A Review on Basics of Artificial Neural Network and its Applications in Dosage Form Design

This article is an attempt to make the existing and future generation of pharmaceutical formulators aware of all the essential aspects of emerging technique of artificial neural network (ANN).

A brief description of various components of ANN as well as a description of its working, which is necessary to provide clear comprehension to a novice reader, is included in this review. The review also sheds light on the various applications of artificial neural networks, which has observed an explosion of interest in recent years.

It also highlights the key factors to which the sweeping success of ANN can be attributed. It also encompasses the various advantages offered by ANN over the existing methods and its utilization for the improvement in product formulation development. The review also enlists various dosage form developed, utilizing ANN and various ANN softwares used for this purpose. It is expected that, the reader will be able to carry out research in an impressive manner after gaining thorough understanding of ANN.

Introduction

First implemented in the early 1960’s, neural network only began to develop significantly in the mid 1980’s with the introduction of new neural network architecture and advances in processing technologies. Since then, neural networks have been successfully used in variety of areas such as finance, retail, manufacturing, energy, health, telecommunications and security. The potential applications of artificial neural network (ANN) methodology in the pharmaceutical sciences range from interpretation of analytical data, drug and dosage form design through biopharmacy to clinical pharmacy.

Artificial neural networks (ANNs) are computer system developed to mimic the operations of human brain by mathematically modeling its neurophysiological structure (i.e., nerve cells and the network of interconnections between them). The basic unit of both, the mammalian nervous system and of ANN is the neuron. In the case of mammalian systems, each neuron collects input stimuli and triggers and sends the output to the next neuron in the assembly. In an ANN, computational units are called neurons and strengths of the interconnections between these neurons are represented as the “weights”. ANN attempts to simulate some of the neurological processing ability of the biological brain such as learning and drawing conclusion from experience. Therefore, the problems handled by ANN can be quite varied like-pattern recognition, pattern association, modeling and optimization application. ¹

Need And Benefits Of ANN

Various formulation and process variables relating to effectiveness, safety, and usefulness need to be optimized simultaneously while developing pharmaceutical formulations. A response surface method (RSM) has often been applied to optimize the formulation variables. The optimization procedure based on RSM includes statistical experimental designs, multiple regression analysis, and mathematical optimization algorithms for seeking the best formulation under a set of constrained equations. When the theoretical relationship between the response variables and casual factor are not clear, multiple regression analysis can be applied for the prediction of response variables on the basis of a second order equation.

The prediction of pharmaceutical responses based on second order polynomial equation, however is often limited to low levels, resulting in the poor estimation of optimal formulations. To overcome this limitation of factorial design (FD), artificial neural network (ANN) was incorporated.^2,3,4,5

Other advantages of ANN over conventional statistical technique are:-

· ANN accurately predicts results when the response variables are highly non-linear.

· A neural network also keeps in check the curse of dimensionality problem that bedevils attempts to model nonlinear functions with large number of variables.

· Neural networks are more accommodating to sparse and noisy data than statistical modeling packages. Therefore, literature or historic data can also be used for training.

·No prior knowledge of the underlying statistical nature of the problem is required.

· Neural Network has a unique ability of spotting a pattern in data. Therefore, it can be used to rank formulation variables that are most critical in influencing the parameters of interest.

· Once trained, neural networks are inherently fast and can lead to saving in both time and cost of product development.

· An ANN model, unlike statistical models operates upon the experimental data without data transformations.

·ANN requires no assumption to be made about the nature or significance of interconnections between formulation components or the relationship between the ingredients and the properties of the formulation.

Network Architecture

A neural network can consist of many neurons and the method by which neurons are organized is called as “network architecture”. ANN consists of mostly three types of layers.¹

Input layer to the neural network is the conduit through which data is presented to neural network.

Out put layer of the neural network is what actually presents the results to the user.

Hidden layers-refer to one or more layers of neurons that are arranged
between the input and output layer. Though these layers do not directly interact
with the external environment these layers have tremendous influence on the
final output and hence on the network performance.⁶

Takayama et al. described a mathematical equation to calculate the “weight”. According to him, in each hidden layer and output layer, the processing unit sums its input from the previous layer and then applies the sigmoidal function to compute its output to the next layer.⁴

The data is repeatedly presented to the neural network. With each presentation, the error between the network output is computed and desired output is computed and is fed back to the neural network. The neural network uses this error to adjust its weights such that the error will be decreased. This sequence of events is usually repeated until an acceptable error has been reached or until the network no longer appears to be learning.⁷

Although there are many network architectures, probably one of the most popular and successful is that of the multi-layer perceptron (MLP). This consists of identical neurons that are all interconnected and organized in layers. Neurons in one layer are connected to those in the next layer so that the outputs in one layer become the inputs in the subsequent layer. ⁸

Number Of Neurons Or Nodes In Different Layers

The number of neurons or nodes in the input and output layers is automatically determined by the number of input and output variables in the task to be handled. On the other hand, we need to make two important key decisions with regard to the hidden layers, namely, the number of hidden layers and the number of neurons in each such layer. Using too few neurons in the hidden layer will result in under fitting, which occurs due to failure in adequately detecting the signals in a complicated data set. Using too many neurons in the hidden layers will result in several problems such as over-fitting and an increase in the training time to such an extent that it may be impossible to adequately train the network for the practical purposes.

Therefore, a compromise has to be reached between too many and too few neurons in the hidden layers. There exists no steadfast rule for determining the hidden neuron count. One approach is to start with as few neurons as possible, usually two, train the neural network and test it. The number of hidden neurons is then increased and the process is repeated so long as the overall results of the training and testing improves significantly.6

Second approach for deciding the number of nodes in the hidden layer is to follow Kolmogorov’s theorem. According to Kolmogorov’s theorem, it is understood that twice the number of input nodes plus one is sufficient to compute any arbitrary continuous function (i.e. if we have two input node, then number of nodes in hidden layer to start with, would be calculated as 2 * 2+1=5). The general trend is to start with Kolmogorov’s number of hidden nodes and then go on increasing the number of nodes until a network with the least mean squared error is attained.

To decide the number of hidden layer is a key decision to be made. Although in theory, any number of hidden layers may be added, in general only one hidden layer is required for the majority of pharmaceutical applications. A rule of thumb indicates that 85% of all problems can be learned by neural network with single hidden layer, and this network architecture is most commonly used in formulation development. Multiple hidden layers are only necessary for those applications with extensive non-linear behaviour. ^{3, 9}

Training Of ANN

The first step in handling ANN is training the data set using input (independent variable) and output (dependent variable) using the experimentally obtained results. Training is defined as a search process for the optimized set of weight values, which can minimize the squared error between the estimation and experimental data of units in output layer.

The neural networks are entirely data driven, the implication is that data must be available to train the network and issue of “how much data” is an important factor. In practice, a good model can be developed from 3 to 4 times as many experiments as there are inputs, provided that the data are of good quality. At the beginning of the training process, the connections between the neurons are set to random weight values. During the training process, the input and output data from the training data subset are fed into the network. The difference between training output and actual output values is then calculated. The difference is an error value, which is decreased using a training algorithm during the training process by modifying the values of weights at each neuron. These modifications bring the output of the network closer to the desired output. Once trained, the network can hopefully be used to predict accurate output values for new input data X (independent variable) and Y (dependent variable). ^{1, 3}

Types Of Neural Networks And Type Of Connections

The earliest neural networks proposed by Marvin Minsky consisted of a single layer of interconnected neurons. Unfortunately, a single layer neural network, or what Rosenblatt referred to as preceptron, is not able to do much.

There are two broad classes of neural networks:

> One type is multilayer preceptron network or MLP network, which is a generalization of single layer neural network. This network does not have any feedback, and thus it is also referred to as feed forward neural network.

> The other class of network has feedback, where the output of each neuron, in general, is fed back to itself and all the other neurons. Such networks are referred to as recurrent networks. ¹⁰

The connections between layers are called inter-layer connections and they are of following types-⁶

Fully connected – each neuron on the first layer is connected to every neuron the second layer.

Partially connected- a neuron of the first layer does not have to be connected to all neurons on the second layer.

Bi – directional- there is another set of connections carrying the output of the neurons of the second layer into the neurons of the first layer.

Data Selection For Neural Networks

The ANN model developer needs to follow certain data screening guidelines to ensure integrity in the data. ¹¹

· Choose independent variables, which may exhibit influence on dependent variable. Placket-Burman screening design may be adopted to reduce the number of independent variables.

· Numeric and nominal variables can be handled. All the other variables need to be converted into these forms, or should be discarded.

· A large data set is required (the more the number of variables, the more is the number of cases required). For pharmaceutical applications, if the volume of data is small we can consider using ensembles and resampling.

· Cases with missing values can be used, if necessary, but outliers may cause problems. Therefore, we need to check data and remove the outliers. If we have sufficient data we can discard the cases with missing values.

· Redundant variables are minimized or eliminated.

Learning In Neural Networks

The process of adjusting the weights to make the network learn the relationship between the inputs and targets is called learning or training. A prescribe set of well defined rules for the solution of a learning problem is called learning algorithm. Learning algorithms differ from each other in the way in which the adjustment to a synaptic weight of a neuron is formulated. In principle, almost all learning algorithms for neural networks are iterative optimization algorithms. There are two main categories for learning, namely supervised learning and unsupervised learning.⁶

Supervised learning-

The vast majority of artificial neural network solutions have been trained with supervision. In supervised learning data are presented to neural networks as records, each of which corresponds to a formulation experiment. Each record contains both inputs and outputs. The network is initialized by putting small random weights and an output is calculated. The output is compared with the observed data. Weights that are usually randomly set to begin with, are then adjusted by the network and are compared to the desired and actual output. The learning method tries to minimize the current errors of all processing elements. This global error reduction is created over time by continuously modifying the input weights until acceptable network accuracy is reached. The method used most frequently for this is called back propagation. Back propagation can be standard incremental back propagation (here the weights are updated after each pattern) or standard batch propagation (here the weights are updated only after all the patterns have been presented to network). ^{3, 6}

When no further learning is necessary, the weights are typically frozen for the application. Some network types allow continual training, at a much slower rate, while in the operation. This helps a network to adapt to gradually changing conditions. After a supervised network performs well on the training data, it is important to see what it can do with data it has not seen before. If a system does not give reasonable outputs for this test set, the training period is not over. Therefore, this testing is critical to insure that the network has not simply memorized a given set of data but has learned the general patterns involved within application. ⁶

Unsupervised learning

Unsupervised learning is sometimes called self-supervised learning. With unsupervised learning, there is no feedback from the environment to indicate if the outputs of the network are correct. A sequence of input vectors is provided, but no target vectors are specified. The network must discover the features, regulations, correlations, or categories in the input data automatically. Thus, unsupervised learning involves trial and error type strategies and these are the type of situations which one often encountered in practice. These networks use no external influences to adjust their weights. Instead they internally monitor their performance. These network look for regularities or trends in the input signals and makes adaptations according to the function of the network.

When the system uses input data to change its weight to learn the domain knowledge, the system could be in training mode or learning mode. When the system is being used as a decision aid to make recommendations, it is in the operation mode, this is also sometimes called recall. ⁶

Learning Rules

These rules are mathematical algorithms used to update the connection weights. Given below is few of the major rules-⁶

Hebbian learning rule- according to this rule, if a neuron receives input from another neuron and if both are highly active (mathematically have the same sign), the weight between the neurons should be strengthened. For the neurons operating in the opposite phase, the weights between them should be weakened. If there is no correlation, the weights should remain unchanged.

Correlation learning rule- it is based on similar principles as the Hebbian learning rule. It assumes that weights between simultaneously responding neurons should be largely positive and between the neurons with opposite reaction should be largely negative. Instead of actual response, the desired response is used for weight change calculation.

Competitive learning rules- here the output neurons of an ANN compete among themselves to become activated or fired, with the result that only one output neuron, or one neuron per group, is on at one time. An output neuron that wins the competition is called winner neuron. One way of inducing competition among the output neurons is to use lateral inhibitory connections between them.

The delta rule- this is basically an error correction learning rule. It is one of the most commonly used. This rule is based on the simple idea of continuously modifying the strengths of input connections to reduce the difference (the delta) between the desired output value and the actual output of processing element. This rule changes the synaptic weights in the way that minimizes the mean squared error of the network. This rule is also referred to as Widrow- Hoff Learning rule or Least Mean square (LMS) learning rule. Out of the above mentioned rules the most popular one is the delta rule.

Learning Materials For Anns

Learning in neural networks obviously implies that some learning material should be provided to it to learn from. In case of ANN any non-numerical data must be processed in such a way to obtain a numeric representation. A “data set” is a matrix containing several samples. In Ann methodology, the data set is often sub divided into “training” and “test” sets. A training set is a set of examples used for learning, which is to fit the parameters [i.e., weights] of the classifier. A validation set is a set of examples used to tune the parameters [i.e., architecture, not weights] of a classifier, for example, number of hidden units.

A test set is a set of examples used only to assess the performance [generalization] of a fully specified classifier. Training sets needs to be fairly large to contain all the needed information if the network is to learn the features and relationship that are important. Not only do the sets have to be large but also the training session must include a wide variety of data. ⁶

Network Validation

The primary risk in developing a model is that of over training, a situation in which the neural network starts to reproduce the noise specific to a particular sample in the training data, which may cause it to lose its ability to predict accurately. There are certain techniques that are used to avoid this; the most popular of this is network validation. The testing of the network predictivity is done by reserving some of the data, which is excluded from the training data sets. The network is used to predict the outputs for these reserve data records, and the calculated outputs are compared with the observed values. If they are found to be sufficiently close, the network is considered to be sufficiently predictive and the network is said to be validated. ³

Generalization

Generalization is the ability of a neural network to produce reasonable responses to input patterns that are similar, but not identical, to training patterns. Once it is claimed that neural network has been trained properly or it is said that the neural network has learned the concept. Then it is expected that neural network produces the correct output for previously unknown inputs, but belonging to the same concept class. Then, the trained neural network has the capability to generalize. For example, if we have trained a neural network using several images (poses) of the leopard. If the neural network has been well trained it is expected that when one presents another image (pose) of leopard, which was not a part of training set, the neural network should be able to recognize the presented image as a image of leopard. This is what is meant by generalization.¹⁰

Disadvantages Of ANN

The major disadvantage of ANN is that, they are by nature black boxes; the relationship that the network finds cannot be expressed easily in mathematical form. The primary risk in developing a model is that of overtraining, a situation in which the neural network starts to reproduce the noise specific to a particular sample in the training data, which may cause it to lose its ability to predict accurately. This disadvantage can be removed as mentioned earlier by performing network validation .³

ANN requires the use of sophisticated software’s whereas the (response surface methodology) RSM can be done using the earliest software such as EXCEL.

Applications Of Ann In Product Formulation Development

Table below enlists various dosage forms, which have been designed or studied using the technique of ANN.

Softwares Available To Handle ANN Problems

A large number of integrated computer programs based on ANN are now commercially available. These programs are now being used widely and are gaining more and more acceptance in Pharma sector. Examples of such programs based on ANN, which have been used to design or study different dosage forms are enlisted below-

Conclusion

Over the past few years neural networks have gained more acceptances in modeling pharmaceutical formulation than in any comparable field. The main business benefits offered by ANN are enlisted below-

·Enhancement of product quality and performance at low cost.

·Shorter time to market

·Development of new products

·Improved customer response

·Improved confidence

Overall the use of ANN offers a new dimension to pharmaceutical systems study because of its unique advantages, such as nonlinear processing capacity and the ability to model poorly understood systems. It is very suitable for simulations and optimization and for the exact study of systems from all points of view, without performing additional experiments. ¹⁸

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Neelima .R. Mehta completed Bachelors in pharmacy from Gujarat
University in 2003,currently working as a research scholar in the department
of pharmaceutics and pharmaceutical technology of L.M College of pharmacy of
Gujarat University and recipient of two gold medals for scoring highest marks
in the subject of pharmaceutical technology and clinical pharmacology for the
year 2003.

M.C. Gohel*

Pricipal, L. M. College of Pharmacy, P. O. Box 4011, Navarangpura, Ahmedabad
380 009. E-mail: mukeshgohel@hotmail.com

*Corresponding author.