Numerical investigation of the mechanical properties of the additive manufactured bone scaffolds fabricated by FDM: the effect of layer penetration and post-heating

In recent years, thanks to additive manufacturing technology, researchers have gone towards the optimization of bone scaffolds for the bone reconstruction. Bone scaffolds should have appropriate biological as well as mechanical properties in order to play a decisive role in bone healing. Since the fabrication of scaffolds is time consuming and expensive, numerical methods are often utilized to simulate their mechanical properties in order to find a nearly optimum one. Finite element analysis is one of the most common numerical methods that is used in this regard. In this paper, a parametric finite element model is developed to assess the effects of layer adhesion on the mechanical properties of bone scaffolds. To be able to validate this model, some compression test specimens as well as bone scaffolds are fabricated with biocompatible and biodegradable poly lactic acid using fused deposition modeling. All these specimens are tested in compression and their elastic modulus is obtained. Using the material parameters of the compression test specimens, the finite element analysis of the bone scaffold is performed. The obtained elastic modulus is compared with experiment indicating a good agreement. Accordingly, the proposed finite element model is able to predict the mechanical behavior of fabricated bone scaffolds accurately. In addition, the effect of post-heating of bone scaffolds on their elastic modulus is investigated. The results demonstrate that the numerically predicted elastic modulus of scaffold is closer to experimental outcomes in comparison with as-build samples.


Introduction
Tissue engineering is ''an interdisciplinary field that bring the principles of engineering and life sciences together to develop biological substitutes in order to restore, maintain, or improve tissue function or a whole organ'' (Godbey and Atala, 2002). Although treatment methods like allograft and autograft are the gold standard for treatment of some diseases and tumors, they have undeniable deficiencies. As an outstanding example, fracture, nonunion and infection are some complicated drawbacks of more than 30% of the allograft procedures and also requiring high volume of bone in autograft method (DE LONG et al., 2007;Doyle et al., 2015). Therefore, researchers have gone toward preparation of suitable structural frameworks named bone scaffold to provide a support for cells (Jariwala et al., 2015;Poh, 2014). Such structures should have appropriate geometrical and mechanical properties in order to provide suitable bone treatment (Giannitelli et al., 2014;Sanz-Herrera et al., 2008;Yang et al., 2001). In this regard, Dias et al. (Dias et al., 2014) proposed a topology optimization algorithm for designing scaffolds that satisfy both mass transport and mechanical load bearing capacity.
In addition to the desirable shape for defected site, bone scaffolds should have enough porosity and pore interconnectivity to provide the possibility of cell ingrowth and nutrition exchange (Brown, 2000;Hollister and Lin, 2007;Mullender et al., 2004). In addition, the base material's properties such as biocompatibility and bioresorbability are of vital Importance for the design of bone scaffolds. Furthermore, a bone scaffold should have appropriate surface chemistry and adequate mechanical properties with respect to its application (Hutmacher, 2000). Until now, both synthetic and natural polymers have been studied as scaffolds for bone tissue engineering applications . The results of these investigations show that a polymer-based scaffold should have a three-dimensional porous matrix.
There are various processing methods for producing bone scaffolds (Widmer and Mikos, 1998) from conventional ones like phase separation (Gao et al., 2003), emulsion freezedrying (Whang et al., 1995), gas foaming (Harris et al., 1998), fiber templates (Thomson et al., 1995) and porogen leaching (Mikos et al., 1993;Zhou et al., 2005) to additive manufacturing (AM) techniques (Hutmacher, 2000;Moroni et al., 2006). Over the past decades, due to the possibility of fabricating complex microstructures with controllable pore shape and size, AM techniques have been widely utilized for fabrication of bone scaffolds. In fact, these techniques are able to eliminate various drawbacks of conventional methods, e.g. uncontrollable structure.
AM techniques are divided into seven categories including powder bed fusion, extrusionbased, material jetting, binder jetting, sheet lamination, directed energy deposition and vat photopolymerization processes (Gibson et al., 2015). Fused deposition modeling (FDM), which is based on depositing a thread of molten thermoplastic material onto a substrate, is a low cost extrusion based AM technique. In addition to various significant benefits, like lack of any need to solvent, FDM presents unique features of ease and flexibility in material selection, processing and simplicity of fabrication process. Also, using from materials in filament shape allows nonstop production without consuming any time for replacing feedstock (Zein et al., 2002). A schematic of FDM process is shown in Figure 1.

Figure 1. Schematic diagram of the FDM machine
Although FDM has become more and more popular in the last decade, fabrication of numerous compressive specimens as well as bone scaffolds is really time-consuming causing it to not be economically recommended. Accordingly, finite element method (FEM) is used to overcome this deficiency by predicting the mechanical response of FDM parts before fabrication (Martínez et al., 2013) causing the reduction of the final fabrication cost by decreasing the required experimental measurements (Liu and Zheng, 2010). Also, if the mechanical behavior of bulk material of tissue scaffolds are identified, then with the assistance of FEM, it is possible to predict the behavior of complex formations such as mechanical response at microscopic level during the cell differentiation (Sahai et al., 2016). There are several studies in the literature which are concentrated on the numerical analysis of bone scaffolds, especially using the finite element method. This method has been utilized effectively for the prediction of mechanical properties of additive manufactured scaffolds (Giannitelli et al., 2014). Boccaccio et al. (Boccaccio et al., 2011) developed computational mechno-regulation models for determining porosity as well as structural response of scaffolds during the time. Wieding et al. (Wieding et al., 2014) optimized the geometrical parameters of porous scaffolds to match the elastic modulus of human cortical bone. Laurent et al. (Laurent et al., 2014) proposed a finite element model for predicting the geometrical evolution of a biodegradable polymer scaffold for ligament tissue engineering. FEM is also used to predict the mechanical response of bone scaffolds as well as cellular lattices structures Kadkhodaei, 2015, 2013;M R Karamooz Ravari et al., 2015;Mohammad Reza Karamooz Ravari et al., 2015;Ravari et al., 2014). The results of these investigations show a good agreement with those obtained from experimental measurements. Apart from FEM literature, there are plenty of studies on the experimental work in this area. As an outstanding example, Sudarmadji et al. (Sudarmadji et al., 2011) fabricated polymeric tissue scaffolds with various structures as well as porosity values implementing selective laser sintering technique. They reported the stress-strain curves of the performed compression tests and showed that the stiffness of the fabricated scaffolds matched with the properties of the cancellous bone. Additionally, Scaffaro et al. (Scaffaro et al., 2016) reported that pore architecture has a paramount effect on the mechanical properties by performing various compression tests. Ang et al. (Ang et al., 2007) worked on the fabrication of PCL/HA composites as a structure which could be applied in tissue engineering. They reported that the obtained composition had improved compressive properties rather than polymeric structures fabricated by PCL with respect to the performed mechanical tests.
The main goal of this study is to develop a finite element model for predicting the elastic mechanical response of porous polymeric bone scaffolds fabricated by fused deposition modeling approach. Hence, some bone scaffolds are fabricated by FDM technique using appropriate geometrical parameters reported in the literature. For this purpose, a specialized program is developed as a G-Code for the fabrication of bone scaffolds via FDM machine. To be able to characterize the bulk material of the bone scaffolds for modeling purposes, some compression test samples are fabricated too. All the samples are tested in mechanical compression and their stress-strain response is obtained. Considering the amount of layers' adhesion, a parametric finite element model is developed to simulate the mechanical properties of the bone scaffolds. The layer adhesion is defined as the inter-layer bonding of the extruded struts as it was defined by Gurrala and Regalla (Gurrala and Regalla, 2014). The elastic modulus obtained numerically is compared with the experimentally measured one and a good agreement is observed. Moreover, the effects of struts' diameter and layer adhesion on the elastic modulus of the bone scaffolds are investigated. Finally, the effect of post-heating is studied and experimental results are compared with the outcomes of the proposed finite element model.

Materials & methods
In this section, first of all, the fabrication process of the bone scaffold is presented. Then, the mechanical compression test is briefly reviewed. Finally, the proposed finite element model is presented.

Fabrication of scaffold
As mentioned before, fabrication of bone scaffolds are performed based on parameters reported in other researches. One of the most important biological features which should be taken into account is the pore size of the bone scaffolds (Annabi et al., 2009;Cicuéndez et al., 2012;Sondergaard et al., 2012;Zimmermann et al., 2008). The appropriate range of porosity for bone regeneration was determined through experimental investigations of biomaterials (Yang et al., 2001). Zein et al. (Zein et al., 2002) suggested that bone scaffolds' pore size should be in the range of 160 -700 micron. A library for the structure of bone scaffolds produced via additive manufacturing was reported by Chua et al (Cheah et al., 2003a(Cheah et al., , 2003b.
In this study, all the scaffolds are designed with the pore size and struts' diameter of 350 and 700 micron, respectively. For this purpose, a G-Code program is developed so that it contains all the considerable parameters like the amount of struts' diameter and pore size. This G-code data will then be used as the input of FDM machine.
Poly lactic acid (PLA), a biocompatible and biodegradable polymer, supplied by Shenzhen Esun Industrial Company (natural grade) is used for the fabrication of bone scaffolds. Some properties of the PLA polymer filaments applied in the fabrication process are shown in Table 1.  Figure 2 shows one porous bone scaffold fabricated by FDM machine.

Characterization 2.2.1. Compression tests
Since the bone scaffolds are used as bone implants, their compressive mechanical response is of importance. To assess the compressive response of the fabricated bone scaffolds, specimens are prepared based on ISO 604/B1 standard (ISO 604:2002, Plastics-Determination of compressive properties, 2002. According to this standard, samples are cut from larger blocks into 10 10 3 mm 3 and tests are carried out with a velocity of 1 mm/min a b (strain rate of approximately 42 10 -4 S -1 ) and a preload of 1.5 N. All the compression tests are performed on HOUNSFIELD (H50KS) (Shakopee, USA). Figure 3 demonstrates

Microscopic images
To be able to characterize the microstructure of the fabricated scaffolds, some microscopic images are taken. All these images are captured by the versatile digital microscope (Dino-Lite Company, Netherlands) with 50 times magnification. The height of the microscope is changed in order to achieve an appropriate quality.

Finite element model
For predicting the mechanical behavior of the fabricated bone scaffolds, a python script is developed to generate parametric finite element model through the finite element package ABAQUS 6.11-1. In this subsection, this finite element model is presented in details.
As shown in Figure 4, the finite element model is constructed by repeating some cylinders with the diameter of D in X, Y, and Z directions. The axis of the cylinders of each layer is perpendicular to that of its upper and lower layers. N x , is the number of cylinders in x direction, N z the number of cylinders in z direction, N yx the number of cylinders parallel to x in y direction, and N yz the number of cylinders parallel to z direction in y direction. The cylinder of a layer is penetrated to those of its upper and lower one. This value is defined with δ m as the amount of inter-layer bonding, meaning the amount of layer adhesion. The distance between two neighbor cylinders in the layers parallel to X and Z axis can be different which are indicated by parameters R x and R z , respectively. Moreover, P x and P z are defined as the amount of extra material exceeding from the main borders of scaffold in x and z direction, respectively. To be able to model the uniaxial compression test, the upper and lower layers of the bone scaffold is cut with the value of δ end . It is worth mentioning that PLA used in this research has lower shrinkage rather than other materials like ABS. Consequently, as one of the model assumptions, the effect of shrinkage is not included in the developed model.  According to what mentioned above, the geometry of the finite element model can be described using D, R x , R z , P x , P z, δ m , δ end , N x , N yx , N yz, and N z parameters. Referring to the model, the bone scaffold's dimension in x, y, and z directions can be calculated using the following equations respectively.

Results
In the following subsection, first, the microstucture of the fabricated bone scaffolds as well as their compressive mechanical response are presented. Then, the results of finite element simulations are discussed. Figure 6 shows one fabricated bone scaffold and its microscopic images. Using the microscopic images, the pore size and struts' diameter measured to be 0.7 ± 0.12 and 0.35 ± 0.08 mm, respectively. As it can be seen, the average value of these two parameters is nearly equal to that defined in the G-code. Also, the amount of scaffold's porosity is measured by Archimedes principle which is about 40 percent.

Finite element model
The geometrical parameters obtained from microscopic images are used to generate the finite element model. Table 2 shows the geometrical parameters used for the present simulations. In addition, the value of loading parameter, Δ, is supposed to be 0.2 mm. Using these geometrical parameters the dimensions of the bone scaffold is calculated to be about 10.17, 3.06, and 10.17 mm in x, y, and z directions, respectively. All the simulations are performed on 2.93 GHz processors with 24 cores and 24 GB RAM provided by National High-Performance Computing Center of Isfahan University of Technology. The model is meshed using 10-node modified quadratic tetrahedron elements with four integration points denoted by C3D10 in ABAQUS. Figure 9 shows the meshed configuration of the model. As shown in Figure 10, a mesh sensitivity analysis is conducted by repeatedly reducing the mesh size and rerunning the analysis until changes in the results are negligible. Using this method, the value of 0.6 is obtained for the mesh size and used for all the simulations. The numerically calculated elastic modulus of the bone scaffold is about 213.21 MPa which is about 16.11 % higher than that obtained experimentally. This difference can be due to the existence of some microstructural defects in the microstructure of the scaffold. Karamooz  and Karamooz Ravari et al. (M R Karamooz Ravari et al., 2015;Ravari et al., 2014) showed that the microstructural imperfections can severely affect the mechanical response of porous materials as well as cellular lattice structures.

Discussion
In this section, first, the effects of geometrical parameters including struts' diameter and layer adhesion on the elastic modulus of the bone scaffold is investigated using finite element approach. Finally, the effect of post-heating on the elastic modulus of fabricated bone scaffolds as well as compression test samples are assessed through experimental and numerical investigations. Figure 11 shows the elastic modulus of the bone scaffold for three different values of struts' diameter. According to this figure, the elastic modulus increases by increasing the value of struts' diameter as a result of lower porosity. Although increase the amount of strut diameter enhances the bone scaffold elastic modulus, its biological features such as pore size will be affected. In a fixed value of porosity, increase the amount of strut diameter (by having low numbers of wider ligaments) lead to restricted conditions for transporting nutrition because of a considerable decrease in pore size. This is where that the importance of being a balance between mechanical and biological properties shows itself. Figure 11. Investigation of the effect of struts' diameter on the elastic modulus of bone scaffold Additionally, strut diameter determines fusion which has an inevitable effect on the mechanical properties of bone scaffolds. Numerous studies were reported on the bone scaffolds fabricated by melt electrospinning with smaller strut diameter rather than FDM technique Visser et al., 2015). While in methods like FDM the strut diameter is restricted to greater than 100 micron, melt electrospinning could obtain lower diameters (Brown et al., 2011). For evaluating whether other techniques which could provide smaller strut diameter have any effect on the mechanical properties or not, another study is done. In a fix amount of porosity (about 40%), three groups of scaffolds are investigated from mechanical point of view with strut diameter of 0.49, 0.62 and 0.7 mm. As it is shown in Figure 12, smaller strut diameter, in a fix amount of porosity, has higher elastic modulus. Thus, methods like meltspinning could be utilized as an effective method for fabricating scaffolds with enhanced elastic modulus in comparison with FDM technique. The effect of layer adhesion on the elastic modulus of the fabricated bone scaffolds is shown in Figure 13. It can be concluded from this figure that there is a direct correlation between layer adhesion and elastic modulus. The elastic modulus increases almost linearly by the value of layer adhesion.

Investigation of post-heating effect on the elastic modulus
To achieve desirable futures of a fabricated part, post-heating of those parts may be applied. In this study, the proposed model does not include post-heating. However, it is suggested that post heating could enhance mechanical properties (Perego et al., 1996). To do so, some scaffolds with the struts' diameter of 700 and pore size of 350 micron are heated up to 3 more than crystallization temperature of the PLA which is about 115 . They are kept for 300 seconds at this temperature and then cooled down to the room temperature. Figure  As it can be seen, the elastic modulus of the post-heated scaffold as well as bulk sample is higher than that of the as-build samples. It can be justified in such a way that by holding the samples at a sufficiently high temperature for a reasonably enough time, the layers of the material stick to each other more than the layers of the as-build samples. In other words, as a hypothesis, it is assumed that this increase in due to raise the amount of inter-layer bonding amongst solidified struts. Accordingly, a more uniform material distribution is obtained causing higher stress level in the stress-strain curve in a specific value of strain. In addition, there might be some micro-pores in the structure of the as-build samples which would be filled after post heating of the samples which lead to more pronounced mechanical properties. Beyond the effect of layer adhesion on the mechanical properties of the FDM parts, this factor could affect tribological behavior of them as a paramount factor which plays a decisive role in their friction coefficient and friction force. It was reported that the wear mechanism of the FDM parts fabricated by ABS is according to de-lamination (Boparai et al., 2015). Consequently, post heating could increase adhesion bonding which could enhance tribological properties of FDM parts generally such as greater wear resistance as well as lower friction coefficient. In addition, control of accuracy and precision is really important in FDM parts. Berger (Berger, 2015) reported the aspects of accuracy in the additive manufactured plastic gears. Although increase of the layer adhesion could improve mechanical properties, it could decrease the dimensional accuracy. Thus, for those applications which dimensional accuracy is important, post heating could decrease the accuracy in despite of increasing the layer adhesion.
The numerically calculated elastic modulus of the bone scaffold is about 210.32 MPa which is 0.02 % higher than that obtained experimentally. It shows that developed model could predict the elastic modulus of post-heated bone scaffolds more accurately in comparison with as-build ones. Due to strict adhesion of layers and existence of fewer pores in the postheated bulk samples, their stress-strain response is more accurate in comparison with that b of the as-build samples. In addition, the layers of the as-build bone scaffolds are more defected than those of the post-heated samples. However, the effects of these defects are not taken into account in the finite element model. According to what mentioned above, the predictions of the model is more accurate for the post-heated samples.

Conclusions
The main goal of the present study is to investigate the mechanical response of polymeric bone scaffolds fabricated by fused deposition modeling. To do so, some bone scaffolds are designed and fabricated using suitable geometrical parameters. To be able to characterize the bulk material of the bone scaffolds, some compression test specimens are also fabricated. All the specimens are tested in compression and their elastic modulus are obtained. Using the material parameters of the compression test samples as the bulk material of the bone scaffold, a parametric finite element model is also developed to predict the elastic response of the bone scaffolds. The obtained numerical elastic modulus is compared with the experimentally measured one showing a good agreement. In addition, the effect of layer adhesion which is inseparable part of additive manufactured parts is investigated. The results show that by increasing the value of layer adhesion, the elastic modulus increases significantly. Finally, the effect of post-heating of bone scaffold as well as compression test samples on their mechanical response is investigated. The results show that post-heating of both bone scaffold and compression test sample increases the value of their elastic modulus. The numerically obtained elastic modulus is about 213.21 MPa and 210.32 MPa for as-build and post-heated scaffolds respectively. These values are about 16.11% and 0.02% higher than the corresponding experimentally measured value. Based on the achieved outcomes, presented finite element model is an efficient numerical model for the investigation of the mechanical response of the bone scaffolds fabricated by FDM technique, especially post-heated ones.