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Biomaterials 83 (2016) 127e141

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Biomaterials

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Review

Topological design and additive manufacturing of porous metals forbone scaffolds and orthopaedic implants: A review

Xiaojian Wang a, 1, Shanqing Xu a, 1, Shiwei Zhou a, Wei Xu b, Martin Leary b,Peter Choong c, M. Qian b, Milan Brandt b, Yi Min Xie a, b, *

a Centre for Innovative Structures and Materials, School of Engineering, RMIT University, GPO Box 2476, Melbourne 3001, Victoria, Australiab Centre for Additive Manufacturing, School of Engineering, RMIT University, GPO Box 2476, Melbourne 3001, Victoria, Australiac Department of Surgery, University of Melbourne, St. Vincent's Hospital, Melbourne 3001, Victoria, Australia

a r t i c l e i n f o

Article history:Received 23 July 2015Received in revised form31 December 2015Accepted 1 January 2016Available online 6 January 2016

Keywords:Additive manufacturingTopology optimizationBone scaffoldPorous metalsOrthopaedic implantsBiomaterials

* Corresponding author. Centre for Innovative StrucEngineering, RMIT University, GPO Box 2476, Melbou

E-mail address: mike.xie@rmit.edu.au (Y.M. Xie).1 Equal contribution.

http://dx.doi.org/10.1016/j.biomaterials.2016.01.0120142-9612/© 2016 Elsevier Ltd. All rights reserved.

a b s t r a c t

One of the critical issues in orthopaedic regenerative medicine is the design of bone scaffolds and im-plants that replicate the biomechanical properties of the host bones. Porous metals have found them-selves to be suitable candidates for repairing or replacing the damaged bones since their stiffness andporosity can be adjusted on demands. Another advantage of porous metals lies in their open space for thein-growth of bone tissue, hence accelerating the osseointegration process. The fabrication of porousmetals has been extensively explored over decades, however only limited controls over the internalarchitecture can be achieved by the conventional processes. Recent advances in additive manufacturinghave provided unprecedented opportunities for producing complex structures to meet the increasingdemands for implants with customized mechanical performance. At the same time, topology optimi-zation techniques have been developed to enable the internal architecture of porous metals to bedesigned to achieve specified mechanical properties at will. Thus implants designed via the topologyoptimization approach and produced by additive manufacturing are of great interest. This paper reviewsthe state-of-the-art of topological design and manufacturing processes of various types of porous metals,in particular for titanium alloys, biodegradable metals and shape memory alloys. This review alsoidentifies the limitations of current techniques and addresses the directions for future investigations.

© 2016 Elsevier Ltd. All rights reserved.

1. Introduction

Bone is a complex tissue that continually undergoes dynamicbiological remodelling, i.e., the coupled process whereby osteo-clasts resorb mature bone tissue followed by osteoblasts thatgenerate new bone to maintain healthy homeostasis of bone [1].This unique feature of bone underpins its ability to remodel itself torepair damage. However, when a bone defect exceeds a critical non-healable size, external intervention is required to supplement self-healing if the defect is to be bridged [2]. Despite recent advances inbiomaterials and tissue engineering, repair of such a critical-sizedbone defect still remains a challenge. The optimal choice is to useautograft (patients' own tissue) [3]. However, harvesting autograft

tures and Materials, School ofrne 3001, Victoria, Australia.

tissue creates the morbidity associated with a second surgical site.An alternative choice is allograft tissue (taken from another per-son), which carries the risk of transmissible disease and depends onlogistic circumstances (limited availability). The insufficiencies ofapplication of autograft and allograft tissue have led to greaterresearch efforts to identify biomimetic materials and structuresthat are suitable for skeletal repair without the inherent problems.

Metals and alloys have a long history of application as boneimplants [4e7]. Among them, the use of stainless steels, cobalt (Co)based alloys (CoCrMo), and titanium (Ti) and its alloys are wellestablished due to their good biocompatibility, satisfactory me-chanical strength and superior corrosion resistance [5]. However,implants made of these materials are usually much stiffer thannatural bones, leading to stress shielding - a major source for boneresorption and eventual failure of such implants [5]. Cortical bone(compact bone) has elastic moduli ranging from 3 to 30 GPa, whiletrabecular or cancellous bone has significantly lower elastic moduliof 0.02e2 GPa. Most current implant materials have much higher

X. Wang et al. / Biomaterials 83 (2016) 127e141128

moduli than those of bones, e.g., Ti6Al4V has a modulus of around110 GPa and CoCrMo alloys have a modulus of around 210 GPa[5,6,8]. Therefore, to avoid stress shielding at the bone-implantinterface, the equivalent Young's modulus and yield stress have tobe adjusted when using these bulk materials. An effective methodis to introduce adjustable porosity or relative density as proposedby Gibson and Ashby [9] for isotropic materials.

Traditional methods for fabricating open-cell porous metalsinclude liquid state processing (direct foaming, spray foaming, etc.),solid state processing (powder metallurgy, sintering of powdersand fibres, etc.), electro-deposition and vapour deposition [10,11].Although the shape and size of the pores can be adjusted bychanging the parameters of these manufacturing processes, only arandomly organized porous structure can be achievable. However,additive manufacturing (AM) technologies can fabricate porousmetals with predefined external shape and internal architecture[2,12e14]. Metal-based additive manufacturing (MAM) techniques,such as selective laser melting (SLM) and electron beam melting(EBM), are computer controlled fabrication process based on layer-wise manufacturing principles. SLM [15e17] and EBM [18,19] areincreasingly used for the fabrication of porous metals with complexarchitecture. Instead of using electron beam as the energy source inEBM, the SLM technology uses laser beam with adjustable wave-length. Therefore, EBM can only process conductive metalswhereas SLM can process polymer or ceramics as well as metal.Furthermore, due to more diffuse energy (larger heat-affectedzone), EBM process has larger minimum feature size, medianpowder particle size, layer thickness, resolution and surface finish[20]. The robust application of MAM technologies requires exten-sive material, process and design knowledge, specific to each MAMtechnology [21]. MAM system behaviour is subject to significantstochastic error and experimental uncertainties, requiring that“assumptions are necessary to simplify the problem” [22]. Sourcesof error include: complex and transient heat transfer phenomena[23], geometric effects [24] with poorly defined powder thermalproperties [25]. MAM prediction error can lead to excess melt pooltemperature [26], resulting in undesirable microstructure, residualstress, local porosity, and surface roughness. Understanding theeffects of design decisions on temperature related process defects iscritically important to the process control. Comprehensive reviewsof AM technologies can be found elsewhere [27,28].

Recent successes in orthopaedic regenerative medicine havepromised an exciting future of AM technology. The world's firstadditively manufactured mandible was implanted in a patient byDr. Jules Poukens and his team in 2012 in Belgium [29]. A full lowerjaw implant (mandible in Fig. 1) was coated with hydroxyapatiteand implanted in an 83 year old lady. The porous implant wasslightly heavier than a natural jaw, and provided robust attachmentof muscles and sufficient space for nerves [29]. Skull re-constructions with AM parts have been performed successfully byusing digital design and AM. Mertens et al. [30] successfullyreconstructed a class III defect using AM manufactured titaniumimplants, which provided bothmidfacial support and a graft fixture(midface defect in Fig. 1). Jardini et al. [31] in Brazil designed andAM fabricated a customized implant for the surgical reconstructionof a large cranial defect. In 2014, Prof. Peter Choong, an Australiansurgeon from St Vincent's Hospital, together with scientists fromthe Commonwealth Scientific and Industrial Research Organization(CSIRO) and Anatomics, successfully implanted the world's first 3D-printed titanium heel bone into a patient [32].

Typical design and application approaches of porous metallicimplants normally include the design of scaffold, AM and post-processing (heat-treatment and surface modification) as illus-trated in Fig. 1. This review aims to identify the current status andthe future directions of design-oriented AM technology in

producing porous metallic structures for bone tissue repair, with aparticular emphasis on topological design of internal architectureof porous metals for bone implants.

2. Structure and properties of bone

2.1. Structure of bone

Bone is a natural composite containing both organic compo-nents (mainly type-I collagen, but also type-III, type-IV collagenand fibrillin) and inorganic crystalline mineral (e.g., hydroxyap-atite, HA) [1,22,33,34], as illustrated in Fig. 2. The structure ofbone is similar to reinforced concrete that is used in the buildingindustry. The function of HA crystals and collagen molecules arelike the steel rod and cement to concrete: one part providesflexibility and the other provides strength and toughness. Type-Icollagen is a triple helix of ~1.5 nm in diameter and ~300 nm inlength. It is the primary organic components of bone. Other non-collagenous proteins include glycoproteins and bone specificproteoglycans [1]. Hydroxyapatite is the inorganic component ofbone and is plate-shaped of 50 � 25 nm in size and 1.5e4 nmthick [35]. The HA crystals are oriented in a periodic array in thefibrils, preferentially with their c axis parallel to the collagen fi-brils [35]. These two phases account for about 95 wt. % of the drybone.

Bone has a hierarchical structure. Each level performs diversemechanical, biological and chemical functions. The hierarchicallevels of bone include macroscale, microscale, sub-microscale,nanoscale, and sub-nanoscale (Fig. 2). The macroscale level rep-resents the overall shape of the bone. Bone can be classified ascompact bone (cortical bone), and trabecular bone (cancellousbone). Compact bone is almost solid, with only ~3e5% spaces forosteocytes, canaliculi, blood vessels, and erosion cavities etc.There are large spaces in trabecular bone. The pores in trabecularbone are filled with bone marrow, and the porosity varies be-tween 50 and 90% [1,36e38]. The building block of compact boneis the osteons, which are of the size ranging from 10 to 500 mm,whereas the trabecular bone is made of a porous network oftrabeculae. At the micron- and nano-scales, aggregated type-Icollagen and HA form the collagen fibril. The reinforcedcollagen fibre is a universal building element for both compactand trabecular bones.

2.2. Mechanical properties of bone

Mechanical properties of bone vary significantly with age,anatomical site and bone quality. It continues to be a major scien-tific challenge to fully understand the mechanics of living bones[36e38]. Among the various biomechanical properties of bone(stiffness, strength, creep and fatigue), elastic modulus has attrac-ted the most research interest because of its critical importance forcharacterizing various bone pathologies and guiding artificialimplant design. The elastic modulus and strength of bone areanisotropic. Compact bone is both stronger and stiffer when loadedlongitudinally along the diaphyseal axis than the radial transversedirections (Table 1). It is also stronger in compression than intension. Trabecular bone is an anisotropic and porous composite.Like many biological materials, trabecular bone displays time-dependent behaviour as well as damage susceptibility during cy-clic loading [41]. The mechanical properties of trabecular bonedepend on not only the porosity, but also the architecturalarrangement of the individual trabeculae. The physical and me-chanical properties of human bone are summarized in Table 1(values are averaged from reported data) [1,26,34,36e38,42,43].

Fig. 1. Schematic diagram for the design, additive manufacturing, heat-treatment, surface modification of porous metallic structures and the latest orthopaedic regenerativemedicine examples. Images adapted from Refs. [29e31].

Fig. 2. Hierarchical structural organization of bone. Image adapted from Refs. [35,39,40].

X. Wang et al. / Biomaterials 83 (2016) 127e141 129

2.3. Requirements for the design of orthopaedic implants

A successful porous metallic implant would restore the functionof bone and promote regeneration of bone tissue at the damagedsite. An ideal bone scaffold should possess the following

characteristics: (1) biocompatibility; (2) suitable surface for cellattachment, proliferation and differentiation; (3) highly porouswith an interconnected pore network for cell ingrowth and trans-port of nutrients and metabolic waste; (4) mechanical properties tomatch the requirements of the surrounding tissues to reduce or

Table 1Mechanical properties of human bones, average values from literature [1,26,34,36e38,42,43].

Porosity Modulus (GPa) Strength (MPa) Poisson's ration

Compact Bone 3e5% Longitudinal 17.9 ± 3.9 Tension 135 ± 15.6 0.4 ± 0.16Compression 205 ± 17.3

Transverse 10.1 ± 2.4 Tension 53 ± 10.7 0.62 ± 0.26Compression 131 ± 20.7

Shear 3.3 ± 0.4 Shear 65 ± 4.0Trabecular Bone Up to 90% Vertebra 0.067 ± 0.045 2.4 ± 1.6

Tibia 0.445 ± 0.257 5.3 ± 2.9Femur 0.441 ± 0.271 6.8 ± 4.8

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eliminate stress shielding, and to meet anatomic loading re-quirements to avoid mechanical failure [44e48]. Porous metals areimplanted to repair bone defects of critical size and, in most cases,serve as load-bearing devices. Bone is usually anisotropic withdifferent stiffness and strength in different directions, but normallythere are no extremely weak directions [49]. Therefore, suitableporous metals will approximate the stiffness of surrounding bones,making them effective for load transfer and alleviating the stressshielding effect.

The key characteristics to design porous metallic implantsinclude the careful selection of porosity, pore size, and pore inter-connectivity, aiming to achieve satisfactory clinical outcomes.These structural features have a profound effect on mechanicalproperties and biological performance of the metallic implants.Bone regeneration in porous implants in vivo involves recruitmentand penetration of cells from the surrounding bone tissue andvascularization [50]. Higher porosity may facilitate these processesand benefit the bone ingrowth. For instance, more bone ingrowthwas found in porous titanium coatings of higher porosity after theimplants were placed into a canine model for 8 weeks [51]. Simi-larly, bone ingrowth was shown to be deeper and greater in porouspolymer scaffolds of higher porosity [52].

The influence of pore size on the bone ingrowth is still contro-versial in literature [53e57]. The optimal pore size for mineralizedbone ingrowth is claimed to be 100e400 mm in the research by Italaet al. [53]. They implanted triangle-shaped titanium implants ofdifferent plate thickness with pore size ranging from 50 to 125 mminto rabbit femur and found that there was no clear lower limit ofpore size for consistent bone ingrowth [53]. Recently Braem et al.[55] assessed the feasibility of early bone ingrowth into a pre-dominantly microporous Ti coating in the compact bone of rabbittibiae and found that new bone formed in micropores of less than10 mm. Large pores are believed to favour vascularization. Bai et al.[56] suggested an upper limit of pore size for vascularization, 400mm, beyond which no significant difference was observed withincreasing pore size. Kuboki et al. [54] found that, when the poresize ranged from 300 to 400 mm, the implantation of porous hy-droxyapatite scaffolds into rats showed higher alkaline phosphatesactivity, osteocalcin content and bone ingrowth. However, Naoya etal. [57] implanted 300 mm, 600 mm and 900 mm AM manufacturedporous Ti scaffolds into rabbit tibia and they found 600 mm and 900mm scaffolds demonstrated significantly higher bone ingrowth than300 mm scaffolds. In addition to vascularization, specific surfacearea of scaffolds is another essential factor with respect to fixationability. Scaffolds with smaller pores are considered to have largersurface area and therefore more space for bone tissue ingrowth.

Another important feature of bone implants is the permeabilityof the porous metal since the transportation of cells, nutrients andgrowth factors require the flow of blood through the porous scaf-folds. In simple terms, permeability is characterised by usinggradient pressure to push liquid through porous material. Zhanget al. [58,59] stated that permeability may influence vascular

invasion and the supply of nutrients required to sustain cell growthand may also provide an outlet for the removal of cell debris,thereby increasing its osteoconductive potential. High permeabilityof titanium implants enhances the osseointegration process[58,59]. Further research on the effect of permeability of porousmetallic implants is in demand.

In summary, porosity, pore size and pore interconnectivity arekey factors that will significantly influence the mechanical prop-erties and biological performance of scaffolds such as boneingrowth and transportation of cells and nutrients. However, theeffects of these factors on scaffold performance are complicated,even conflicting to each other in certain circumstances. Forexample, increasing the porosity may enhance the biological pro-cesses, but it can decrease the stiffness and strength drastically [9].Therefore, finding the optimal topologies for scaffolds is of criticalimportance. However, conventional CAD-based design techniquesare inefficient and usually fail to obtain the optimal scaffold designbecause a prohibitively large number of trials would be required inorder to achieve a balanced performance, e.g., desirable stiffnessand good permeability. On the contrary, topology optimizationtechniques are capable of quickly finding the optimal topologieswhich satisfy multiple objectives and constraints simultaneously toprovide site-specific biological performance.

3. Topological design of porous metallic structures fororthopaedic implants

3.1. Porous metallic implants and topology optimization techniques

Asmentioned previously, bone is a 3D inhomogeneous structurewith elaborate features from macro-to nano-scales. While it isimpossible, and perhaps unnecessary, to recreate all details ofnatural bone in the porous metallic implant, ideally the implantshould have similar hierarchical configurations on multiple scales.It is essential that the implant should possess properties similar tothe host bone and the ambient tissue [60]. This calls for a well-established design methodology integrating structural stiffnesswith fluid permeability to allow the implant to have both adequaterigidity to resist the physical loading and sufficient permeability totransfer cells, nutrients, etc. Fully solid metals, e.g. titanium, areunsuitable because they are inherently impermeable, preventingcells from invading inside to proliferate and form extra cellularmatrix. Moreover, the Young's modulus of human bones (Table 1) ismuch lower than that of solid metals. Such a stiffness mismatch isregarded as one of the most significant problems in implant designas the resulting stress shielding would often lead to implantationfailures.

Recently, porous metals were used in orthopaedic surgeries toreplace damaged bones. Porous scaffolds are geometrically similarto natural hard tissues which are composed of constituting ma-terials penetrated by interconnected pores [61]. Porous metals canbe designed to duplicate the properties of bones if their structures

Fig. 3. Approaches for scaffold design: representative unit cells and blocks. Images adapted from Refs. [14,62e64,71,72,74,80,106e108].

X. Wang et al. / Biomaterials 83 (2016) 127e141 131

could be designed digitally and fabricated using advancedmanufacturing technology. Conventional porous scaffolds typically

consist of a vast number of randomly shaped pores in differentsizes and therefore it is almost impossible to quantitatively analyse

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their properties. To obtain a simplified model, researchers usuallyassume that scaffolds are constructed of periodically-repeatingunit cells along all directions and the architecture of the microunit cells can distinctly define the macro properties of the scaf-folds. Typical traditional design strategies of periodic bone scaf-folds include Computer Aided Design (CAD), image-based designand implicit surfaces [62], as illustrated in Fig. 3. CAD-based designare obtained by using various CAD tools. The widely used library ofconstructing units always involves Platonic and Archimedeanpolyhedral solids, which can also be used to construct functionalgraded scaffolds [63e66]. Computer-aided system for tissue scaf-folds (CASTS) is a further development based on these scaffold li-braries, aiming to efficiently automate the entire design process fordesired topologies [67e69]. Bio-inspired design is an alternative toimprove the mechanical performance of bone scaffolds and enrichthe scaffold library [70e72]. Other CAD-based approaches mayalso be used in designing scaffolds [14]. Image-based design, asproposed by Hollister et al. [73], is based on Computed Tomogra-phy (CT) or Magnetic Resonance Image (MRI) data for recon-struction of a defect. It uses Boolean combination of defect imageand architecture image (could be from empirical or bio-inspiredshapes) to create 3D scaffold image [12,73e75]. Implicit surfacemodelling uses single mathematical equations to freely introducepore shapes such as triply periodic minimal surfaces (TPMS),which is highly flexible in designing scaffolds [62,76e80]. CAD-based randomization approach starts from cell elements to fill aspecific volume in computer software, where standard cell ele-ments are usually packaged while new cell elements can also becreated [81,82]. This method can effectively imitate real bones bythe randomization process, thus promoting the bone attachmentand bone cell in-growth, as well as increasing the damagetolerance.

While the aforementioned methods enable scaffolds to obtaindesirable stiffness and permeability, these approaches demand avast number of attempts to achieve anticipated properties. Oftenthe resulting design is far from the optimum. One of the mainchallenges in the application of porous scaffolds to orthopaedicimplants is the adaptation of their mechanical and biomedicalproperties to those of natural bones. The implanted scaffolds areplaced in a complex environment and their performance is affectedby many factors. Some of them such as high permeability and goodstiffness are competing with each other since a larger pore size isobtained usually at the cost of a lower mechanical strength [83].Hence, to increase the mass transfer, while retaining a strongsupporting framework, there is a need to maintain a delicate trade-off between the porosity of the fabricated scaffold and its strength[10].

Topology optimization e a mathematical method capable ofrearranging the materials to attain desired properties whilesatisfying prescribed constraints e can complement the trial-and-error approach and provide a powerful tool to design complexscaffolds with features on multiple scales. It is a branch ofcomputational mechanics and was originally developed in struc-tural engineering [84]. It has been widely used for designingstructures and materials for desirable mechanical performanceand physical properties. Through two decades of development, thismethod has gone far beyond the traditional structural engineeringcontext [85].

Typically, there are two ways to define a structure in topologyoptimization. The first is a point-by-point description in which avoid (r¼ 0) or a solid (r¼ 1) phase in a local element is representedby an elemental density r [86]. The Evolutionary Structural Opti-mization (ESO) [87,88] and the Solid Isotropic Material withPenalization (SIMP) methods [86,89] use this type of descriptionand have gained considerable success in solving a wide range of

engineering optimization problems. In the field of computationalmaterial design, the topology optimization approach is termed asan “inverse homogenization” method because the homogenizationmethod [90,91] is used to calculate the effective properties of a unitcell and the material distribution is rearranged through topologyoptimization to enable the material to attain target properties. Theseminal work of inverse homogenization was conducted by Sig-mund in the 1990s for the design of materials with prescribedelastic properties [92,93]. Thereafter, great achievements wereobtained in the design of exceptional material properties includingnegative thermal expansion coefficient [94] and negative refractionindex [95]. Later, this method was extended to the design of scaf-fold materials with their stiffness matrices matching those ofanisotropic native bones [75,96,97]. By using the SIMP basedstructural optimization, Guest and Prevost [98] developed a to-pology optimization technique to find a scaffold with pores in theshape of a Schwartz primitive structure, resulting in the maximumpermeability. They also combined bulk modulus and permeabilityin a single objective function and tailored these two competingproperties in a multi-physics optimization problem [99]. Using asimilar density-based optimization method, scaffolds with elastictensors similar to those of natural bones were designed; and theperformance of these scaffolds in subsequent tissue ingrowth wasinvestigated [100]. It is found that bone remodeling is at its bestwhen the scaffold elastic tensor matches or is slightly higher thanthe elastic properties of the host bone.

The last row in Fig. 3 shows the porous structures with themaximum bulk and shear moduli, respectively, at a given porosity.These unit cells were obtained using the Bi-directional Evolu-tionary Structural Optimization (BESO) method [101e105], whichshows faster convergence and unambiguous material definition[106e109]. The BESO method, which allows the material to beadded and removed simultaneously during the optimization pro-cess, is an extension of the original evolutionary ESO methodproposed by Xie and Steven [87,88]. As shown in Fig. 3 on topologyoptimization, various unit cells with maximal bulk modulus,maximal shear modulus, prescribed stiffness ratios in three di-rections, and functionally graded structures can be obtainedthrough the BESO method.

The second class of topology optimizationmethods, representedby the level-set algorithm [110], focus on tracking phase bound-aries. In the level-set method, the interfaces of two phases areimplicitly defined by the zero-level contour of a high-dimensionallevel-set function. The level-set method provides an effectivetechnique to represent smooth boundaries and to control topologychanges [111]. A variational level-set technique for periodic mate-rial design problems governed by NaviereStokes and Maxwell'sequations was developed to attain material with maximal perme-ability [112]. Level-set topology optimization enables the no-slipboundary condition of fluids in Stokes flow to be naturally satis-fied [113]. Periodic structures of scaffolds with the maximal effec-tive diffusivity aimed at providing an ideal environment fornutrient transportation were studied by a level-set based optimi-zation method [114].

There have been tremendous advances in recent years in thearea of using topology optimization techniques to design multi-functional materials with periodic structures, as shown in acomprehensive review by Cadman [115]. Several of these de-velopments are directly related to the design of scaffolds. Bothstiffness and diffusive transport properties were considered byHollister [12,44] and Challis et al. [116]. Using topology optimiza-tion, Hollister and co-workers also created an interbody fusion cagefor improved arthrodesis [117]. The outcomes of their researchwere used in clinic to support bone regeneration for craniofacialreconstruction [12].

X. Wang et al. / Biomaterials 83 (2016) 127e141 133

3.2. Constraints in structural design for additive manufacturing

Although AM can theoretically produce structures in any shape,the quality of the structures may vary significantly depending onthe design and fabrication parameters [118]. Therefore, it isnecessary to consider the processability of the designed partsduring the topological design process, including the constraints andlimitations of AM technologies. However, there is still limitedresearch on creating design guidelines to achieve this goal. Kranzet al. [119] experimentally investigated the restrictions of LaserAdditive Manufacturing (LAM) of Ti6Al4V and presented acomprehensive structured catalogue. In their research, restrictionsand recommendations were presented based on experimentalmeasurements of different characteristics such as cavities (powderremoval, volume reduction), walls (edges, corners and thickness),bores (size, orientation and tooling), gap (dimension, form), hollowcylinder, overhangs and support structures. They also found thatthe quality of AM parts was highly dependent on the materials,machines and process parameters. Therefore, similar guidelinescould be achieved through similar methodology on different ma-terial systems. Among many parameters, frequently discussed oneincludes overhanging structures, which may lead to some unde-sirable defects [120,121]. In an AM process, the overhangingstructure is not supported by solidified section or bottom substratewhen it is being built. Therefore, the overhanging structure isstrongly influenced by the orientation of building (Fig. 4 (a)-(d))[121]. Therefore, the critical fabrication angle is of great importancesince it determines the form of overhanging structure, hence theprocessability [120]. Fig. 4 (e) [120] shows the sketch of a circularpore with overhanging arc AB, which can be processable if thefabrication angle were larger than the critical value qc. Otherwise,supporting structures have to be used, which are normally avoidedto prevent damage of parts in post-processing. A better choice indesign is to adopt structures with special geometrical arrangementsuch as an octahedral lattice, whose lateral schematic is shown inFig. 4 (f) [120]. When the downward sloping surface CD has a largerfabrication angle than the critical angle qc, no supporting structures

Fig. 4. Examples of overhanging structures: (a)e(c) structures having downward sloping facprocessability of a circular pore and (f) improved design of a pore. Images reproduced from

are required.There were also attempts to design structures so that they could

be fabricated using AM without support [122]. This approach isinteresting and useful, but may not be generally applicable toscaffold designs. Other researchers examined the suitability of us-ing SIMP and BESO topology optimization algorithms to designstructures for AM [123].

4. Current status of AM and topology optimization inproducing porous metallic structures

AM technologies are superior to conventional fabrication tech-niques for producing porous metallic implants with complex andcustomized structures, as shown in Fig. 5. In addition to the geo-metric flexibility, composites with two or more phases can bemanufactured. These advantages enable AM to become a promisingtool for the production of biomedical implant devices, controlleddrug delivery systems, and engineered tissues [124e135]. Examplesinclude artificial joints and load-bearing implants produced by AMusing biocompatible materials such as hydroxyapatite, Ti, Ta andCoeCreMo alloys [2,44,127,134] and customized prostheses such asintervertebral spacers [135]. There has been growing research in-terest in using topology optimization to design bone scaffolds andorthopaedic implants [75,96e100,136e144], however significantchallenges still remain before these concepts could be used inclinical practice. An important issue that may not be neglectedwhen applying topology optimization to scaffold design is toconsider the differences in physical, chemical and mechanicalproperties of base materials produced by AM and conventionalfabrication techniques. The material property in AM process maygreatly affect the final topological shape of scaffold, which maydiffer from the original CAD model obtained from topology opti-mization. Moreover, good understanding of the change in me-chanical properties in AM process may assist more accurate optimaldesign in topology optimization procedure. This sectionwill reviewthe status of research on AM fabrication of three main families ofalloys and the application of topology optimization.

e and (d) adjusting downward sloping faces by changing the orientation of the part, (e)Refs. [120,121].

Fig. 5. Photographs of additive manufactured bone scaffolds: Ti6Al4V implants in sheep cervical spine (a) [135] NiTi scaffold for pseudoelastic applications (b) [161]; biodegradableMg stent after expansion (c) [162]; as-produced plain Ti scaffold (d) and the scaffolds with homogeneous and thick CaP coatings (e), (f) [152]; as produced Ti6Al4V scaffold (g),scaffold after HCl etching treatment (h) and the corresponding enlarged view (i) [18].

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4.1. Biocompatible Ti alloys

Metals in biological systems may experience corrosion andrelease ions, which may result in many adverse physiological ef-fects [4,145]. Therefore, the biocompatibility (defined by thetoxicity and carcinogenicity from the release of metal ions) of anyimplant must be quantified to decrease the patient's risk and thefailure of the implantation [4]. The cytotoxicity of typical surgicalimplant alloys and pure metals have been broadly studied in thepast decades [146e149]. It is now commonly accepted that vana-dium (V) may cause sterile abscess and aluminium (Al) may causescar tissue, whereas titanium (Ti), zirconium (Zr), niobium (Nb) andtantalum (Ta) exhibit excellent biocompatibility [4].

Another important motivation behind the design of biocom-patible Ti alloys is the opportunity to decrease the modulus of Tialloys by adding b-stabilizing elements. As mentioned above, the b-stabilizing elements should be biocompatible. Various b-type Tialloys composed of low modulus biocompatible elements (i.e., Ta,Nb, Zr, Mo) were developed. These alloys exhibited lower modulusthan the commonly used Ti6Al4V. One example is Ti13Nb13Zr[146], which showed improved bone biocompatibility and amodulus of 79 GPa. Other b-type Ti alloys which exhibited lowermodulus (~55e65 GPa) included Ti29Nb13Ta4.6Zr [147] andTi35Nb5Ta7Zr [149].

In recent years, AM produced porous Ti alloy scaffolds werewidely reported with Ti6Al4V in dominance, such as the Ti6Al4Vimplants in sheep cervical spine in Fig. 5 (a) [135]. Ryan et al. [150]

combined the multi-stage AM technology with the powder met-allurgy process to produce porous Ti alloy scaffolds using waxtemplates generated by CAD. The pore size of their designs rangedfrom 200 to 400 mm and the porosity reached 66.8%. This methodcould achieve controlled porous structure and ensure high reso-lution in manufacturing. The resulting microstructure and surfaceroughness were similar to parts manufactured by conventionalmethods. This method could also be extended to the fabrication ofother metallic structures which are difficult to be directly made byAM. Murr et al. [14] manufactured different porous Ti6Al4V im-plants using AM based on micro-CT scan and CAD models built byMaterialise software. They studied the influence of geometric fea-tures of unit cells on the mechanical properties of the porousstructures and found that when the porosity changed from 59% to88%, the elastic modulus decreased from 3.03 to 0.58 GPa, whichproved that the elastic modulus of porous metals could be readilyadjusted through the porosity. Similarly Pattanyak et al. [17] stud-ied porous Ti implants based on micro-CT scan on human cancel-lous bones, which focused on structures with complicated internalstructures for bone ingrowth applications. The implants weremanufactured via SLM using Ti powder of less than 45 mm in size.They found that the compressive strength decreased from 120 to35 MPa when the porosity changed from 55% to 75%. Hollanderet al. [151] produced a variety of Ti6Al4V implants, ranging fromporous cylinder to solid human vertebra model with irregularshapes.

Porous Ti6Al4V structures were shown to be effective in

X. Wang et al. / Biomaterials 83 (2016) 127e141 135

supporting cell growth and new bone tissue growth, and cell basedstudy suggested that Ti6Al4V possesses high cyto-biocompatibility[55,152e156]. In vitro studies were performed with porous Ti6Al4Vstructures. Cell spreading and proliferation were observed acrossthe entire surface and inside the porous structure [156]. A similarstudy was performed by Van Bael et al. [155], which suggested thatenhanced cell seeding and proliferation were achieved on porousstructures. Porous Ti6Al4V scaffolds were found performing well inanimal models since induced new bone growth and osseointegra-tionwere achieved on both bare and surface-coated porous Ti6Al4Vstructures [135,152]. Although porous Ti6Al4V had been widelystudied, the potential release of toxic ions led researchers towardslooking for safer alternative alloys. Therefore, Ti alloys such asTi24Nb4Zr8Sn, Ti7.5Mo and Ti40Nb were designed and fabricatedby AM, which exhibited comparable mechanical properties to theircounterparts by conventional manufacturing approaches[157e160].

There was significant research interest in using topology opti-mization for the design of porous Ti alloy scaffolds [116,136e144].While early works mainly focused on the theoretical considerationof the structural design of the unit cells, recent efforts put moreemphasis on integrating topology optimization (the design aspect)with AM (the fabrication aspect), e.g. Refs. [116,136].

4.2. Shape memory alloys

Shape Memory Alloys (SMA) are capable of regaining theiroriginal shape after severe deformations when stimulated byexternal environments [163,164]. Due to this unique property,SMAs have found their way in orthopaedic implant applications.Typical SMAs include NiTi or nitinol which normally containsapproximately 50 at% Ni and 50 at% Ti. The shape memory effect inNiTi comes from the austenite/martensite phase transformationsince martensite is a low temperature stable phase with theabsence of stress whereas austenite is a high temperature stablephase [165,166]. Currently, more than 90% of all commercial SMAsare based on NiTi and its ternary alloys - NiTiCu and NiTiNb [167].Solid NiTi has a modulus of 48 GPa, which is much lower than otherTi alloys. Furthermore, NiTi allows for relatively large reversibledeformation of up to 8%. NiTi has higher stiffness than bone undertendon, and is able to deform over a large strain range at an almostconstant stress (plateau stress) [161,168]. Due to these character-istics, NiTi has beenwidely used inmedical devices, such as surgicaltools, stents, orthodontic wires, plates and staples for bone frac-tures. A NiTi scaffold for pseudoelastic application is shown in Fig. 5(b) [161]. Main attractive features of SMAs are: (1) capability torecover the original shape after large deformation (pseudo-elas-ticity), (2) capability to recover the original shape from a stabledeformed shape when heated (shape memory effect) and (3) a highdamping capacity.

For biomedical applications, the presence of Ni in NiTi has beena continuous concern since Ni is one of the highest sensitivities inmetallic allergy tests [169,170]. Therefore, attempts were madeeither to develop surface modification techniques or to use sub-stitution elements to mitigate this effect without sacrificing thebiocompatibility [160,171e175]. For example, TiNb and the relatedTiNbX system (where X ¼ Zr, Ta, Hf) were developed whichexhibited elastic strains as high as 4.2% [175].

Common methods for making porous NiTi structures are basedon powder metallurgy (PM) and self-propagating high temperaturesynthesis (SHS) of a mixture of elemental powders (Ni and Ti) orpre-alloyed NiTi powder with space holding materials [176e178].After removing space holding materials at relatively low tempera-ture, the structures are further sintered at high temperature[176e178]. Due to high reactivity of Ti and Ni, the sintering of

porous structures is normally done in high vacuum. However, thesemethods have difficulties in precisely controlling the porousstructures of NiTi, i.e., pore size and pore shape. To overcome thisproblem, AM technologies such as SLM have been used to produceNiTi implants [179e184]. It was shown that AM produced NiTi partsexhibited similar mechanical properties as those fabricated byconventional methods such as casting [181,182].

In contrary to the substantial research on Ti alloys, no reports onthe application of topology optimization in the design of SMAscaffolds involving AM fabrication can be found in the literature upto date.

4.3. Biodegradable metals

Biodegradable materials, including both polymer-based andmetal-based ones, are used for some medical implants which willgradually degrade in human body over a period of time [185]. Insome clinical cases, biomaterials are only needed temporarily in thebody and are expected to support the healing process and todisappear after the healing process is completed. Fig. 5 (c) shows abiodegradable Mg stent after expansion [162]. Compared topolymer-based materials, biodegradable metals have higher stiff-ness and strength, and are more suitable for load bearing condi-tions. As the degradable alloys (mainly magnesium and iron basedalloys) are expected to degrade inside human body, the maincompositions of the alloys should be metallic elements that can bemetabolized, and demonstrate appropriate degradation rates in thehuman body [186]. Due to its unique characteristics, Mg alloys wereused to manufacture cardiovascular stents [162] and bone screws[187]. The degradable magnesium alloy bone screws were foundclinically equivalent to the conventional Ti screws; and no foreignbody reaction, osteolysis, or systemic inflammatory reaction wereobserved for the Mg alloy screws [187].

A key parameter that needs to be considered in designing abiodegradable metallic implant is its degradation rate in humanbody. Pure Mg is known to have a fast degradation in high chloridephysiological environment but it may produce hydrogen gas at ahigh rate from corrosion, which cannot be dealt with by the hosttissue. Fe-based biodegradable materials are known to exhibit aslow degradation rate. Animal tests showed that large portions ofthe pure Fe stent remained intact in the blood vessels 12 monthspost-surgery [188]. Alloying is a typical method to adjust thedegradation rate of a metal. For instance, by adding elements suchas Y, Sr, Zn, Zr and Ca, Mg alloys were shown to have much lowerdegradation rates in comparison with pure Mg. Such alloys alsoexhibited high strength, which is desirable for load-bearing appli-cations. In addition to alloying, amorphous structures like metallicglass alloys MgZnCa showed low degradation rate and highstrength [189,190]. However, metallic glass alloys are generallydifficult to manufacture, which would add the cost to the applica-tion of this type of material [190].

Porous Mg alloy implants were investigated as temporary bonereplacements in an animal model [191,192]. They were shown to beable to enhance bone remodelling and appropriate host response.However, porous Mg alloys degrade too rapidly in vivo, which mayleave subcutaneous gas cavities [193]. Since an open porousimplant has large surface area, only alloys with slow degradationrate should be considered for making the porous structure, e.g. Mg-4wt.% Y. The element yttrium helps promote grain refinement, thusresulting in a slow degradation and sufficient cyto-compatibility[193]. Nguyen et al. [194] manufactured porous Mg alloys usingSLM and suggested that the dimension, surface morphology andthe oxygen pick-up of the laser-melted Mg were strongly depen-dent on the laser processing parameters. Due to the high evapo-ration rate at elevated temperatures, few attempts were made to

X. Wang et al. / Biomaterials 83 (2016) 127e141136

fabricate Mg scaffolds directly using AM [195]. Instead, a techniquecombining 3D printing and gravity casting was shown to be effec-tive in producing topologically-ordered porous Mg structures[196,197], where a porous NaCl mould was created using SLM andthen Mg alloy was cast into the mould. After removing the NaCl,porous Mg structure with porosity of 41% and pore size of 1 mmwas obtained. The compressive strength of the porous Mg was re-ported to be 13 MPa, which is comparable to porous Mg producedby powder metallurgy [197].

A review on porous biodegradable metals for hard tissue scaf-folds can be found in Ref. [198]. A theoretical study of topologicaldesign of polymeric scaffolds considering the effect of biodegra-dation was conducted by Chen et al. [199]. No reports on theapplication of topology optimization in the design of biodegradablemetallic scaffolds involving AM fabrication have appeared in theliterature so far.

5. Heat-treatment and surface modification of porousmetallic structures produced by AM

5.1. Heat-treatment

The mechanical properties of AM produced materials dependheavily on the processing parameters, including building layerthickness, scan speed, energy density and focal offset distance[200,201]. Usually AM (SLM or EBM) produced materials haverelatively high yield stress (Ti6Al4V, ~1000 MPa) and ultimatetensile strength (Ti6Al4V, ~1150 MPa), but a relatively low ductility(Ti6Al4V, less than 10%) [200,202,203]. In order to improve themechanical properties of AM produced porous biomaterials so thatthey can mimic the human tissues and fulfil the desired functions,post-treatment is of critical importance. It is known that the mi-crostructures of as-built materials by AM are very different fromthose by traditional casting or forging approaches. AM is a layer-wise build-up process with high cooling rates that lead to signifi-cant internal thermal stresses in the structure. During the buildingprocess, the scanning by either a laser (for SLM) or an electronbeam (for EBM) may cause the instabilities of the melt pool,resulting in increased porosity and high surface roughness[200,204]. Therefore, heat-treatment for changing the microstruc-tures is routinely applied in most applications to meet the productrequirements. The post-treatment process also enables the reduc-tion of thermal stresses in AM produced structures. For Ti6Al4V,post heat-treatment is typically performed within the a þ b region(where a to b phase transition temperature Tb is 995 �C), which cancontrol the morphology and size of the a-phase without signifi-cantly influencing the prior-b grain size. Heat-treatment above Tbleads to a complete dissolution of the a phase and the coarsening ofprior-b grains [200]. A proper heat-treatment process may sub-stantially improve the mechanical properties of AM producedmaterials. Thone et al. [205] observed significant improvement inductility and fatigue strength after heat-treatment of SLM producedTi6Al4V. They revealed that the tensile strength of heat-treatedTi6Al4V slightly decreased from 1080 MPa to 945 MPa but theelongation at failure increased significantly from 1.6% to 11.6%,along with remarkably prolonged fatigue life of parts from 28,900to 290,000 cycles [205]. The improvements in the mechanicalproperties after post heat-treatment are mainly due to the elimi-nation of thermal stresses and the changes of microstructures. Onthe other hand, an adequate selection of AM processing variablescan facilitate in-situ heat treatment. The microstructure of Ti6Al4Vmade by SLM is often dominated by a0 martensite due to rapidcooling, which can be decomposed to lamellar a þ b structureduring SLM process by tuning the processing variables [201]. Afterthe optimization of processing conditions, Xu et al. [201] produced

Ti6Al4V with comparable or better mechanical properties thanforged Ti6Al4V.

5.2. Surface modification

Surface modification plays an important role in enhancing thebiological performance of AM produced porous biomaterials,particularly bioactivity and biocompatibility [206e212]. Ti alloysare normally covered by one layer of 3e7 nm thick native oxide,namely TiO2, which provides excellent chemical inertness, corro-sion resistance and biocompatibility. In the human body, Ti alloyimplants may experience non-specific protein adsorption andinterrogation of neutrophils and macrophages, which may attractfibroblasts to an encapsulation process. To ensure an effectivebiological bond between Ti alloy implants and surrounding bones,surface modification is essential to improve the conductivity ofbones or the bioactivity of titanium [7,213]. The surfacemorphology of Ti alloy implants depends on the history of materialprocessing. For AM produced porous Ti alloys, powders tend tobecome small liquid spheres when heated up by laser or electronbeams [18]. Such a “balling” effect is a complex metallurgical pro-cess that leads to a rough surface and residual powder particles[179]. These loosely connected powder particles can be removedthrough blasting or other post-processing methods beforeimplantation.

Surface modification or activation of Ti surface can be achievedby various techniques such as plasma spray, physical or chemicalvapour deposition, ion implantation, electrochemical oxidation,acidic or alkali etching, solegel, heat-treatment, and surfacemachining or grinding. For porous metallic structures, there aretwo main approaches, based on surface coating and surfacecorrosion.

A popular coating-based method is solegel process, which is asimple yet versatile method for creating oxide coatings at relativelylow temperatures. For implants with a complex topology, dipcoating is normally used. The solegel process may deposit thin(<10 mm) inorganic coatings. The chemical composition and mi-crostructures of the coating can be better controlled by the solegelprocess than by other methods. Other advantages of the solegelprocess include homogeneity and low cost. Brie et al. [214] usedsolegel to form a bioceramic coating (CaP) on porous Ti6Al7Nbimplants. The coating uniformly covered the external and internalsurfaces of the implants; and the coated porous structures exhibi-ted improved biocompatibility. Other methods include electrolyticdeposition (ED) and plasma spray. ED can produce CaP coatingshaving a thickness of a few microns to several hundred microns,which can be controlled by applying appropriate current densityand processing time [152]. This may also assist to control the sur-face morphology of CaP coatings from needle-like to plate-likestructures. Coating through ED can produce uniformly and fullycovered surface, which makes it suitable for functionalizing porousstructures. Chai et al. [152] found that the bioactivity of the CaPcoated Ti6Al4V scaffold (surface morphology is shown in Fig. 5 (d)to (e)) was significantly improved and it was possible to produceosteoinductive “bio-units” for the repair of bone defects.

Corrosion-based surface treatment involves interfacial chemicalreactions of structures in corrosive solution. Such chemical pro-cesses include alkali treatment [215e217], acid etching [179] andanodization treatments [218,219]. Fig. 5 (h) to (i) show the surfacemorphology of scaffold before and after HCl etching treatment [18].The chemical reaction may produce a thin oxide layer (of TiO2, forexample) on the surface of the metal, usually resulting in improvedbioactivity. The thickness of the active layer can be controlled fromtens of nanometer to hundreds of microns by adjusting processingvariables. Alkali treatment was initially introduced by Kim et al.

X. Wang et al. / Biomaterials 83 (2016) 127e141 137

[215] to improve the bioactivity of Ti implants owing to a biologi-cally active bone-like apatite layer on Ti surface. Anodization is amature electrochemical process capable of producing protectivelayers on the metal surface with adjustable surface microstructureand crystal structure [218,219]. Special care should be taken withregard to the possible negative effect on mechanical propertiesafter corrosion-based surface treatment. It was reported that alkalitreatment might result in the deterioration of mechanical strengthof porous Ti alloy scaffolds and also cause the embrittlement of thestruts in the scaffolds [209].

6. Challenges and future directions

Additive manufacturing provides unprecedented opportunitiesfor producing customized medical implants as this technology canfabricate structures of complex external shapes and intricate in-ternal architectures. Topology optimization has become a powerfuldigital tool for the design of optimal structures and materials. Theintegration of these two technologies sees a promising future indesigning and manufacturing biocompatible orthopaedic implantswith desired mechanical properties and minimal side effects onpatients in clinical applications. Key challenges and future di-rections in integrating the two technologies are as follows:

i) A comprehensive and reliable database containing detailedinformation on the mechanical and biological properties ofhuman bones is yet to be established. This database shouldinclude properties of bones for different age, gender groupsand at different locations. Such information is required as thedesign “target” of the topology optimization process.

ii) Sophisticated topology optimization algorithms capable ofdealing with multi-functional designs on multiple lengthscales simultaneously needs to be developed. Preliminarystudies along this line can be found in Refs. [220,221].

iii) Topological design of the lattice structures that can be easilyproduced by AM and exhibit anisotropic mechanical prop-erties similar to human bones is another promising direction,despite that the fact that there has been extensive researchon topology optimization based on continuum models.

iv) Constraints and limitations of current AM technologies, suchas the critical angle of the overhanging structure and thedifficulty in removing the supporting structure, should beinvolved in newly-developed topology optimization algo-rithms so that the “optimized” designs could actually befabricated by AM.

v) The long-term in vivo material/biological performance ofporous metallic implants that are designed through topologyoptimization techniques and produced by AM needs to berigorously assessed in order to ascertain the advantages anddrawbacks of such implants.

vi) Novel alloying systems capable of enhancing the mechanicaland biological performance of porous metallic implants arein great demand, together with new post-treatment tech-nologies for improving the bioactivity and biocompatibility.

7. Conclusions

In this paper, the current status of the topological design ofporous metallic implants and the fabrication of such implants usingadditive manufacturing is reviewed. First the mechanical proper-ties of human bones are discussed. Then it is demonstrated thattopology optimization is a powerful digital tool that can be used toobtain optimal internal architectures for porous implants whichnot only satisfy multifunctional requirements but also mimic

human bones. Furthermore it is shown that additive manufacturingis the most promising and disruptive technology in the fabricationof porous orthopaedic implants designed through topology opti-mization. To further improve the mechanical and biological per-formance of these structures, both post-treatment and surfacemodification are necessary. Based on these discussions, challengesand future directions of the integration topology optimization withadditive manufacturing are identified. This review provides usefulinformation to researchers and practitioners who are working invarious areas of the truly multidisciplinary topic of bone implantdesign and fabrication.

Acknowledgements

This work was supported by the Australian Research Council(DP140100213 and LP140100607).

References

[1] J.D. Currey, Bones: Structure and Mechanics, Princeton University Press,2002.

[2] S. Bose, S. Vahabzadeh, A. Bandyopadhyay, Bone tissue engineering using 3Dprinting, Mater. Today 16 (2013) 496e504.

[3] J. Parthasarathy, 3D modeling, custom implants and its future perspectives incraniofacial surgery, Ann. Maxillofac. Surg. 4 (2014) 9e18.

[4] M. Abdel-Hady Gepreel, M. Niinomi, Biocompatibility of Ti-alloys for long-term implantation, J. Mech. Behav. Biomed. Mater. 20 (2013) 407e415.

[5] M. Long, H. Rack, Titanium alloys in total joint replacement - a materialsscience perspective, Biomaterials 19 (1998) 1621e1639.

[6] M. Niinomi, Recent research and development in titanium alloys forbiomedical applications and healthcare goods, Sci. Tech. Adv. Mater. 4 (2003)445e454.

[7] X. Liu, P.K. Chu, C. Ding, Surface modification of titanium, titanium alloys, andrelated materials for biomedical applications, Mater. Sci. Eng. R. 47 (2004)49e121.

[8] P.C. McAfee, I.D. Farey, C.E. Sutterlin, K.R. Gurr, K.E. Warden,B.W. Cunningham, The effect of spinal implant rigidity on vertebral bonedensity: a canine model, Spine 16 (1991) S190eS197.

[9] L.J. Gibson, M.F. Ashby, Cellular Solids: Structure and Properties, CambridgeUniversity Press, 1999.

[10] G. Ryan, A. Pandit, D.P. Apatsidis, Fabrication methods of porous metals foruse in orthopaedic applications, Biomaterials 27 (2006) 2651e7260.

[11] J. Banhart, Manufacture, characterisation and application of cellular metalsand metal foams, Prog. Mater. Sci. 46 (2001) 559e632.

[12] S.J. Hollister, Porous scaffold design for tissue engineering, Nat. Mater. 4(2005) 518e524.

[13] S. Van Bael, G. Kerckhofs, M. Moesen, G. Pyka, J. Schrooten, J.P. Kruth, Micro-CT-based improvement of geometrical and mechanical controllability ofselective laser melted Ti6Al4V porous structures, Mater. Sci. Eng. A 528(2011) 7423e7431.

[14] L.E. Murr, S.M. Gaytan, F. Medina, H. Lopez, E. Martinez, B.I. MacHado,D.H. Hernandez, L. Martinez, M.I. Lopez, R.B. Wicker, J. Bracke, Next-gener-ation biomedical implants using additive manufacturing of complex cellularand functional mesh arrays, Phil. Trans. R. Soc. A 368 (2010) 1999e2032.

[15] P. Fischer, V. Romano, H.P. Weber, N.P. Karapatis, E. Boillat, R. Glardon,Sintering of commercially pure titanium powder with a Nd:YAG laser source,Acta Mater. 51 (2003) 1651e1662.

[16] J.M. Williams, A. Adewunmi, R.M. Schek, C.L. Flanagan, P.H. Krebsbach,S.E. Feinberg, S.J. Hollister, S. Das, Bone tissue engineering using poly-caprolactone scaffolds fabricated via selective laser sintering, Biomaterials 26(2005) 4817e4827.

[17] D.K. Pattanayak, A. Fukuda, T. Matsushita, M. Takemoto, S. Fujibayashi,K. Sasaki, N. Nishida, T. Nakamura, T. Kokubo, Bioactive Ti metal analogous tohuman cancellous bone: fabrication by selective laser melting and chemicaltreatments, Acta Biomater. 7 (2011) 1398e1405.

[18] P. Heinl, L. Müller, C. K€orner, R.F. Singer, F.A. Müller, Cellular Ti-6Al-4Vstructures with interconnected macro porosity for bone implants fabri-cated by selective electron beam melting, Acta Biomater. 4 (2008)1536e1544.

[19] J. Parthasarathy, B. Starly, S. Raman, A. Christensen, Mechanical evaluation ofporous titanium (Ti6Al4V) structures with electron beam melting (EBM),J. Mech. Behav. Biomed. Mater. 3 (2010) 249e259.

[20] I. Gibson, D.W. Rosen, B. Stucker, Additive Manufacturing Technologies,second ed., Springer, 2015, p. 138.

[21] E. Atzeni, L. Iuliano, P. Minetola, A. Salmi, Redesign and cost estimation ofrapid manufactured plastic parts, Rapid Prototyp. J. 16 (2010) 308e317.

[22] J. Cole, M.H. van der Meulen, Whole bone mechanics and bone quality, Clin.Orthop. Relat. Res. 469 (2011) 2139e2149.

[23] B. Vrancken, R. Wauthle, J.P. Kruth, J. Van Humbeeck, Study of the influence

X. Wang et al. / Biomaterials 83 (2016) 127e141138

of material properties on residual stress in selective laser melting, in: Pro-ceedings of the Solid Freeform Fabrication Symposium, 2013, p. 393.

[24] J.P. Kruth, P. Mercelis, J. Van Vaerenbergh, T. Craeghs, Feedback control ofselective laser melting, in: 3rd International Conference on AdvancedResearch in Virtual and Rapid Prototyping, Leiria, Portugal, 2007, pp. 24e29.

[25] M. Rombouts, Selective Laser Sintering/melting of Iron-based Powders (PhDthesis), Catholic University of Leuven, Heverlee Belgium, 2006.

[26] L. Facchini, Microstructure and Mechanical Properties of Biomedical AlloysProduced by Rapid Manufacturing Techniques (PhD thesis), University ofTrento, Italy, 2010.

[27] W.E. Frazier, Metal additive manufacturing: a review, J. Mater. Eng. Perform.23 (2014) 1917e1928.

[28] D. Gu, W. Meiners, K. Wissenbach, R. Poprawe, Laser additive manufacturingof metallic components: materials, processes and mechanisms, Int. Mater.Rev. 57 (2012) 133e164.

[29] Xillo, The World's First 3D Printed Total Jaw Reconstruction, 2011. Availablefrom, http://www.xilloc.com/patients/stories/total-mandibular-implant/.

[30] C. Mertens, H. L€owenheim, J. Hoffmann, Image data based reconstruction ofthe midface using a patient-specific implant in combination with a vascu-larized osteomyocutaneous scapular flap, J. Cranio. Maxill. Surg. 41 (2013)219e225.

[31] A.L. Jardini, M.A. Larosa, C.A. de Carvalho Zavaglia, L.F. Bernardes,C.S. Lambert, P. Kharmandayan, D. Calderoni, R.M. Filho, Customised tita-nium implant fabricated in additive manufacturing for craniomaxillofacialsurgery, Virtual Phys. Prototyp. 9 (2014) 115e125.

[32] CSIRO Produces 3D Heel in World First Surgery, 2014. Available from, http://www.csiro.au/en/News/News-releases/2014/3D-Heel-In-World-First-Surgery2014.

[33] R. Narayan, P. Colombo, Advances in Bioceramics and Porous Ceramics, JohnWiley & Sons, 2009, p. 169.

[34] T.M. Keaveny, E.F. Morgan, G.L. Niebur, O.C. Yeh, Biomechanics of trabecularbone, Ann. Rev. Biomed. Eng. 3 (2001) 307e333.

[35] U.G.K. Wegst, H. Bai, E. Saiz, A.P. Tomsia, R.O. Ritchie, Bioinspired structuralmaterials, Nat. Mater. 14 (2015) 23e36.

[36] K. Choi, J.L. Kuhn, M.J. Ciarelli, S.A. Goldstein, The elastic moduli of humansubchondral, trabecular, and cortical bone tissue and the size-dependency ofcortical bone modulus, J. Biomech. 23 (1990) 1103e1113.

[37] J.Y. Rho, R.B. Ashman, C.H. Turner, Young's modulus of trabecular and corticalbone material: ultrasonic and microtensile measurements, J. Biomech. 26(1993) 111e119.

[38] J.Y. Rho, L. Kuhn-Spearing, P. Zioupos, Mechanical properties and the hier-archical structure of bone, Med. Eng. Phys. 20 (1998) 92e102.

[39] E.N. Marieb, K. Hoehn, Human Anatomy & Physiology, ninth ed., PearsonEducation, 178, 2013.

[40] G.J. Tortora, B.H. Derrickson, Principles of Anatomy and Physiology, thir-teenth ed., Wiley, 187, 2011.

[41] T.M. Keaveny, J.M. Buckley, Biomechanics of vertebal Bone, in: S.M. Kurtz,A.A. Edidin (Eds.), Spine Technology Handbook: Elservier, 2006, pp. 64e65.

[42] J.W. Melvin, Fracture mechanics of bone, J. Biomech. Eng. 115 (1993)549e554.

[43] A. Sharir, M.M. Barak, R. Shahar, Whole bone mechanics and mechanicaltesting, Vet. J. 177 (2008) 8e17.

[44] S.J. Hollister, Scaffold design and manufacturing: from concept to clinic, Adv.Mater. 21 (2009) 3330e3342.

[45] R.S. Langer, J.P. Vacanti, Tissue engineering: the challenges ahead, Sci. Am.280 (1999) 86e89.

[46] R. Langer, J.P. Vacanti, Tissue engineering, Science 260 (1993) 920e926.[47] L.G. Cima, J.P. Vacanti, C. Vacanti, D. Ingber, D. Mooney, R. Langer, Tissue

engineering by cell transplantation using degradable polymer substrates,J. Biomech. Eng. 113 (1991) 143e151.

[48] R. Langer, L.G. Cima, J.A. Tamada, E. Wintermantel, Future directions inbiomaterials, Biomaterials 11 (1990) 738e745.

[49] S. Bernard, Q. Grimal, P. Laugier, Accurate measurement of cortical boneelasticity tensor with resonant ultrasound spectroscopy, J. Mech. Behav.Biomed. Mater. 18 (2013) 12e19.

[50] V. Karageorgiou, D. Kaplan, Porosity of 3D biomaterial scaffolds and osteo-genesis, Biomaterials 26 (2005) 5474e5491.

[51] B.J. Story, W.R. Wagner, D.M. Gaisser, S.D. Cook, A.M. Rust-Dawicki, Vivoperformance of a modified CSTi dental implant coating, Int. J. Oral Maxillofac.Implants 13 (1998) 749e757.

[52] K.U. Lewandrowski, J.D. Gresser, S.P. Bondre, A.E. Silva, D.L. Wise,D.J. Trantolo, Developing porosity of poly (propylene glycol-co-fumaric acid)bone graft substitutes and the effect on osteointegration: a preliminaryhistology study in rats, J. Biomater. Sci. Polym. Ed. 11 (2000) 879e889.

[53] A.I. It€al€a, H.O. Yl€anen, C. Ekholm, K.H. Karlsson, H.T. Aro, Pore diameter ofmore than 100 mm is not requisite for bone ingrowth in rabbits, J. Biomed.Mater. Res. 58 (2001) 679e683.

[54] Y. Kuboki, Q. Jin, H. Takita, Geometry of carriers controlling phenotypicexpression in BMP-induced osteogenesis and chondrogenesis, J. Bone Jt.Surg. 83 (2001) S105eS115.

[55] A. Braem, A. Chaudhari, M. Vivan Cardoso, J. Schrooten, J. Duyck, J. Vleugels,Peri- and intra-implant bone response to microporous Ti coatings withsurface modification, Acta Biomater. 10 (2014) 986e995.

[56] F. Bai, Z. Wang, J. Lu, J. Liu, G. Chen, R. Lv, J. Wang, K. Lin, J. Zhang, X. Huang,The correlation between the internal structure and vascularization of

controllable porous bioceramic materials in vivo: a quantitative study, TissueEng. Part A 16 (2010) 3791e3803.

[57] N. Taniguchi, S. Fujibayashi, M. Takemoto, K. Sasaki, B. Otsuki, T. Nakamura,T. Matsushita, T. Kokubo, S. Matsuda, Effect of pore size on bone ingrowthinto porous titanium implants fabricated by additive manufacturing: anin vivo experiment, Mater. Sci. Eng. C 59 (2016) 690e701.

[58] Z. Zhang, D. Jones, S. Yue, P.D. Lee, J.R. Jones, C.J. Sutcliffe, E. Jones, Hierar-chical tailoring of strut architecture to control permeability of additivemanufactured titanium implants, Mater. Sci. Eng. C 33 (2013) 4055e4062.

[59] S. Yang, K.F. Leong, Z. Du, C.K. Chua, The design of scaffolds for use in tissueengineering. Part I. Traditional factors, Tissue Eng. 7 (2001) 679e689.

[60] D.M. Robertson, L. St Pierre, R. Chahal, Preliminary observations of boneingrowth into porous materials, J. Biomed. Mater. Res. 10 (1976) 335e344.

[61] P. Griss, G. Heimke, Record of discussion on stability of joint prostheses, in:D. Williams (Ed.), Biocompatibility of Implant Materials, Sector Publishing,London, 1976, pp. 52e68.

[62] S.M. Giannitelli, D. Accoto, M. Trombetta, A. Rainer, Current trends in thedesign of scaffolds for computer-aided tissue engineering, Acta Biomater. 10(2014) 580e594.

[63] M.A. Wettergreen, B.S. Bucklen, B. Starly, E. Yuksel, W. Sun,M.A.K. Liebschner, Creation of a unit block library of architectures for use inassembled scaffold engineering, Comput. Aided Des. 37 (2005) 1141e1149.

[64] N. Chantarapanich, P. Puttawibul, S. Sucharitpwatskul, P. Jeamwatthanachai,S. Inglam, K. Sitthiseripratip, Scaffold library for tissue engineering: a geo-metric evaluation, Comp. Math. Methods Med. 2012 (2012) 40785.

[65] C.K. Chua, K.F. Leong, C.M. Cheah, S.W. Chua, Development of a tissue en-gineering scaffold structure library for rapid prototyping. Part 2: parametriclibrary and assembly program, Int. J. Adv. Manuf. Technol. 21 (2003)302e312.

[66] C.K. Chua, K.F. Leong, C.M. Cheah, S.W. Chua, Development of a tissue en-gineering scaffold structure library for rapid prototyping. Part 1: investiga-tion and classification, Int. J. Adv. Manuf. Technol. 21 (2003) 291e301.

[67] N. Sudarmadji, J.Y. Tan, K.F. Leong, C.K. Chua, Y.T. Loh, Investigation of themechanical properties and porosity relationships in selective laser-sinteredpolyhedral for functionally graded scaffolds, Acta Biomater. 7 (2011)530e537.

[68] M.W. Naing, C.K. Chua, K.F. Leong, Y. Wang, Fabrication of customised scaf-folds using computer-aided design and rapid prototyping techniques, RapidPrototyp. J. 11 (2005) 249e259.

[69] C.M. Cheah, C.K. Chua, K.F. Leong, C.H. Cheong, M.W. Naing, Automatic al-gorithm for generating complex polyhedral scaffold structures for tissueengineering, Tissue Eng. 10 (2004) 595e610.

[70] J. Nam, B. Starly, A. Darling, W. Sun, Computer aided tissue engineering formodeling and design of novel tissue scaffolds, Comput. Aided Des. Appl. 1(2004) 633e640.

[71] B.S. Bucklen, W.A. Wettergreen, E. Yuksel, M.A.K. Liebschner, Bone-derivedCAD library for assembly of scaffolds in computer-aided tissue engineering,Virtual Phys. Prototyp. 3 (2008) 13e23.

[72] W. Sun, B. Starly, J. Nam, A. Darling, Bio-CAD modeling and its applications incomputer-aided tissue engineering, Comput. Aided Des. 37 (2005)1097e1114.

[73] S.J. Hollister, R.A. Levy, T.M. Chu, J.W. Halloran, S.E. Feinberg, An image-basedapproach for designing and manufacturing craniofacial scaffolds, Int. J. OralMaxillofac. Surg. 29 (2000) 67e71.

[74] M.H. Smith, C.L. Flanagan, J.M. Kemppainen, J.A. Sack, H. Chung, S. Das,S.J. Hollister, S.E. Feinberg, Computed tomography-based tissue-engineeredscaffolds in craniomaxillofacial surgery, Int. J. Med. Robot. Comp. 3 (2007)207e216.

[75] S.J. Hollister, R.D. Maddox, J.M. Taboas, Optimal design and fabrication ofscaffolds to mimic tissue properties and satisfy biological constraints, Bio-materials 23 (2002) 4095e4103.

[76] S.C. Kapfer, S.T. Hyde, K. Mecke, C.H. Arns, G.E. Schr€oder-Turk, Minimalsurface scaffold designs for tissue engineering, Biomaterials 32 (2011)6875e6882.

[77] S. Rajagopalan, R.A. Robb, Schwarz meets Schwann: Design and fabrication ofbiomorphic and durataxic tissue engineering scaffolds, Med. Image Anal. 10(2006) 693e712.

[78] D.J. Yoo, Porous scaffold design using the distance field and triply periodicminimal surface models, Biomaterials 32 (2011) 7741e7754.

[79] D.J. Yoo, Computer-aided porous scaffold design for tissue engineering usingtriply periodic minimal surfaces, Int. J. Precis. Eng. Manuf. 12 (2011) 61e71.

[80] B. Derby, Printing and prototyping of tissues and scaffolds, Science 338(2012) 921e926.

[81] L. Mullen, R.C. Stamp, P. Fox, E. Jones, C. Ngo, C.J. Sutcliffe, Selective lasermelting: A unit cell approach for the manufacture of porous, titanium, bonein-growth constructs, suitable for orthopedic applications. II. Randomizedstructures, J. Biomed. Mater. Res. Part B Appl. Biomater. 92 (2012) 178e188.

[82] A. Atala, J.J. Yoo, Essentials of 3D Biofabrication and Translation, AcademicPress, 2015, p. 32.

[83] M.M. Dewidar, J.K. Lim, Properties of solid core and porous surface Ti-6Al-4Vimplants manufactured by powder metallurgy, J. Alloys Compd. 454 (2008)442e446.

[84] M.P. Bendsoe, O. Sigmund, Topology Optimization: Theory, Methods andApplications, Springer Science & Business Media, 2003.

[85] S. Zhou, W. Li, G. Sun, Q. Li, A level-set procedure for the design of

X. Wang et al. / Biomaterials 83 (2016) 127e141 139

electromagnetic metamaterials, Opt. Express 18 (2010) 6693e6702.[86] M. Zhou, G.I.N. Rozvany, The COC algorithm, Part II: topological, geometrical

and generalized shape optimization, Comput. Methods Appl. Mech. Eng. 89(1991) 309e336.

[87] Y.M. Xie, G.P. Steven, A simple evolutionary procedure for structural opti-mization, Comput. Struct. 49 (1993) 885e896.

[88] Y.M. Xie, G.P. Steven, Basic Evolutionary Structural Optimization, Springer,1997.

[89] M.P. Bendsøe, Optimal shape design as a material distribution problem,Struct. Optim. 1 (1989) 193e202.

[90] E. S�anchez-Palencia, Non-homogeneous Media and Vibration Theory,Springer-Verlag, 1980.

[91] A. Bensoussan, J.L. Lions, G. Papanicolau, Asymptotic Analysis for PeriodicStructures, Elsevier Science, 1978.

[92] O. Sigmund, Materials with prescribed constitutive parameters: an inversehomogenization problem, Int. J. Solids Struct. 31 (1994) 2313e2329.

[93] O. Sigmund, Tailoring materials with prescribed elastic properties, Mech.Mater 20 (1995) 351e368.

[94] O. Sigmund, S. Torquato, Design of materials with extreme thermal expan-sion using a three-phase topology optimization method, J. Mech. Phys. Solids45 (1997) 1037e1067.

[95] J. Zhou, J. Dong, B. Wang, T. Koschny, M. Kafesaki, C.M. Soukoulis, Negativerefractive index due to chirality, Phys. Rev. B 79 (2009), 121104(R).

[96] C.Y. Lin, N. Kikuchi, S.J. Hollister, A novel method for biomaterial scaffoldinternal architecture design to match bone elastic properties with desiredporosity, J. Biomech. 37 (2004) 623e636.

[97] B.C. Chen, Optimal Design of Material Microstructures and Optimization ofStructural Topology for Design-dependent Loads (PhD thesis), University ofMichigan, 2000.

[98] J.K. Guest, J.H. Pr�evost, Design of maximum permeability material structures,Comput. Methods Appl. Mech. Eng. 196 (2007) 1006e1017.

[99] J.K. Guest, J.H. Pr�evost, Optimizing multifunctional materials: design of mi-crostructures for maximized stiffness and fluid permeability, Int. J. SolidsStruct. 43 (2006) 7028e7047.

[100] S. Sturm, S. Zhou, Y.W. Mai, Q. Li, On stiffness of scaffolds for bone tissueengineering-a numerical study, J. Biomech. 43 (2010) 1738e1744.

[101] O.M. Querin, G.P. Steven, Y.M. Xie, Evolutionary structural optimisation(ESO) using a bidirectional algorithm, Eng. Comput. 15 (1998) 1031e1048.

[102] X.Y. Yang, Y.M. Xie, G.P. Steven, O.M. Querin, Bidirectional evolutionarymethod for stiffness optimization, AIAA J. 37 (1999) 1483e1488.

[103] X. Huang, Y.M. Xie, Convergent and mesh-independent solutions for the bi-directional evolutionary structural optimization method, Finite Elem. Anal.Des. 43 (2007) 1039e1049.

[104] X. Huang, Y.M. Xie, Bi-directional evolutionary topology optimization ofcontinuum structures with one or multiple materials, Comput. Mech. 43(2009) 393e401.

[105] X. Huang, Y.M. Xie, Evolutionary Topology Optimization of ContinuumStructures: Methods and Applications, Wiley, 2010.

[106] X. Huang, A. Radman, Y.M. Xie, Topological design of microstructures ofcellular materials for maximum bulk or shear modulus, Comput. Mater. Sci.50 (2011) 1861e1870.

[107] X.Y. Yang, X. Huang, J.H. Rong, Y.M. Xie, Design of 3D orthotropic materialswith prescribed ratios for effective Young's moduli, Comput. Mater. Sci. 67(2013) 229e237.

[108] A. Radman, X. Huang, Y.M. Xie, Topology optimization of functionally gradedcellular materials, J. Mater. Sci. 48 (2013) 1503e1510.

[109] A. Radman, X. Huang, Y.M. Xie, Maximizing stiffness of functionally gradedmaterials with prescribed variation of thermal conductivity, Comput. Mater.Sci. 82 (2014) 457e463.

[110] S. Osher, J.A. Sethian, Fronts propagating with curvature-dependent speed:algorithms based on Hamilton-Jacobi formulations, J. Comput. Phys. 79(1988) 12e49.

[111] M.Y. Wang, X. Wang, D. Guo, A level set method for structural topologyoptimization, Comput. Methods. Appl. Mech. Eng. 192 (2003) 227e246.

[112] S. Zhou, Q. Li, A variational level set method for the topology optimization ofsteady-state Navier-Stokes flow, J. Comput. Phys. 227 (2008) 10178e10195.

[113] V.J. Challis, J.K. Guest, Level set topology optimization of fluids in Stokes flow,Int. J. Numer. Methods Eng. 79 (2009) 1284e1308.

[114] C.C. Chang, S. Zhou, Q. Li, Optimization of effective diffusivity by iso-surfacemodeling, in: 10th World Congress on Structural and MultidisciplinaryOptimization Orlando, Florida, USA, 2013.

[115] J.E. Cadman, S. Zhou, Y. Chen, Q. Li, On design of multi-functional micro-structural materials, J. Mater. Sci. 48 (2013) 51e66.

[116] V.J. Challis, A.P. Roberts, J.F. Grotowski, L.C. Zhang, T.B. Sercombe, Prototypesfor bone implant scaffolds designed via topology optimization and manu-factured by solid freeform fabrication, Adv. Eng. Mater. 12 (2010)1106e1110.

[117] C.Y. Lin, C.C. Hsiao, P.Q. Chen, S.J. Hollister, Interbody fusion cage designusing integrated global layout and local microstructure topology optimiza-tion, Spine 29 (2004) 1747e1754.

[118] D. Wang, Y. Yang, R. Liu, D. Xiao, J. Sun, Study on the designing rules andprocessability of porous structure based on selective laser melting (SLM),J. Mater. Process Tech. 213 (2013) 1734e1742.

[119] J. Kranz, D. Herzog, C. Emmelmann, Design guidelines for laser additivemanufacturing of lightweight structures in TiAl6V4, J. Laser Appl. 27 (2015)

S14001.[120] X.B. Su, Y.Q. Yang, P. Yu, J.F. Sun, Development of porous medical implant

scaffolds via laser additive manufacturing, Trans. Nonferrous. Met. Soc. China22 (Suppl. 1) (2012) s181es187.

[121] F. Calignano, Design optimization of supports for overhanging structures inaluminum and titanium alloys by selective laser melting, Mater. Des. 64(2014) 203e213.

[122] M. Leary, L. Merli, F. Torti, M. Mazur, M. Brandt, Optimal topology for ad-ditive manufacture: a method for enabling additive manufacture of support-free optimal structures, Mater. Des. 63 (2014) 678e690.

[123] A. Aremu, I. Ashcroft, R. Hague, R. Wildman, C. Tuck, Suitability of SIMP andBESO topology optimization algorithms for additive manufacture, in: 21stAnnual International Solid Freeform Fabrication Symposium - an AdditiveManufacturing Conference, SFF 2010, Austin, TX: University of Texas atAustin (Freeform), 2010, pp. 679e692.

[124] S.T. Becker, H. Bolte, O. Krapf, H. Seitz, T. Douglas, S. Sivananthan, J. Wiltfang,E. Sherry, P.H. Warnke, Endocultivation: 3D printed customized porousscaffolds for heterotopic bone induction, Oral Oncol. 45 (2009) e181e188.

[125] A. Fukuda, M. Takemoto, T. Saito, S. Fujibayashi, M. Neo, DeepakK. Pattanayak, T. Matsushita, K. Sasaki, N. Nishida, T. Kokubo, T. Nakamura,Osteoinduction of porous Ti implants with a channel structure fabricated byselective laser melting, Acta Biomater. 7 (2011) 2327e2336.

[126] I. Gibson, D.W. Rosen, B. Stucker, Additive Manufacturing Technologies,Springer, 2010.

[127] L. Hao, R. Harris, Customised implants for bone replacement and growth, in:P. B�artolo, B. Bidanda (Eds.), Bio-materials and Prototyping Applications inMedicine, Springer, US, 2008, pp. 79e107.

[128] P. Heinl, L. Müller, C. K€orner, R.F. Singer, F.A. Müller, Cellular Tie6Ale4Vstructures with interconnected macro porosity for bone implants fabricatedby selective electron beam melting, Acta Biomater. 4 (2008) 1536e1544.

[129] T.B. Kim, S. Yue, Z. Zhang, E. Jones, J.R. Jones, P.D. Lee, Additive manufacturedporous titanium structures: through-process quantification of pore and strutnetworks, J. Mater. Process Tech. 214 (2014) 2706e2715.

[130] L. Mullen, R.C. Stamp, W.K. Brooks, E. Jones, C.J. Sutcliffe, Selective lasermelting: a regular unit cell approach for the manufacture of porous, tita-nium, bone in-growth constructs, suitable for orthopedic applications,J. Biomed. Mater. Res. B 89 (2009) 325e334.

[131] L.E. Murr, K.N. Amato, S.J. Li, Y.X. Tian, X.Y. Cheng, S.M. Gaytan, E. Martinez,P.W. Shindo, F. Medina, R.B. Wicker, Microstructure and mechanical prop-erties of open-cellular biomaterials prototypes for total knee replacementimplants fabricated by electron beam melting, J. Mech. Behav. Biomed.Mater. 4 (2011) 1396e1411.

[132] L.E. Murr, S.M. Gaytan, F. Medina, H. Lopez, E. Martinez, B.I. Machado,D.H. Hernandez, L. Martinez, M.I. Lopez, R.B. Wicker, J. Bracke, Next-gener-ation biomedical implants using additive manufacturing of complex, cellularand functional mesh arrays, Phil. Trans. R. Soc. A 368 (2010) 1999e2032.

[133] B. Stevens, Y. Yang, A. Mohandas, B. Stucker, K.T. Nguyen, A review of ma-terials, fabrication methods, and strategies used to enhance bone regener-ation in engineered bone tissues, J. Biomed. Mater. Res. B 85 (2008)573e582.

[134] V.K. Balla, S. Bodhak, S. Bose, A. Bandyopadhyay, Porous tantalum structuresfor bone implants: fabrication, mechanical and in vitro biological properties,Acta Biomater. 6 (2010) 3349e3359.

[135] J. Yang, H. Cai, J. Lv, K. Zhang, H. Leng, C. Sun, Z. Wang, Z. Liu, In vivo study ofa self-stabilizing artificial vertebral body fabricated by electron beammelting, Spine 39 (2014) E486eE492.

[136] D. Xiao, Y. Yang, X. Su, D. Wang, J. Sun, An integrated approach of topologyoptimized design and selective laser melting process for titanium implantsmaterials, Bio Med. Mater. Eng. 23 (2013) 433e445.

[137] C.Y. Lin, T. Wirtz, F. LaMarca, S.J. Hollister, Structural and mechanical eval-uations of a topology optimized titanium interbody fusion cage fabricated byselective laser melting process, J. Biomed. Mater. Res. Part A 83 (2007)272e279.

[138] H.G. Chuah, I.A. Rahim, M.I. Yusof, Topology optimisation of spinal interbodycage for reducing stress shielding effect, Comput. Methods. Biomech. Bio-med. Eng. 13 (2010) 319e326.

[139] G. Chen, G.J. Pettet, M. Pearcy, D.L.S. McElwain, Modelling external boneadaptation using evolutionary structural optimisation, Biomech. ModelMechanobiol. 6 (2007) 275e285.

[140] C.L. Chang, C.S. Chen, C.H. Huang, M.L. Hsu, Finite element analysis of thedental implant using a topology optimization method, Med. Eng. Phys. 34(2012) 999e1008.

[141] A. Tovar, S.E. Gano, J.E. Renaud, J.J. Mason, Topology and shape optimizationof an interbody fusion implant for lumbar spine fixation, in: 2003 ASMEDesign Engineering Technical Conferences and Computers and Informationin Engineering Conference, Chicago, 2003, pp. 1351e1358.

[142] S. Shuib, M.I.Z. Ridzwan, A.Y. Hassan, M.N.M. Ibrahim, Topology optimisationof hip prosthesis to reduce stress shielding, in: 9th International Conferenceon Computer Aided Optimum Design in Engineering, 2005, WITPress, Skia-thos, 2005, pp. 257e266.

[143] D.M. Xiao, Y.Q. Yang, X.B. Su, D. Wang, Z.Y. Luo, Topology optimization ofmicrostructure and selective laser melting fabrication for metallic biomate-rial scaffolds, Trans. Nonferrous. Met. Soc. China 22 (2012) 2554e2561.

[144] M. Fraldi, L. Esposito, G. Perrella, A. Cutolo, S.C. Cowin, Topological optimi-zation in hip prosthesis design, Biomech. Model Mechanobiol. 9 (2010)

X. Wang et al. / Biomaterials 83 (2016) 127e141140

389e402.[145] N. Hallab, K. Merritt, J.J. Jacobs, Metal sensitivity in patients with orthopaedic

implants, J. Bone Jt. Surg. 83 (2001) 428e436.[146] J. Davidson, A. Mishra, P. Kovacs, R. Poggie, New surface-hardened, low-

modulus, corrosion-resistant Ti-13Nb-13Zr alloy for total hip arthroplasty,Bio Med. Mater. Eng. 4 (1994) 231e243.

[147] D. Kuroda, M. Niinomi, M. Morinaga, Y. Kato, T. Yashiro, Design and me-chanical properties of new b type titanium alloys for implant materials,Mater. Sci. Eng. A 243 (1998) 244e249.

[148] Y. Okazaki, Y. Ito, K. Kyo, T. Tateishi, Corrosion resistance and corrosion fa-tigue strength of new titanium alloys for medical implants without V and Al,Mater. Sci. Eng. A 213 (1996) 138e147.

[149] S. Steinemann, G. Winter, J. Leray, Evaluation of Biomaterials, Willey, NewYork, 1980.

[150] G.E. Ryan, A.S. Pandit, D.P. Apatsidis, Porous titanium scaffolds fabricatedusing a rapid prototyping and powder metallurgy technique, Biomaterials 29(2008) 3625e3635.

[151] D.A. Hollander, M. Von Walter, T. Wirtz, R. Sellei, B. Schmidt-Rohlfing,O. Paar, H.J. Erli, Structural, mechanical and in vitro characterization ofindividually structured Ti-6Al-4V produced by direct laser forming, Bio-materials 27 (2006) 955e963.

[152] Y.C. Chai, G. Kerckhofs, S.J. Roberts, S. Van Bael, E. Schepers, J. Vleugels,F.P. Luyten, J. Schrooten, Ectopic bone formation by 3D porous calciumphosphate-Ti6Al4V hybrids produced by perfusion electrodeposition, Bio-materials 33 (2012) 4044e4058.

[153] J. Markwardt, J. Friedrichs, C. Werner, A. Davids, H. Weise, R. Lesche,A. Weber, U. Range, H. Meißner, G. Lauer, B. Reitemeier, Experimental studyon the behavior of primary human osteoblasts on laser-cused pure titaniumsurfaces, J. Biomed. Mater. Res. A 102 (2014) 1422e1430.

[154] D.K. Pattanayak, A. Fukuda, T. Matsushita, M. Takemoto, S. Fujibayashi,K. Sasaki, N. Nishida, T. Nakamura, T. Kokubo, Bioactive Ti metal analogous tohuman cancellous bone: fabrication by selective laser melting and chemicaltreatments, Acta Biomater. 7 (2011) 1398e1406.

[155] S. Van Bael, Y.C. Chai, S. Truscello, M. Moesen, G. Kerckhofs, H. Van Oos-terwyck, J.P. Kruth, J. Schrooten, The effect of pore geometry on the in vitrobiological behavior of human periosteum-derived cells seeded on selectivelaser-melted Ti6Al4V bone scaffolds, Acta Biomater. 8 (2012) 2824e2834.

[156] A. Bandyopadhyay, F. Espana, V.K. Balla, S. Bose, Y. Ohgami, N.M. Davies,Influence of porosity on mechanical properties and in vivo response ofTi6Al4V implants, Acta Biomater. 6 (2010) 1640e1648.

[157] H.C. Hsu, S.C. Wu, S.K. Hsu, M.S. Tsai, T.Y. Chang, W.F. Ho, Processing andmechanical properties of porous Tie7.5 Mo alloy, Mater. Des. 47 (2013)21e26.

[158] Y. Yao, X. Li, Y.Y. Wang, W. Zhao, G. Li, R.P. Liu, Microstructural evolution andmechanical properties of TieZr beta titanium alloy after laser surfaceremelting, J. Alloys Compd. 583 (2014) 43e47.

[159] L. Zhang, D. Klemm, J. Eckert, Y. Hao, T. Sercombe, Manufacture by selectivelaser melting and mechanical behavior of a biomedical Tie24Nbe4Zre8Snalloy, Scr. Mater. 65 (2011) 21e24.

[160] K. Zhuravleva, M. B€onisch, K.G. Prashanth, U. Hempel, A. Helth, T. Gemming,M. Calin, S. Scudino, L. Schultz, J. Eckert, A. Gebert, Production of porous b-Type Ti-40Nb alloy for biomedical applications: comparison of selective lasermelting and hot pressing, Materials 6 (2013) 5700e5712.

[161] C. Haberland, M. Elahinia, J.M. Walker, H. Meier, J. Frenzel, On the devel-opment of high quality NiTi shape memory and pseudoelastic parts by ad-ditive manufacturing, Smart Mater. Struct. 23 (2014) 104002.

[162] R. Erbel, C. Di Mario, J. Bartunek, J. Bonnier, B. de Bruyne, F.R. Eberli, P. Erne,M. Haude, B. Heublein, M. Horrigan, C. Ilsley, D. B€ose, J. Koolen, T.F. Lüscher,N. Weissman, Temporary scaffolding of coronary arteries with bioabsorbablemagnesium stents: a prospective, non-randomised multicentre trial, Lancet369 (2007) 1869e1875.

[163] M.T. Andani, N. Shayesteh Moghaddam, C. Haberland, D. Dean, M.J. Miller,M. Elahinia, Metals for bone implants. Part 1. Powder metallurgy andimplant rendering, Acta Biomater. 10 (2014) 4058e4070.

[164] P. Bartolo, J.P. Kruth, J. Silva, G. Levy, A. Malshe, K. Rajurkar, M. Mitsuishi,J. Ciurana, M. Leu, Biomedical production of implants by additive electro-chemical and physical processes, CIRP Ann. Manuf. Technol. 61 (2012)635e655.

[165] W.J. Buehler, J.V. Gilfrich, R.C. Wiley, Effect of low-temperature phasechanges on the mechanical properties of alloys near composition TiNi,J. Appl. Phys. 34 (1963) 1475e1477.

[166] M.H. Elahinia, M. Hashemi, M. Tabesh, S.B. Bhaduri, Manufacturing andprocessing of NiTi implants: a review, Prog. Mater. Sci. 57 (2012) 911e946.

[167] L. Petrini, F. Migliavacca, Biomedical applications of shape memory alloys,J. Metall. 2011 (2011) 501483.

[168] N.B. Morgan, Medical shape memory alloy applications-the market and itsproducts, Mater. Sci. Eng. A 378 (2004) 16e23.

[169] A. Biesiekierski, J. Wang, M. Abdel-Hady Gepreel, C. Wen, A new look atbiomedical Ti-based shape memory alloys, Acta Biomater. 8 (2012)1661e1669.

[170] R. K€oster, D. Vieluf, M. Kiehn, M. Sommerauer, J. Kahler, S. Baldus,T. Meinertz, C.W. Hamm, Nickel and molybdenum contact allergies in pa-tients with coronary in-stent restenosis, Lancet 356 (2000) 1895e1897.

[171] E.G. Obbard, Y.L. Hao, T. Akahori, R.J. Talling, M. Niinomi, D. Dye, R. Yang,Mechanics of superelasticity in Ti-30Nb-(8-10)Ta-5Zr alloy, Acta Mater. 58

(2010) 3557e3567.[172] M. Lai, Y. Gao, B. Yuan, M. Zhu, Indirect determination of martensitic

transformation temperature of sintered nickel-free Ti-22Nb-6Zr alloy by lowtemperature compression test, Mater. Des. 60 (2014) 193e197.

[173] F. Yang, D.R. Coughlin, P.J. Phillips, L. Yang, A. Devaraj, L. Kovarik, R.D. Noebe,M.J. Mills, Structure analysis of a precipitate phase in an Ni-rich high-tem-perature NiTiHf shape memory alloy, Acta Mater. 61 (2013) 3335e3346.

[174] R. Santamarta, R. Arr�oyave, J. Pons, A. Evirgen, I. Karaman, H.E. Karaca,R.D. Noebe, TEM study of structural and microstructural characteristics of aprecipitate phase in Ni-rich Ni-Ti-Hf and Ni-Ti-Zr shape memory alloys, ActaMater. 61 (2013) 6191e6206.

[175] S. Miyazaki, H.Y. Kim, H. Hosoda, Development and characterization of Ni-free Ti-base shape memory and superelastic alloys, Mater. Sci. Eng. A438e440 (2006) 18e24.

[176] J.Y. Xiong, Y.C. Li, X.J. Wang, P.D. Hodgson, C.E. Wen, Titanium-nickel shapememory alloy foams for bone tissue engineering, J. Mech. Behav. Biomed.Mater. 1 (2008) 269e273.

[177] B.Y. Li, L.J. Rong, Y.Y. Li, V.E. Gjunter, Synthesis of porous Ni-Ti shape-memory alloys by self-propagating high-temperature synthesis: reactionmechanism and anisotropy in pore structure, Acta Mater. 48 (2000)3895e3904.

[178] B.Y. Li, L.J. Rong, Y.Y. Li, V.E. Gjunter, Recent development in producingporous Ni-Ti shape memory alloys, Intermet 8 (2000) 881e884.

[179] W. Hoffmann, T. Bormann, A. Rossi, B. Müller, R. Schumacher, I. Martin, M. deWild, D. Wendt, Rapid prototyped porous nickeletitanium scaffolds as bonesubstitutes, J. Tissue Eng. 5 (2014) 1e14.

[180] T. Habijan, C. Haberland, H. Meier, J. Frenzel, J. Wittsiepe, C. Wuwer,C. Greulich, T.A. Schildhauer, M. K€oller, The biocompatibility of dense andporous Nickel-Titanium produced by selective laser melting, Mater. Sci. Eng.C 33 (2013) 419e426.

[181] C. Haberland, Additive Verarbeitung von NiTi-Formged€achtniswerkstoffenmittels Selective-Laser-Melting, Shaker, 2012.

[182] H. Christoph, E. Mohammad, M.W. Jason, M. Horst, F. Jan, On the develop-ment of high quality NiTi shape memory and pseudoelastic parts by additivemanufacturing, Smart Mater. Struct. 23 (2014) 104002.

[183] T. Bormann, M. de Wild, F. Beckmann, B. Müller, Assessing the morphologyof selective laser melted NiTi-scaffolds for a three-dimensional quantifica-tion of the one-way shape memory effect, Proc. SPIE (2013)868914e868918.

[184] S. Bernard, V. Krishna Balla, S. Bose, A. Bandyopadhyay, Compression fatiguebehavior of laser processed porous NiTi alloy, J. Mech. Behav. Biomed. Mater.13 (2012) 62e68.

[185] H. Hermawan, Biodegradable Metals: State of the Art. Biodegradable Metals,Springer, Heidelberg, 2012, pp. pp.13e22.

[186] Y.F. Zheng, X.N. Gu, F. Witte, Biodegradable metals, Mater. Sci. Eng. R. 77(2014) 1e34.

[187] H. Windhagen, K. Radtke, A. Weizbauer, J. Diekmann, Y. Noll, U. Kreimeyer,R. Schavan, C. Stukenborg-Colsman, H. Waizy, Biodegradable magnesium-based screw clinically equivalent to titanium screw in hallux valgus sur-gery: short term results of the first prospective, randomized, controlledclinical pilot study, Biomed. Eng. Online 12 (2013) 62.

[188] M. Peuster, C. Hesse, T. Schloo, C. Fink, P. Beerbaum, C. von Schnakenburg,Long-term biocompatibility of a corrodible peripheral iron stent in theporcine descending aorta, Biomaterials 27 (2006) 4955e4962.

[189] B. Zberg, P.J. Uggowitzer, J.F. Loffler, MgZnCa glasses without clinicallyobservable hydrogen evolution for biodegradable implants, Nat. Mater. 8(2009) 887e891.

[190] B. Zberg, E.R. Arata, P.J. Uggowitzer, J.F. L€offler, Tensile properties of glassyMgZnCa wires and reliability analysis using Weibull statistics, Acta Mater. 57(2009) 3223e3231.

[191] F. Witte, H. Ulrich, C. Palm, E. Willbold, Biodegradable magnesium scaffolds:part II: peri-implant bone remodeling, J. Biomed. Mater. Res. Part A 81 (2007)757e765.

[192] F. Witte, J. Reifenrath, P.P. Müller, H.A. Crostack, J. Nellesen, F.W. Bach,D. Bormann, M. Rudert, Cartilage repair on magnesium scaffolds used as asubchondral bone replacement, Materwiss Werksttech 37 (2006) 504e508.

[193] K. Bobe, E. Willbold, I. Morgenthal, O. Andersen, T. Studnitzky, J. Nellesen,W. Tillmann, C. Vogt, K. Vano, F. Witte, In vitro and in vivo evaluation ofbiodegradable, open-porous scaffolds made of sintered magnesium W4short fibres, Acta Biomater. 9 (2013) 8611e8623.

[194] T.L. Nguyen, M.P. Staiger, G.J. Dias, T.B.F. Woodfield, A novel manufacturingroute for fabrication of topologically-ordered porous magnesium scaffolds,Adv. Eng. Mater. 13 (2011) 872e881.

[195] F. Geng, L. Tan, B. Zhang, C. Wu, Y. He, J. Yang, K. Yang, Study on b-TCP coatedporous Mg as a bone tissue engineering scaffold material, J. Mater. Sci. Tech.25 (2009) 123e129.

[196] M.P. Staiger, A.M. Pietak, J. Huadmai, G. Dias, Magnesium and its alloys asorthopedic biomaterials: a review, Biomaterials 27 (2006) 1728e1734.

[197] N.T. Kirkland, I. Kolbeinsson, T. Woodfield, G.J. Dias, M.P. Staiger, Synthesisand properties of topologically ordered porous magnesium, Mater. Sci. Eng. B176 (2011) 1666e1672.

[198] A.H. Yusop, A.A. Bakir, N.A. Shaharom, M.R. Abdul Kadir, H. Hermawan,Porous biodegradable metals for hard tissue scaffolds: a review, Int. J. Bio-mater. 2012 (2012) 10 pages, 641430.

[199] Y. Chen, S. Zhou, Q. Li, Microstructure design of biodegradable scaffold and

X. Wang et al. / Biomaterials 83 (2016) 127e141 141

its effect on tissue regeneration, Biomaterials 32 (2011) 5003e5014.[200] B. Vrancken, L. Thijs, J.P. Kruth, J. Van Humbeeck, Heat treatment of Ti6Al4V

produced by selective laser melting: microstructure and mechanical prop-erties, J. Alloys Compd. 541 (2012) 177e185.

[201] W. Xu, M. Brandt, S. Sun, J. Elambasseril, Q. Liu, K. Latham, K. Xia, M. Qian,Additive manufacturing of strong and ductile Ti-6Al-4V by selective lasermelting via in situ martensite decomposition, Acta Mater. 85 (2014) 74e84.

[202] E. Brandl, D. Greitemeier, Microstructure of additive layer manufactured Ti-6Al-4V after exceptional post heat treatments, Mater. Lett. 81 (2012) 84e87.

[203] T. Vilaro, C. Colin, J.D. Bartout, As-fabricated and heat-treated microstruc-tures of the Ti-6Al-4V alloy processed by selective laser melting, Metall.Mater. Trans. A 42 (2011) 3190e3199.

[204] T. Bormann, B. Müller, M. Schinhammer, A. Kessler, P. Thalmann, M. de Wild,Microstructure of selective laser melted nickel-titanium, Mater. Charact. 94(2014) 189e202.

[205] M. Th€one, S. Leuders, A. Riemer, T. Tr€oster, H. Richard, Influence of heat-treatment on selective laser melting products - eg Ti6Al4V, in: Twenty-third Annual International Solid Freeform Fabrication (SFF) Symposium,2012.

[206] S. Amin Yavari, J. van der Stok, Y.C. Chai, R. Wauthle, Z. Tahmasebi Birgani,P. Habibovic, M. Mulier, J. Schrooten, H. Weinans, A.A. Zadpoor, Boneregeneration performance of surface-treated porous titanium, Biomaterials35 (2014) 6172e6181.

[207] A. Fukuda, M. Takemoto, T. Saito, S. Fujibayashi, M. Neo, S. Yamaguchi,T. Kizuki, T. Matsushita, M. Niinomi, T. Kokubo, T. Nakamura, Bone bondingbioactivity of Ti metal and Ti-Zr-Nb-Ta alloys with Ca ions incorporated ontheir surfaces by simple chemical and heat treatments, Acta Biomater. 7(2011) 1379e1386.

[208] W.Q. Yan, T. Nakamura, M. Kobayashi, H.M. Kim, F. Miyaji, T. Kokubo,Bonding of chemically treated titanium implants to bone, J. Biomed. Mater.Res. 37 (1997) 267e275.

[209] X. Wang, Y. Li, P.D. Hodgson, C. Wen, Biomimetic modification of porousTiNbZr alloy scaffold for bone tissue engineering, Tissue Eng. A 16 (2009)309e316.

[210] X. Wang, Y. Li, J. Lin, P. Hodgson, C. Wen, Apatite-inducing ability of titaniumoxide layer on titanium surface: the effect of surface energy, J. Mater. Res. 23

(2008) 1682e1688.[211] X. Wang, Y. Li, J. Lin, P.D. Hodgson, C. Wen, Effect of heat-treatment atmo-

sphere on the bond strength of apatite layer on Ti substrate, Dent. Mater. 24(2008) 1549e1555.

[212] X. Wang, Y. Li, J. Lin, Y. Yamada, P. Hodgson, C. Wen, In vitro bioactivityevaluation of titanium and niobium metals with different surface mor-phologies, Acta Biomater. 4 (2008) 1530e1535.

[213] V. Goriainov, R. Cook, J.M. Latham, D.G. Dunlop, R.O.C. Oreffo, Bone andmetal: an orthopaedic perspective on osseointegration of metals, Acta Bio-mater. 10 (2014) 4043e4057.

[214] I.C. Brie, O. Soritau, N. Dirzu, C. Berce, A. Vulpoi, C. Popa, M. Todea, S. Simon,M. Perde-Schrepler, P. Virag, O. Barbos, G. Chereches, P. Berce, V. Cernea,Comparative in vitro study regarding the biocompatibility of titanium-basecomposites infiltrated with hydroxyapatite or silicatitanate, J. Biol. Eng. 8(2014) 14.

[215] H.M. Kim, F. Miyaji, T. Kokubo, T. Nakamura, Preparation of bioactive Ti andits alloys via simple chemical surface treatment, J. Biomed. Mater. Res. 32(1996) 409e417.

[216] B.H. Lee, J.K. Kim, Y.D. Kim, K. Choi, K.H. Lee, In vivo behavior and mechanicalstability of surface-modified titanium implants by plasma spray coating andchemical treatments, J. Biomed. Mater. Res. A 69 (2004) 279e285.

[217] S. Nishiguchi, T. Nakamura, M. Kobayashi, H.M. Kim, F. Miyaji, T. Kokubo, Theeffect of heat treatment on bone-bonding ability of alkali-treated titanium,Biomaterials 20 (1999) 491e500.

[218] K. Das, V.K. Balla, A. Bandyopadhyay, S. Bose, Surface modification of laser-processed porous titanium for load-bearing implants, Scr. Mater. 59 (2008)822e825.

[219] A. Apolinario, C.T. Sousa, J. Ventura, J.D. Costa, D.C. Leitao, J.M. Moreira,J.B. Sousa, L. Andrade, A.M. Mendes, J.P. Araújo, The role of the Ti surfaceroughness in the self-ordering of TiO2 nanotubes: a detailed study of thegrowth mechanism, J. Mater. Chem. A 2 (2014) 9067e9078.

[220] Z.H. Zuo, X. Huang, J.H. Rong, Y.M. Xie, Multi-scale design of compositematerials and structures for maximum natural frequencies, Mater. Des. 51(2013) 1023e1034.

[221] X. Yan, X. Huang, G. Sun, Y.M. Xie, Two-scale optimal design of structureswith thermal insulation materials, Compos. Struct. 120 (2015) 358e365.

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