Porous materials created with conventional techniques.
Bone scaffolds with graded porosities or graded cellular bone scaffolds are new innovations of bone replacements and biomedical bone implants, especially in cases of long-bone defects, multitissue regenerations, and functional-controlled bone prostheses. The concepts of graded cellular bone scaffolds are based on the complexity of bone characteristics (graded hierarchical structures and heterogeneity), which aims to closer replicate the multifunctions of bone tissues. The designs of graded cellular bone scaffolds are highly fascinating with the relative anatomical, biological, and mechanical similarity to the replaced bones. While it is difficult for the graded designs to replicate the actual bone models, additive manufacturing (AM) techniques with computer-aided designs successfully create well-controlled models with comparable bone properties. Potential advantages of graded cellular bone scaffolds are enormous. Graded pores can direct types of cell regenerations for multitissue regenerations. Furthermore, graded pores promote a greater load-sharing to adjacent bone tissues than conventional scaffolds do, while both mechanical properties are similar. To summarize, bone implants with graded cellular structures can be fabricated using AM techniques, and their mechanical and biological performances can be tailored by modifying the internal architectures.
- graded cellular structure
- bone scaffolds
- stress shielding
- additive manufacturing techniques
Bone tissue engineering (TE) scaffold has been considered to be a potential technology for repairing and/or replacing damaged bone tissues and organs. The main function of a scaffold serves as a three-dimensional (3D) template for cell organization and tissue development to eliminate the drawbacks of autologous and allogeneic bone transplantations . The major requirements for the scaffolds are biocompatibility, suitable pore size, and porosity for cell attachment and proliferation, and an adequate mechanical strength under physiological loading conditions. Such scaffolds have been successfully utilized in broad areas including repair of long-bone and osteochondral defects, maxillofacial and spinal surgery, cranial reconstruction, and drug delivery systems.
Although bioceramics and polymers are commonly used to make bone-tissue scaffolds, their mechanical strengths are inadequate to withstand a high loading. Metallic cellular structures, however, have been attractive for application in orthopedic bone implants, since the porous architecture promotes bone anchorage and provides suitable stiffness . On the other hand, dense metals, such as those used for total hip replacement (THR), are often too stiff and can shield the adjacent bone tissue and cause loosening of the implants . The implants based on the concepts of bone TE scaffolds would shift the trend of using porous metallic implants.
A functionally graded structure for bone tissue engineering is a porous biomaterial where the porosity changes with a specific gradient in space . This gradient porosity similarly behaves as a graded structure of bones . Anatomically, graded structures of bone are illustrated with the surface cortical bone toward the inner cancellous bone. The porous structure inside the cancellous bone promotes nutrient and waste transportations for biological functions. Furthermore, the graded structures of bone are also controlled by the mechanical functions required for each area. Many studies have demonstrated that graded cellular bone TE showed the advantages to engineer material with specific structural, morphological, and mechanical properties [6, 7].
2. Fabrications of graded cellular bone scaffold
The scaffolds behave as a structure that promotes tissue formation, therefore the types of cell formations (fibroblast, chondroblast, and osteoblast) are controlled by the pore size, porosity, and surface properties of the scaffolds. The production of implant materials with high porosity allows good and fast bone growth, while the low-porosity materials can withstand early physiological mechanical stress .
Pompe et al.  reported that functionally graded material could give the implant a suitable strength to withstand the physiological loading, and that the graded porosity structure can optimize the material’s response to external loading. A similar feature of graded cellular bones might prove favorable to an artificial bone implant. Bone TE scaffolds with the graded cellular structures like bone structures could be fabricated using conventional and additive manufacturing techniques .
2.1. Conventional techniques
The porous materials can be created using porogens as a void spacer. The possible spacers  used are various, depending on the particle size and removing techniques, such as sodium chloride, carbomide, poly (methyl methacrylate), magnesium, and so on. The spacers used are subsequently removed by dissolving with solvents or burning-out (Figure 1).
Porous materials created with this technique use porogens to create the voids. The pore size is related to the porogen size. There are many types of porogens used as shown in Table 1.
Using magnesium as a spacer is suitable for porous metal fabrication during powder compaction and sintering process, since it has a relatively high strength and elastic modulus (45 GPa) and high melting temperature (650°C) compared to polymeric spacers . Graded porosity scaffolds are further created as the composite-laminated materials. Material-porogen mixtures of different porosities are prepared with paste and filled into a mold layer by layer to form laminated multiporous layers (Figure 2) .
Although the pore sizes are related to sizes of a spacer, an uncontrolled microstructure contributes to internal stress concentrations located around the structural defects . This technique is, therefore, applied to create biomaterials with pores in nano- to micro-scale, and is combined with an additive manufacturing technique to control the micro- to macro-scale architectures.
2.2. Additive manufacturing (AM) techniques
AM techniques have been introduced to TE, recently. The benefits of AM techniques improve the well-defined architectures of the scaffold fabrications according to the designs controlled by computer-based methods. Mimicking the porous structures of bone tissues, an internal architecture of the scaffolds, significantly affects nutrient diffusion, cell adhesion, and matrix deposition of the regenerated tissues. Scaffolds have to be carefully designed to match specific mechanical, mass transport, and biological requirements; however, customizing the architecture to better suit these requirements remains a challenging issue.
Computer-aided designs (CAD) and computational simulations using finite element analysis (FEA) have played a major role in the reduction of in vitro and in vivo experimental efforts and costs. Furthermore, the accuracy of FEA results is acceptable to predict a design optimization before the manufacturing. An overview of this design paradigm is reported in Figure 3.
The images in STL file are directly processed with computer-aided manufacturing (CAM) in order to print the specimens in layer. Selective laser melting (SLM) techniques have shown capability of 3D cellular structure production through printing of layered structures based on CAD (Figure 4) [19–21]. During SLM, metallic powder is melted by a scanning laser beam , featured by excellent reproducibility and efficiency . The limitations of SLM are the quality of the print which depends on the process setting parameters. Poor setting parameters such as layer thickness, laser-beam spot, laser power, and hatching space contribute to incomplete melting of the metal powders. Furthermore, the minimum scale that can process is limit the lattice thickness and pores in hundreds micrometer. Although, the scale limitation of the print is larger than nano-scale of the real bone, these SLM-processed structures are adequately to allow bone ingrowth (>300 μm).
The methodological approaches for the design of scaffold architectures are classified into the architecture formed by the repetition of unit cells (cellular structures) or that consisting of lattices (lattice domain). This collection of unit cells is also known as computer-aided system for tissue scaffolds (CASTS). Chua et al. [23, 24] and Cheah et al.  have developed a parametric library of scaffold structures and an algorithm to automate the entire process of matching desired anatomical shapes in order to reduce the time-consuming processes. Figure 5 shows examples of the unit cells used in CASTS.
Limmahakhun et al.  emphasized that the internal architectures of scaffolds play a crucial role in determining the overall mechanical and biological performances. It is interesting to note that the mechanical response from a cellular structure depends on the loading modes. The cubic structure [0° ± 90°] has much higher compression stiffness but lower shear and torsion stiffness than that in octahedron-type structures [±45°]. The pillar octahedron combined with the strut characteristics featured along 0° and ±45° demonstrates high compression, shear, and torsional stiffness (26.94, 18.93, and 9.52 MPa, respectively). To this end, for axially loaded applications, such as bone implants to fix long-bone defects, the cubic structure is the best choice because of its high stiffness under compressive force. High fatigue life under compression loading was observed in cubic unit cells . On the other hand, when subjected to a combined loading (compression, shear, and torsion), such as femoral hip implants, the pillar octahedron is an appropriate architecture as it provides the greatest shear and torsional stiffness and high compressive stiffness. Note that the pillar octahedral structure also has the greatest accumulated stress during the stress relaxation test .
Unit geometry directly controls the tortuosity, a measure of flow distance that travels in the porous materials . The strut intersection in the middle of octahedral types diverts the fluid from the straight direction and slows down the flow rate (Figure 6b). The low flow rate when pipetting a cell suspension onto the pillar octahedral shapes would favor cell adherence (Figure 6d–f), while the high flow rates of cubic and truncated octahedral shape contribute to cell deposition at the bottom of the well. The greater cell proliferation of the pillar octahedron could be attributed to the greater surface areas of these polyhedral structures that are printed with 3D printing techniques, compared with the cubic and octahedron (Figure 6a). Together with its better cell proliferation rate, pillar octahedral structure has demonstrated balanced mechanical and biological properties.
CAD-based methods [28, 29] and implicit surface modeling (ISM) methods [18, 30] are common to create the cellular structures with porosity-graded structures, since the internal architectures are fully controlled with no hanging edge [18, 31]. For the CAD-based methods, graded structures of the pillar octahedral scaffolds could be attained by varying the architectural parameters, such as lattice diameter (t) and unit size (L) (Figure 7).
The graded cellular bone scaffolds with desired porosity and pore size on each location could be done using manual or automatic algorithm processes. The primitive unit cell that is recommended by the author’s works is the pillar octahedral shape . Our findings proved that this unit has balanced mechanical and biological performances for bone tissue regenerations. Figure 8 shows an example of pillar octahedral unit cells with different porosities and graded patterns; axially and radially graded patterns, fabricated with cobalt chromium (CoCr) alloys using SLM techniques. Manually mating the unit cells inside the graded cellular bone scaffolds could be fully controlled with no error, however it is time-consuming.
On the other hand, ISM allows scaffold architectures to be easily described using a single mathematical equation, with freedom to introduce different pore shapes and architectural features, including pore-size gradients. Although, automatically processing time based on the algorithm is more convenient compared to the CAD-based method, the algorithm that could perfectly serve the required graded internal architectures of the scaffolds with no internal defect is more complexity. While many of the ISM are available, both of the Schwarz’s Diamond and Schoen’s Gyroid shapes are preferable in promoting cell migration and tissue ingrowth . Furthermore, these techniques are suitable to create the graded cellular structures.
3. The effects of graded cellular bone scaffolds
Designing an architecture of the scaffolds that mimics the complex structure of bone tissue is the new generation of bone tissue engineering . Scaffolds with graded cellular structures behave similar to the bone that is replaced. Furthermore, porosity gradation affects the types of cell regeneration and promotes the environment to be more suitable for cell functions. While the biological cell interactions are directly influenced by the porosity gradation, the mechanical performance which is affected by porosity and cellular structures could be modified to match the desired functionalities. The improved tissue regeneration rate of graded cellular structures led the research community to find the possible models of bone tissue engineering. However, such model has not been developed yet.
3.1. Biological cell interactions
Different layers of the tissue perform different roles in maintaining the organ functions. Each cell type has individual specific functions and is important for tissue formations. Bone, cartilage, and ligament are formed simultaneously as a bone and joint structure, as a result of tissue formation by osteoblast, chondrocyte, and fibroblast cell-types, respectively. The graded cellular bone scaffolds are critical for multitissue regenerations such as bone and cartilage tissues  and ligament-bone interface . These cell types have obviously different environments, thus scaffolds should be tailored with different pore sizes and porosities. For example, fibroblasts (cell size 20–50 μm) can span void spaces up to 200 μm . On the other hand, the preferred pore diameter for osteoblast (cell size 20–30 μm ) is 100–350 μm .
Beside the pore size, porosity and pore interconnection also facilitate bone ingrowth. The scaffold with porosity >90% and pore interconnection promotes more cell infiltration, proliferation and extracellular matrix deposition, since it has a better flow mechanic for nutrient and waste transportation  and allows cellular signals between interconnecting networks . Furthermore, the graded cellular structures also increase the fluid permeability and flow, which enhances the cell diffusion throughout the whole scaffolds [40, 41].
Since different pore sizes affect the type of cell formations, graded cellular scaffolds potentially produce the multi-tissue grafts on the bone-ligament interface by following the phenotypic gradients that exist at the natural ligament-bone interface. In addition to the graded features in architectures, graded features in terms of different material compositions also promote biologic functions like bone materials. Two materials with spatially graded fraction of polymer and hydroxyapatite (HA), fabricated with co-electrospinning techniques, are found to be metabolically active from the study of rat bone marrow stromal cell cultures . Gene expression of bone morphogenic protein-2 and osteopontin was elevated on mineral-containing regions as compared to regions without mineral, which confirmed osteoblastic phenotypic maturation of this polymeric-HA graded scaffolds by day 28.
Computational study has been utilized to optimize the best porosity distribution in functionally graded scaffolds for bone tissue engineering . Based on the porosity distribution law, the graded scaffolds with tri-linear law promote larger amounts of bone formation compared to the models of bi-linear, linear, and constant laws. Alternatively, the more the complexity of porosity distribution laws (i.e., with increasing number of coefficients, Ai), the better the scaffold geometry can be tailored. A larger number of design variables increases the probability that optimizes a geometry to match the specific boundary and loading conditions.
The effect of the loading conditions appears more critical. Boccaccio et al.  showed that the loading conditions are essential in determining optimal porosity distribution. For a pure compression loading, it was predicted that the changes of the pore dimension are marginal, and using a graded cellular bone scaffold allows the formation of amounts of bone slightly larger than those obtainable with a homogeneous porosity scaffold. For a pure shear loading, instead, bone formations of graded cellular bone scaffolds are significant compared to a homogeneous porosity scaffold. While increasing the pore diameters leads to an increased value of the scaffold Young’s modulus, increasing a porosity distribution law makes a scaffold generate larger amounts of bone formations. Graded porosity characteristics contribute to optimized loading distributions, which enhances sensing signal to maximize osteoblastic cellular activities, as termed as mechanobiologic signal.
3.2. Mechanical performances
A scaffold should have the mechanical properties sufficient to maintain integrity until the new tissue regeneration. Bioceramics (hydroxyapatite, bioglass, etc.) and metals (titanium, tantalum, cobalt chrome, etc.) have been commonly used as a biomaterial for bone tissue regeneration. The limitation of bioceramics is their brittleness and contributes to easily break after replacements. While greater stiffness, endurance, and strength of metals are preferred, the higher stiffness of metals shields the stress distributed to the adjacent bone tissue and leads to bone resorption called “stress shielding.” Therefore, the mechanical properties of the scaffolds should match that of the native tissue to both prevent stress shielding and give proper mechanical performances.
Despite the types of materials used for fabrications, the relative modulus of cellular materials (E/Es) has a power law relation to the relative density (ρo/ρs), based on Gibson and Ashby model :
where E and Es are the moduli of base and cellular materials and ρo and ρs are the density of base and cellular materials. This relationship depends on the unknown coefficients (ϕ and n) which are a factor of each cellular unit.
The cellular structures with various relative densities can be created by varying the diameter of the beam thickness (Figure 7). The moduli and strength of those cellular scaffolds can be predicted upon the relative density, as shown in an example of cobalt chrome (CoCr) cellular structures (Figure 9). It is clear that the elastic modulus (stiffness), yield stress, and ultimate compressive strength of cellular structures increase with decrease in the porosity. The CoCr cellular structures of pillar octahedron have stiffness and compressive strengths between 2.33–3.14 GPa and 113–523 MPa, respectively, which are comparable to those of cortical bone tissues (2.73–17 GPa  and 100–150 MPa ). In addition, these CoCr cellular structures also demonstrated a greater energy absorption (24.6–116.86 MJ/m3) than bone tissues.
Unfortunately, the quality of the SLM-built is a major concern that affects the scaffold reproductions. Although FEA could predict the modulus of cellular scaffolds, the accuracy of the prediction is low . Poor correlation between FEA and physical testing results from an incomplete melting of the metal powders. Internal voids of the printed scaffolds increase the stress concentration, and crack may occur, weakening the scaffold constructs (Figure 10). Completely selective-melting process in each layer of the manufacture plays a main role to minimize such error of the prediction.
The mechanical properties of titanium alloys fabricated with SLM have been extensively studied under static and fatigue loadings [19, 21, 47–51]. Although titanium cellular structures have similar stiffness as bone tissues, fatigue is still a technical issue, which mainly resulted from poor design of the internal architectures [19, 52]. Naturally, the implant is expected to have similar properties as bone. Structural gradient has been observed in bone tissues, depending on required functions, such as load-bearing capacity and biological properties . However, under axial compression, there is no benefit of graded cellular bone scaffolds over a uniformed bone scaffold with the same relative density . Figure 11 shows that CoCr graded cellular structures have similar elastic modulus, yield strength, and compressive strength as the uniformed cellular structures. CoCr cellular scaffolds and graded cellular scaffolds with the porosity ranging from 40 to 70% exhibit elastic modulus around 2.7–3.1 GPa, which is in the same level of bone stiffness [44, 53]. Therefore, mechanical properties of the cellular bone scaffolds are mainly related to the relative density rather than the porosity-graded characteristics.
The opposite findings were noticed with the bioceramic graded cellular scaffolds. Wang et al.  studied a novel calcium polyphosphate bioceramic scaffold with a graded pore structure similar to the bimodal structure of cortical and cancellous bones (Figure 12). The compressive strength of porosity-graded calcium polyphosphate (PG-CPP) scaffolds was better than that of homogeneous calcium polyphosphate (H-CPP) scaffolds, which was significant (p < 0.05) at each time point. This fact is also noted that, after 28 days of degradation, the compressive strength of PG-CPP scaffolds was even greater than that of primary H-CPP.
It is still controversial whether the graded cellular scaffolds can improve the mechanical properties of the constructs compared to homogeneous scaffolds. The bioceramic scaffolds with a porosity-graded structure in this study have a much better mechanical property. PG-CPP gives a prolonged deflection besides the elastic deformation which indicates that the porosity-graded scaffolds exhibit a different fracture behavior from that of the homogeneous scaffolds. Furthermore, PG-CPP exhibits nonbrittle fractures whereas the H-CPP fractures catastrophically. Hence, it may be inferred that the mechanical properties of the porosity-graded scaffold can be substantially improved by a graded porous structure . To end this, types of materials used for fabrications, internal structures of the scaffolds, and the design of graded scaffolds play an important role to control the mechanical properties of the graded cellular scaffolds.
Although both homogeneous and porosity-graded metallic bone scaffolds show a reasonable mechanical strength, the benefits of cellular graded structures optimized the functions required for such scaffold. Metallic cellular structures have lighter weight than solid metals, since an introduction of pores inside the materials. The stiffness of cellular structures can be tailored to match that of bone, according to the design and density of the scaffold’s architectures. The stiffness of the cellular bone scaffolds is related to the porosity, following a nonlinear relationship as reported by Gibson and Ashby . Therefore, the cellular bone scaffolds share more of the stress to an adjacent bone tissue than the solid counterpart due to the lower stiffness of the scaffolds.
Basically, the cellular structural implants with low stiffness properties reduce the peri-prosthetic bone-stress shielding, yet increase the bone-implant interface failure. Figure 13 shows that more peri-implant bone-stress shielding occurs with the high-stiffed implant, and finally increases higher risks of the implant loosening. The initial stability of a femoral stem is necessary for biological bony ingrowth, which can be secured by minimizing relative micromotion at the bone-implant interfaces. Excessive micromotions (>150 μm) allow fibrous connective tissue to grow, which prevents bone ingrowth between the contact surfaces and leads to aseptic loosening and failure of the implant [54–56]. Although homogeneous cellular implants increase stress sharing to peri-prosthetic bone due to lower construct stiffness, the greater interface failure due to excessive micromotions (>150 μm) adversely causes an initial implant instability and inhibits bone osseointegration.
According to computational study , the porous femoral stem with uniform relative density of 50% is approximately three times more flexible than the titanium stem. This implant can qualitatively simulate the behavior of an implant made out of tantalum foam using the well-defined cellular structures. The amount of bone resorption and the interface failure index of this stem are about 34% and 2.87, respectively, and the interface failure is maximum (0.71) at the edge of the proximal region. Compared to the solid titanium implant, the amount of bone resorption decreases by 50%, whereas the maximum interface failure increases about 40%. This shows that a decrease in the implant stiffness with uniform porosity distribution aiming at reducing bone resorption has the undesirable effect of increasing the risk of interface failure at the proximal region.
Kuiper and Huiskes  showed that the use of a graded material in an orthopedic stem can lead to a reduction of both stress shielding and bone-implant interface failure. The bone resorption and interface failure of graded cellular stems are 16% and 1.15, respectively . The peak value of the local interface failure is 0.25. Compared to the titanium stem, both the amount of bone resorption and the peak of interface failure were decreased by 76 and 50%, respectively. With respect to the uniformly distributed cellular implant, the decrease in bone resorption and interface failure peak is of 53 and 65%, respectively. A graded cellular implant with optimized relative density distribution is thus capable of reducing concurrently both the conflicting objective functions. In particular, bone resorption reduces as a result of the cellular material which makes the implant more compliant; the interface stress and micromotions, on the other hand, are minimized by the optimized gradients of cellular material.
Furthermore, for designing the scaffolds with functionally graded structures to mimic the graded structures of the host bone, the stress sharing to the adjacent bone is increased around 50% compared to the uniformed cellular bone scaffolds . The degree of proximal bone-stress sharing depends on a porosity-graded orientation. In case of intramedullary implants, such as femoral stems, the scaffolds with porosity gradient along a longitudinal plane present the maximum stress distribution to the proximal bone (Figure 14).
Graded cellular implants are functionally designed to match the mechanical and morphological properties of bones. While the graded metallic cellular implants exhibit mechanical properties similar to the uniformed cellular implants, the graded one is more capable of preventing bone-stress shielding and promoting larger amounts of bone ingrowth to the implants. The optimized designs of biomimetic graded cellular implants are complex depending on the functional objectives of the constructs.
The graded cellular bone scaffolds show logical concepts for bone tissue engineering. Cellular structures with graded pore sizes and porosities could mimic the graded structure in bones . The advantage of graded cellular structures over the uniformed cellular structures is that the former provide more realistic environment for biological and mechanical functions. For stress-sharing orthopedic applications, the axially graded cellular structure demonstrated balanced mechanical performances and maximized proximal stress transfers around a peri-implant material . Instead of using the uniformed cellular structures, we believe incorporating graded cellular structures in a structure like femoral prosthesis that will improve the load distribution in adjacent bones, greater bone osteointegration, and optimum nutrient permeability of the components .