Experimental validation of 3D printed patient-specific implants usingdigital image correlation and finite element analysis

Alok Sutradhar a,b,n, Jaejong Park b, Diana Carrau c, Michael J. Miller a

a Department of Plastic Surgery, The Ohio State University, Columbus, OH 43210, USAb Department of Mechanical and Aerospace Engineering, The Ohio State University, Columbus, OH 43210, USAc College of Medicine, The Ohio State University, Columbus, OH 43210, USA

a r t i c l e i n f o

Article history:Received 19 March 2014Accepted 2 June 2014

Keywords:Craniofacial implantsTopology optimizationSegmental bone defectDigital image correlationMasticatory simulation

a b s t r a c t

With the dawn of 3D printing technology, patient-specific implant designs are set to have a paradigmshift. A topology optimization method in designing patient-specific craniofacial implants has beendeveloped to ensure adequate load transfer mechanism and restore the form and function of the mid-face. Patient-specific finite element models are used to design these implants and to validate whetherthey are viable for physiological loading such as mastication. Validation of these topology optimizedfinite element models using mechanical testing is a critical step. Instead of inserting the implants into acadaver or patient, we embed the implants into the computer-aided skull model of a patient and, fusethem together to 3D print the complete skull model with the implant. Masticatory forces are applied inthe molar region to simulate chewing and measure the stress–strain trajectory. Until recently, straingages have been used to measure strains for validation. Digital Image Correlation (DIC) method is arelatively new technique for full-field strain measurement which provides a continuous deformationfield data. The main objective of this study is to validate the finite element model of patient-specificcraniofacial implants against the strain data from the DIC obtained during the mastication simulationand show that the optimized shapes provide adequate load-transfer mechanism. Patient-specific modelsare obtained from CT scans. The principal maximum and minimum strains are compared. Thecomputational and experimental approach to designing patient-specific implants proved to be a viabletechnique for mid-face craniofacial reconstruction.

& 2014 Elsevier Ltd. All rights reserved.

1. Introduction

Craniofacial segmental defects that are caused due to blastinjury or tumor ablation require reconstructive procedures invol-ving large bone replacement implants. Such defects remain achallenging problem for reconstructive surgeons as it is difficultto create a complicated 3D structure that satisfies significantfunctional and aesthetic roles of the midface. Proper reconstruc-tion and replacement are needed not only to obliterate the defect,but also to address the issues of swallowing, orbital function,vision, mastication, speech and restoration of facial contour andself-image [1]. These defects are patient-specific and the implantsshould depend on the loads and the dimensions of the missingbone defect. Large segmental bone defects of the midface typicallyrequire bone grafts for a successful outcome and, advances inmicrovascular free flaps have greatly increased reconstructive

options. Virtual surgical planning, stereolithography modeling,and prefabricated osteotomy bone cutting templates have madesurgical planning of osteotomies easier [2–4]. However, for most ofthese cases, no structural analysis or design principles are usedwhich often results in unfavorable circumstances such as fractureor high stress concentrations. Advances in 3D printing technologyhave opened a new dawn in patient-specific implant design.Recently, a bioresorbable airway splint has been successfullycreated and implanted in an infant using a 3D printer [5]. Thiswork demonstrated innovative creation of implants for patient-specific anatomical condition using a multi-disciplinary approachinvolving high-resolution imaging, computer aided design andbiomaterial based 3D printing. For a large segmental defect,finding the correct and optimized shape of the bone replacementstill remains a question. Reconstruction is typically done heuris-tically without adequate surgical preplanning and structuralanalysis. To address this problem, a technique named topologyoptimization has been introduced into designing bone replace-ment in our previous work [6,7]. Topology optimization is amethod of finding a structure with optimal load paths to transfera number of loads to defined supports. This method is widely used

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Computers in Biology and Medicine

http://dx.doi.org/10.1016/j.compbiomed.2014.06.0020010-4825/& 2014 Elsevier Ltd. All rights reserved.

n Corresponding author at: Department of Plastic Surgery, The Ohio StateUniversity, 915 Olentangy River Road, Suite 2109, Columbus, OH 43212, USA.Tel.: þ1 614 293 7655; fax: þ1 614 293 9024.

E-mail address: alok.sutradhar@osumc.edu (A. Sutradhar).

Computers in Biology and Medicine 52 (2014) 8–17

in designing components for the automobile industry and lately indesigning aircraft components. For example, it has been success-fully applied to design the main wing box rib of Airbus A380 [8].

Surgical outcome can be enhanced by taking an interdisciplin-ary approach. Custom tissue fabrication can be considered anoption to replace the region of defect ideally [9]. A potentialstrategy to achieve this objective for craniofacial reconstruction isto apply bone formation technique to patient specific solutionsobtained from computer aided design (CAD) with computationalmethods [7]. The solution is optimized for functional restorationwhen combined with soft tissue repair and appropriate prostheticseven though the design may deviate from the original humanbone geometry. The objective function of topology optimizationalgorithm is to minimize compliance within the structure.Although only mechanical loadings were considered, it was foundthat topology optimization gives a shape similar to human naturalskeleton without a defect when applied to cross-section on avertical plane through first molar [7]. Understanding how func-tional physiological loads (e.g., required for biting) are transferredto the bone-implant interface enables better design of implantsupported prosthesis as well [10,11].

Traditional strain measurement technique in experiments usesstrain gauges. Although they are known to be reliable and robust[12], strain gauges only give discrete data by averaging the realstrains between the tips of strain gauge. The result of thistechnique tends to be affected by environment and requirespreparation of the surface and wiring [13]. In general, local strainmeasurements are essential because complexity in geometries andinhomogeneity result in substantial variation over the structure.Recently, a technique named Digital Image Correlation (DIC) hasbeen developed that captures full field strain data with a goodresolution on the surface of the model from images. This relativelynew method can be applied to complex geometries. Theories anddetailed information of the method can be found in Refs. [14,15].This DIC technique is used extensively in experiments to char-acterize the specimen’s behavior. Using this method, full fieldstrain of splinted and non-splinted implant prostheses has beencaptured [16]. Also, various kinds of computational models forcomposite hemipelvis [12] and, proximal femur [12,17] have beenvalidated with DIC.

The principal aim of this paper is twofold. (i) To experimentallyvalidate that the finite element model correctly captures the stressstrain contour of the skull model subjected to masticatory forcesand (ii) to validate that the designed implant appropriatelytransfer the masticatory forces by keeping the maximum stressbelow ultimate stress. In order to do this, a bone replacement

shape for a patient with massive facial injury with large bone lossin midface is designed using the topology optimization method.The solution is then embedded in the skull with computer-aidedengineering software to obtain a skull model. Then, the skullmodel with the embedded implant is fabricated by a 3D printer.Mastication activity is simulated in the experiment and alsomodeled by finite element analysis (FEA). This work is expectednot only to evaluate the solution of topology optimization but alsoto appraise the idea of using topology optimization to designmacroscopic bone replacement shapes for midface defects. The fullfield strain data from mechanical testing via DIC is compared withthat from FE (Finite element) model under same boundary andloading conditions to validate the FE model. FE model of skull isfurther analyzed to investigate the practicality of the skull in termsof load transfer mechanism and structural integrity.

2. Materials and methods

2.1. Model preparation

A skull model of massive facial injury with large bone loss inthe midface is extracted from the CT scan using software Amira(FEI Visualization Science Group, MA, USA) as shown in Fig. 1. Thedefect is in the center of midface and is asymmetrically extendedbilaterally. Using measurement tools, the appropriate designdomain is extracted. Within the design domain, supports areprovided on the lateral surfaces for contact and fixation betweenthe implant and uninjured portion of facial skeleton. A set ofupward forces representing the forces of mastication are appliedon bottom surface in the dental profile and, another set of down-ward forces are provided in the center of the top surface tosimulate the trauma forces that may be transferred from theupper region of skeleton. Appropriate holes are embedded tomimic eye, nasal cavities and space for hard palate. The illustrationof design domain and respective boundary conditions are shownin Fig. 1.

2.2. Topology optimization

Topology optimization suggests the best material distributionwithin a design domain by seeking where to put the material(solid) and where not to (void). The topology can be defined by thedensity at different locations within the domain. The density isusually considered a design variable and can assume 0 or 1 with0 representing the void and 1 representing the solid. The topology

Fig. 1. Selection of design domain and required design considerations to obtain boundary and cavity information.

A. Sutradhar et al. / Computers in Biology and Medicine 52 (2014) 8–17 9

optimization method used in this work iteratively optimizes theelemental densities in the design domain to minimize the com-pliance (maximize the stiffness) of the final structure whilesatisfying the volume fraction constraint. This objective functionand constraints can be mathematically expressed as follows,

minimizeρ

Cðρ;udÞ ¼ fTud

subject to : KðρÞ ud ¼ f

VðρÞ ¼ZΩρ dV rVs ð1Þ

where C is the compliance, ρ is the density vector, f is the globalload vector and ud is the global displacement vector. K is the globalstiffness matrix, Ω is the design domain, and Vs is the volumefraction constraint. Employing the Solid Isotropic Material withPenalization (SIMP) method [18,19], the problem is relaxed fordensity to have any value between 0 and 1 with small lower boundof ρmin¼0.001 to avoid singularities during calculating for equili-brium. Also, a parametric equation of Young’s modulus for localstiffness is defined. Thus, following is added in the problem.

0 o ρmin o ρ o 1

EðxÞ ¼ ρðxÞpE0 ð2Þwhere p is the penalization factor and E0 is the Young’s modulus ofthe material in the solid phase.

In this work, we used the multi-resolution topology optimiza-tion (MTOP) method [20]. In MTOP, different discretizations areemployed for analysis, design and optimization. The details of thismethod can be found in [7,20] and for basic theory and introduc-tion of the topology optimization the readers are referred to [21].Two level of discretization are used in MTOP, B8 elements fordisplacement (analysis) and 125 density elements inside a B8element for density (visualization) and design variable (optimiza-tion). Based on conditions shown in Fig. 1, a total of28�20�12¼6720 B8/n125 elements are used in the topologyoptimization algorithm. The design parameter Vs (volume con-straint) is chosen as 12%. The penalization factor (p) is selected as3 to satisfy the Hashin–Shtrikman bounds [19]. The load ratiobetween the top and the bottom forces depends on the relativeimportance given to them for different patient-specific conditions.The load ratio between top and bottom forces is chosen to be 10and the number of iteration is limited to 50 with a condition toterminate the process if density change in domain between

iterations is less than 0.001. The result is shown in Fig. 2(a). Also,if the user wants to emphasize the equal importance between thetop and the bottom forces, load ratio of the top and bottom forcescan be changed to 1. In this case, a different solution is obtainedwhich is depicted in Fig. 2(b). Both the respective topologyoptimization solutions in Fig. 2. are represented with iso-surfaces with density of 0.25.

In order to embed the topology optimized bone replacementinto the skull, the mandible is separated by cutting the image datanear upper condyles in mandible via image segmentation. Thebone replacement implant is then scaled and positioned. Adenture is included during the embedding process. Once all thecomponents are properly positioned, their stereolithography arecombined in a Boolean fashion. Note that the embedded model isre-meshed to alleviate the discrepancies in mesh size betweencomponents. The procedure is visually shown in Fig. 3.

2.3. Mechanical testing

A realistic mastication activity is selected to be simulated byapplying appropriate force over molar region on one side ofoptimized solution embedded skull model (see Fig. 4(a)) whilethe skull model is held stationary. The stereolithography of skullmodel is sent to Dimension SST 1200es (Stratasys Ltd., MN, USA), a3D printer, to fabricate three skull models for the repetitivemechanical testing. This 3D printer uses Fused Deposition Model-ing (FDM) technique with ABSplus TM-P430. The elastic modulusof this thermoplastic (2320 MPa, 330000 psi) is obtained from themanufacturer. Custom fixture, which is inspired by medical halodevice [22], is designed in SolidWorks (SolidWorks Corp., MA,USA) and fabricated. The fixture is attached onto the XY table ofthe Instron 1321 (Instron, MA, USA) servo-hydraulic load frame.XY table is adjusted so that load is applied over the expected molar

Fig. 2. Implant shapes from different load ratios considered in the design process.Multiresolution topology optimization (MTOP) is used in both scenarios (a) F1/F2¼10, (b) F1/F2¼1.

Fig. 3. Embedding MTOP solution into the skull to acquire final skull model formechanical investigation.

A. Sutradhar et al. / Computers in Biology and Medicine 52 (2014) 8–1710

region in the skull model. Aluminum cylindrical load applicator(see Fig. 4(b)) is used. This load applicator is hinged in the middleso that the top portion is flexible to ensure better contact with theskull model. The cross sectional area of the load applicator iscomparable to the area of two molar teeth in the skull model. Thefinal configuration is shown in Fig. 4(b).

The mechanical behavior of skull model is analyzed by mea-suring full-field strain using the 3D digital image correlationtechnique in the region where most deformation is expectedas depicted in Fig. 4(a). Successive images are taken at the constantspeed of 2 frames per second with a pair of GRAS-20S4M-C(Point Grey Research, BC, Canada) cameras (resolution: 1624

Fig. 4. (a) Proposed scenario (mastication) for the mechanical testing, (b) setup for mechanical testing of the skull model.

Fig. 5. (a) The final configuration of the mechanical testing and data capturing cameras, (b) schematic of the final configuration, (c) load history applied in the model duringmechanical testing for three consecutive tests.

A. Sutradhar et al. / Computers in Biology and Medicine 52 (2014) 8–17 11

Fig. 6. Deformation of specimen (ABSplus) under uniaxial compressive loading (a) before loading, (b) after loading, (c) stress strain curve obtained from compression testing.

Fig. 7. (a) Finite element mesh of the skull model, (b) boundary and loading conditions for finite element model.

A. Sutradhar et al. / Computers in Biology and Medicine 52 (2014) 8–1712

�1224 pixel) equipped with 35 mm Schneider (Scheneider Optics,NY, USA) lenses. The final configuration of the cameras in theexperiment is shown in Fig. 5. The external surface of the skullmodel is sparingly painted with black and white spray paint togive a speckle pattern. The deformation of the model surface iscalculated by the Vic-3D software (Correlated solutions, Inc., SC,USA) by monitoring the changes in this speckle pattern in thedigital image sequence.

A calibration panel that has a set of points with known spacingis used to calibrate the data acquisition system. The calibrationpanel is oriented differently in each calibration images from bothcameras so that they can be used to define 3D Cartesian coordinatesystem in Vic-3D. The contour of the skull model is captured bystereo triangulation in the defined 3D Cartesian coordinate system.The MTS FlexTest (MTS, MN, USA) controller is set to apply a linearramp load on the skull model with a maximum magnitude of

120 lbs (ffi534 N) starting from 5 lbs (ffi22.2 N) of preloadthrough cylindrical load applicator. Load histories of the threemechanical tests are shown in Fig. 5.

2.4. 3D printing and material property

In order to successfully replicate the mechanical testing, thematerial property of the printing material (ABSplus) is required.The tensile property of ABSplus which can be obtained from themanufacturer (Stratasys Ltd., MN, USA), could not be directlyapplied because compressive stress dominates in the study. Hence,we performed our own mechanical testing to obtain the compres-sive material properties of ABSplus material used in the 3Dprinting. Additional cylindrical specimens with 12 mm diameterand 24 mm height are 3D printed to characterize its propertyunder compression. Printing layer with respect to load of thisspecimen is controlled such that it is consistent with the skullmodel. Similar setup with that of the mechanical testing of skullmodel is employed. A ramp load that generates strain rate of8.333E�4 is chosen (50% strain in 600 s) (see Fig. 6). 3D digitalimage correlation technique is used to capture the mechanicalbehavior of the specimen during loading. In the sequence of theimages, a virtual extensometer is positioned in specimen’s long-itudinal direction to extract engineering strain. Stress and strainrelationship is extracted by correlating extracted engineeringstrain with the loading profile. The testing is repeated three times

Fig. 8. (a) Maximum principal strain distribution, (b) minimum principal strain distribution, (c) vertical strain component distribution in the skull model under masticationsimulation at approximately 530 N.

Table 1Quantitative comparison of strain values from three specimens in mechanicaltesting.

Test 1 Test 2 Test 3 Average Max % difference

e1 0.0191 0.0177 0.0165 0.01777 7.48e2 �0.0282 �0.0233 �0.0233 �0.02610 10.7eyy �0.0218 �0.0198 �0.0198 �0.02067 5.47

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with the three specimens. The resulting three true and engineer-ing stress strain plots are shown in Fig. 6. The average elasticmodulus of the ABSplus from the three samples is computed to be2.074 GPa.

2.5. Finite element analysis

The stereolithography of the skull model is meshed using 3Dvolumetric elements. The mesh consists of 155195 linear tetrahe-dral (C3D4) elements and 41492 nodes in the skull model.

Commercial FEA software Abaqus (Dassault Systèmes, Vèlizy-Villacoublay, France) is used for the simulation of the experiment.

Elastic modulus of 2.074 GPa and material yield strength using0.2% offset method of 53 MPa from the compressive specimentesting are used with manufacturer provided Poisson’s ratio of0.35. Plastic behavior is also taken into account in the FE model byintroducing plastic strain values. The boundary conditions tomatch the mechanical testing of skull model are employed. Theyinclude four areas in upper cranium and two areas in the bottommost portion of skull model. Their movement and rotation underthe load is prohibited by fixing the nodes in these areas. A load of

Fig. 9. Vertical strain distribution comparison between (a) FEA, and (b) mechanical testing. Horizontal strain distribution strain distribution comparison between (c) FEA,and (d) mechanical testing at approximately 267 N.

Fig. 10. (a) Five selected elements in the skull model for quantitative comparison of vertical strain with the mechanical testing results, (b) tabulated values show thecomparison.

A. Sutradhar et al. / Computers in Biology and Medicine 52 (2014) 8–1714

267 N which is the half of the maximum load in the mechanicaltesting is applied on 23 nodes in the region of first and secondmolar teeth as concentrated forces (magnitude of 11.61 N each invertical direction). (See Fig. 7(b)).

3. Results and discussion

The full field strains captured from mechanical testing on threeskull models are compared with one another to ensure thereliability of the 3D printed skull models as well as the setup ofthe mechanical testing. Maximum and principal strains andvertical strain components in the area of interest (as shown inFig. 4(a)) are calculated. The applied loading resulted in positivemaximum principal strain (tensile), whereas minimum principalstrain was negative (compressive) in most areas of the domain.The strain fields from the three tests match quite well qualitativelyas shown in Fig. 8. Quantitative comparisons of strains generatedin the Vic-3D are tabulated in Table 1. The maximum difference ofapproximately 10% is observed in the minimum principal strain(compressive). The heterogeneity of the printed material is aprobable factor of this discrepancy. The way fused decomposition

works; it creates anisotropy in the object due to the voids in thedirection parallel to the printing layers. Also, any mismatch in thealignment of skull model with the load applicator may affect theresult. The direction of load depends on how the skull is fixed.During the testing preparation, skull models may have a minorshift from their initial position. Overall, the results from threemechanical testing match well.

The result from the finite element analysis shows that themodel will not experience any plastic deformation with a load of267 N as the maximum von-Mises stress is 41.74 MPa which is lessthan the experimental yield stress of 53 MPa. Recognizing com-pression in vertical direction dominates in this study, verticalstrain component is compared between the results from themechanical testing and the FEA. Quick visual comparison demon-strates that FEA of skull model successfully follows the straincontours from mechanical testing (see Fig. 9). Five elements thatare located in the most critical region as shown in Fig. 10 areselected to check the quantitative agreement between FEA and themechanical testing. In these locations, the maximum differencebetween the vertical strain results from FEA simulation and the

Fig. 11. A cross section of a 3D printed specimen showing printed materialheterogeneity.

Table 2Mechanical properties of human skull bone from [25].

Tangentialcompressiveproperty

No. ofspecimens

No. ofdonors

Mean Standarddeviation

Skull to skullsignificantdifferences

Modulus (GPa) 219 14 5.584 3.034 YesPoisson’s ratio 327 18 0.22 0.11 NoUltimate strength(MPa)

210 14 96.53 35.85 No

Ultimate strain(�10�3)

210 14 51 32 No

Fig. 12. (a) Plot of stress directional components (potential new load transfer paths), (b) possible load transfer paths in the MTOP solution with the same load ratios betweentop and bottom forces, (c) load transfer paths (buttresses) in uninjured human skull.

A. Sutradhar et al. / Computers in Biology and Medicine 52 (2014) 8–17 15

mechanical testing result is 6.2%, which is reasonably acceptable.Again, this disagreement is possibly due to the material inhomo-geneity during the 3D printing process as shown in Fig. 11. If thematerial of skull model was purely isotropic, a better agreementwould have been obtained. Also, using finer speckle pattern andshorter camera-specimen distance the accuracy might beimproved as discussed in Ref. [12]. Yet, compressive strain (εyy)discrepancies are between 2% and 6% which indicate that FEAmodel effectively can represent the compressive behavior frommechanical testing.

Reconstructive surgery of mid-face requires adequate loadtransfer to restore the functional role such as proper load transfer,as well as the aesthetic role like proper facial proportions [23]. Anew load transfer mechanism may be traced from the FEA of skullmodel. The directional components of stresses are plotted in themid-face in Fig. 12. The results show that significant amount ofload is transferred through the topology optimized solution nearnasal cavity which resembles nasomaxillary buttress [24]. Also,considerable horizontal load is transferred to the midface via thelower portion of topology optimized solution, which is similar tothe zygomaticomaxillary buttress and pterygomaxillary buttress inan uninjured skull. Similar buttresses can be traced in the implantdesigned using different load ratio in Fig. 2(b). This demonstratesthat the new designed implant transfers the load in the correctmanner.

Human bone is a very complex and highly anisotropic materialin general. While simple anatomic theory of bone exists (stiff anddense cortical bone surrounds soft and coarse cancellous bone),obtaining mechanical property of specific locations in the humanskeleton system is still arduous. In this work, instead of perform-ing testing in a cadaver, 3D printing technology is used. Althoughthis approach is convenient, it does not capture the inhomogeneityand the anisotropy of a real human bone. In order to check thefeasibility of the implants, we perform simulation using bonematerial properties. In [25], the mechanical properties of humanskull were obtained experimentally and it was inferred that theskull bone is fairly isotropic in direction tangent to the skull.Experimental tangential compressive properties from their workare provided in Table 2. The compressive modulus and Poisson’sratio from Table 2 are used in the FEA. The boundary conditionsremain the same as the initial test but the load is increased from264 N to 534 N which is close to the reported maximum humanmasticatory force found in the literature [26]. The purpose of thissimulation is to test structural fidelity of topology optimizedsolution. The results (see Fig. 13) indicate that maximum stressof 74.1 MPa stays below ultimate strength of 96.53 MPA in [25],Similarly, the principal maximum strain (9.30E�3) and principal

minimum strain (�10.1E�3) are below ultimate strain of 51E�3in [25]. Thus, topology optimized solution embedded skull wouldsurvive the maximum masticatory force reported.

In the topology optimization routine, upward vertical forceswere applied to mimic loads from teeth while downward forceswere applied to simulate traumatic forces. However, the exacttopology would depend on the specific dimensions of the defect.In real life, major mastication forces are applied on the posteriorzone of the maxilla in the molar area. For the presented example,the created topology might produce an unfavorable Anterior–Posterior (AP) spread with more tensile strains on the anteriorportion. This might induce bone loss in the future. These specificsituations can be easily dealt with patient-specific cases, anddefect dimensions. Based on these different scenarios, the locationof the loading may be critical to avoid unfavorable AP spread.Designs for different patient-specific defects have been developedin Ref. [6].

Using an engineering technique like the topology optimizationto design bone replacement shapes can alleviate the uncertaintythat exists when deciding on an implant shape for adequate load-transfer. The designs can be used as guidelines for osteotomies aswell as in designing tissue engineered scaffolds for bone regenera-tion. The main purpose for repairing damaged andmissing tissue is topreserve a three-dimensional space that will maintain structuralintegrity by providing an efficient load-transfer mechanism underphysiological loading.

4. Conclusion and future work

In this work, the mechanical feasibility of implants designed bythe topology optimization method for craniofacial reconstructivesurgery is examined. A mastication simulation using a finite elementmodel that was generated from patient’s CT scan is validated withmechanical testing. The specimen for the mechanical testing wasobtained using a 3D printer. The FEA results show that topologyoptimized solutions have the potential to restore destroyed buttresssystems and recover the structural integrity of the facial skeleton toendure a maximum masticatory force around 534 N. The digitalimage correlation technique for full field strain measurementresulted in a simple experiment. Also, the use of 3D printing hasenabled us to work with patient-specific model with a fullyembedded implant. In the era of patient-specific implant designs,using topology optimization method in order to find the structurallyoptimized solution can eliminate the uncertainty of choosing heur-istic shapes for critical surgeries like mid-face reconstruction. This

Fig. 13. FEA result of skull model under 534 N of masticatory load with isotropic skull bone mechanical property (a) von-Mises stress, (b) maximum principal strain,(c) minimum principal strain.

A. Sutradhar et al. / Computers in Biology and Medicine 52 (2014) 8–1716

will also help in designing fixation and additional prosthesis toimprove the quality of life for the patients.

Currently, we are exploring to include biological variables (e.g.,oxygen level) in the topology optimization algorithm for the bonereplacements [27]. Also, we are looking into different impactloading configurations, stress concentrations and fracture analysisin the implants.

Funding

National Science Foundation through the CMMI Award no.1032884.

Conflict of interest statement

None.

Acknowledgement

The work was funded by National Science Foundation throughthe CMMI Award no. 1032884. Diana Carrau was supported by theMDRS Roessler fellowship from College of Medicine, The OhioState University. We would like to acknowledge Dr. Jeremy Siedt,Department of Mechanical and Aerospace Engineering, The OhioState University for facilitating the mechanical testing of the skullmodel and Professor Blaine Lilly and Mr. Richard Teynor forhelping with the 3D printing. Finally, we thank Dr. Tam H Nguyen(Northeastern University) and Professor Glaucio H Paulino (Uni-versity of Illinois at Urbana-Champaign) for their assist with thetopology optimization framework.

References

[1] N.D. Futran, E. Mendez, Developments in reconstruction of midface andmaxilla, Lancet Oncol. 7 (2006) 249–258.

[2] Y. Shen, J. Sun, J. Li, M.M. Li, W. Huang, A. Ow, Special considerations in virtualsurgical planning for secondary accurate maxillary reconstruction with vas-cularised fibula osteomyocutaneous flap, J. Plast. Reconstr. Aesthet. Surg. 65(2012) 893–902.

[3] A.K. Antony, W.F. Chen, A. Kolokythas, K.A. Weimer, M.N. Cohen, Use of virtualsurgery and stereolithography-guided osteotomy for mandibular reconstruc-tion with the free fibula, Plast. Reconstr. Surg. 128 (2011) 1080–1084.

[4] Y. He, H.G. Zhu, Z.Y. Zhang, J. He, R. Sader, Three-dimensional modelsimulation and reconstruction of composite total maxillectomy defects withfibula osteomyocutaneous flap flow-through from radial forearm flap, OralSurg. Oral Med. Oral Patho. Oral Raiol. Endod. 108 (2009) e6–e12.

[5] D. Zopf, S.J. Hollister, M.E. Nelson, R.G. Ohye, G.E. Green, Bioresorbable airwaysplint created with a three-dimensional printer, N. Engl. J. Med. 368 (2013)2043–2045.

[6] A. Sutradhar, J. Park, D. Carrau, T.H. Nguyen, M.J. Miller, G.H. Paulino,Computational modeling of craniofacial bone replacements, Med. Biol. Eng.Comput. (2013) (in review).

[7] A. Sutradhar, G.H. Paulino, M.J. Miller, T.H. Nguyen, Topological optimizationfor designing patient-specific large craniofacial segmental bone replacements,Proc. Nat. Acad. Sci. U.S.A. 107 (2010) 13222–13227.

[8] L. Krog, T. Alastair, G. Rollema, Application of topology, sizing and shapeoptimization methods to optimal design of aircraft components, in: ProductDesign, Altair Engineering Inc, UK, 2011.

[9] H. Kang, J.P. Long, G.D.U. Goldner, S.A. Goldstein, S.J. Hollister, A paradigm forthe development and evaluation of novel implant topologies for bone fixation:implant design and fabrication, J. Biomech. 45 (2012) 2241–2247.

[10] R. Tiossi, M.A.A. Vasco, L.S. Lin, H.J. Conrad, O.L. Bezzon, R.F. Ribeiro, A.S.L. Fok,Validation of finite element models for strain analysis of implant-supportedprostheses using digital image correlation, Dent. Mater. 29 (2013) 788–796.

[11] R. Tiossi, L. Lin, R.C.S. Rodrigues, Y.C. Heo, H.J. Conrad, M.d.G.C. de Mattos, R.F. Ribeiro, A.S.L. Fok, Digital image correlation analysis of the load transfer byimplant-supported restorations, J. Biomech. 44 (2011) 1008–1013.

[12] A.S. Dickinson, A.C. Taylor, H. Ozturk, M. Browne, Experimental validation of afinite element model of the proximal femur using digital image correlationand a composite bone model, J. Biomech. Eng. 133 (2011) 014504.

[13] J.W. Dally, W.F. Riley, Experimental Stress Analysis, third ed., McGraw-HillCollege, Boston, MA, 1991.

[14] W.H. Peters, W.F. Ranson, Digital imaging techniques in experimental stress-analysis, Opt. Eng. 21 (1982) 427–431.

[15] T.C. Chu, W.F. Ranson, M.A. Sutton, W.H. Peters, Applications of digital-image-correlation techniques to experimental mechanics, Exp. Mech. 25 (1985)232–244.

[16] N.L. Clelland, J.D. Seidt, L.G.D. Daroz, E.A. McGlumphy, Comparison of strainsfor splinted and nonsplinted implant prostheses using three-dimensionalimage correlation, Int. J. Oral Maxillofac. Implants 25 (2010) 953–959.

[17] J. Op Den Buijs, D. Dragomir-Daescu, Validated finite element models of theproximal femur using two-dimensional projected geometry and bone density,Comput. Methods Prog. Bio. 104 (2011) 168–174.

[18] G.I.N. Rozvany, M. Zhou, T. Birker, Generalized shape optimization withouthomogenization, Struct. Optimiz. 4 (1992) 250–252.

[19] M.P. Bendsoe, O. Sigmund, Material interpolation schemes in topologyoptimization, Arch. Appl. Mech. 69 (1999) 635–654.

[20] T.H. Nguyen, G.H. Paulino, J.H. Song, C.H. Le, Improving multiresolutiontopology optimization via multiple discretizations, Int. J. Numer. MethodsEng. 92 (2012) 507–530.

[21] M.P. Bendsoe, O. Sigmund, Topology Optimization Theory, Methods andApplications, Springer, Berlin, 2003.

[22] P.S. Walker, D. Lamser, R.W. Hussey, A.B. Rossier, A. Farberov, J. Dietz, Forces inthe halo-vest apparatus, Spine 9 (1984) 773–777.

[23] R. Bluebond-Langner, E.D. Rodriguez, Application of skeletal buttress analogyin composite facial reconstruction, Craniomaxillofac. Trauma Reconstr. 2(2009) 19–25.

[24] T. Nagasao, T. Nakajima, A. Kimura, T. Kaneko, H. Jin, T. Tamaki, The dynamicrole of buttress reconstruction after maxillectomy, Plast. Reconstr. Surg. 115(2005) 1328–1340 (discussion 1341).

[25] J.h. McElhaney, J.L. Fogle, J.W. Melvin, R.R. Haynes, V.L. Roberts, N.M. Alem,Mechanical properties of cranial bone, J. Biomech. 3 (1970) 495–511.

[26] J.H. Koolstra, Dynamics of the human masticatory system, Crit. Rev. Oral Biol.Med. 13 (2002) 366–376.

[27] A. Matzavinos, C.Y. Kao, J.E.F. Green, A. Sutradhar, M.J. Miller, Avner Friedman,Modeling oxygen transport in surgical tissue transfer, Proc. Natl. Acad. Sci. U.S.A. 106 (2009) 12091–12096.

A. Sutradhar et al. / Computers in Biology and Medicine 52 (2014) 8–17 17