NN-GVEIN: Neural Network-Based Modeling of Velocity Profile inside Graft-To-Vein Connection

Transcription

1 Proceedings of 5th International Symposium on Intelligent Manufacturing Systems, Ma1y 29-31, 2006: Sakarya University, Department of Industrial Engineering1 NN-GVEIN: Neural Network-Based Modeling of Velocity Profile inside Graft-To-Vein Connection Nurullah Arslan Industrial Engineering Department, Fatih University, Buyukcekmece, Istanbul, Turkey Phone: ext 2026, fax: Alexander Nikov Industrial Engineering Department, Fatih University, Buyukcekmece, Istanbul, Turkey Phone: ext 1038, fax: Ferhat Karaca Environmental Engineering Department, Fatih University, Buyukcekmece, Istanbul, Turkey Phone: ext 1050, fax:

2 NN-GVEIN: Neural Network-Based Modeling of Velocity Profile inside Graft-To-Vein Connection Arslan N, Nikov A, and Karaca F Abstract This paper presents the application of backpropagation neural networks (NN) to modeling of flow field inside in vitro arteriovenous graft-to-vein connection The flow field was analyzed using the experimental laser Doppler method The experimental results were used as input data for the neural networks-based modeling Experimental studies are very time consuming and expensive Whereas the NN modeling technique is time saving and cheap compared to experimental methods In this study, the advantage is that this approach does not require the model structure to be known a priori, in contrast to most of the modeling techniques The results showed that this method is a feasible technique for modeling of flow velocity profiles inside graft-to-vein connection The NN algorithm and NN structure are adaptively determined based on minimization of mean squared error The model showed good modeling performance Submission area: Systems Modeling and Simulation 855

3 NN-GVEIN: Neural Network-Based Modeling of Velocity Profile inside Graft-To-Vein Connection 1 Introduction Dialysis patients are in high risk if their blood is not cleaned using dialysis machine They have to be connected to the dialysis machine three to four days and four to five hours a day during the week The connection sides can be arteriovenous fistulae or arteriovenous (AV) graft Experimental studies were done inside the AV graft to vein connections [1-4] The velocity measurements were performed at specified location inside the connection The critical flow regions such as turbulence, low wall shear stress, secondary flow and stagnation points were found These are the regions which are very important in the formation of stenosis and thrombosis The formation of these regions inside the connection can cause the lower patency rate In this study the blood flow analysis performed inside an AV graft to vein connection experimentally was compared to the modeling done by backpropagation neural networks (NN) This modeling method can be applied to flow in different regions of the cardiovascular system such as by-pass graft, AV graft, aneurysms 2 Description of NN-GVEIN Model For modeling the velocity profile of the flow field inside graft-to-vein connection a neural networks-based model (NN-GVEIN) was proposed The neural network structure is presented in Figure 1 INPUT HIDDEN LAYER OUTPUT LAYER (1) Input parameter (2) Input parameter (3) Input parameter (k-2) Input parameter Output parameter (k-1) Input parameter (k) Input parameter tan-sigmoid function Linear transfer function +1 0 n +1 0 n -1 tansig -1 purelin Figure 1 Neural network structure 856

4 Four input parameters of NN-GVEIN model were defined They are essential for accurate modeling of the flow field inside graft-to-vein connection data As output blood stream velocities (Ui) were selected ( Table 1) Table 1 Parameters of NN-GVEIN Model PARAMETERS Input Parameters 1 Measurement location X mm 2 Vertical location Y mm 3 Graft angle α (now α =5) degrees 4 Flow rate (now=25) mm 3 /s Output Parameters Velocity U = u + v cm/s i x y DIMENSIONS Silinmiş: Table 1 3 Velocity Profiles Modeling by NN-GVEIN In the following the NN-GVEIN model is applied for modeling the velocity profiles of the flow field inside AV graft connection For this purpose are collected experimental data Based on mean squared error the best-fitting NN algorithm for the experimental data set is selected Also the optimal NN structure is determined 31 Experimental data collection Experimental data were collected inside an in vitro model of AV graft In vivo flow and geometric data were taken from the hemodialysis patients in the hospital using color Doppler ultrasound Then this data was used to make the in vitro model and to set the flow condition for experimental system In vitro data was collected using laser Doppler anemometer at thirteen different locations inside the in vitro model Figure 2 illustrates the experimental data cm/s Figure 2 Experimental data inside in-vitro model 857

5 32 Selection of the best backpropagation algorithm Thirteen neural networks - backpropagation algorithms (BP) were compared in order to select the best fitting BP algorithm of data gathered For all algorithms a two-layer network, with tan-sigmoid transfer function at hidden layer and a linear transfer function at output layer were used Ten neurons were used at hidden layer The training results are given in Table 2 Table 2 Comparison of backpropagation algorithms Silinmiş: Table Backpropagation Algorithms R-values Mean Squared Error Levenberg-Marquardt backpropagation One step secant backpropagation BFGS quasi-newton backpropagation Powell-Beale conjugate gradient backpropagation Polak-Ribiere conjugate gradient backpropagation Resilient backpropagation (Rprop) Scaled conjugate gradient backpropagation Fletcher-Powell conjugate gradient backpropagation Gradient descent with adaptive linear backpropagation Gradient descent with momentum backpropagation Gradient descent with momentum & adaptive lr backprop Gradient descent backpropagation Batch training with weight and bias learning rules The best BP algorithm with minimum training error (0 0348) is the Levenberg-Marquardt algorithm (Figure 3) The training stopped after 11 iterations because the validation error started to increase (Figure 3) The result here is reasonable, since the test set error and the validation set error have similar characteristics, and it doesn't appear that any significant change over fitting has occurred A regression analysis of network response between the network output and the corresponding target was performed The outputs of the regressions are given in Table 2 Taking into account the nonlinear dependence of the data the output seems to track the targets reasonably The R-value for Levenberg- Marquardt algorithm is Silinmiş: Table 2 858

6 7 6 Training Validation Test 5 4 Squared Epoch Figure 3 Training, validation, and test square mean errors for Levenberg-Marquardt algorithm 33 Construction of optimal NN structure With increasing of neuron number the squared mean error is decreasing for the training set The checking error decreases up to a certain point in the training and then it increases This increase represents the point of model over fitting However, increasing neuron number over 7 neurons causes not reasonable result, since the test set error and the validation set error have not similar characteristics, and a significant change over fitting occurred ( Figure 4) Therefore, the optimal neuron number for gbellmf algorithm is 7 neurons ( Figure 4) The optimal neural network structure for NN-GVEIN model is given on Figure 5 Mean Squared Error Neuron Number Silinmiş: Figure 4 Silinmiş: Figure 4 Silinmiş: Figure 5 Figure 4 Dependence between mean square error (for training) and neuron numbers 859

7 INPUT HIDDEN LAYER OUTPUT LAYER 1 1 Measurement location X 2 Vertical location Y 3 Graft angle a (now a =5) 2 Velocity (Ui) 4 Flow rate (now=25) 6 7 Figure 5 Optimal neural network structure for NN-GVEIN model 34 Velocity Profile Forecasting The jackknife is a non-parametric method for estimating a sampling distribution for a statistics [5-11] For a given sample data set and a desired statistics (eg, the mean), the jackknife computes the desired statistic with an element deleted Based on Jackknife method mean square errors (MSE) were calculated for each measurement point (Table 3) On Figure 6 the velocity profiles of experimental data and the data forecasted by NN- GVEIN for five locations inside the proximal vein segment (X= 12, 20, 28, 36 and 40) are displayed Silinmiş: Table 3 Silinmiş: Figure 6 Table 3 MSE values for each section Section # MSE Average

8 Figure 6 NF-GVEIN model results obtained by jackknife method 4 Conclusions A model based on NN was proposed for modeling the flow field inside graft to vein connection The experimental data and data found with NN model were compared at five different locations inside the proximal vein segment (X= 12, 20, 28, 36 and 40) Thirteen different NN algorithms were analyzed in order to determine the best one with lowest error The optimal NN structure was determined The velocity profiles inside graft model found by NN-GVEIN were very close to the experimental velocity profiles (Figure 6) The highest MSE was at X = 12 and the least MSE was at X = 20 This confirmed the applicability of NN-GVEIN for modeling of velocity profiles inside graft-to-vein connection and thus significantly reducing the costs for experimental data collection Acknowledgements Nurullah Arslan would like to thank to the department of Mechanical and Industrial engineering of the University of Illinois at Chicago for using the laser Doppler anemometer of the department References [1] Arslan, N, (1999), "Experimental Characterization of Transitional Unsteady Flow Inside a Graft-to- Vein Junction", PhD thesis, The University of Illinois at Chicago [2] Loth, F, Fischer, PF, Arslan, N, Bertram, CD, Lee, SE, Royston, TJ, Song, RH, Shaalan, WE, Bassiouny, HS, (2003), "Transitional flow at the venous anastomosis of an arteriovenous graft: Potential activation of the ERK1/2 mechanotransduction pathway," Journal of Biomechanical Engineering, Vol [3] Arslan N, Loth F, Bertram C, and Bassiouny, (2005), "Transitional flow field characterization inside an arteriovenous graft-to-vein anastomosis under pulsatile flow conditions", European Journal of Mechanics B/Fluids [4] Shu, MC, and Hwang, NHC, (1991), Haemodynamics of Angioaccess Venous Anastomoses, Journal of Biomedical Engineering, Vol 13, pp [5] Arvesen, JN, (1969), Jackknifing U-statistics, Ann Math Statist 40, [6] Jones, HL, (1974), Jackknife estimation of functions of stratum means, Biometrika 61, [7] Miller, RJ, (1974), The Jackknife -a review, Biometrika 61, 1-15 [8] Quenouille, MH, (1949), Approximate tests of correlation in time series, JR Statist Soc B ll, [9] Thorburn, D, (1977), On the asymptotic normality of the Jackknife, Scand J Statist 4,

9 [10] Thorburn, D, (1976), Some asymptotic properties of Jackknife statistics, Biometrika 63, [11] Tukey, J, (1958), Bias and confidence in not quite large samples (abstract), Ann Math Statist 29,