on the surface of the implant. Loading of the skull and PMMA implant is assumed to be equivalent to the weight of the head itself. Specifically, a weight of 5 kg [13] is assumed based on simplified measurements on small number of specimens. This load was applied to the model as a pressure force of 50N distributed over a small area as indicated in Fig 1. The global boundary conditions were held constant across all configurations by fixing the skull base in the proximity of the spinal region [14]. Table 1. Stiffness coefficients used in representing fixation devices. Stiffness units Tension 2000 N/mm Torsion 153.85 Nmm/rad Strong axis bending 399.8 N/mm Strong axis shear 16.87 N/mm Weak axis bending 73.04 N/mm Weak axis shear 0.49 N/mm https://doi.org/10.1371/journal.pone.0179325.t001 Evaluation of treatment design options for PMMA based skull reconstructions: FEA study of 6 cases PLOS ONE | https://doi.org/10.1371/journal.pone.0179325 June 13, 2017 3 / 16 Model configurations Each of the 6 cases were modeled and simulated individually. The arrangement of the fixation plates and the location of the external load (50N) for each case were determined by the chief surgeon according to the requirements for corresponding treatment. The surgeon’s recommendations were designated as model configurations for each case (total 70 configurations). For the sake of brevity, these configurations are presented in Fig 1 through a scheme. The defect cases large enough to make variation of load location possible have their respective positions indicated by alphabetized patches. The number and arrangement of the fixation devices are illustrated through unique markers (for a case). To be able to identify these configurations in this work, they were systematically labeled using a three-character code. The first character in the code (a number) denotes the specific case, the second character (a letter) denotes the point of loading, and the third character (a number) denotes the fixation device arrangement. Table 2. Material properties. Bone PMMA Young’s Modulus E b = 15000 MPa E PMMA = 3000 MPa Poisson’s Ratio μ b = 0.3 μ PMMA = 0.38 Yield strength -σ y,PMMA = 65 MPa References [15,16] [17–19] https://doi.org/10.1371/journal.pone.0179325.t002 Fig 1. Skull reconstruction plans modeled for 6 cases with large defects. Models for each case illustrate the implant shape and location (red); fixation device numbers and arrangement (markers at implant boundaries); and loading locations for incident 50N static loads (labeled circular patches: A, B or C). Of note, the different layouts of the fixations devices on the periphery of the implant—in terms of numbers and position—are illustrated in corresponding marker styles. These layouts are assigned an identifying number indicated in the adjacent legend for each case. https://doi.org/10.1371/journal.pone.0179325.g001 Evaluation of treatment design options for PMMA based skull reconstructions: FEA study of 6 cases PLOS ONE | https://doi.org/10.1371/journal.pone.0179325 June 13, 2017 4 / 16 For instance, label “4B2” denotes Case 4, Load B and fixation arrangement 2 (scheme defined in Fig 1). The element/node counts for the 6 models were around 850k/1100k and the configuration details are described below: Case 1. Seven variations in the titanium plate position and three variations in load sites were assessed. In arrangements "1" through "5", 3 titanium plates were used. In arrangements "6" and "7", 4 and 5 titanium plates were used, respectively. All 21 configurations analyzed in this case are labeled as follows: 1A1-1A7, 1B1-1B7, and 1C1-1C7. Case 2. In this case, seven variants of titanium plate position and three variants of load were assessed. In configurations "1" through "5", 3 titanium plates were used. In configurations "6" and "7", 4 and 5 titanium plates were used, respectively. The 21 configurations analyzed in this case are labeled as follows: 2A1-2A7, 2B1-2B7, 2C1-2C7. Case 3. In this case, four variants of titanium plate position and three variants of load were used. In configurations "1" and "2", 3 titanium plates were used. In configurations "3" and "4", 4 and 5 titanium plates were used, respectively. The 12 configurations analyzed in this case are labeled 3A1-3A4, 3B1-3B4, 3C1-3C4. Case 4. In this case, four variants of titanium plate position and two variants of load were used. In configurations "1" and "2", 2 titanium plates were used. In configurations "3" and "4", 3 and 4 titanium plates were used, respectively. 8 configurations analyzed in this case are labeled 4A1-4A4, 4B1-4B4. Case 5. In this case, four variants of titanium plate positions and a single loading condition were used. In configurations "1" and "2", 2 titanium plates were used. In configurations "3" and "4", 3 and 4 titanium plates were used. 4 configurations analyzed in this case are labeled 5A1-5A4. Case 6. In this case, four variants of titanium plate position and a single loading condition were used. In configurations "1" and "2", 2 titanium plates were used. In configurations "3" and "4", 3 titanium plates were used. 4 configurations analyzed in this case are labeled 6A1-6A4. Configuration assessment The performance of each configuration was analyzed in terms of stresses and strains induced in each component of the assembly. Stress intensity and displacement in the PMMA implant, shear/normal forces in fixation plates, and the induced strain in the bone are important parameters that could affect the overall clinical outcome. Therefore a metric, called assessment factor (AF), was formulated as a weighted combination of the aforementioned parameters. This factor was based on a multi-criteria decision-making (MCDM) approach known as Weighted Sum Method (WSM) [20]. This method is commonly used and widely popular in the field of computational mechanics. For an analysis of M alternatives (A i for i = 1, 2, . . . M) and N criteria (C j for j = 1, 2, . . . N), the favorableness of the i-th alternative can be calculated by the following expression: AFi¼X N j¼1 wjyij ð1Þ Where, AF i is the WSM-score or the assessment factor of the i-th alternative, y ij is the value of the i-th alternative with respect to the j-th criterion and w j is the weighting factor of the j-th criterion. The latter expresses the importance of C j . Throughout this study, the alternatives are all configurations within each case; e.g. for the Case 1, the alternatives are A = {1A1, 1A2, 1A3, 1A4. . . 1C5, 1C6, 1C7}. The criteria evaluated here are C = {SINT, EPTO, UNORM, FNORM, FSHEAR}, where SINT = stress intensity in the PMMA [MPa] Evaluation of treatment design options for PMMA based skull reconstructions: FEA study of 6 cases PLOS ONE | https://doi.org/10.1371/journal.pone.0179325 June 13, 2017 5 / 16 EPTO = strain intensity in the bone [–] UNORM = total normal displacement (normal to brain surface) of PMMA plate [mm] FNORM = normal force in the titanium plate [N] FSHEAR = total shear force in the titanium plate [N] These parameters represented nominal values in specific regions of interest. These values were evaluated to represent a typical biomechanical condition of the case/configuration and to be a basis for a comparative analysis (S1 File,S1 Table). Since these parameters have different dimensions and different units, Eq 1cannot be used directly and the source data must be modified (normalized) first. Assuming a linear dependency between the normalized values and the actual values, 0 is assigned to the worst value of C j and 1 is assigned to the best value of C j . Therefore, the normalized values can be calculated as follows: uij ¼yij dj hjdjð2Þ Where, d j and h j are maximum and minimum values of C j , respectively. Finally, the assessment factor for the normalized values can be calculated using following expression: AFi¼X N j¼1 wjuij ð3Þ The best alternative is the one that satisfies following expression: AFBEST ¼maxðAFiÞ;for i ¼1;2;3;...;Mð4Þ On the contrary, the least favorable alternative is the one that minimizes the assessment factor as follows: AFWORST ¼minðAFiÞ;for i ¼1;2;3;. . . ;Mð5Þ The importance of the individual criteria plays a significant role and the weighting factors must be chosen carefully. In doing so, their sum must equal 1. In case of uncertainty or in the case that all criteria are assumed to be equally important (as is the case in the present study), the weighing factors can be calculated as follows: wj¼1 Nð6Þ Therefore, in this study the weighting factors are 0.2 for all evaluated criteria. For the final comparison, the assessment factors within each case were additionally normalized by mean value of all AFs and their standard deviation using following expression: AF i¼AFim sð7Þ Where, μis the mean value of assessment factors within the assessed case and σis the standard deviation of assessment factors within the assessed case. This adjustment allows the best configuration to be presented with a positive AF and, the worst configurations with negative AF. The assumption of weighting factors equality for all evaluated quantities may be debatable. Choice of different weights might lead to determining of different best/worst configuration within the case. In order to verify the best/worst configuration choice, a testing study within the WSM was carried out using all possible non-trivial permutations of participating criteria. Evaluation of treatment design options for PMMA based skull reconstructions: FEA study of 6 cases PLOS ONE | https://doi.org/10.1371/journal.pone.0179325 June 13, 2017 6 / 16 Since five parameters were evaluated and taken as a basis for MCDM, a total of 2 5 –1 = 31 nontrivial permutations were tested for the best/worst configurations. In other words, the configurations were evaluated firstly based on only one parameter (i.e. individually SINT, EPTO, UNORM, FNORM, FSHEAR), secondly based on combinations of two parameters (SINT +EPTO, SINT+UNORM. . ..), etc., and finally based on the combination of all parameters. Frequencies of best/worst combinations throughout all non-trivial permutations were determined. The most frequent best/worst combination was assumed to be the solution of this verification study. Results The various configurations for each case (Case 1 through Case 6) were simulated under static loading conditions and the results were analyzed for the following mechanically relevant parameters–total displacements (PMMA implant), stress intensity (PMMA implant), strain intensity (bone), and normal and shear forces (fixation plate). The values obtained were used to calculate the assessment factors. The best and worst case configurations based on this factor are illustrated in Fig 2 (cases 1, 2 & 3) and Fig 3 (cases 4, 5 & 6). The configurations with the second best performance in each case are illustrated separately in Fig 4. In the following subsections, the extreme values of the evaluated parameters are listed. Case 1 Among the 21 configurations, the maximum values observed for each parameter were–displacement: 1.26 mm (1B1); stress intensity: 11.45 MPa (1A3); strain intensity: 1.91x10 -3 (1B1); normal force: 53.29 N (1B1); shear force: 19.83 N (1B1). The calculated assessment factor AF i  for each configuration is illustrated in Fig 5. 1B1 was the worst performer and 1C1 was the best performer. Fig 2 illustrates stress, strain and displacement plots for the best/worst configurations. Fig 6 shows a typical example of the verification study based on the permutation approach. The results show that the best/worst configurations for this case as presented above apply for most of analyzed permutations of weighting factors in consideration. Case 2 Among the 21 configurations, the maximum values observed for each parameter were–displacement: 0.32 mm (2B5); stress intensity: 5.07 MPa (2A2); strain intensity: 1.41x10 -3 (2B7); normal force: 51.14 N (2B1); shear force: 24.02 N (2C3). The calculated assessment factor AF i  for each configuration is illustrated in Fig 5. 2B5 was the worst performer and 2A7 was the best performer. Fig 2 illustrates stress, strain and displacement plots for the best/worst configurations. Case 3 Among the 12 configurations, the maximum values observed for each parameter were–displacement: 0.37 mm (3C1); stress intensity: 5.08 MPa (3C1); strain intensity: 1.30x10 -3 (3C1); normal force: 36.62 N (3B2); shear force: 10.76 N (3C2). The calculated assessment factor AF i  for each configuration is illustrated in Fig 5. 3C1 was the worst performer and 3A4 was the best performer. Fig 2 illustrates stress, strain and displacement plots for the best/worst configurations. Case 4 In the 8 configurations, the following were the observed maximum values–displacement: 0.34 mm (4A2); stress intensity: 7.14 MPa (4A2); strain intensity: 1.08x10 -3 (4A1); normal force: Evaluation of treatment design options for PMMA based skull reconstructions: FEA study of 6 cases PLOS ONE | https://doi.org/10.1371/journal.pone.0179325 June 13, 2017 7 / 16 Fig 2. Stress intensity, strain intensity and displacement plots of best/worst performers within each case (cases 1 through 3). The configuration details are illustrated using the marking scheme introduced in Fig 1. In the illustrations–stress intensity is in PMMA implant, strain intensity is in the bone and the total displacements are for the PMMA implant. https://doi.org/10.1371/journal.pone.0179325.g002 Evaluation of treatment design options for PMMA based skull reconstructions: FEA study of 6 cases PLOS ONE | https://doi.org/10.1371/journal.pone.0179325 June 13, 2017 8 / 16 Fig 3. Stress intensity, strain intensity and displacement plots of best/worst performers within each case (cases 4 through 6). The configuration details are illustrated using the marking scheme introduced in Fig 1. 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