Effective parameters on conductivity of mineralized carbon nanofibers: an investigation using artificial neural networks

Abstract

The aim of this study was to predict the effects of different parameters on the conductivity of mineralized PAN-based carbon nanofibers by the artificial neural network (ANN) method. The conductivity of CNFs was investigated as a function of various parameters, including simulated body fluid (SBF) concentration, immersion time and CNFs diameter. In order to conduct ANN modeling, the considered parameters and experimental outputs were categorized into (i) training, (ii) validating and (iii) testing datasets, which were subsequently analyzed using three different training algorithms, including scaled conjugate gradient, Bayesian regularization, and Levenberg–Marquardt back-propagation. The comparison study between three artificial neural network models indicates that all back-propagation methods could be employed to estimate the cathodic current accurately. The results of cyclic voltammetry demonstrated that the cathodic current increased as a function of decreasing simulated body fluid concentration, immersion time and carbon nanofiber diameter. The Pearson correlation coefficients were significant at less than the 0.01% level for all prediction models. Among the studied algorithms, the scaled conjugate gradient back-propagation method produced the highest R-value at 0.92. Based on the promising results of the current approach, the mineralized CNFs can be tailored in a way to construct electro-conductive scaffolds capable of manipulating the activities of bone cells through electrical stimulation and could be utilized in bone tissue engineering.

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1. Introduction

Electrical stimulation (ES) of damaged bone tissue was considered as an effective treatment means due to the piezoelectric characteristics of the bone.¹ Electrical stimulations initiate various cellular and molecular events such as enhancement of protein synthesis in the extra cellular matrix (ECM), cell proliferation, mineralized nodule formation, and enzymatic activities.^2–5 Certain molecules that are targeted by the electrical stimulation of bone include S6 ribosomal subunit kinase, insulin receptor substrate-1 and endothelial nitric oxide synthase, expression of mRNA for osteoblast-specific BMP2, RUNX2, BSP, DLX5 and ALP proteins.^6–10 The implementation of ES has been shown to trigger fast fracture consolidation, fracture resistance, increased fracture callus, cortical thickening and reduced disuse osteoporosis.^11–14 ES can be conducted by two approaches: (i) direct coupling, where cell culture or the patient body are stimulated by inserted or implanted electrodes,^15,16 or (ii) indirect coupling, that causes capacitive, inductive, and combined coupling effects in a remote manner.^17–19 The shortcomings of the direct coupling methods include generation of dangerous faradic by-products, reduced levels of molecular oxygen, and changes in pH,^15,20,21 whilst biological side effects of high voltage (e.g., 100 V) is the main drawback of the capacitive coupling methods.²²

Electro-conductive scaffolds have been recently developed to act as the novel high potential tools to mediate delivery of the electrical stimulus to the cells. Accordingly, electro-conductive polymers, such as polyaniline²³ and polypyrrole (PPy),²⁴ are used either alone or in combination with different polymers²⁵ for bone tissue engineering. However, they suffer from poor mechanical strength, thus, they are combined with carbon nanofibers to have their mechanical strength improved. The combination of CNFs with hydroxyapatite ceramic integrates the mechanical properties, electroconductivity and fibrous nature of CNFs with the osteoconductivity, biocompatibility and bioactivity of hydroxyapatite. Accordingly, the CNFs–HA composites are considered as ideal electro-conductive scaffolds capable to conduct electrostimulation of bone cells. Electrospun carbon nanofibers which have shown promising application in the bone tissue scaffold possess excellent biocompatibility, high stability, good electric conductivity and strong mechanical strength.^26–28 Since the conductivity of the electro conductive scaffolds could directly affect bone formation and remodeling, it is better to use a modeling approach to estimate CNFs conductivity before the mineralization process starts. Various methods such as artificial neural network (ANN) and response surface methodology (RSM) modeling are used for predicting the effects of different parameters on outputs of interest.^29,30 However, ANN models might be more applicable due to their great efficacy.

ANN models are known as descriptive approaches capable to process unknown parameters in various scientific and industrial fields including; medicine, traffic, electronics, space, and banking. Accordingly, they have been used to predict the influence of multi variable parameters on the interested outputs such as the effect of concentration, high voltage amplitude, nozzle tip and collector distance, and flow rate on the diameter of electrospun chitosan/polyethylene oxide (PEO) nanofibers.³¹ The characteristics and mechanism of action of influencing factors on the diameter of electrospun gelatin nanofiber have been addressed by theoretical approaches.³⁰ We have already reported some techniques to predict the effect of CNFs diameter, electrodeposition time and pH on the thickness of CNFs layer and cathodic current in polyacrylonitrile-based Pt coated CNFs electrodes.³² Here, we used different training algorithms including scaled conjugate gradient (SCG), Levenberg–Marquardt back-propagation (LM) and Bayesian regularization (BR) to investigate the effects of CNFs diameter, SBF concentrations and immersion time on the conductivity of CNFs.

2. Material and methods

2.1. Materials

Polyacrylonitrile (PAN) (MW: 80 000 g mol⁻¹) was purchased from Polyacryl Company (Iran). Dimethylformamide (DMF) was obtained from Merck Company (Merck, USA). The stock solutions of PAN/DMF were prepared by dissolving PAN in DMF at 60 °C with continuous and vigorous magnetic stirring for 12 h.

2.2. Preparation of CNFs

CNFs were prepared based on our reported method.³³ Briefly, the PAN/DMF solutions (9, 11 and 13 wt%) were used to construct CNFs with different diameters. The PAN solution was electrospun using needle-based electrospinning setup (Fanavaran Nano Meghyas Ltd., Co., Tehran, Iran). The PAN solution was fed to the tip of nozzle, a blunted 18-gauge stainless needle, using the electronically controlled injection module. An electrical field was applied between nozzle and collector at a high voltage of 20 kV to direct and accelerate the jet flow of PAN solution toward the collector. The electrospun PAN nanofibers were collected on the aluminum foil which was wrapped around the rotating anode drum. The resulted mat went through two stages of heat treatments; (i) stabilization, in air atmosphere at 290 °C for 4 h with a heating rate of 1.5 °C min⁻¹ and (ii) carbonization, at 1000 °C for 1 h under a high-purity nitrogen atmosphere with the heating rate of 4 °C min⁻¹ in a tube furnace (Azar, TF5/25-1720, Iran). The resulted constructions of CNFs were treated chemically in the subsequent stages.

2.3. Mineralization of CNFs

CNFs were activated in a concentrated NaOH solution (5 M) and then mineralized in the Simulated Body Fluid (SBF) solution at concentrations of 1, 3 and 3×, according to the approved protocol³⁴ (Table 1). The nucleation and formation of mineral phase was conducted via immersion of CNFs in NaOH solution stirred for 24 h at 45 °C. The resulted mineralized CNFs (M-CNFs) were then rinsed with deionized water several times, dried at 80 °C for 24 h and stored in a cool and dry space away from light. The activated CNFs were soaked in SBF solutions at 37 °C for 24, 48 and 72 h before application. The SBF solution was replaced during the course of experiments by a fresh one on a daily basis.

Table 1 Chemical composition of SBF solution

Order	Reagents	Amount
		1×	2×	3×
1	NaCl	6.5465 g	13.093 g	19.6395 g
2	NaHCO3	2.2682 g	4.5346 g	6.8046 g
3	KCl	0.373 g	0.746 g	1.119 g
4	Na2HPO4·2H2O	0.1419 g	0.2838 g	0.4257 g
5	MgCl2·6H2O	0.3049 g	0.6098 g	0.9147 g
6	1 M HCl	9 ml	9 ml	9 ml
7	CaCl2·2H2O	0.3675 g	0.735 g	1.1025 g
8	Na2SO4	0.071 g	0.142 g	0.213 g
9	(CH2OH)3CNH2	6.057 g	12.114 g	18.171 g
10	1 M HCl	30 ml	30 ml	30 ml

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2.4. Conductivity of CNFs

The conductivity of fabricated mineralized CNFs was measured by a computer controlled μAutolab type III potentiostat (Eco Chemie, Utrecht, The Netherlands). For this purpose, the M-CNFs were cut to small spheres (diameter of 5 mm), and suspended in a saturated KCl solution. The electrical conductivity of M-CNFs was measured by means of the extent of their interaction with two copper wire electrodes immersed in the M-CNFs containing solution. The current flowing throw the corresponding electrodes was recorded by CV with a scan rate of 100 mV s⁻¹ that cycled for 20 times. Different characteristics of CNFs such as; diameter (nm), SBF concentration and immersion time were used as the main inputs for ANN analysis.

2.5. Artificial neural network

The artificial neural network (ANN) considers three processing element or node classifications; input, hidden and output layers, each with one or more nodes, are considered in this method.^30,31 The method is a non-linear statistical data modeling approach that approximate various arbitrary complex functions, correlates the complex relationships between inputs and outputs and finds the dominant patterns in the simulated data. The input dataset is divided into training, validation and testing classes. After network designing, the training dataset is used for ANN training and is validated and tested subsequently. The output of interest is finally predicted based on the strength of connections between the neurons in the input, hidden and output layers.³²

In this study, three ANN models each with different training algorithms were used for data analysis. The predictive networks were developed based on three layers feed forward network with tangent sigmoid activation function in hidden layers and linear activation function in the output layer, using MATLAB software (version 2012). The multilayer feed forward networks were trained using the most commonly used algorithms including; scaled conjugate gradient (SCG), Levenberg–Marquardt back-propagation (LM) and Bayesian regularization (BR). Input, hidden and output layer sizes of the ANNs were 3, 10 and 1, respectively based on empirical formulas were presented to calculate hidden layer size.³⁵ The single hidden layer ANNs were selected due to their flexible learning rate and fast convergence to linear target functions.³⁶

Data division for training, validation, and testing procedures was performed randomly. The percentage ratios of the training, validation and number of tests used in ANNs modeling were 70% (19), 15% (4) and 15% (4), respectively. The validation dataset was added to the training one and no Bayesian regularization performed. The percentage ratios of the training and number of tested data used in ANNs modeling were 85% (23) and 15% (4), respectively. To minimize the effects of the dataset sizes and evaluate its effect on the results, another ANN model was developed based on the Bayesian regularization algorithm with the percentage ratios of 75% (21) and 25% (6) for the training and tests dataset, respectively. The characteristic factors of CNFs including; diameter (nm), SBF concentration (×) and immersion time (h), were considered as the neural networks inputs; and the cathodic current (μA) was predicted as an output. In the experimental section, 27 samples were prepared based on the effects of three parameters involved in fabrication of mineralized CNFs.

The selected range of the variables and the levels of the parameters are in the following based on our preliminary studies and Wu et al. study:²⁸

The selected range for CNFs diameter was 92, 130 and 170 nm.

The selected range for SBF concentrations were 1, 2 and 3× (1, 2 and 3 times concentrated SBF).

The selected range for immersion times were 24, 48 and 72 h.

Data normalization was performed using mapminmax functions based on eqn (1) in the pre-processing step before ANN modeling. Mapminmax functions with the following algorithm normalized the minimum and maximum values to [−1, 1]:

where Y_min and Y_max are −1 and 1, respectively. The X is the data which is normalized. X_max and X_min are the maximum and minimum values of X.

The schematic diagram of the artificial neural network model is shown in Fig.1.

Fig. 1 Schematic diagram of ANN model.

The training parameters of neural networks for ANNs modeling, measured and predicated cathodic currents are listed in Table 2.

Table 2 ANN training parameters

Levenberg–Marquardt back propagation
Training algorithm	Trainlm
Maximum epochs	2000
Maximum training time	1800
Performance goal	0
Minimum gradient	1 × 10^−12
Maximum validation checks	6
Mu	0.001
Mu decrease ratio	0.1
Mu increase ratio	10
Maximum mu	10 000 000 000
Scaled conjugate gradient backpropagation
Training algorithm	Trainscg
Maximum epochs	2000
Maximum training time	1800
Performance goal	0
Minimum gradient	1 × 10^−12
Maximum validation checks	6
Sigma	5 × 10^−5
Lambda	5 × 10^−7
Bayesian regularization backpropagation
Training algorithm	Trainbr
Maximum epochs	2000
Maximum training time	1800
Performance goal	0
Minimum gradient	1 × 10^−12
Maximum validation checks	6
Mu	0.005
Mu decrease ratio	0.1
Mu increase ratio	10
Maximum mu	10 000 000 000

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The ANNs modeling were further pursued by usage of the training parameters of neural networks for the experimental dataset (Table 3).

Table 3 The experimental data set for ANNs modeling

Sample no.	CNFs diameter (nm)	SBF concentration (×)	Immersion time (h)	Measured cathodic current (μA)	Predicted cathodic current (μA)
					LM	BR 1	BR 2	SCG
1	92	1	24	3.44	3.31	3.42	3.38	3.42
2	92	1	48	3.27	3.23	3.24	3.20	3.22
3	92	1	72	3.04	3.07	3.09	3.05	3.07
4	92	2	24	3.35	3.36	3.32	3.32	3.31
5	92	2	48	3.16	3.19	3.14	3.13	3.11
6	92	2	72	2.94	2.97	2.98	2.98	3.01
7	92	3	24	3.2	3.22	3.24	3.24	3.27
8	92	3	48	3.02	2.99	3.05	3.04	3.06
9	92	3	72	2.9	2.86	2.92	2.89	2.88
10	130	1	24	3.42	3.42	3.39	3.36	3.40
11	130	1	48	2.92	3.06	3.20	3.20	3.11
12	130	1	72	3.03	2.99	3.03	3.05	2.90
13	130	2	24	3.31	3.24	3.28	3.31	3.36
14	130	2	48	2.93	3.16	3.10	3.11	3.10
15	130	2	72	3.11	2.95	2.95	2.94	3.02
16	130	3	24	3.18	3.18	3.21	3.20	3.19
17	130	3	48	2.99	3.05	3.01	3.01	2.98
18	130	3	72	2.88	2.86	2.90	2.90	2.92
19	170	1	24	3.41	3.39	3.36	3.35	3.44
20	170	1	48	3.24	3.22	3.17	3.16	3.17
21	170	1	72	3.01	2.95	3.01	3.01	2.97
22	170	2	24	3.3	3.44	3.27	3.28	3.44
23	170	2	48	3.07	3.11	3.10	3.11	3.10
24	170	2	72	2.87	2.93	2.92	2.94	2.85
25	170	3	24	3.18	3.20	3.20	3.17	3.13
26	170	3	48	2.98	3.05	2.99	3.01	2.85
27	170	3	72	2.84	2.83	2.87	2.86	2.86

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3. Results and discussion

3.1. Circular voltammetry of M-CNFs

Experimental study showed that there was an inverse relation between CNFs diameter, SBF concentration and immersion time with conductivity (Table 3). The fiber conductivity enhanced by CNFs diameter decreasing due to their increased surface area. In addition, SBF concentration and immersion time increasing led to higher coverage of CNFs surface with mineral phase which decreases the fibers surface area and conductivity. Nguyen Thi Xuyen and colleagues³⁷ showed that with decreasing CNFs diameter the conductivity of fibers prominently increased, that was consistent with the results of our previous studies³² indicating an increase in the nanofiber surface area and conductivity as a result of decreased CNFs diameter.

3.2. ANN models of M-CNFs

The main objective of this study was to develop the most efficient ANN model to predict the cathodic current in M-CNFs. Three different ANN models were developed in MATLAB, based on the SBF concentration, CNFs diameter and immersion time input parameters. Having the approach had trained, output parameter, the cathodic current, was predicted by three back-propagation algorithms; scaled conjugate gradient (SCG), Levenberg–Marquardt (LM) and Bayesian regularization (BR) algorithm. Bayesian regularization mode I was utilized for the ANN model using the Bayesian regularization back-propagation algorithms with the percentage ratios of 85% (23) and 15% (4) for the training and testing datasets, respectively. In the Bayesian regularization mode II, the Bayesian regularization back-propagation algorithms was implemented with the percentage ratios of 75% (21) and 25% (6) for the training and testing datasets, respectively. The results indicated the potential capability of three different back-propagation algorithms in identification and prediction of the SBF concentration and immersion time effects on the cathodic current in M-CNFs.

3.2.1. Effects of SBF concentration and immersion time on the cathodic current in M-CNFs. The interaction of SBF concentration was measured and the extent of their correlation investigated. The maximum and minimum cathodic currents were found to be 3.42 and 2.88 μA which were related to the low SBF concentration (1×) and immersion time (24 h), and high SBF concentration (3×) and immersion time (72 h), respectively (Fig. 2).

Fig. 2 Effects of the measured interaction of SBF concentration and immersion time on the cathodic current in M-CNFs. Experimental results are compared with the theoretical investigations manifested by Levenberg–Marquardt, Bayesian regularization modes I and II, scaled conjugate gradients approaches. The letter C represents current (μA), Im T is immersion time (h), and SBF C is SBF concentration (×).

As shown in Fig. 2, the cathodic current could increase as a function of the SBF concentration and the immersion time decreasing. This relationship could be attributed to the higher coverage of CNFs surface with mineral phase via the SBF solution concentration and the immersion time increasing which led to the surface area decreasing.

3.2.2. Effects of CNFs diameter and immersion time on the cathodic current in M-CNFs. CNFs with different diameter and immersion time represented varying cathodic currents. The results indicated an inverse relationship between the cathodic current, CNFs diameter and immersion time. The cathodic current (about 3.33 μA) was maximum in low CNFs diameter (92 nm) and low immersion time (24 h). The minimum cathodic current is about 2.91 μA in high CNFs diameter (170 nm) and high SBF immersion time (72 h) (Fig. 3).

Fig. 3 Effects of the measured interaction of CNFs diameter and immersion time on the cathodic current in M-CNFs. Experimental results are compared with the theoretical investigations manifested by Levenberg–Marquardt, Bayesian regularization modes I and II, scaled conjugate gradients approaches. The letter C represents the current (μA), Im T is immersion time (h) and CFNs D is CNFs diameter.

As shown in Fig. 3, the conductivity increased by CNFs diameter and immersion time decreasing. The increased immersion time led to higher CNFs surface coverage with mineral phase which reduced the conductivity subsequently. In addition, the conductivity enhanced by the CNFs diameter decreasing because of increasing the nanofibers surface area.

3.2.3. Effects of CNFs diameter and SBF concentration on the cathodic current in M-CNFs. The cathodic current of M-CNF was changed due to the interaction of CNFs diameter with SBF solution that was investigated by both practical and theoretical approaches and revealed a promising correlation. As shown in Fig. 4, the cathodic current increased by CNFs diameter and SBF concentration increasing. The cathodic current was maximum (3.25 μA) in smallest CNFs (92 nm) and at minimum SBF concentration (1×). However, the minimum cathodic current was about 3 μA in high CNFs diameter (170 nm) at high SBF concentration (3×).

Fig. 4 Effects of the measured interaction of CNFs diameter and SBF concentration on the cathodic current in M-CNFs. Experimental results are compared with the theoretical investigations manifested by Levenberg–Marquardt, Bayesian regularization modes I and II, scaled conjugate gradients approaches. The letter “C” represents the current (μA), SBF C is SBF concentration (×) and CNFs D is CNFs diameter (nm).

The results indicate that there is an inverse relationship between the cathodic current, CNFs diameter, and SBF concentration (Fig. 4). This can be attributed to the increased surface area caused by decreasing CNFs diameter and SBF concentration. With increasing SBF concentration, more ions were accessible to form the mineral phase on the accessible surfaces of CNFs which caused a decrease in the CNFs bare surface area. These results are in agreement with findings of our previous work which indicated that decreasing CNFs diameter leads to improvement in voltammetric response.³³ In another study we have used ANN model to predict the effects of different input parameters on the conductivity of CNFs electrodes. The results show that lowering the CNFs diameter and electrodeposition time of Pt on CNFs electrode leads to increase conductivity.³²

3.2.4. Correlation between observed and predicted cathodic currents in M-CNFs. The linear regression analysis was used to determine the correlation between the observed and predicted cathodic currents. The correlation between the observed and cathodic currents was predicted using scaled conjugate gradient (SCG), Levenberg–Marquardt (LM) and the mode I and II models of the Bayesian regularization (BR) (Fig. 5).

Fig. 5 Correlation between the observed and predicted cathode current in M-CNFs. The relationship was predicted using Levenberg–Marquardt (LM) (a), scaled conjugate gradient (SCG) (b) and Bayesian regularization (BR) mode I and II models (c and d).

The regression (r) and significant coefficients determined by the Pearson correlation between the observed and the cathodic currents was predicted using the scaled conjugate gradient (SCG), Levenberg–Marquardt (LM) and Bayesian regularization (BR) mode I and II models (Table 4). The Pearson correlation coefficients (r) between the observed (C_O) and predicted (C_P) cathodic currents are determined using eqn (2):

where n represents the data number.

Table 4 Pearson correlation between the observed and predicted cathodic current in M-CNFs

Training algorithm			Measured currents (μA)	Predicted currents (μA)
a Correlation is significant at the 0.01 level (2-tailed).
Levenberg–Marquardt	Measured currents (μA)	Pearson correlation	1	0.904^a
		Sig. (2-tailed)		0.000
		N	27	27
	Predicted currents (μA)	Pearson correlation	0.904^a	1
		Sig. (2-tailed)	0.000
		N	27	27
Bayesian regularization mode I	Measured currents (μA)	Pearson correlation	1	0.910^a
		Sig. (2-tailed)		0.000
		N	27	27
	Predicted currents (μA)	Pearson correlation	0.910^a	1
		Sig. (2-tailed)	0.000
		N	27	27
Bayesian regularization mode II	Measured currents (μA)	Pearson correlation	1	0.905^a
		Sig. (2-tailed)		0.000
		N	27	27
	Predicted currents (μA)	Pearson correlation	0.905^a	1
		Sig. (2-tailed)	0.000
		N	27	27
Scaled conjugate gradient	Measured currents (μA)	Pearson correlation	1	0.922^a
		Sig. (2-tailed)		0.000
		N	27	27
	Predicted currents (μA)	Pearson correlation	0.922^a	1
		Sig. (2-tailed)	0.000
		N	27	27

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The Pearson correlation coefficients between observed and cathodic currents were predicted using scaled conjugate gradient (SCG), Levenberg–Marquardt (LM) and Bayesian regularization (BR) mode I and II models and showed the values of 0.904, 0.910, 0.905 and 0.922, respectively (P < 0.01). As it can be inferred from the Fig. 5, there is a good agreement between the measured and predicted cathodic current values for every ANN prediction model implemented in this study. To find out the optimal back-propagation algorithm, the development and evaluation of ANN models were performed using a similar randomly selected datasets for training, validation and testing procedures. In addition, the estimation and predictive capability of ANN model was determined with RMSE, AAD and SEP (as shown in Tables 1–3 in ESI†).

3.2.5. Selection of the best ANN model. In this study, the correlation strength between the measured and predicted values was measured by means of the correlation coefficients (R). An exact linear relationship found to be feasible between the measured and predicted values if the linear correlation coefficient R equals one. There will be a good agreement between the measured and predicted values when the R value is greater than 0.90.

The predicted cathodic current values were plotted versus the measured values for each ANN model and a linear relationship was identified between the effecting factors and the resulted cathode current. The algorithms and equations used to find the fitness and the regression values for training, validation and testing datasets for different ANN models are listed in Table 5.

Table 5 Correlation between training, validation and testing datasets and different ANN models

Training algorithms	Training	Validation	Test	All
Scaled conjugate gradient	Output = 0.92 × target + 0.24	Output = 0.98 × target + 0.03	Output = 1.3 × target − 0.77	Output = 0.95 × target + 0.15
	R = 0.95395	R = 0.93327	R = 0.8598	R = 0.92214
Levenberg–Marquardt	Output = 0.93 × target + 0.23	Output = 0.71 × target + 0.82	Output = 0.92 × target + 0.37	Output = 0.86 × target + 0.44
	R = 0.96708	R = 0.9363	R = 0.87209	R = 0.90379
Bayesian regularization mode I	Output = 0.82 × target + 0.55	—	Output = 0.61 × target + 1.3	Output = 0.8 × target + 0.64
	R = 0.92005		R = 0.84683	R = 0.90977
Bayesian regularization mode II	Output = 0.78 × target + 0.69	—	Output = 0.72 × target + 0.91	Output = 0.76 × target + 0.75
	R = 0.89943		R = 0.93649	R = 0.90518

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19, 4, and 4 data were randomly selected for training, validation and test steps, respectively. In training procedure, ANN was modeled and the relationship between the ANN and experimental results (for training dataset including 19 data) were evaluated using the regression analysis. Then the ANN model was validated and tested using the validation (4 data) and test (4 data) dataset. In these steps, the relationship between the ANN and experimental results were also evaluated for the validation and test datasets (in other words; the relationship between the 4 data estimated by the ANN model and 4 data obtained by experiments were studied in validation and test steps). In the final stage, overall r is achieved based on the line fitting for 27 samples. Therefore, this quantity is the most comprehensive index to evaluate the relationship between the ANN and experimental results and goodness of the back-projection algorithms.

Bayesian regularization mode I was used for the ANN model based on the Bayesian regularization back-propagation algorithms with the percentage ratios of 85% (23) and 15% (4) for the training and testing datasets, respectively. Bayesian regularization mode II was used for the ANN model based on the Bayesian regularization back-propagation algorithms with the percentage ratios of 75% (21) and 25% (6) for the training and testing datasets, respectively.

The highest regression value (0.96708) was achieved by Levenberg–Marquardt method for the training dataset. There was almost identical regression value identified in validation datasets for the scaled conjugate gradient and Levenberg–Marquardt methods. The highest regression value (0.93649) for the test dataset was obtained by Bayesian regularization method. The regression value was calculated for all input data and the scaled conjugate gradient (SCG) back-propagation method showed the highest regression value (0.92214).

The comparison study between three artificial neural network models suggests that back-propagation methods can be employed to estimate the cathodic current accurately. Among the implemented algorithms, the scaled conjugate gradient (SCG) back-propagation method produced the highest R value at 0.92. The approved ANN model showed R values of 0.95395, 0.93327 and 0.8598 for training, validation and testing data, respectively. The R value of higher than 0.9 indicated that higher number of predicted values were consistent with the measured ones. Therefore, in this study, the SCG algorithm was considered as the optimal back-propagation method for ANN training.

3.2.6. Correlation between output and training, validation, testing for ANN model. Correlation between the resulted output and training, validation, testing and all input data was investigated for the ANN model (Fig. 6). The analysis revealed a linear relationship with a slope of 0.92, 0.98, 1.3 and 0.95 and regression value of 0.95395, 0.93327, 0.8598, and 0.92214.

Fig. 6 Training, validation and testing dataset for the ANN model. The plots are based on the scaled conjugate gradient back propagation and all input data.

Based on the scaled conjugate gradient (SCG) model an error histogram with 20 bins was produced for the ANN model shown in Fig. 7.

Fig. 7 Error histogram for the ANN model based on the scaled conjugate gradient back propagation (bin number is 20).

4. Conclusion

According to our findings, all back-propagation methods can be employed to estimate the cathodic current accurately. To the best of our knowledge this is the first report on using 3 different algorithms for predicting the effects of input parameters on cathodic current of mineralized CNFs. The scaled conjugate gradient propagation algorithm was the best algorithm to predict the cathodic current values. In addition 3D graphs indicated that decreasing diameter of CNFs, SBF concentration and immersion time led to increased conductivity in mineralized CNFs. Based on the promising findings of this study, the mineralized CNFs possess the potential characteristics of an electro-conductive scaffold and form appropriate platform capable to deliver electrical stimulus for various purposes including bone tissue engineering and fabrication.

Acknowledgements

This project was supported by Tehran University of Medical Sciences (TUMS), grant No. 94-02-87-28669.

References

1. E. Fukada and I. Yasuda, J. Phys. Soc. Jpn., 1957, 12, 1158–1162.
2. Z. Friedenberg, E. Andrews, B. Sinolenski, B. Pearl and C. Brighton, Plast. Reconstr. Surg., 1971, 48, 95–96.
3. Y. S. Shayesteh, B. Eslami, M. M. Dehghan, H. Vaziri, M. Alikhassi, A. Mangoli and A. Khojasteh, J. Prosthodontics, 2007, 16, 337–342.
4. Y.-h. Lee, J.-h. Rah, R.-w. Park and C.-i. Park, Yonsei Med. J., 2001, 42, 194–198.
5. J. A. Spadaro, Bioelectromagnetics, 1997, 18, 193–202.
6. B. Ercan and T. J. Webster, Int. J. Nanomed., 2008, 3, 477.
7. H.-P. Wiesmann, M. Hartig, U. Stratmann, U. Meyer and U. Joos, Biochim. Biophys. Acta, Mol. Cell Res., 2001, 1538, 28–37.
8. M. Hartig, U. Joos and H.-P. Wiesmann, Eur. Biophys. J., 2000, 29, 499–506.
9. M. Schnoke and R. J. Midura, J. Orthop. Res., 2007, 25, 933–940.
10. Y. Yang, C. Tao, D. Zhao, F. Li, W. Zhao and H. Wu, Bioelectromagnetics, 2010, 31, 277–285.
11. K. Schindler, C. E. Elger and K. Lehnertz, Epilepsy Res., 2007, 77, 108–119.
12. J. F. Connolly, H. Hahn and O. Jardon, Clin. Orthop. Relat. Res., 1977, 124, 97–105.
13. C. T. Brighton, G. T. Tadduni, S. R. Goll and S. R. Pollack, J. Orthop. Res., 1988, 6, 676–684.
14. J. A. Ogden and W. O. Southwick, Skeletal Radiol., 1981, 6, 187–192.
15. B. Ercan and T. J. Webster, Biomaterials, 2010, 31, 3684–3693.
16. I. S. Kim, J. K. Song, Y. L. Zhang, T. H. Lee, T. H. Cho, Y. M. Song, D. K. Kim, S. J. Kim and S. J. Hwang, Biochim. Biophys. Acta, Mol. Cell Res., 2006, 1763, 907–916.
17. C. T. Brighton, W. Wang, R. Seldes, G. Zhang and S. R. Pollack, J. Bone Jt. Surg., Am. Vol., 2001, 83, 1514–1523.
18. R. Huo, Q. Ma, J. J. Wu, K. Chin-Nuke, Y. Jing, J. Chen, M. E. Miyar, S. C. Davis and J. Li, J. Surg. Res., 2010, 162, 299–307.
19. H. T. H. Au, I. Cheng, M. F. Chowdhury and M. Radisic, Biomaterials, 2007, 28, 4277–4293.
20. D. R. Merrill, M. Bikson and J. G. Jefferys, J. Neurosci. Methods, 2005, 141, 171–198.
21. J. Spadaro and R. Becker, Med. Biol. Eng. Comput., 1979, 17, 769–775.
22. S. Meng, M. Rouabhia and Z. Zhang, Electrical stimulation in tissue regeneration, INTECH Open Access Publisher, 2011.
23. M. A. Whitehead, D. Fan, G. R. Akkaraju, L. T. Canham and J. L. Coffer, J. Biomed. Mater. Res., Part A, 2007, 83, 225–234.
24. S. Meng, Z. Zhang and M. Rouabhia, J. Bone Miner. Metab., 2011, 29, 535–544.
25. S. Meng, M. Rouabhia, G. Shi and Z. Zhang, J. Biomed. Mater. Res., Part A, 2008, 87, 332–344.
26. H. Liu, Q. Cai, P. Lian, Z. Fang, S. Duan, X. Yang, X. Deng and S. Ryu, Mater. Lett., 2010, 64, 725–728.
27. B. Han, X. Zhang, H. Liu, X. Deng, Q. Cai, X. Jia, X. Yang, Y. Wei and G. Li, J. Biomater. Sci., Polym. Ed., 2014, 25, 341–353.
28. M. Wu, Q. Wang, X. Liu and H. Liu, Carbon, 2013, 51, 335–345.
29. N. Naderi, F. Agend, R. Faridi-Majidi, N. Sharifi-Sanjani and M. Madani, J. Nanosci. Nanotechnol., 2008, 8, 2509–2515.
30. M. Naghibzadeh and M. Adabi, Fibers Polym., 2014, 15, 767–777.
31. N. Ketabchi, M. Naghibzadeh, M. Adabi, S. S. Esnaashari and R. Faridi-Majidi, Neural Computing and Applications, 2016, 1–13.
32. M. Adabi, R. Saber, M. Naghibzadeh, F. Faridbod and R. Faridi-Majidi, RSC Adv., 2015, 5, 81243–81252.
33. M. Adabi, R. Saber, R. Faridi-Majidi and F. Faridbod, Mater. Sci. Eng., C, 2015, 48, 673–678.
34. S. Jalota, S. B. Bhaduri and A. C. Tas, Mater. Sci. Eng., C, 2008, 28, 129–140.
35. W. Yu, H. He and N. Zhang, Advances in Neural Networks-ISNN 2009: 6th International Symposium on Neural Networks, ISNN 2009 Proceedings, Wuhan, China, Springer, 26–29 May 2009.
36. T. Nakama, in Advances in Neural Networks – ISNN 2011: 8th International Symposium on Neural Networks, ISNN 2011 Proceedings, Part I, Guilin, China, ed. D. Liu, H. Zhang, M. Polycarpou, C. Alippi and H. He, Springer Berlin Heidelberg, Berlin, Heidelberg, 2011, pp. 270–279,  DOI:10.1007/978-3-642-21105-8_32.
37. N. T. Xuyen, E. J. Ra, H.-Z. Geng, K. K. Kim, K. H. An and Y. H. Lee, J. Phys. Chem. B, 2007, 111, 11350–11353.

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Footnote

† Electronic supplementary information (ESI) available. See DOI: 10.1039/c6ra21596c

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