Using An Artificial Intelligence Technique to Optimize Calcium Phosphates Synthesis Conditions

Transcription

1 Using An Artificial Intelligence echnique to Optimize Calcium Phosphates Synthesis Conditions Mitra Asadi-Eydivand Department of Computer Engineering and Information echnology, Amirkabir University of echnology ehran, Iran Abstract he most widely used calcium phosphatebased bioceramic is biphasic calcium phosphate (BCP) consist of hydroxyapatite and tricalciumphosophate. Bioactivity and biodegradation of BCP is controlled by varying HA/CP ratio. In this study, a biphasic calcium phosphate composite (HA/b-CP) was synthesized through a wet chemical method. he structure and the composition of the resulting powders were characterized by different analytical techniques. o estimate and predict the synthesis conditions, a back-propagation neural network (BPNN) which has 2 inputs and 1 output was designed. Some experimental samples have been prepared to train the BPNN to get it to estimate the output parameters. hen BPNN is tested using some samples that have not been used in the training stage. o prepare the training and testing data sets, some experiments were performed. he effects of the ph of reactants and the Ca:P ratios of reactants, as input parameters, have been investigated on the Ca:P ratio of products, as output parameters. he comparison of the predicted values and the experimental data indicates that the developed model has an acceptable performance to estimate the Ca:P ratio of products in HA/beta-CP composite powder. Keywords- Artificial Neural Network; Biphasic Calcium Phosphate; Hydroxyapatite; ricalcium Phosphate; Synthesis I. INRODUCION Calcium phosphate-based ceramics have been very popular implanted materials for biological applications during past decades due to their similarity to human bone, biocompatibility and directly bone bonding. he most widely used calcium phosphates are hydroxyapatite (HA) and betatricalcium phosphate (b-cp) [1-2].With the development of computer technology and artificial intelligence theory, optimization of process parameters based on Artificial Neural Network (ANN) are designed in order to discover the proper condition to generate ideal biphasic calcium phosphates[1-4]. Insomuch as the experimental methods are time-consuming and expensive, computational models such Amir Hossein Hakami Vala/ Arghavan Farzadi/ Soheila Ali Akbari Ghavimi/ Mehran Solati-Hashjin Nanobiomaterials Laboratory (NBML), Biomedical Engineering Faculty Amirkabir University of echnology ehran, Iran as artificial neural networks (ANN) have been used for minimizing these deficiencies via estimating the results. ANN is a flexible mathematical structure which is capable of identifying complex nonlinear relationships between input and output data sets. ANN models have been found useful and efficient, particularly in problems for which the characteristics of the processes are difficult to describe using physical equations [5]. A neural network consists of an interconnected group of artificial neurons, and it processes information using a connectionist approach to computation. he objective of this study is providing a back-propagation trained artificial neural network, which has 2 inputs and 1 output. Some data obtained from synthesizing of (HA/b- CP) composite were used to train the artificial neural network (ANN). o predict the proper synthesis condition of biphasic calcium phosphate, including hydroxyapatite and tricalcium phosphate the influence of input parameters, the ph and the initial Ca/P ratio of reactants, on output parameters, Ca/P ratio of products, have been investigated. II. MAERIALS AND MEHODS A. Synthesis and Characterization of Powders Calcium nitrate tetrahydrate with the chemical formula of Ca(NO 3 ) 2.4H 2 O and diammonium hydrogen phosphate with the formula of (NH4)2HPO4 were used as starting materials and sources of Ca and P respectively. HNO3ANDNH4OH WERE USED O ADJUS HE PH OF HE SOLUION mixture during the process. o prepare BCP powders by wet chemical method, diammonium hydrogen phosphate solution was added drop wise the calcium nitrate tetrahydrate solution under stirring conditions. he suspension was centrifuged and calcined at 1100 C. he chemical composition (Ca, and P contents) was determined by inductively coupled plasma (ICP) atomic emission spectroscopy using an ICP (AES ARL 3410) spectrometer. he effects of the initial Ca/P molar ratio and the ph of the solution on the composition of the precipitates are given in able I.

2 ABLE I.HE CONDIION FOR PREPARAION OF CALCIUM PHOSPHAE POWDERS A 20 C ph of Reactants Ca:P Ratio ( Reaction Products) Ca/P =1 Ca/P =1.5 Ca/P =1.67 Ca/P =2 Reactants In order to verify the performance of network, four extra samples were prepared and characterized by XRD and FIR. Phase analyses of powders were determined by X-ray diffraction (Philips PW 3710). he XRD data were collected over 2θ range of using Cu-Kα radiation ( mm). Phase identification was achieved by comparing the diffraction patterns of samples with ICDD (JCPDS) standards. Fourier transform infrared spectroscopy (Bruker IFS 48) using pellets of powdered samples mixed with KBr was performed to evaluate the functional groups of specimens. he FIR spectra were obtained over the region cm -1. B. Neural Network In this Study, the Neural Network oolbox software from Matlab has been used. hree back-propagation networks with three layers in each one with 5,10,50 neurons and hyperbolic tangent sigmoid transfer functions in hidden layer were designed. he network will be trained with the Levenberg-Marquardt back-propagation algorithm (trainlm). he Levenberg-Marquardt algorithm was designed to approach second-order training speed without having to compute the Hessian matrix[6]. he Levenberg-Marquardt algorithm was designed to approach second-order training speed without having to compute the Hessian matrix. When the performance function has the form of a sum of squares (as is typical in training feed forward networks), then the Hessian matrix can be approximated as equation (1): H = J J (1) And the gradient can be calculated as equation (2): g = J e (2) J is the Jacobian matrix that contains first derivatives of the network errors with respect to the weights and biases, and e is a vector of network errors. he Jacobian matrix can be computed by a standard back propagation technique that is much less complicated than computing the Hessian matrix. he Levenberg-Marquardt algorithm uses this approximation instead of the Hessian matrix in the equation (3): x 1 = xk [ J J µ I] k + + When the scalar µ is zero, this equation turns to be Newton's method, using the approximate Hessian matrix. When µ is large, the equation becomes gradient descent with a small step size. Newton's method is faster and more accurate near an error minimum, so the aim is to shift toward Newton's method as fast as possible. herefore, µ is decreased after each successful step (reduction in performance function) and is increased only when a trial step would increase the performance function. In this way, the performance function is always reduced at each iteration of the algorithm. In the other words, the training process continues until the validation error cannot be decreased anymore [7, 8]. he training process ran for each set of data shown in able I. he inputs and target data set were randomly divided into three sets as follows, he samples that were used for training the network that fit connection weights. he samples that were used for validation, measure network generalization; if the generalization stops improving, the training is terminated. he samples that had been used for testing were used as a completely independent test of network generalization. [9] In this paper, 41 samples were used for training, 3 samples for generalization and 8 samples for testing. he difference between three designed networks is between their number of hidden layer sneurons /n (n=5, 10, 50) means these three networks with n neurons in hidden layer. III. 1 J e RESULS AND DISCUSSION he Fig. 1 displays the network's outputs with respect to target for training, validation and test sets. Vertical axis is the output, and horizontal axis is the target. For a perfect fit, the data should fall along the 45-degree line where the network outputs are equal to the targets. According to Fig (1-a), that amount of slop in the all three processes of training, validation and test is and Y-intercepts is 0.13 that indicates less difference between targets and outputs. In Fig (1-b) the network which has 15 neurons in its hidden layer, the slope is nearer to line Y=X and the amount is shows better prediction than previous network. he slope of the line fitted to data points of network with 50 neurons in its hidden layer is that shows less accuracy in (3)

3 prediction, Fig (1-c). So, between three networks with 5, 10 and 50 neurons in hidden layer, the second one has the highest accuracy in prediction. 0432). In addition, the intensity of the HA peaks increases from BCP1 to BCP2 and BCP3 to BCP4 indicating that the amount of β-cp decreases as the amount of the ph of suspension is increased during the preparation procedure (at constant Ca/P ratio). (a) Figure 1(a-c). Neural networks regression plots a: /5, b: /10, c: /50 he FIR spectra of BCP powders is shown in Fig 3. he spectra illustrates the hydroxyl bond stretch at 3550 cm -1 and -2 HOP 4 at 970 cm -1 corresponding to HA and β-cp structure respectively. he vibrational bands of the phosphate ions are observed in all the samples. As there is an insignificant amount of hydroxyapatite in BCP3 and BCP4 samples, the hydroxyl band disappears and forms a relatively broad-band stretch over the range of cm -1 due to the adsorbed molecules of water. By increasing the amount of tricalcium phosphate phases in BCP2, BCP3 and BCP4 samples, the hydroxyl band at 633 cm -1 reduces in peak area. he hydroxyl vibrational band disappears in BCP1 sample. (c) According to able II, for four extra samples, the peaks of these samples were indexed according to standard patterns (JCPDS). he diffractograms of the samples BCP2 and BCP3 show additional peaks rather than the HA peaks. he peaks were identified to be corresponding to β-cp and indexed according to the standard card (JCPDS ). he intensity of the additional peaks increases from BCP2 to BCP3 indicating that the amount of β-cp decreases as the excess amount of the Ca/P ratio of reactants is increased during the preparation procedure (at constant ph). he sample BCP1 shows peaks of β-cp. his indicates that single phase β-cp was successfully synthesized at temperatures 1100 C [10]. he XRD pattern of BCP4 in Fig. 2 shows well-characterized peaks of pure, and the peaks were indexed according to the standard pattern (JCPDS 09- (b) BCP1 BCP2 BCP3 BCP4 ABLE II. HE EXPERIMENAL DAA OF FOUR BCP POWDERS Sample β-cp β-cp-riched-bcp HA-riched-BCP HA Initial Ca/P ratio ph Aging time For investigation of network accuracy, 4 extra data were run by the networks, and the predicted results were close to the experimental results. For these 4 supplementary data, the

4 network with 10 neurons in its hidden layer has the highest accuracy. (b) Figure 2. XRD patterns of BCP sample Figure3. FIR patterns of BCP samples According to Fig 4., the slope of the regression lines of network 5,10,50 neurons in its hidden layer were 1, 0.99, and 0.90 respectively. So far, prediction of product Ca/P using a network with ten neurons is proposed. (a) (c) Figure 4(a-c). Neural networks regression plots for four extra data a: 413-8/5, b: /10, c: /50 IV. CONCLUSION Biphasic calcium phosphate synthesis condition can be predicted by an ANN approach using the initial Ca/P ratio and ph as inputs and reactants Ca/P ratio as output. By changing the configuration of network, the amount of error can be optimized for having the best prediction. Levenberg-Marquardt back propagation algorithm was designed in which the neural network with 50 neurons has the maximum errors in predicting the reactant Ca/P ratios due to over-fitting caused by using too many neurons in the hidden layer. he ANN with 10 neurons in hidden layer has minimum errors in predicting Ca/P ratio of products, and fewer numbers of neurons can decrease the time it takes to train the network. his well-trained ANN with 10 neurons is expected to be very helpful and powerful for predicting the biphasic calcium phosphate synthesis condition.

5 REFERENCES [1] A. Farzadi,M. Solati-Hashjin, F. Bakhshi, A. Aminian, Synthesis and characterization of hydroxyapatite/ β -tricalcium phosphate nanocomposites using microwave irradiation, Ceramics International, Vol. 37, pp. 65 7, 2011 [2] S. J. Kalita, A. Bhardwaj, H. A. Bhatt, Nanocrystalline calcium phosphate ceramics in biomedical engineering, Materials Science and Engineering C, Vol. 27, pp , [3]. V. hamaraiselvi, S. Rajeswari, Biological evaluation of bioceramic materials A Review, rends Biomater. Artif. Organs, Vol.18, pp. 9-17, [4] I. Mobasherpour, M. Solati-Hashjin, A. Kazemzadeh, Synthesis of nanocrystalline hydroxyapatite by using precipitation method, Journal of Alloys and Compounds, Vol. 430, pp , [5] M. Paliwal and U.A. Kumar, Neural networks and statistical techniques: A review of applications. Expert Systems with Applications, 36 (2009) [6] I. Mukherjee, S. Routroy, Comparing the performance of neural networks deeloped by using Levenberg- Marquardt and Quasi- Newton with the gradient descent algorithm for modelling a multiple response grinding process, Exper Systems with Application, 39 (2012) [7] M.A. Costa, A.P. Braga, B. R. Menezes, Improving generalization of MLPs with sliding mode control and the Levenberg Marquardt algorithm, Neurocomputing, 70 (2007) [8] M.A. Costa, A.P. Braga, B. R. Menezes, Improving generalization of MLPs with sliding mode control and the Levenberg Marquardt algorithm, Neurocomputing, Vol. 70, pp , [9] Abraham, A., 129: Artificial Neural Networks. Handbook of Measuring System Design, PH Sydenham and R. horn, eds. John Wiley & Sons, [10] A. Esin, N. Mahmutyazıcıoğlu, S. Altıntaş, Drying and sintering of ceramic based parts using microwave heating, Key Engineering Materials, Vol. 264, pp , 2004