HRV and BPV neural network model with wavelet based algorithm calibration

Measurement 42 (2009) 805–814

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HRV and BPV neural network model with wavelet based algorithm calibration G. Postolache a, L. Silva Carvalho c, O. Postolache b, P. Girão b,*, I. Rocha c a

Escola Superior de Saúde, Universidade Atlântica, Antiga Fábrica da Pólvora de Barcarena 2730-036, Oeiras, Portugal Instituto de Telecomunicações, IST, Av. Rovisco Pais, 1, 1049-001 Lisboa, Portugal Instituto de Medicina Molecular, Unidade de Sistema Nervoso Autónomo, Faculdade de Medicina, Universidade de Lisboa, Av. Professor Egas Moniz - 1649-028 Lisboa, Portugal b c

a r t i c l e

i n f o

Article history: Received 20 December 2006 Received in revised form 30 December 2008 Accepted 5 January 2009 Available online 10 January 2009

Keywords: Autonomic nervous system Wavelet transform Neural network model

a b s t r a c t The heart rate and blood pressure power spectrum, especially the power of the low frequency (LF) and high frequency (HF) components, have been widely used in the last decades for quantification of both autonomic function and respiratory activity. Discrete Wavelet Transform (DWT) is an important tool in this field. The paper presents a LF and HF fast estimator that uses artificial neural networks and Daubechies DWT processing techniques. Radial Basis Function and Multilayer Perceptron neural networks were designed and implemented for fast assessment of cardiovascular autonomic nervous system control. The training values to design the networks were obtained after heart rate and blood pressure wavelets processing. The designed neural structures assure a faster evaluation tool of the sympathetic and parasympathetic autonomic nervous system control of the cardiovascular function. Ó 2009 Elsevier Ltd. All rights reserved.

1. Introduction Heart rate and arterial blood pressure are the fundamental physiological parameters for assessment of cardiovascular and hemodynamic functions in basic medical research as well as in clinical practice. During the last two decades, the spectral analysis of heart rate variability (HRV) and blood pressure variability (BPV) have been providing important insights into neuronal control of the heart and blood vessels functions and considerable diagnostic utility in assessing cardiovascular and respiratory autonomic nervous system function [1–7]. A number of studies have suggested that the measurement of variability has important prognostic cardiovascular implications [8,9]. Many studies refer to the Fast Fourier Transform as one of the important methods to obtain the low frequency (LF) and high frequency (HF) infor* Corresponding author. Tel.: +351 218417289; fax: +351 218417672. E-mail addresses: [email protected] (G. Postolache), [email protected] (O. Postolache), [email protected] (P. Girão). 0263-2241/$ - see front matter Ó 2009 Elsevier Ltd. All rights reserved. doi:10.1016/j.measurement.2009.01.003

mation [1,2] but time length constrains (not less than 5 min) and required stationarity make this method less attractive for short time intervals (5–30 s) associated to autonomic nervous system changes. Digital wavelet transforms proved to be a good solution [7,9–13] for time–frequency analysis of heart rate and blood pressure signals allowing time visualization of the contribution of the LF signal component (related with sympathetic outflow), of the HF signal component (related with parasympathetic outflow and respiratory rhythm) and of the LF/HF ratio as an indicator of the balance between sympathetic and parasympathetic outflows. Previous works of the authors in the autonomic nervous system assessment were related to the design and implementation of wavelet-based algorithms for the evaluation of heart rate variability and blood pressure variability on rats [10,13]. Several correlations between the results of wavelet analysis and real physiological evoked response to experimentally induced changes were underlined based on wavelet analysis. With this approach, relative contributions of the two branches of the autonomic nervous system

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(sympathetic and parasympathetic systems) are assessed. Likewise, information from short-time cardiovascular signal analysis can be inferred on autonomic nervous system outflow. In this work special attention was granted to the design and implementation of an automatic system for the measurement of physiological parameters on rats that provides estimation of cardiovascular autonomic modulation based on intelligent algorithms. A study related to fast modeling methods of multivariable systems was carried out. In this way design aspects such as the selection of an optimal sampling frequency of the measured signal and the analog-to-digital converter’s resolution were considered. Intelligent algorithms, such as artificial neural networks and fuzzy systems showed to be important candidates for fast estimation of systems’ internal parameters [14,15] particularly for autonomic nervous system control of the cardiovascular function. Different solutions based on neural networks modeling are reported in the literature both for static and dynamic characteristics of different kind of systems including biological systems [16–18]. Artificial Neural Networks (ANN), with their remarkable ability to

derive meaning from complicated or imprecise data, can be used to extract patterns and detect trends that are too complex to be noticed by either humans or other computer techniques. A trained neural network can be thought of as an ‘‘expert” in the category of information it has been given to analyze. Thus, considering ANN advantages such as high degree of generalization and parallel computing [19], the present paper proposes a novel solution for fast evaluation of cardiovascular autonomic modulation based on neural networks using a DWT calibration algorithm.

2. LF and HF reference estimator based on wavelets Time series were constructed from electocardiograms (Neurolog) and blood pressure signals from 20 male Wistar rats (400–460 g), anesthetized (a-chloralose, 100 mg/kg) with spontaneous respiration (10 rats) or artificially ventilated and paralysed (pancuronium bromide, 4 mg/kg/h) (10 rats). The femoral artery and vein were catheterised for pressure measurement (pressure transducer Sensonor 840 driven by a Lectromed Ltd. amplifier) and the admin-

Fig. 1. RR interval and systolic arterial pressure (SAP) variability in rat with spontaneous respiration (N, number of signals; t, analysed time interval).

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istration of drugs, respectively. Rats were artificially ventilated (Harvard Rodent Ventilator, model 683) with a mixture of oxygen and small amount of room air. The cycling rate was set as 62 ± 2 cycles/min. The temperature was controlled at 38.5–39.5 °C using a rectal probe and a Harvard homeothermic blanket. All recorded variables were acquired (Instrutech VR100B, Digitimer Ltd.) and recorded on videotape. On-line analysis of blood pressure and heart rate was made using a computer-based data acquisition system with data capture and analysis software (PowerLab 8SP, ChartWindow). The electrocardiogram (ECG) and blood pressure signals of each rat were acquired for 5 min at sampling frequency fS = 2 kHz using the Neurolog Digitimeter Ltd. card. Signals from pharmacological induced inhibition in vagal tone (atropine hydrochloride, 2 mg/kg) or cardiac sympathetic blockade (labetolol, 2 mg/kg) in spontaneously breathing rats were also introduced in the analysis. Thereafter, signals from five episodes of 5 s (1 min between each one) from each rat with spontaneous or artificially respiration and six episodes of 5 s (baseline, first 50 s, 2 and 5 min after atropine or labetolol) from six rats were processed by the software. In Fig. 1 are represented a set of five episodes of 5 s R–R interval and systolic arterial pressure (SAP) obtained from rats with spontaneous respiration.

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The pattern of variability of cardiovascular signals observed in the rats with spontaneous respiration diminished with sympathetic and parasympathetic blockade, and with artificial respiration (Fig. 2). The software block diagram of the LF–HF estimation based on wavelets was described elsewhere [10] and synthesized in Fig. 3. In summary, a time series of R–R intervals derived from ECG and systolic blood pressure (SBP) is spline interpolated and re-sampled according to the Shannon theorem to produce 2n samples (128 samples in this case). Wavelets coefficients for details associated to 0.01 and 3 Hz frequency intervals are calculated and the energy distribution on the frequency axis investigated. R–R and SBP signals are decomposed with orthonormal Daubechies wavelets of order 12 into seven wavelet scales (j = 7). LF and HF components of signals are obtained by merging the detail signals at scale 6 (0.1–0.4 Hz) and at scales 3, 4 and 5 (0.5–3 Hz), respectively. The decomposed VLF signals corresponded to the detail at scale 7. Wavelet-filtered components are obtained by summing wavelet detail coefficients for each scale separately and the instantaneous power for the reconstructed detail signals is calculated as the square of the positive values of the wavelets details corresponding to low frequency and high frequency signal components.

Fig. 2. Representation of variability of R–R interval in sets of 5 s ECG signals recorded in rats with spontaneous respiration, after inhibition of parasympathetic (atropine) and sympathetic (labetolol) heart control and with artificial respiration.

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peak detector ECG (ti)

Spline cubic interpolation RR or SAP x(t ) analyse i

resampling

SAP (ti)

Pre-processing

fRS computation

dx

ax Wavelet Estimator

LFDWT HFDWT Cardiac Autonomous Nervous System Control Fig. 3. The wavelet-based estimator of cardiac autonomic nervous system control as reference estimator.

An example of LF and HF value obtained from cardiac and blood pressure signal after DWT decomposition is represented in Fig. 4a and b. The normalized LF and HF components were obtained by calculating the ratio of LF and HF variability with respect to the total power after subtracting the power of the VLF component (detail 7 of decomposition). Low frequency component (d6 detail of decomposition) from blood pressure and cardiac signal reflects tonus of the sympathetic control of the vessels and heart. Parasympathetic autonomic control of the heart is highly correlated with high frequency component of the cardiac signal (d5, d4, d3). High frequency oscillation in systolic blood pressure signal is mechanically induced by respiratory function. A reference result of LF, HF estimation based on DWT (reference algorithm) is presented in Fig. 5. Acting on both sympathetic control of the heart and vessels, labetolol injection produced higher variability on rats’ cardiac signal. Great variation on parasympathetic tonus (HFn-RR) was produced to physiological changes induced by artificially ventilation, atropine and labetolol injection, revealing an imbalance on autonomic outflow to the heart. Decreased blood pressure produced by labetolol administration was correlated with a higher decreased in sympathetic outflow to the vessels (LFn-

SAP). The normalized LF and HF components obtained by the DWT algorithm was used for neural network design.

3. Autonomic modulation estimator based on neural networks Neural Networks (NNs) are efficient function approximators and represent an important solution in dynamic systems modeling [20,21]. In the present case, multi-input, multi-output Multilayer Perceptron (MLP) and a Radial Basis Function (RBF) neural network architectures were designed in order to materialize the cardiovascular autonomic modulation fast estimator based on the HRV and BPV evaluation.

3.1. General processing scheme To obtain the LF and HF components that reflect the cardiovascular autonomic modulation a hybrid architecture expressed by a cubic spline interpolation block (CSpline), a time delay line (TDL) [22], and a multiple input – multiple output neural network (MIMO-NN) is proposed (Fig. 6).

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Fig. 4. Representation of wavelet decomposition of 5 s cardiac signal recorded in rats with spontaneous respiration (a). VLF corresponds to wavelet coefficients of detail d7; LF component corresponds to detail d6 and HF corresponds to wavelet coefficients from details d5, d4, d3 of heart rate signal decomposition. DWT decomposition of 5 s of SBP signal (b). LF component could be visualized in detail d6 of wavelet decomposition of the systolic blood pressure. HF component that is related with respiratory trends correspond to details d5, d4 e d3 of wavelet decomposition of blood pressure signal.

The interpolated signal (sint) is re-sampled at a TRS period by the tape delay line (TDL) using a set of 127 delay cells. The re-sampling frequency is automatically calculated (included in 16–28 Hz) in order to obtain 128 samples for 5 s time interval. The sig-

nals with sampling frequency lower than 15 Hz were not input to the neural network block. The re-sampled and normalized signals ðsnorm int Þ are applied to the designed MIMO-NN that estimates the LF and HF components.

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R-sp

A

L

R-art

1.00

0.95

HFn-RR

0.90

0.85

0.80

0.75 0

10

20

30

40

50

60

N

R-sp

A

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R-art

0.5

0.4

LFn - SAP

0.3

0.2

0.1

0.0

0

10

20

30

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N Fig. 5. The normalized LFn-SAP and HFn-RR components obtained using wavelets coefficients from DWT decomposition of signals from rats with spontaneous respiration (R-sp), atropine (A) and labetolol (L) injection and artificial respiration (R-art).

3.2. NN architecture and training The neural network architectures designed to materialize the MIMO-NN block were the Multilayer Perceptron and Radial Basis Function [19,23]. In both cases, the input layer is characterized by 128 input elements and receives the RR or SBP samples while the output is expressed by two linear neurons that deliver the LFNN and HFNN values. The training and test data are the elements of an input ma-

trix including RR or SBP re-sampled signals (e.g. 128  60) and of an output matrix including the LFDWT and HFDWT obtained upon application of the wavelet-based processing algorithm considered as a calibration or reference algorithm. The input-output training set is taken from different experiments (eg. base-line condition, atropine or labetolol injection) associated to autonomic nervous system modulation. Elements of MLP-NN hidden layers and training algorithms are presented next.

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s(mΔt)

TDL C-Spline

sint(jT)

T

sint(jT-T)

x T

sint(jT-126T)

T

sint(jT-127T)

0.172

Snorm sintnorm (jT-127T)

sintnorm (jT) MIMO -NN

LFNN

HFNN

Fig. 6. NN processing scheme for the autonomous cardiovascular modulation assessment: TDL – time delay line characterized by 127 T delay cells, C-Spline – cubic spline interpolation of cardiovascular signals, Snorm-normalization block, MIMO – multiple input multiple output neural network processing block (MLP-NN – Multilayer Perceptron or RBF-NN Radial Basis Function neural network).

3.2.1. MLP-NN case The MLP-NN includes a hidden layer with 5–15 tansignoid neurons and an output layer with two linear neurons that deliver the HF and LF values characterizing the autonomic modulation for a given experience expressed by fluctuations in the RR or SBP signals. The neural network weights and biases of hidden (W1,B1) and output layers (W2,B2) were obtained using Levenberg Marquardt training algorithm [19] and a training set expressed by 128  60 input matrix and 2  60 target matrices. Each column of the input matrix includes 128 sampled values that constitute the 128 NNs input nodes and which were extracted from the RR or SAP signals. The target matrices (output matrix) is represented by the normalized LF and HF numerical values as results of wavelet processing block, (Fig. 4), applied to RR or SAP signals. A study concerning the dependence of the number of hidden neurons (nhidden = 5  15) and LF and HF components estimation was performed and presented in the results section. 3.2.2. RBF-NN case The radial basis function ANN (RBF-NN) is also a fully connected feedforward artificial neural network architecture. It includes only 3 layers: input, hidden and output layer. The input and output layer are similar to the MLPNN case: 128 input neurons, 2 linear output neurons. The hidden layer includes a variable number of neurons with gaussian activation functions [19,23]. The individual activation function of each hidden layer neuron is given by: 2

2

uðxÞ ¼ ekXCk =2r

ð1Þ

where vector X represents the input values of the neuron, C is the vector of neuron center coordinates and r the width of the radial function. This type of networks creates a local approximation of a non-linear input–output function. The local approximation, instead of the global approximation performed by MLP-ANN, implies the utilization of higher number of hidden neurons (more than 60 neurons in our case) for the same degree of accuracy. Otherwise, the RBF-NN requires reduced design times for a good modeling performance when a large number of training vectors are available.

Referring to the training, it consists of 2 separate phases. During the first phase the parameters of the radial basis functions, centers and widths, are set using an unsupervised training mode until their values are stabilized. In a second phase the weights of the connections between hidden and output neurons are established using a supervised training mode (backpropagation type) that minimizes the errors between NN outputs (LFNNi and HFNNi values) and correspondent targets, (LFDWTi and LDWTi) for a given set of input training vectors, RRi.., i = 1 . . . 60 in our case. 4. NN processing results The performance of the designed MLP-NNs and RBFNNs depends on the internal architectures chosen (number of neurons, transfer functions), data training, and training algorithm. After training, the designed networks were tested using the validation input matrix and corresponding LF–HF output matrix whose elements were obtained using the mentioned wavelet algorithm. The absolute and relative approximation errors are calculated for different network types (MLP and RBF) and for different internal parameters (number of neurons, spread values etc). The absolute and relative approximation errors for LF and HF were calculated using the following relations:

eaa jLF ¼ LFNN  LFDWT ; ear jLF ¼ eaa jHF ¼ HFNN  HFDWT ; ear jHF

eaa jLF  100½% LFDWT eaa jHF ¼  100½% LFDWT

ð2Þ ð3Þ

Thus, for the particular case of RR-interval signals associated with sympathetic/parasympathetic variations, the MLP-NN approximation performance is expressed by eaajLF and eaajHF (Fig. 7). Analyzing Fig. 7, one can notice that an MLP-NN with 5 hidden neurons represents in our case a good solution considering the modeling accuracy and the computational load. The maximum of the relative approximation error associated to LF and HF components calculation obtained for the considered testing set was 0.02% and 0.01%, respectively. In order to maintain the maximum of the relative approximation error lower than 1% for new different real situations (baseline individual variations and induced

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2 LF HF

-3

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(1)

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(3)

0

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-1 -1.5

-4

0

10 20 Mtest

30

-2

-4 0

10 20 Mtest

30

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10 20 Mtest

30

Fig. 7. The distribution of absolute errors calculated for the NN model validation set (128  21) and for different MLP-NN architecture (1) MLP-NN with 5 hidden neurons, (2) MLP-NN with 10 hidden neurons (3) MLP-NN with 15 hidden neurons.

changes in autonomic nervous system control), the MLPNN requires new training for larger training sets (e.g. 128  500) which will conduct to better LF and HF estimation model characterized by high generalization capabilities. The results obtained with the RBF-NN prove the better learning capabilities of this type of network. However, the generalization performance depends strongly on the spread parameter (sf) used in the RBF-NN training phase. Several results concerning the LF and HF estimation based on RBF-NN are shown in Figs. 8 and 9. As shown in Fig. 8, using a testing set (128  21 – Mtest) provided also by the DWT based reference algorithm, the RBF-NN estimator of the cardiac autonomic ner-

vous system control with a limited number of neurons (up to 15 neurons) performs the estimation of the LF and HF components with low accuracy when compared to MLPNN. However, increasing the number of neurons to 60, the RBF-NN estimation accuracy increases and is better than MLP-NN (Fig. 9), the accuracy depending also on the spread factor (sf) used in the network training phase. To obtain an RBF-NN with high generalization capabilities, sf needs to be maintained high (sf > 10). In order to perform the LF and HF estimation for BPV signals, different types of MLP-NN and RBF-NN were designed and tested. Several results concerning the LF and HF estimation error (eaajLF and eaajHF) obtained for the best designed neural network (MLP-NN and RBF-NN case)

Fig. 8. The distribution of absolute errors calculated for the NN model validation set (128  21) and for different RBF-NN architecture (1) RBF-NN with 5 hidden neurons, (2) RBF-NN with 10 hidden neurons (3) RBF-NN with 15 hidden neurons.

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x 10

4 (1 )

-8

5

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-7

(3 )

(2 )

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eaa|LF, eaa|HF

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3 2 1

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10 Mtest

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0

LF HF

10 Mtest

-2

20

0

10 Mtest

20

Fig. 9. The distribution of absolute errors calculated for the RBF-NN model validation set (128  21) for different values of training spread factor-sf: (1) sf = 2; (2) sf = 10; (3) sf = 20.

a

b x 10-16

0.05

6

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Fig. 10. The distribution of absolute errors of LF and HF estimation (a) MLP-NN (10 hidden neurons) estimator (b) RBF-NN, (sf = 20) estimator for a validation set (128  60).

are presented in Fig. 10. The results indicate that the RBFNN is a usefully solution considering the accuracy of RBFNN estimator and the training times (shorter than in the MLP-NN cases). 5. Conclusion A fast solution for the HRV and BPV evaluation based on MLP or RBF neural networks is proposed and tested. For optimal results special attention was also granted to the signal conditioning and acquisition of physiological signals that provide accurate samples to input the artificial neural network processing architecture. It should be emphasized that the work reported here can be seen as a step towards a fast and low computational on-line HRV and BPV dynamics assessment. The following conclusions may be drawn:

The use of data obtained from a wavelet algorithm as reference data for neural network training is extremely useful and justifies itself in the present application considering that the scaled and time-shifted wavelets are a better representation of local phenomena in the original signal. Using MLP-NN or RBF-NN a short time (5 s on rats) assessment of the two branches of the autonomic nervous system (expressed by LF and HF numerical values) can be on-line achieved. The approximation relative errors obtained on neural network testing phase are less than 1% for the LF component and HF components of the RR-interval signal for both types of the designed neural networks, MLP-NN and RBFNN. Better results can be obtained extending the training set and optimising the MLP-NN architectures. Compared to the wavelet algorithm for LF and HF components evaluation, the neural network based method is

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characterized by less complexity reflected in lower computation load but requires a hard training phase supported on large amount of training data for different physiological situation. Acknowledgments The work now reported was not possible without the leadership and direct involvement of Prof. Luı´s Silva-Carvalho. A world-known researcher particularly in experimental Physiology, he was, until his dead in November 2008, the Head of the Instituto de Fisiologia, Faculdade de Medicina, Universidade de Lisboa in which worked or with which collaborate the other authors of this paper who deeply regret the departure of Prof. Silva-Carvalho before the work was published. R.I.P., Prof. Silva-Carvalho! References [1] Task Force of the European Society of Cardiology and the North American Society of Pacing and Electrophysiology. Heart rate variability. Standards of measurement, physiological interpretation and clinical use. Circulation, vol. 93, 1996, pp. 1043–1065. [2] M. Malik, A.J. Camm, Heart Rate Variability, Futura Publishing Company, Inc., Armonk, NY, 1995. [3] S. Cerutti, A.M. Bianchi, L.T. Mainardi, Advanced spectral methods for detecting dynamic behaviour, Autonomic Neuroscience: Basic and Clinical 90 (2001) 41–46. [4] G. Parati, A. Frattola, M. Di Rienzo, P. Castiglioni, G. Mancia, Broadband spectral analysis of blood pressure and heart rate variability in very elderly subjects, Hypertension 30 (1997) 803– 808. [5] G. Parati, J.P. Saul, M. Di Rienzo, G. Mancia, Spectral analysis of blood pressure and heart rate variability in evaluating cardiovascular regulation, Hypertension 25 (1995) 1276–1286. [6] M. Pagani, F. Lombardi, S. Guzzetti, O. Rimoldi, R. Furlan, P. Pizzinelli, G. Sandrone, G. Malfatto, S. DellÓrto, E. Piccaluga, M. Turiel, G. Baselli, S. Cerutti, A. Malliani, Power spectral analysis of heart rate and arterial pressure variabilities as a marker of sympatho-vagal interaction in man and conscious dog, Circulation Research 59 (1986) 178–193. [7] J.L. Ducla-Soares, M. Santos-Bento, S. Laranjo, A. Andrade, E. DuclaSoares, J.P. Boto, L. Silva-Carvalho, I. Rocha, Wavelet analysis of autonomic outflow of normal subjects on head-up tilt, cold pressor test, Valsava manoeuvre and deep breathing, Experimental Physiology 92 (4) (2008) 677–686.

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