Hadi Samadiana,
Seyed Salman Zakariaeeb,
Mahdi Adabia,
Hamid Mobashericd,
Mahmoud Azamie and
Reza Faridi-Majidi*a
aDepartment of Medical Nanotechnology, School of Advanced Technologies in Medicine, Tehran University of Medical Sciences, Tehran, Iran. E-mail: refaridi@sina.tums.ac.ir
bDepartment of Medical Physics, School of Medicine, Ilam University of Medical Sciences, Ilam, Iran
cLaboratory of Membrane Biophysics and Macromolecules, Institute of Biochemistry and Biophysics, University of Tehran, Tehran, Iran
dBiomaterials Research Center (BRC), University of Tehran, Tehran, Iran
eDepartment of Tissue Engineering, School of Advanced Technologies in Medicine, Tehran University of Medical Sciences, Tehran, Iran
First published on 10th November 2016
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.
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.
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 |
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]:
![]() | (1) |
The schematic diagram of the artificial neural network model is shown in Fig.1.
The training parameters of neural networks for ANNs modeling, measured and predicated cathodic currents are listed in Table 2.
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![]() ![]() ![]() |
![]() |
|
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![]() ![]() ![]() |
The ANNs modeling were further pursued by usage of the training parameters of neural networks for the experimental dataset (Table 3).
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 |
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.
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.
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
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 (CO) and predicted (CP) cathodic currents are determined using eqn (2):
![]() | (2) |
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 | 0.904a |
Sig. (2-tailed) | 0.000 | |||
N | 27 | 27 | ||
Predicted currents (μA) | Pearson correlation | 0.904a | 1 | |
Sig. (2-tailed) | 0.000 | |||
N | 27 | 27 | ||
Bayesian regularization mode I | Measured currents (μA) | Pearson correlation | 1 | 0.910a |
Sig. (2-tailed) | 0.000 | |||
N | 27 | 27 | ||
Predicted currents (μA) | Pearson correlation | 0.910a | 1 | |
Sig. (2-tailed) | 0.000 | |||
N | 27 | 27 | ||
Bayesian regularization mode II | Measured currents (μA) | Pearson correlation | 1 | 0.905a |
Sig. (2-tailed) | 0.000 | |||
N | 27 | 27 | ||
Predicted currents (μA) | Pearson correlation | 0.905a | 1 | |
Sig. (2-tailed) | 0.000 | |||
N | 27 | 27 | ||
Scaled conjugate gradient | Measured currents (μA) | Pearson correlation | 1 | 0.922a |
Sig. (2-tailed) | 0.000 | |||
N | 27 | 27 | ||
Predicted currents (μA) | Pearson correlation | 0.922a | 1 | |
Sig. (2-tailed) | 0.000 | |||
N | 27 | 27 |
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†).
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.
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 |
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.
![]() | ||
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.
Footnote |
† Electronic supplementary information (ESI) available. See DOI: 10.1039/c6ra21596c |
This journal is © The Royal Society of Chemistry 2016 |