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Fabrication of mechanically enhanced hydroxyapatite scaffold with the assistance of numerical analysis

Hydroxyapatite (HAp) has been found to be incompetent as it relates to its mechanical integrity, which somewhat restricts its use for load-bearing clinical applications. Several studies have been conducted doping HAp with foreign elements in order to enhance its mechanical integrity. However, it has been established that foreign elements usually trade off the phase structure and biological integrity of HAp. To avoid this challenge, this study presents a numerical analysis with the aim to fabricate a pure HAp scaffold with high mechanical strength, considering compaction and sintering protocols. The X-ray diffraction (XRD) and Fourier transformed infrared (FTIR) spectroscopy of raw bovine bones (RB) and HAp sintered at 900, 1000, and 1100 °C showed calcium phosphate contents of the bulk materials. It was also observed that increase in sintering temperature made prominent characteristic peaks of HAp phase to become narrower on the XRD patterns. The scanning electron microscope (SEM) analysis on the powdery samples showed that sintering temperature reduced HAp particle size, which resulted to the enhancement noticed in the mechanical properties of the fabricated HAp. Taguchi design analysis on the individual hardness and compressive strength revealed 1100 °C as the optimal sintering temperature, but a disparity in compaction load displaying 5 KN for high hardness and 15 KN for high compressive strength. Conversely, Taguchi grey relational analysis gave common optimal settings for high hardness and compressive strength to fabricate mechanically enhanced HAp scaffold, and are 1100 °C sintering temperature and 5 KN compaction load. Significantly, this study revealed that compaction load has a very high percentage of contribution of 90.15% compared to sintering temperature having a contribution of 7.79%. Confirmation analysis also proved that the experimental grey relational grade of 0.7824 is within 95% confidence interval.


Introduction
Hydroxyapatite (HAp) of biowastes (coral, bovine, or marine algae derived) or from synthetic source is commercially available for use in bone repair, substitution, and augmentation and as scaffolds in tissue engineering for bone regeneration. HAp is also used as abrasives to roughen metal implant surfaces and as source material for depositing bioactive coatings on orthopedic and dental implants. These materials can also be used as transfection agents, drug carriers, and percutaneous devices. HAp has been found to be disadvantaged as it relates to its mechanical integrity which somewhat restricts its use for load-bearing clinical applications. Therefore, extensive studies are geared towards methods that have the potential of enhancing the mechanical properties of HAp without overly compromising its bio-compatibility. These methods stem from tailoring the processing of the HAp powders, carefully optimizing the sintering temperature and its scaffold compaction loading [1][2][3][4][5].
Taguchi design strategy includes diminishing the variety in a cycle through hearty plan of tests. The general target of the strategy is to deliver top-notch product for minimal expense to the producer. The Taguchi strategy was created by Dr. Genichi Taguchi of Japan who kept up that variety. Taguchi fostered a technique for planning analyses to explore what various boundaries mean for the mean and change of a cycle execution trademark that characterizes how well the interaction is working. The test configuration proposed by Taguchi includes utilizing symmetrical clusters to put together the boundaries influencing the cycle and the levels at which they ought to be shifts. Rather than testing all potential blends like the factorial plan, the Taguchi technique tests sets of mixes. This takes into consideration the getting of data to figure out which factors most influence product quality with a base measure of experimentation, thereby saving time and resources. Several studies have been conducted employing Taguchi experimental design technique to fabricate pure HAp or composite HAp. Ranito et al. [6] used Taguchi design technique to investigate the effect and to optimize pH, reaction temperature, reagent concentration, and flow rate addition on Ca/P ratio of the synthesized HAp. The design analysis revealed that pH was the most influencing factor affecting HAp Ca/P ratio. Cizek et al. [7] employed Taguchi DOE and analysis of variance to investigate the effect of six different spraying conditions, namely, net power (5, 10, and 15 kW), main gas (40, 70, and 100 schf), auxiliary gas (20,50, and 80 schf), carrier gas (6, 9, and 12 schf), feed rate (2, 3, and 4 rpm), and spraying distance (50, 100, and 150 mm) on particles temperature and velocity of the sprayed HAp. It was observed that the Taguchi technique was able to reveal the three most influencing factors affecting the HAp particle temperature and velocity, and are net power, main gas flow, and spraying distance. Sadat-Shojai et al. [8] employed Taguchi orthogonal array to investigate the effect of pH (4, 6, and 9), flow rate of PO −2 4 precursor (5, 20, and 80 ml/h), temperature (50, 100, and 200 °C), and time (20,60, and 100 h) on the characteristics of HAp. This technique revealed the significant effect of pH and temperature on HAp fundamental characteristics. Ben-Arfa et al. [9] used Taguchi design to investigate the effect of pH, synthesis temperature, synthesis time, drying temperature, and calcination temperature on crystallite size, surface area, Ca/P ratio, and mol % of the synthesized HAp. The result revealed that calcination temperature was the only and most significant factor affecting the crystallite size and surface area of the synthesized HAp, while Ca/P ratio was mainly influenced by pH. Kadhim et al. [10] employed Taguchi design technique in the mixture of chitosan and HAp through electrophoretic deposition (ED). The design was used to optimize deposition parameters (voltage, time, concentration, and temperature) for better mixture coating layers, such as thickness, porosity, nanoroughness, and microroughness. The design revealed the optimum conditions to be 22 µm thickness, 3.53% porosity, 4.48 nm nanoroughness, and 3.85 µm microroughness. Ebrahimi et al. [11] utilized Taguchi design to investigate the effect of nanostructured alumina (3, 5, and 7 wt%), microstructured titanium (5, 10, and 15 wt%), and sintering temperature (1100, 1150, and 1200 °C) on the phase stability, structural and mechanical properties of HAp, and it was observed that with the help of Taguchi design, quantitative effect and the percentage of contributions of the considered factors on the properties of HAp were identified. Reger et al. [12] used Taguchi design to investigate and optimize Sr +2 , Zn +2 , Ag + , and F − ion doping on HAp crystallite size and crystallinity. Their results showed that crystallite size and crystallinity of HAp were significantly influenced by Sr +2 and Zn +2 doping compared to Ag + and F − doping. It was concluded from their study that doping composition with HAp can be tailored for desirable functional properties, namely, strength, bioactivity, and degradation for diverse implant applications. Nosrati et al. [13] employed Taguchi design to optimize hydrothermal processing time, total pressure, temperature, and wt% of graphene for enhanced mechanical properties of HAp. It was found out that hydrothermal temperature is the most influencing factor. Ahmed and Rehman [14] employed electrophoretic deposition (ED) to coat stainless steel substrates with zein/ HAp composite for orthopedic application. Taguchi DOE was used to optimize ED parameters, namely, HAp concentration in the polymer solution, applied voltage, and deposition time. The result revealed the optimum condition for zein/HAp suitable adhesion and higher corrosion resistance, and thereby increases the chance of the use of stainless steel in orthopedics. [2,3] employed Taguchi design technique to optimize sintering temperature (900, 1000, and 1100 °C) and compaction pressure (0 and 500 Pa) for better mechanical properties of HAp. The design revealed that production of HAp with better hardness and compressive strength is feasible with or without compaction pressure, but sintering temperature is an inevitable sintering parameter for better mechanical properties. Abifarin et al. [2] employed Taguchi design to optimize fabrication parameters and kaolin reinforcement for better mechanical properties of HAp. It was concluded that sintering temperature and reinforcement were the most essential factors to consider to fabricate high strength HAp.
The above literature review basically revealed that the addition of foreign elements can enhance the mechanical properties of HAp; however, foreign elements usually trade off the phase structure and biological properties of HAp. To avoid this challenge, this study presents a numerical analysis with the aim to fabricate a pure HAp scaffold with high mechanical strength, considering compaction and sintering temperature protocols. Grey relational analysis (GRA) is one of the most influential numerical analysis to optimize more than one performance characteristics of a system, processes, or materials [15][16][17]. GRA converts composite responses to a singular response that can be recognized by optimization software. Primarily, in this study, we first of all synthesized and characterized HAp from raw bovine bones using modified calcination. After which Taguchi orthogonal array design assisted by numerical analysis was employed in the fabrication of mechanically enhanced HAp scaffold for load-bearing clinical application. Taguchi grey relational analysis is a numerical analysis that is capable of identifying the best combination of HAp processing parameter levels to fabricate mechanically enhanced HAp scaffold suitable for load-bearing and biomedical application.

Hydroxyapatite synthesis and sintering
Raw cow bones (RB) were collected from an Abattoir in Zaria, Nigeria, and were used as a source to produce hydroxyapatite. The collected raw bones were first fired with charcoal to remove the bone's protein, collagen, and some organic components until no smoke was observed. The carbonization was done to avoid build-up smokes and pressure within the closed furnace. The carbonized bones were further taken into the an electric furnace for complete calcination at 900 °C at a ramp rate of 5 °C/min with 2 h of soaking time and allowed to furnace cool. The raw bones and the calcined sample were analyzed with SEM, XRD, and FTIR machines. Next, the calcined sample was crushed with a metallic mortar and pestle and sieved through a 300μm mesh sieve to obtain a fine powder. The powdery sample was cold-compacted in cylindrical shape (25 mm diameter and 10 mm thickness) under 5, 10, and 15 KN with universal testing machine (UTM). The fabricated scaffolds were sintered at 900, 1000, and 1100 °C for 2 h at the heating rate of 5 °C/min. The sintered scaffolds were analyzed with XRD and FTIR machines to know the phase structure and the functional group characteristics. Figures 1 and 2 show the experimental procedures for HAp synthesis and scaffold making, respectively.

Mechanical measurement
The micro hardness (HV) of the sintered scaffolds was investigated via the Vickers indentation with a MHV10002 micro hardness tester. The scaffolds were subjected to an applied load of 300 g for a dwell time of 10 s. A total of 5 indentations were made on each scaffold resulting to 5 hardness values for accuracy. The compressive strength of the scaffolds was performed using a universal testing machine (UTM), equipped with a 5 kN load cell. Five scaffolds were analyzed for each condition for accuracy (see Fig. 2).

Experimental design
According to the described processing procedures in Section 2.1, mechanical properties of HA scaffolds were evaluated with the consideration of two processing parameters, namely, sintering temperature and compaction load, each at three levels as shown in Table 1.
A Taguchi L 9 orthogonal array (OA) was employed with nine runs for the experiments as shown in Table 2. The mechanical characteristics were assessed using two response variables, namely, hardness and compressive strength (see Section 2.2).

Signal to noise (S/N) ratios in the Taguchi design method
The orthogonal arrays were employed in Taguchi method to minimize variance and optimize process parameters. The S/N ratio is used in Taguchi method as a performance characteristic to measure the strength of process and to evaluate the extent of deviation from the desired values [17]. In calculating the S/N ratio, a logarithmic function is computed by assessing the proportion of signal (mean) to the noise (standard deviation) [18]. Higher values of S/N ratios are preferred to minimize noise and the effects of uncontrollable factors [19]. High S/N ratios indicate better quality of a product. The higher-the-better, S/N ratio type was chosen because a higher hardness and compressive strength is desired, and it is shown in Eq. (1) [20,21].
where n is the experimental number; y i symbolizes the response value of the ith experiment in the OA.

Multi-mechanical characteristic optimization using GRA
Taguchi DOE method is sufficient to evaluate the optimal processing parameters for a single mechanical characteristic.
In the situation of two or more mechanical characteristics, with different quality characteristics, multi-mechanical characteristic optimization using GRA is the chosen method. When there is seemingly irregular finite data to be determined, grey analysis can also be employed data [22]. Hence, multi-mechanical characteristic (hardness and compressive strength) optimization of processing parameters in this study is conducted using the subsequent steps in GRA.

Grey relational generation
In data analysis with GRA, the function of the processing parameters is neglected when there is a high standard value and a high reference sequence range. In addition, if there is dissimilar goal compared with the directions of processing parameters, GRA may yield inexact results. Therefore,  pre-processing of data is done to normalize the original reference sequences to a comparable sequence within the range of zero to one [1][2][3][23][24][25]. Normalizing of data into a group of sequences is referred to as grey relational generation. The data in this study was normalized using the largerthe-better as shown in Eq. (2):

Fig. 2 HAp scaffolds making
where x i (k) is the normalized data for the ith experiment, and y i (k) denotes the initial sequence of the mean of the responses.

Grey relational coefficient and grade computation
After normalizing the sequence, the next step is to compute the deviation sequence of the reference sequence as shown in Eq. (3): , and x i (k) are the deviation, reference, and comparability sequences respectively. Next, the grey relational coefficient (GRC) is computed using Eq. (4): where i (k) symbolizes GRC of individual response variables calculated as a function of Δ min and Δ max , the minimum and the maximum deviations of each response variable. is the distinguishing coefficient (0 ∼ 1), but its equal weight of 0.5 is usually assign to each parameter. As reflected in Eq. (5), grey relational grade (GRG) is then calculated by averaging the GRC of each response variable: where i = the value of GRG determined for the ith experiment; n is the aggregate count of the performance characteristics.

Analysis of variance (ANOVA)
ANOVA is employed to know perhaps the processing parameters in the design of the experiment (DOE) have a significant effect on the evaluated material characteristics.
The ANOVA table has also been widely employed to analyze the interactions between processing parameters and the effect of such interactions on the dependent variables [16].
The F-test is used as a measure to investigate the extent of processing parameters controlling the test results. For a 95% confidence level, if the value of "Prob > F" is less than 0.05, the processing parameters and interactions are considered significant [26]. Furthermore, a large F-value signifies that its processing parameter has a significant effect on the performance characteristic. In ANOVA, the adjusted correlation coefficient, R 2 , is used to evaluate the validity of the fitted model. R 2 adj measures the percentage of variation explained exclusively by independent processing parameter and interactions which predominantly affect the response variables. Additional, to conclude that the created models fit the performed experiments well, it is desired that the values of R 2 and R 2 adj should be high and close to each other [16,26] 3 Results and discussion

RB and HAp characterization analysis
The morphological characteristics of the raw bovine bones (RB) and the thermally treated samples at different temperature conditions are revealed in Fig. 3. It is observed that the bulk RB powders contained the largest particle size. In addition, the SEM images of all the samples revealed that particle size reduced with increase in temperature. Reports have shown that powders with lesser particle size tend to exhibit higher mechanical properties [27][28][29]. This observation is in line with the impact of sintering temperature noticed on the mechanical properties of the fabricated HAp scaffold (see Sections 3.3, 3.4, and 3.5).
The phase characteristics of the RB and the synthesized HAp at different sintering temperatures (900, 1000, and 1100 °C) are presented in Fig. 4. The reflected patterns noticed on all the samples show the characteristic peaks of calcium phosphate-based materials. The noticed characteristic patterns on all the samples are in agreement with several results presented in the literature. On the RB sample, the low and the broader peak noticed are as a result of the presence of organic residue. On the other hand, the heated samples (900-1100) reflect sharp and narrower peaks, and as the temperature increases, the reflection becomes narrower and sharper, which is due to the removal of the organic residue and the HAp pure phase formation. This observation can be likened to the increased mechanical properties with increase in sintering temperature, and it is in agreement with the work of Obada et al. [30], Obada et al. [31], and [2,3]. Figure 5 shows the FTIR characteristic patterns of RB and the sintered HAp at different temperature (900, 1000, and 1100 °C). The reflections show the functional groups peculiar to calcium phosphate materials, which was also validated by the XRD analysis. It is interesting to note that the OH group band around 3500 cm −1 becomes narrower with increase in sintering temperature, which is associated to the disappearance of absorbed water after heating. The result is in agreement with the work of Abifarin et al. [32]. Tables 3 and 4 reflect the orthogonal array of the experimental mechanical properties and their corresponding Taguchi S/N ratios of the processed HAp at different conditions. The S/N ratios and the data analysis were obtained using Minitab 16.

Effect of processing parameters on hardness
The experimental hardness value in Table 3 was analyzed and response table for S/N ratios is displayed in Table 5. The processing parameters have been identified from delta statistics in S/N ratios response table, and ranks were made according to delta value. The delta statistics is the difference between the highest and the lowest average value of each processing parameter. The first rank reflects the higher value of delta. Table 5 shows that the sintering temperature with a delta value of 1.22 has a close value with compaction load with 1.15 delta value.
The main effects plot for S/N ratios of the experimental hardness values is generated from Table 5 as shown in Fig. 6. The displayed patterns of the plots for sintering temperature and compaction load indicate that hardness is hugely influenced by change in sintering temperature and compaction load. The plot reveals that increase in sintering temperature increased the hardness S/N ratios, while increase in compaction load decreased the hardness S/N ratios. The reason for the increasing effect of sintering temperature has been recently reported by [2,3]. The reduction in hardness S/N ratios may be associated with the residual stress generated on the surface of the pellets during compaction, meaning, as the compaction load was increased, much stress was generated on the surface, leading to softer surface of the pelletized HAp. It can be concluded from this result that increase in sintering temperature can relieve the stress generated on the surface of the pellets during compaction, but it is safe and economical to employ lesser compaction load which will require lesser sintering temperature to relieve surface stress of the fabricated HAp scaffolds. The results presented in Table 5 and Fig. 4 show that 1100 °C and 5 KN compaction Sequel to determining the processing parameter levels, analysis of variance (ANOVA) was performed to obtain the percentage contribution of each processing parameter's effect on the hardness value. It can be seen that the compaction load having a contribution of 53.20% is the most influencing processing parameter affecting HAp hardness value, followed by the sintering temperature having 43.91%, while residual error has 2.89% which shows that it is insignificant on the HAp hardness value, as it is less than 0.05 [33], [20]; [1][2][3]. In addition, Table 6 shows that the value of R 2 is very high and not close to the value of R 2 adj . The variability is explained by the model and affirmed the validity of this model.

Effect of processing parameters on compressive strength
Similar to hardness analysis, the experimental compressive strength shown in Table 4 was analyzed and response table for S/N ratios is displayed in Table 7. The first rank reflects the higher value of delta. Table 5 shows that the sintering temperature has a delta value of 3.08 and compaction load has a delta value of 1.45.
The main effects plot for S/N ratios of the experimental compressive strength is generated from Table 7 as shown in Fig. 7. The displayed patterns of the plots for sintering temperature and compaction load also indicate that compressive strength is significantly influenced by change in sintering temperature and compaction load. The plot reveals that increase in sintering temperature and compaction load increased the compressive strength S/N ratios of HAp scaffolds. This observation is similar to the case of HAp hardness values, but compaction load has a reverse effect on compressive strength relative to that of hardness value. The reason for the increase in compressive strength as the compaction load increased could be due to the fact that compaction load increased the bulk density of the HAp scaffolds, which is different from material surface hardness. The result shows that to produce a high compressive strength of HAp scaffolds, higher sintering temperature and compaction load are required, i.e., 1100 °C and 15 KN compaction load are the desired processing parameter levels to have high compressive strength HAp scaffold.
In order to obtain the percentage of contribution of each processing parameter's effect on HAp compressive strength, ANOVA was performed, as it is displayed in Table 8. As it was noticed on hardness analysis, compaction load having contribution of 81.18% is the most Fig. 4 XRD characteristic patterns of RB and HAp at 900, 1000, and 1100 °C influencing processing parameter affecting the compressive strength of the fabricated HAp scaffold, followed by the sintering temperature having 17.95%, but residual error was insignificant, having 0.87%. In addition, Table 6 shows high values of R 2 and R 2 adj , and are comparable. This shows the goodness of fit of the model.

Grey relational analysis for the multiple performance characteristics
It is important to determine the optimum processing parameter levels for the fabrication of HAp scaffolds having high hardness value and high compressive strength. The  results displayed under the effect of processing parameters on HAp hardness value and compressive strength showed that 1100 °C sintering temperature is required to produce mechanically enhanced HAp, but for compaction load, 5 KN is required for high hardness value, while 15 KN is required for high compressive strength. Since there must be one parameter level to be considered for compaction load, it is therefore important to employ grey relational analysis (GRA) for optimum processing parameters.  GRA is principally utilized to address issues containing a restricted arrangement of information. It is commonly used to have a full grasp of unsure frameworks with no highly contrasting arrangement. In grey system, black means having no data and white connotes having all data [1-3, 3, 34].
The pre-processing of data with grey relational generation was performed on the experimental mechanical properties of the responses in Tables 3 and 4, in particular, hardness and compressive strength. The reference sequence of the responses within 0 to 1 was gotten by normalizing the data using Eq. (2). Next, the deviation sequences were calculated using Eq. (3). Table 9 shows the reference and deviation sequences acquired after data pre-processing.
After getting deviation sequences, the GRC ( i (k) ) for each response value was determined using Eq. (4). At last, the average of the GRCs was done to get the grey relational grade (GRG). As recorded in Table 10, the processed values of GRGs were used to get the corresponding S/N ratios. A higher value of S/N proportion is helpful and shows that the experimental mechanical properties lie near the ideal normalized value of GRG [35]. Figure 8 displays the plot of GRG versus S/N ratios. It shows that the last experimental mechanical properties run has the most noteworthy S/N ratio. In like manner, the principal rank was appointed to the last experimental run. The significance of the GRG, with plot of S/N ratios in Fig. 6, additionally supplements the above discussion.
After ranking has been done, a response table for the GRG was brought out. The GRG of each factor at the picked level was chosen and found the average value to produce the mean of GRG for singular elements. For example, the processing parameter sintering temperature at level 3 in the seventh, eighth, and ninth runs of the   Table 10 were used for estimation as displayed in Eq. (5). The mean of chosen GRGs was determined by employing the method above to make the response table displayed in Table 11. The grades in the response table are the proportion of the connection between the reference sequences and equivalence sequence of GRA. Higher values of the mean of GRGs show a solid relationship [36]. Consequently, from the response table of GRGs in Table 11, it is feasible to get the combination of the process parameters that boost overall mechanical properties. From Table 11, the highest grey relational grades exist at sintering temperature at level 3, and compaction load at level 1. Thus, to finish up, the optimal processing parameters for the fabrication of mechanically enhanced HAp scaffold are the sintering temperature at 1100 °C and compaction load at 5 KN.

Significance analysis of the processing parameters on GRG values
To examine the significance and percentage of contribution of each processing parameter on the multiple mechanical properties of HAp, an ANOVA was performed for the grey relational grade at a 95% confidence level. Considering Table 9 Reference and deviation sequence after pre-processing of data  the two responses (hardness and compressive strength), Table 12 shows that the compaction load has the most noteworthy impact, of 90.15%, on the GRG, followed by the sintering temperature, with 7.79%, but residual error is insignificant, with 2.06%. The high R values imply the goodness of fit of the model developed.

Confirmation analysis
After knowing the optimal processing parameter levels, the last step is to predict the response, which is shown in Eq. (7): [1-3, 15, 37] where 0 is the maximum average value GRG at the optimal processing parameter level and m implies the average of GRG. q is the number of the processing parameters. From Eq. (7) and Table 11, the grey relational grade was predicted using the optimal processing parameter levels. The predicted GRG is 0.7722, compared with the experimental values, which is 0.7824, and it is the average of experimental numbers 7, 8, and 9.
Confidence interval (CI) is used in Eq. (8) to determine the closeness of the experimental GRG value and the predicted GRG value [1][2][3]38]: F∝(1,fe)=F ratio required for α; α=risk; fe=DOF of error; Ve =variance of error; ηeff=effective number of replications, which is the Eq. (9) below: R= number of replications when the experiment is carried out for confirmation; N= total number of experiments.
Therefore, V e = 0.002188; f e = 4 Total DOF of control factors = 4 R = 1, N = 9 = 0.5 (95% confidence interval)  Ninety-five percent confidence interval of the predicted optimal grey relational grade is given in Eq. (10), as posited by [2,3]: The confidence interval reveals that the experimental grey relational grade, 0.7824, is close to the predicted optimal grey relational grade, which authenticates the efficacy of the optimal processing parameter levels for the fabrication of mechanically enhanced HAp scaffold.

Conclusions and future studies
Having researched on the enhancement of the mechanical properties of HAp with the assistance of numerical analysis, further study is essential on the modeling and mechanical reliability of the fabricated HAp scaffolds. Interaction between the processing parameters on the mechanical response can also be studied. Biological integrity and reliability of the fabricated HAp scaffold are also an important information needed for tissue engineering application.  Publisher's note Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.