Saudi Journal of Kidney Diseases and Transplantation

: 2010  |  Volume : 21  |  Issue : 6  |  Page : 1073--1080

A comparative study of artificial neural network and multivariate regression analysis to analyze optimum renal stone fragmentation by extracorporeal shock wave lithotripsy

Neeraj K Goyal1, Abhay Kumar1, Sameer Trivedi1, Udai S Dwivedi1, TN Singh2, Pratap B Singh1,  
1 Department of Urology, Institute of Medical Sciences, Banaras Hindu University, Varanasi, India
2 Department of Earth Sciences, Indian Institute of Technology, Mumbai, India

Correspondence Address:
Pratap B Singh
Department of Urology, Institute of Medical Sciences, Banaras Hindu University, Varanasi 221 005


To compare the accuracy of artificial neural network (ANN) analysis and multi­variate regression analysis (MVRA) for renal stone fragmentation by extracorporeal shock wave lithotripsy (ESWL). A total of 276 patients with renal calculus were treated by ESWL during December 2001 to December 2006. Of them, the data of 196 patients were used for training the ANN. The predictability of trained ANN was tested on 80 subsequent patients. The input data include age of patient, stone size, stone burden, number of sittings and urinary pH. The output values (predicted values) were number of shocks and shock power. Of these 80 patients, the input was analyzed and output was also calculated by MVRA. The output values (predicted values) from both the methods were compared and the results were drawn. The predicted and observed values of shock power and number of shocks were compared using 1:1 slope line. The results were calculated as coefficient of correlation (COC) (r2 ). For prediction of power, the MVRA COC was 0.0195 and ANN COC was 0.8343. For prediction of number of shocks, the MVRA COC was 0.5726 and ANN COC was 0.9329. In conclusion, ANN gives better COC than MVRA, hence could be a better tool to analyze the optimum renal stone fragmentation by ESWL.

How to cite this article:
Goyal NK, Kumar A, Trivedi S, Dwivedi US, Singh T N, Singh PB. A comparative study of artificial neural network and multivariate regression analysis to analyze optimum renal stone fragmentation by extracorporeal shock wave lithotripsy.Saudi J Kidney Dis Transpl 2010;21:1073-1080

How to cite this URL:
Goyal NK, Kumar A, Trivedi S, Dwivedi US, Singh T N, Singh PB. A comparative study of artificial neural network and multivariate regression analysis to analyze optimum renal stone fragmentation by extracorporeal shock wave lithotripsy. Saudi J Kidney Dis Transpl [serial online] 2010 [cited 2021 Oct 24 ];21:1073-1080
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Artificial neural network (ANN) is a division of the "Artificial Intelligence", other than Case Based Reasoning, Expert Systems, and Genetic Algorithms. The Classical statistics, Fuzzy logic and Chaos theory are also considered to be related areas. The ANN is an information pro­cessing system that simulates the structure and functions of the human intellect. It attempts to reproduce the approach in which the human brain works in processes such as studying, re­membering, reasoning and inducing with a complex network which is executed by com­prehensively connecting various processing units. It is a highly interconnected structure that consists of many simple processing elements (called neurons) capable of performing mas­sively parallel computation for data processing and knowledge representation. The paradigms in this area are based on direct modeling of the human neuronal system. [1] A neural network can be considered as a smart hub that is able to forecast an output pattern when it recognizes and learns a given input pattern. The neural network is first trained by processing a large number of input patterns and shows what out­put resulted from each input pattern. The neural network is able to recognize resemblance when presented with a new input pattern (even in imprecise data) after proper training and re­sults in a predicted output pattern.

Neural networks may be used as a direct re­placement for autocorrelation, multivariable regression, linear regression, trigonometric and other statistical analysis techniques. When data are analyzed using a neural network, it is po­ssible to detect important predictive patterns that were not previously perceptible to a non­expert system. Thus, the neural network can act like an intelligent system. Particular net­work can be distinct using three fundamental components: transfer function, network archi­tecture and learning law. [2] One has to define these components, depending upon the problem to be solved.

 Network Training

A network first needs to be trained before ex­tracting new information. Numerous different algorithms are available for training of neural networks. But the back propagation algorithm (capable to solve complex predicting problems) is the most adaptable and robust technique, which endows with the most proficient lear­ning procedure for multilayer neural networks. It consists of at least three layers: input layer, hidden layer and output layer. Each layer con­sists of a number of elementary processing units called neurons, and each neuron is con­nected to the next layer through weights, i.e. neurons in the input layer will send its output as an input for neurons in the hidden layer and similar is the connection between hidden and output layer. According to the problem to be solved, number of hidden layers and number of neurons in the hidden layer changes. The num­ber of input and output neurons is the same as the number of input and output variables.

To make a distinction between the different processing units, values called biases are intro­duced in the transfer functions. These biases are referred to as the weight of a neuron. Except for the input layer, all the neurons in the back propagation network are connected with a bias neuron and a transfer function. The application of these transfer functions depends on the pur­pose of the neural network. The output layer produces the computed output vectors corres­ponding to the solution.

During training of the network, data are pro­cessed through the input layer to hidden layer, until they reach the output layer (forward pass). In this layer, the output is compared to the mea­sured values (the "true" output). The difference or error between both is processed back through the network (backward pass), updating the in­dividual weights of the connections and the biases of the individual neurons. The input and output data are mostly represented as vectors called training pairs. The process as mentioned above is repeated for all the training pairs in the data set, until the network error converged to a threshold minimum defined by a corres­ponding cost function; usually the root mean squared error (RMS) or summed squared error (SSE).

[Figure 1] the j th neuron is connected with a number of inputs{Figure 1}

x i = (x 1 , x 2, x 3 , xn )

The net input values in the hidden layer will be



xi = input units,

w ij = weight on the connection of ith input and jth neuron,

θj = bias neuron (optional), and

n = number of input units.

So, the net output from hidden layer is cal­culated using a logarithmic sigmoid function

O j = f(netj) = 1/1 + e -(netj+θj)

The total input to the kth unit is



θk = bias neuron and

w jk = weight between jth neuron and kth output.

So, the total output from 1 th unit will be

O k = f(netk).

In the learning process, the network is pre­sented with a pair of patterns, an input pattern and a corresponding desired output pattern. The network computes its own output pattern using its (mostly incorrect) weights and thresholds. Now the actual output is compared with the desired output. Hence, the error at any output in layer k is

e k = t k - O k


t k = desired output and

O k = actual output.

The total error function is given by


Training of the network is basically a process of arriving at an optimum weight space of the network. The descent down error surface is made using the following rule:



η is the learning rate parameter and

E is the error function.

The update of weights for the (n + 1) th pattern is given as:


Similar logic applies to the connections bet­ween the hidden and output layers. [3] Each pass through all the training patterns is called a cycle or an epoch. The process is then repeated as many epochs as required until the error is within the user specified goal is reached fruitfully. This quantity is the measure of how the net­work has learned.

 Multivariate Regression Analysis

The purpose of multiple regressions is to learn more about the relationship between several independent or predictor variables and a de­pendent or criterion variable. The goal of re­gression analysis is to determine the values of parameters for a function, which cause the function to best fit a set of data observations provided. In linear regression, the function is a linear (straight-line) equation. When there is more than one independent variable, then mul­tivariate regression analysis is used to get best­fit equation. Multiple regressions solve the data sets by performing least squares fit. It cons­tructs and solves the simultaneous equations by forming the regression matrix and solving for the co-efficient using the backslash operator.

Renal calculus is a common problem in daily urological practice, and despite the advances in the diagnostic and therapeutic modalities, there is considerable morbidity in managing these cases. Since its introduction in 1980, extracor­poreal shock wave lithotripsy (ESWL) is the only noninvasive treatment of choice for most renal calculi despite its pitfalls. [5],[6],[7] The most distressing condition for an urologist is when stone does not get fragmented after four sittings of ESWL and an alternative treatment is re­quired. This is what is known as optimum frag­mentation (defined as none of the remaining fragments of >4 mm).

The possibility of determining the optimum fragmentation by ESWL [8],[9] before the start of treatment includes the traditional statistical mo­dels to solve such problems. [10] We have already established the application of ANN in optimum renal stone fragmentation by ESWL. [8]

Most centers follow the usual guidelines on indications and contraindications for ESWL, mainly including stone size and the presence or absence of distal obstruction. Other factors influencing stone fragmentation are invariably not considered or may be difficult to assess. So, there is a need to know the modality which assesses the patients who will be best managed by ESWL. There are various studies predicting the fragmentation of stone, i.e. by compute­rized tomography attenuation value of renal stone, [11] spontaneous ureteral calculus passage by an ANN [12] and a neural computational mo­del of stone recurrence after ESWL. [13]

In this study, to further validate the ANN application, we compared this modality with a larger population of patients undergoing ESWL and compared the results with statistical model, i.e. multivariate regression analysis (MVRA).

 Materials and Methods

Our institute is a tertiary health care center. A total of 328 patients with renal calculus were treated by ESWL during December 2001 to December 2006 in our institution. We followed the usual guidelines for indication and contra­indication for ESWL. The patients were treated using an electro hydraulic lithotripter. As per the protocol, we delivered ≤13,000 shocks/ stone, involving not more than four ESWL sittings (with a power range of 14-18 kV and a shock frequency of 60-90/minute). The opti­mum stone fragmentation was defined as no fragments (after fragmentation) of >4 mm. We included 276 patients who had successful frag­mentation and in whom were followed the cri­teria for ESWL strictly, i.e. stone size <2 cm in non-obstructed system. All calyceal stones which were not cleared with ESWL were excluded from study to give it uniform parameters.

Out of 276 patients, the data of 196 patients were used for training the ANN. The network was trained using the MATLAB software sys­tem; the working code for the ANN was cons­tructed so that it was compatible with the ana­lysis and processing of the input data.

Network architecture

Feed forward network was adopted here as this architecture was considered to be suitable for problem based on pattern recognition. Pat­tern matching is basically an input/output map­ping problem. The architecture of the network is shown in [Table 1].{Table 1}

Testing and validation of ANN model

To test and validate the ANN model, the new data set was chosen. These data were not used while training of the network. They validate the use of ANN in a more versatile way. The results are presented in this section to demons­trate the performance of the network. The co­efficient of correlation (COC) between the pre­dicted and observed values is taken as the per­formance measures. The predictability of trained ANN was tested on 80 subsequent patients. The prediction was based on the input data sets. The input data remained the same as that used for the training, which included age of patient, stone size, stone burden, number of si­ttings and urinary pH. The output values (pre­dicted values) were number of shocks and shock power. Of the same 80 patients, the in­put was analyzed and output was calculated by MVRA. The output values (predicted values) from both the methods were compared and re­sults were drawn.

Training of the network was done using one hidden layer with four hidden neurons. As Bayesian regulation [4] was used, there was no danger of over-fitting problems. Hence, the network was trained with 700 training epochs. The performance of the ANN during training is shown in [Figure 2].{Figure 2}

Multivariate regression analysis

MVRA equation for prediction of power = 7.4993 - 0.0403*(AGE) - 0.7371*(SIZE) + 1.4020*(BURDEN) - 0.5457*(SITTINGS) +1.7037*(pH)

MVRA equation for prediction of number of shocks = -20026 - 87*(AGE) - 258*(SIZE) + 1808*(BURDEN) + 767*(SITTINGS) + 4559*(pH)


The ANN COC between the predicted values and observed values highly correlated with each other as given in [Figure 3] and [Figure 4]. [Figure 5] and [Figure 6] show the poor correlation co-efficient for pre­dicted power and shocks by MVRA. [Figure 7] and [Figure 8] show the comparison of measured and predicted power and numbers of shock by ANN and MVRA, respectively.{Figure 3}{Figure 4}{Figure 5}{Figure 6}{Figure 7}{Figure 8}


In our study, we compared the ANN analysis and the MVRA results, which showed a high degree of correlation for the former. The ANN is therefore a better option for pre­diction of power and shock using five impor­tant and easily determined parameters which can save time and complications in patients undergoing ESWL.

Being a non bias system, it does not follow any over fitting and under fitting of datasets as the case may be with MVRA. [Figure 7] and [Figure 8] indicate very clear comparison between mea­sured and predicted shock power and number of shocks using ANN and MVRA. ANN in our model adds on to the quest of predicting fruit­ful outcome of ESWL. [9],[10],[11],[12],[13]


ANN gives better COC because it overcomes the shortcomings of the statistical analysis by MVRA. Hence, ANN is probably a better tool to predict the optimum renal stone fragmen­tation by ESWL. Further use of this model on a larger scale will clarify its role in ESWL.[Table 2]{Table 2}


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