

Year : 2011  Volume
: 22
 Issue : 4  Page : 705711 

Artificial neural network for prediction of equilibrated dialysis dose without intradialytic sample 

Ahmad Taher Azar^{1}, Khaled M Wahba^{2}
^{1} Electrical Communication & Electronics Systems Engineering department, Modern Science and Arts University (MSA), 6th of October City, Egypt ^{2} Systems and Biomedical Engineering Department, Faculty of Engineering, Cairo University, Egypt
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Date of Web Publication  9Jul2011 




Abstract   
Postdialysis urea rebound (PDUR) is a cause of Kt/V overestimation when it is calculated from predialysis and the immediate postdialysis blood urea collections. Measuring PDUR requires a 30or 60min postdialysis sampling, which is inconvenient. In this study, a supervised neural network was proposed to predict the equilibrated urea (C _{eq)} at 60 min after the end of hemodialysis (HD). Data of 150 patients from a dialysis unit were analyzed. C _{eq} was measured 60 min after each HD session to calculate PDUR, equilibrated urea reduction rate _{eq} (URR), and ( _{eq} Kt/V). The mean percentage of true urea rebound measured after 60 min of HD session was 19.6 ± 10.7. The mean urea rebound observed from the artificial neural network (ANN) was 18.6 ± 13.9%, while the means were 24.8 ± 14.1% and 21.3 ± 3.49% using Smye and Daugirdas methods, respectively. The ANN model achieved a correlation coefficient of 0.97 (P <0.0001), while the Smye and Daugirdas methods yielded R = 0.81 and 0.93, respectively (P <0.0001); the errors of the Smye method were larger than those of the other methods and resulted in a considerable bias in all cases, while the predictive accuracy for ( _{eq} Kt/V) _{60} was equally good by the Daugirdas' formula and the ANN . We conclude that the use of the ANN urea estimation yields accurate results when used to calculate ( _{eq} Kt/V).
How to cite this article: Azar AT, Wahba KM. Artificial neural network for prediction of equilibrated dialysis dose without intradialytic sample. Saudi J Kidney Dis Transpl 2011;22:70511 
How to cite this URL: Azar AT, Wahba KM. Artificial neural network for prediction of equilibrated dialysis dose without intradialytic sample. Saudi J Kidney Dis Transpl [serial online] 2011 [cited 2020 Jun 6];22:70511. Available from: http://www.sjkdt.org/text.asp?2011/22/4/705/82647 
Introduction   
Postdialysis urea rebound (PDUR) is due to the intercompartmental equilibration of urea during hemodialysis (HD) and supports the concept of an intradialytic twopool model to calculate the dialysis dose. These compartments are considered to be extracellular and intracellular. ^{[1],[2]} PDUR is a critical problem, which influences the calculation of equilibrated urea (C _{eq)} and increases the risk of inaccurate estimation of the dose of dialysis; ^{[3]} Kt/V is greater than that actually achieved in the HD patients when calculated using the immediate postdialysis blood urea concentration. ^{[4]} Because a delay of 3060 min after dialysis before sampling the urea is inconvenient for both the clinician and patients, several methods have been devised to predict the PDURequilibrated Kt/V. ^{[5],[6],[7],[8],[9],[10],[11],[12],[13]}
Smye et al ^{[5],[13]} predicted C _{eq} concentration using the principle of mass conservation and then employed this C _{eq} to calculate the equilibrated dialysis dose ( _{eq} Kt/V). Daugirdas ^{[6],[7],[8]} proposed a simpler method, where a singlepool Kt/V is modified according to the speed of dialysis (K/V) to obtain a doublepool estimate of Kt/V. These two approaches make some biological assumptions that are not always true, but remain the most accepted models.
Recently, Guh et al applied an artificial neural network (ANN) method to deal with this problem using the AINET neural network, which is a selforganizing system derived from a probabilistic approach. ^{[14]} In this method, a supervised neural network model was proposed to predict the C _{eq} 60 min after the end of HD and we also employed the BlandAltman agreement method to compare the different predictive methods. ^{[15]} The ANN is the wellknown multilayer perceptron (MP) trained with the LevenbergMarquardt (LM) algorithm as shown in [Figure 1]. ^{[16],[17],[18]}
We aim in this study to evaluate the ANN utilization in predicting the rebound of urea and the different input parameter combinations in order to find the most predictive ones and all the results are compared with those of the Smye and Daugirdas models.
Methodology   
We studied 156 stable HD patients in a dialysis unit. The selection criteria included: (a) patients without infections or hospitalizations in the previous 30 days and (b) all the patients who had AV fistulas with blood flow rate (Q _{B} ) ≥300 mL/min. All the patients received HD three times a week with Fresenius machines (model 4008B; Fresenius Medical Care, Bad Homburg, Germany) with variable bicarbonate and sodium. Hollowfiber polysulfone (1.3 m ^{2} and 1.6 m ^{2} low flux dialyzers, Fresenius Medical Care, Bad Homburg, Germany) dialyzers were used. For the purpose of this study, all patients were dialyzed over 240 min, and blood and dialysate flows were fixed at 300 and 500 mL/min, respectively. The mean age of the patients was 48.2 ± 13.4 years, and the mean predialysis body weight ( _{pre} BW) was 68.8 ± 15.5 kg. The mean ultrafiltration (UF) (difference between preand postdialysis body weights) was 8.54 ± 5.15 mL/min. All blood samples were obtained at the midweek HD session. Four blood samples were obtained from the arterial line at different times for urea determinations: (1) urea predialysis (C _{pre} ) at the beginning of the procedure, (2) intradialysis urea (C _{int} ) at the middle of the HD session, (3) urea postdialysis (C _{post} ) at the end of the HD session, and (4) equilibrated urea (C _{eq} ) at 60 min after the end of HD. To extract the blood samples for the determination of the intradialysis urea (C _{int} ) and postdialysis urea (C _{post} ), the Q _{B} was slowed to 50 mL/min and the blood was extracted 15 s later. In this situation, access recirculation stops or ceases, and the dialyzer inlet blood reflects the arterial urea concentration. The intradialysis sample (C _{int} ) was obtained 80 min after the beginning of the HD session in order to make the results comparable with those reported by Guh et al ^{[14]} and because Smye et al ^{[5]} originally proposed that the intradialysis sample be obtained between 60 min after the beginning of the session and before the last 20 min of the end of it.
A. Methods for estimating equilibrated urea concentration (C _{eq} )
1. Gold Standard method: The true C _{eq} measured from the blood samples taken at 60 min after the end of the HD session was used as a "gold standard" for postdialysis C _{eq} and urea rebound (UR) was calculated as:
2. Smye method: ^{[5]} The value of equilibrated BUN (C _{eq} ) was calculated from the Smye method according to the following equation:
where C _{eq} is the concentration at the equilibrium; C _{o,} C _{s} , and C _{post} are urea concentrations at the start, at time s and at the end of dialysis, respectively; t is the dialysis time (in minutes), t _{s} is the time when the C _{s} sample was taken.
3. ANN Method: ANN is proposed in this paper as a predictor of the C _{eq} . NNs are mathematical models that grew out of early attempts to model the behavior of the human central nervous system. They usually consist of a set of simple processing units ("neurones") that are highly interconnected through coefficients called weights ("synapses"). The NNs resemble the brain in two main aspects: (a) knowledge is acquired by the network from its environment through a learning process and (b) interneuron connection strengths, known as synaptic weights, are modified during the learning process and used to store the acquired knowledge. ^{[17]} The chosen model was the MP, which is a feedforward ANN model with one input layer (equal in size to the number of input variables), hidden layers (none, one, or several), and an output layer. ^{[17],[18]} Each layer is connected by numerical coefficients called weights resembling neural synapses. The ANN was trained with a modified back propagation algorithm, which is a supervised learning strategy that consists of the modification of the weight values in order to minimize an error function, when an input/ output pair is presented to the net. ^{[17],[19]} The LM training algorithm was used, which is an intermediate optimization algorithm between the GaussNewton method and gradient descent algorithm, addressing the shortcomings of each of those techniques. ^{[16]} LM uses gradient descent to improve on an initial guess for its parameters and transforms to the GaussNewton method as it approaches the minimum value of the cost function. Once it approaches the minimum, it transforms back to the gradient descent algorithm to improve the accuracy. The net was trained to predict the C _{eq} from the following independent variables: Predialysis BUN (C _{pre} ), dialysis time in minutes (T _{d} ), blood flow rate (BFR), ultrafiltration rate (UFR) and postdialysis BUN (C _{post} ) as shown in [Figure 2]. Different net sizes were tested in order to look for the most appropriate number of hidden nodes. Once the net size selection was made, different parameter combinations were tested to build the ANN model, in order to see their influence in the prediction process and evaluate their importance in the predictive model. The hidden layers were given a logistic sigmoid transfer function and the output layer consisted of a single node with a linear transfer function.  Figure 2: Comparison plot between equilibratedBUN and other prediction methods.
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B. Equilibrated Kt/V formulas
A singlepool Daugirdas formula was used to calculate the singlepool Kt/V (Kt/V _{sp} ): ^{[7]}
where R = U _{post} /U _{pre} , UF is ultrafiltration, W is the postdialysis body weight, and t is the duration of the dialysis session in hours.
1. Gold standard Method: To derive the "gold standard" equilibrated Kt/V ( _{eq} Kt/V), we use the Kt/V _{sp} of equation 3, substituting the "equilibrated" postdialysis BUN for the immediate postBUN when computing R:
where the C _{eq60} is the measured urea concentration from a blood sample taken at 60 min after the end of HD. The _{eq} (Kt/V) _{60} was used as a reference for comparison purposes.
2. Smye Method: The equilibrated Kt/V using Smye method can be calculated by the following formula:
where C _{eqSmye} is the estimated C _{eq} with the intradialysis urea sample explained above.
3. The equilibrated Kt/V using ANN method can be calculated by the following formula:
where the C _{eqANN} is the ANN estimation of C _{eq} .
4. The doublepool Daugirdas formula ^{[7]} was also used to estimate the _{eq} Kt/V ( _{eq} Kt/V _{Dau} ):
All the estimated _{eq} Kt/V ( _{eq} Kt/V _{Dau} , _{eq} Kt/V _{Smye} and _{eq} Kt/V _{ANN} ) were compared against the "gold standard equilibrated Kt/V" _{eq} (Kt/V) _{60.}
C. Training process of the ANN
In the net size selection process, complete data were randomly mixed and two training/ test set pairs were built as follows: (A) training: first 70% of the samples, test: last 30% of the samples; (B) training: last 70% of the samples, test: first 30% of the samples. In this way, the jackknife method ^{[18]} is applied for validation purposes. The mean squared error (MSE) between the net's output and the C _{eq} of the test sets was averaged over ten training procedures (five for each training/test set pair) and the net size, which achieved the lowest MSE, was selected. Once the net size and the input parameters were selected, a new net was trained with an early stopped method to improve generalization. In this technique, the available data were divided into three subsets. The first subset is the training set, which is used for computing the gradient and the network weights (60% of the samples). The second subset is the validation set (20% of the samples). The error on the validation set is monitored during the training process. The third subset is the test set (20% of the samples). The validation error normally decreases during the initial phase of training, as does the training set error. However, when the network begins to over fit the data, the error in the validation set typically begins to rise. When the validation error increases for a specified number of iterations, the training is stopped, and the weights and biases at the minimum of the validation error are returned. ^{[16]} This net (ANN) was used to predict the C _{eq} .
D. Comparison analysis
All the methods (the selected ANN, Smye and Daugirdas methods) were compared against the C _{eq} measured from the blood samples taken at 60 min after the end of the HD session. In all cases, the following coefficients were used: (i) correlation: index of direct association between two methods and (ii) BlandAltman agreement method: ^{[8]} this method is based on the analysis of the average and the standard deviation of the difference between the model and the "gold standard", against the true value ("gold standard"). All methods of equilibrated Kt/V were compared using the same analysis as explained above. The results were compared against the "gold standard Kt/V" _{eq} (Kt/V) _{60} equation 4.
Results   
An ANN with two hidden nodes was selected because it achieves the lowest MSE and is robust to different initialization procedures of the ANN initial weights.
The ANN model showed more accuracy and better correlation coefficient (R) than the Smye method [Table 1]. In all the patients, the ANN achieved an R = 0.91 versus an R = 0.75 (P <0.0001) obtained with the Smye method.
The results of urea rebound prediction methods are summarized in [Table 2]. The mean percentage of true urea rebound measured after 60 min of the HD session was 19.6 ± 10.7. The mean urea rebound observed from the ANN was 18.6 ± 13.9%, while the means of urea rebound using Smye and Daugirdas methods were 24.8 ± 14.1% and 21.3 ± 3.49%, respectively. The ANN model achieved an R = 0.97, while the Smye and Daugirdas methods yielded R = 0.81 and 0.93, respectively (P <0.0001). The percentage errors of the Smye method were bigger than the percentage errors achieved by Daugirdas and ANN methods for both the mean and the standard deviation.
The C _{eq} estimated from the Smye method and ANN model was used to estimate the _{eq} (Kt/V). _{eq} (Kt/V) was also estimated with doublepool Daugirdas formula (equations 7 and 8). All these estimates were compared against the "gold standard KtV" _{eq} (Kt/V) _{60} calculated using equation 4. The true _{eq} (Kt/V) _{60} was 1.13 ± 0.34, while the the _{eq} (Kt/V) using Smye, Dauigirdas and ANN were 0.93 ± 0.46, 1.08 ± 0.54 and 1.17 ± 0.23, respectively. [Table 3] shows that the value of the calculated _{eq} (Kt/V) using the C _{eq} Smye estimation was the smallest of those calculated by the other methods. In addition, Smye had the smallest correlation coefficient and the biggest percentage error, not only showing a considerable bias in all cases, but also showing the highest level of inaccuracy. Finally, the predictive accuracy for _{eq} (Kt/V) _{60} was equally good by the Daugirdas and the ANN formulas.
Discussion   
ANN has been successfully applied in many biomedical problems and we have demonstrated in this study their ability to accurately predict the C _{eq} with the corresponding benefits for the true dose calculations for HD patient without the need for an intradialytic sample. The ANN model is more accurate than the Smye formula because the ANN model showed, from a BlandAltman point of view, lower mean and standard deviation errors. The analysis of % error against the % of urea rebound showed that the ANN is very robust to the level of urea rebound. The Smye method overestimated for % UR by about 26.6%. The _{eq} Kt/V estimated with the C _{eq} calculated with the Smye formula is not appropriate because it shows a great dispersion. The BlandAltman analysis showed that the Smye method underestimated the _{eq} (Kt/V) _{60} by about 17.7%. This bad result could be explained by the consideration discussed above. The Daugirdas rate equation is accurate and the results agree with the results of the HEMO study. ^{[12]} The _{eq} (Kt/V) calculated with the C _{eq} estimated by the ANN is also accurate, and it showed a lower bias and greater robustness to noisy data. However, the ANN model performed better than the Daugirdas method as shown in [Figure 3]. It was found that the rate equation only slightly underestimated true _{eq} (Kt/V) _{60} by about 4.8%, while the ANN method overestimated the true values by about 3.7% as shown in [Figure 4].  Figure 4: Comparison plot between true equilibrated Kt/V and other methods.
Click here to view 
The intrinsic nonlinearities involved in the ANN model render this approach very promising to directly estimate the _{eq} (Kt/V) without the previous estimation of the C _{eq} . The results presented here suggest that the ANN, based on limited clinical parameters, is an excellent alternative method to other traditional urea kinetic models (UKM) for accurately predicting equilibrated urea concentrations and urea rebound in HD patients. Future studies should focus on the evaluation and analysis of new noninvasive variables in order to find the most significant ones. We conclude that this study found the ANN model a very promising analysis tool to estimate urea rebound in HD patients.
Acknowledgments   
The authors thank all the medical staff at the Nephrology Department in Ahmad Maher Teaching Hospital, Cairo, Egypt, for their invaluable support during the course of this study.
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Correspondence Address: Ahmad Taher Azar Menoufeya, Menouf, Ahmad Orabi Square, Azar Building Egypt
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PMID: 21743214
[Figure 1], [Figure 2], [Figure 3], [Figure 4]
[Table 1], [Table 2], [Table 3] 

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