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Residual Stenosis Estimation of Arteriovenous Grafts Using a Dual-Channel Phonoangiography With Fractional-Order Features Yi-Chun Du, Wei-Ling Chen, Chia-Hung Lin, Chung-Dann Kan, and Ming-Jui Wu
Abstract—The residual stenosis estimation of an arteriovenous shunt is a valuable for evaluating outcomes of percutaneous transluminal angioplasty (PTA) treatment and surgical revision. This paper proposes a dual-channel phonoangiography (PCG) with fractional-order features to estimate the residual of stenosis estimation of arteriovenous shunt. The auscultation technique provides a noninvasive tool to monitor the degrees of arteriovenous grafts (AVGs). Then, support methods, such as the Burg autoregressive (AR) method and self-synchronization error formulation (SSEF), are used to extract fractional-order features between the loop site (L-site) and venous anastomosis site (V-site). Using 2-D patterns (nonlinear mapping), a generalized regression neural network (GRNN) is designed as a nonlinear estimate model to indicate the outcome of surgical revision or AVG stenosis upon routine monthly examinations. For 42 long-term follow-up patients, the results of examination show the proposed GRNN-based screening model efficiently estimates residual stenosis. Index Terms—Arteriovenous graft (AVG), fractional-order feature, generalized regression neural network (GRNN), phonoangiography (PCG).
I. INTRODUCTION RTERIOVENOUS shunts (AVS) are vital for end-stage renal disease (ESRD) for patients receiving hemodialysis therapy. The bridge accesses of AVS are anastomosed between arteries and veins, including Brescia-Cimino arteriovenous fistulas (AVFs) or synthetic loop grafts (AVGs) made of politetrafluoroethylene (PTFE) for hemodialysis [1], [2]. Due to repeat puncturing of the accesses or long-term use, AVS stenosis and dysfunction are caused by inadequate arterial inflow, venous
A
Manuscript received October 3, 2013; revised April 14, 2014; accepted March 11, 2014. Date of publication June 5, 2014; date of current version March 2, 2015. This work was supported in part by the National Science Council of Taiwan under contracts NSC 102-2218-E-218-006 and NSC 101-2221-E244-001. The Institutional Review Board (IRB) of the National Cheng-Kung University Hospital approved this study under contract ER-99-186. Y.-C. Du is with the Department of Electrical Engineering, Southern Taiwan University of Science and Technology, Tainan 71005, Taiwan (e-mail: terrydu@ mail.stust.edu.tw). W.-L. Chen is with the Department of Biomedical Engineering, National Cheng Kung University, Tainan 70101, Taiwan, and also with the Department of Engineering and Maintenance, Kaohsiung Veterans General Hospital, Kaohsiung 81362, Taiwan (e-mail: [email protected]). C.-H. Lin is with the Department of Electrical Engineering, Kao-Yuan University, Kaohsiung 82151, Taiwan (e-mail: [email protected]). C.-D. Kan is with Department of Surgery, National Cheng Kung University Hospital, Tainan 70101, Taiwan (e-mail: [email protected]). M.-J. Wu is with the Department of Internal Medicine, Yong-Kang Veterans Hospital, Tainan 71051, Taiwan (e-mail: [email protected]). Color versions of one or more of the figures in this paper are available online at http://ieeexplore.ieee.org. Digital Object Identifier 10.1109/JBHI.2014.2328346
outflow occlusion, or total occlusion [2], [3]. In clinical examinations, the traditional imaging method of angiography, along with duplex and Doppler sonography offer promising methods for evaluating dysfunction hemodialysis accesses. Under normal conditions, blood flow in the supply arteries and through the graft are monophasic, peak systolic velocities range from 1.0 to 4.0 m/s, with end-diastolic velocities of 0.6–2.0 m/s, and the draining veins have arterial pulsations with peak velocities of 0.3–1.0 m/s [4], [5]. Compared with the adjacent normal segment, increasing velocities could be shown by duplex and color Doppler sonography in the region of a focal site. Then, PTA treatment or placement of venous stents has been used to repair the intimal hyperplasia, aneurysmal deformability, and thrombosed accesses. However, operational principles must be taken into account, and extra learning about the limitations by the patients themselves is necessary in homecare applications. According to a previous study [6], inflow stenosis occurs in 29% (36/122) of graft cases (total 122 patients), all of whom have a coexisting stenosis on the venous side and that inflow stenosis accounts for 40% (41/101) of fistula cases (total 101 patients), 54% (22/41) of whom have a coexisting dysfunction on the venous side. This shows that the venous side is a site worth measuring to evaluate the conditions of AVS. The findings of other studies [7], [8] also indicate that the V side is a usual site for monitoring AVS function. According to these promising results, the phonography technique is used to estimate the degree of stenosis (DOS). However, the changes in frequency and amplitude are dependent on the stenosis sites, monitoring sites, and severity degree. Only one monitoring site shows slight variations between the frequency features and the DOSs. Therefore, a dual-channel phonoangiography (PCG)-based auscultation method is proposed to enable efficient and accurate estimation of AVS stenosis, as shown in Fig. 1. According to previous promising results [7]–[10], frequencybased features and fractional-order self-synchronization error formulations (SSEF) are used to calculate dynamic errors with changes depending on the DOS. Thus, we propose a highdimensional mapping mechanism, such as generalized regression neural network (GRNN) [11], [12], to model the relationship between ΔDOS and 2-D fractional-order features. The proposed method automates the procedure of complex nonlinear system design in real-time applications, and provides a prediction model-based on flexible curve approximation using a swarm-intelligence algorithm (SIA) [13]–[15] to update the GRNN’s parameters in a dynamic modeling environment.
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DU et al.: RESIDUAL STENOSIS ESTIMATION OF AVGS USING A DUAL-CHANNEL PCG
Fig. 1.
Auscultation method and dual-channel stethoscope placement.
A synthetic tube is implanted under the skin of the forearm/upper arm. The same tube can be used repeatedly when changing needle placement. However, it presents problems than do AVFs in clinical usages, such as clots, infection, and frequent replacement. The patency rate, infection rate, and thrombosis rate of AVGs are higher than those of AVFs, so patients with AVGs are assessed to validate the proposed method. For long-term follow-up patients, the results show that the proposed method is more efficient for residual stenosis estimation. II. TECHNOLOGICALLY SUPPORT Technologically support for feature extraction and SSEF is described below. A. Feature Extraction The PCG signals were acquired using two medical use of electronic stethoscopes (3M Littmann, Model 4100, K051790, MN, USA) in this study. It can detect sounds between 1 Hz to 2 kHz from the heart, vessels, lungs, and other body sounds with the use of a selective frequency undergoing a physical assessment. The stethoscopes offer amplification (18 times the amplification, 25 dB), processing, filtering, and recording functions, as well wireless (infrared transmission) data transfers to compatible PC and tablet PC for further analysis. It has three operation modes: bell (20–500 Hz), diaphragm (20–700 Hz), and extended range (1–20 kHz) modes. Therefore, high-pitch stenosis murmurs between 25 Hz and 2.5 kHz [7], [10] can be acquired with a sampling rate of 4 kHz (Nyquist Theorem). In order to remove the unwanted ambient noises, the filter provides extended frequency response mode for auscultation. Auscultations were performed with dual-channel electronic stethoscopes at the loop site (L-site) and venous anastomosis site (V-site), as shown in Fig. 1.
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On a tablet PC, Hilbert transform and a 5-Hz low-pass digital filter smoothed PCG signals were then used to obtain the peaks of the envelope of the periodic PCG signal. Tracking the peak values, the segmentation process was used to find the minimum value before and after the detected peaks [7], [8]. A reliable acquisition window can be obtained to acquire PCG signals in the segmentation process stage. For analyzing each PCG signal, a 25–200 Hz band-pass filter was implemented to remove the baseline wander and could maintain the main characteristic frequencies in the signal preprocessing stage. Then, the wellknown Burg autoregressive (AR) method [16], [17] was used to estimate the frequency spectra by fitting an autoregressive model of a given specific order. Referring to previous studies [7], [8], [18], an AR model parameters and model order can be determined by the Levinson– Durbin recursion [17]. It is based on minimizing the total sum of the forward and backward prediction errors using the final prediction error criterion. We suggest the AR model order 8 for constructing the Burg AR model with prediction coefficients. This model was used to smooth the frequency spectra and it tends to favor peaky spectra. Thus, the spectral peaks of frequency spectra, the region of 25–800 Hz, can be identified by the Burg AR method. Depending on frequency-based features, it provides key information for residual stenosis estimation. B. Self-Synchronization Error System Chaotic systems (CSs) are widely used in nonlinear physical applications and physical informatics [19], [20]. Generally, an original CS consists of a master system (MS) and a slave system (SS), which can be described as Master System : X˙ = AX + f (X) Slave System : Y˙ = AY + f (Y ) + U
(1) (2)
where X ∈ RN and Y ∈ RN denote the state vector, A is a N × N system matrix, f(X) and f(Y) are the nonlinear vector functions, and term U can be designed as a nonlinear controller to approach the MS for nonlinear control applications [19], [20]. In order to implement nominal plant, dimension N = 3 for a nonlinear CS was chosen for signal processing applications [21]. Consider the nominal Chen-Lee CS, X ࢠ R3 , Y = R3 , where X = [x1 , x2 , x3 ]T , Y = [y1 , y2 , y3 ]T , U = [u1 , u2 , u3 ]T , and matrices, Am or As , is a 3 × 3 system, denoted by the subscripts m and s for MS and SS as ⎡ ⎤ a −x3 0 ⎢x b 0⎥ 3 ⎥ Am = AX + f (X) = ⎢ ⎣ ⎦ 1 x2 0 c 3 ⎤ ⎡ a −y3 0 ⎢y b 0⎥ 3 ⎥ (3) As = AY + f (Y ) = ⎢ ⎦ ⎣ 1 y2 0 c 3
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This results in coupling variables for tracking the dynamic responses between the MS and SS. This system offers good symmetrical behavior and is used in this study [20], [21]. In order to track self-synchronization errors, the control term u1 = u2 = u3 = 0 is used, and we hypothesize that x1 x2 − y1 y2 ≈ (x1 − y1 )(x2 − y2 ), x1 x3 − y1 y3 ≈ (x1 − y1 )(x3 − y3 ), and x2 x3 − y2 y3 ≈ (x2 − y2 )(x3 − y3 ). After defining the error states e = [e1 , e2 , e3 ]T as e1 = (x1 − y1 ), e2 = (x2 − y2 ), and e3 = (x3 − y3 ), subtract (2) from (1), and (x1 − y1 )(x2 − y2 ) = e1 e2 , (x1 − y1 )(x3 − y3 ) = e1 e3 , and (x2 − y2 )(x3 − y3 ) = e2 e3 , the error system can be expressed by ⎡
e˙ 1 ⎣ e˙ 2 e˙ 3
⎤ a −e3 0 ⎡ ⎤ e1 ⎢ b 0⎥ ⎥ ⎣ e2 ⎦ ⎦ = ⎢ e3 ⎦ ⎣ 1 e3 e2 0 c 3 ⎡ ⎤ ⎡ ⎤ ⎡ −e e ⎤ 3 2 a 0 0 e1 ⎥ ⎢ = ⎣ 0 b 0 ⎦ ⎣ e2 ⎦ + ⎣ e1 e3 ⎦ 1 e3 0 0 c e1 e2 3 ⎤
⎡
(4)
According to previous studies, system (4) acts as a chaotic attractor that must satisfy the parameters a, b, and c, under the following specific condition [19], [20]: a > 0, b < 0, c < 0, and 0 0, b = < 0, Γ(2 + α) Γ(2 + α)
c =
cΓ(2) 0.50, Class II: 0.30–0.50, and Class I: < 0.30, after PTA [8]. We monitored three possible anatomy sites, including the A site, loop site (L site), and V site, as shown in Fig. 3. The electronic stethoscope acquired the time-domain PCG signals at the measurement site, as shown in Fig. 4(a). Each segment of PCG signals can be determined between adjacent two minimum values before and after the detected peaks (red-circle symbol), as shown in Fig. 4(b). In Fig. 4, the dynamic errors, Φ1 [i], Φ2 [i], and Φ3 [i], i = 1, 2, 3, . . . , n − 2 (n = 800), can be calculated using (9). When the fractional order q = 0.98 (α = 0.02), the dynamic errors are identified using the system parameters a = 1.983(a = 2), b = −3.966(b = −4), and c = −2.9745(c = −3). Figs. 4(c) and (f) shows the norm of (Φ1 , Φ2 , Φ3 ), index Ψ, on the V site and L site. Referring to a previous study [8], there is no statistical significance in A-sites using statistics analysis (p > 0.05). In this study, we chose dual-channel stethoscopes to measure PCG signals. Fig. 5 shows the average indexes Ψ with three classes on the L and V sites, respectively. The combination patterns of two indexes, ΨL and ΨV , can be separated into three classes, which are denoted by the subscripts L and V for L and V sites. Based on the aim of this research, we select two parameters to estimate the ΔDOS.
III. DUAL-CHANNEL PHONOANIGIOGRAPHY-BASED SCREENING SYSTEM A. Experimental Setup Long-term hemodialysis treatment of patients was chosen for clinical investigation at the Department of Surgery, National Cheng Kung University Hospital, Tainan, Taiwan. The research study was also approved by the hospital research ethics committee and the Institutional Review Board (IRB): ER-99-186. There were 23 females and 19 males with a mean age of 63 ± 10.2 years (52–74 years). The participants’ mean duration of long-term hemodialysis therapy was 48 ± 31 months. Preliminary diagnosis results confirmed the specific degrees by ultrasonic image examination and observation by clinical physicians. In clinical research, the degree of narrowing of the normal vessel is an index for the degree of arteriovenous access. Examination results have confirmed the specific degrees from X-ray images or angiographic images, which are defined as in [7], [8], [18], [25]
d2 (11) DOS = 1 − 2 D where D is the diameter of the normal graft or vessel in the direction of blood flow, d is the diameter of the stenosis lesion. For the surgical results among 42 patients, the overall DOS of
B. Screening System Implementation According to the correlation between ΔDOS and index Ψ, we can utilize “linear” or “exponential” regression to model the relationship between ΔDOS and index Ψ. However, it is not difficult to approximate the scatter data to a function under high dimensionality and nonlinearity. For high-dimensional mapping
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Fig. 4. (a) Phonoangiography (PCG) signal in the time domain. (b) PCG segmentation process, (c), (d), and (e) Frequency spectra, dynamic errors Φ 1 , Φ 2 , and Φ 3 (fractional order q = 0.98), and the index, Ψ, on V site; (f), (g), and (h) Frequency spectra, dynamic errors Φ 1 , Φ 2 , and Φ 3 , and the index, Ψ, on loop site.
Fig. 5.
Average indexes Ψ with three classes on L and V sites.
applications, a “GRNN” is used to model the relationship between ΔDOS and indexes ΨL and ΨV, as shown in Fig. 6. This method has been shown to be effective in a great variety of difficult function mapping and prediction applications [11], [12]. It gives a sufficient number of pattern nodes in the pattern layer and can approximate a nonlinear function. Corresponding pattern nodes allow keep on growing with addition or deletion. The GRNN requires more pattern nodes than a tradition feedforward backpropagation network, but it can be designed in a fraction of the time to train or retrain the network when many training data are available. A continuous learning model can be designed an adaptive mechanism using the optimization algorithms. The feedforward multilayer network consists of four layers, including the input layer, pattern layer, summation layer, and output layer. The curve approximation algorithm of GRNN is summarized as follows:
Fig. 6.
Structure of the GRNN.
Step 1: For each training pattern ψ(k) = [ψL (k), ψV (k)] fork = 1, 2, 3, . . . , K, and create weights wk i , i = 1, 2, between the input layer and pattern layer by
ΨL (k) ΨV (k) , [wk 1 , wk 2 ] = ΨL m ax ΨV m ax T
T (12)
DU et al.: RESIDUAL STENOSIS ESTIMATION OF AVGS USING A DUAL-CHANNEL PCG
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where W 1 = [wk i ] is a K by 2 matrix. It can be extended to work in high-dimensional feature space formed with nonlinear mapping of 2-D input to K-dimensional pattern feature. Step 2: Create weights wk j , j = 1, 2, between pattern layer and summation layer by [wk j ] = [ΔDOS(k), 1]
(13)
where the values of wk 1 are the predicted ΔDOS(k) associated with the pattern [ψ L (k); ψ(k)]. Connection weights from the overall pattern nodes to another summation nodes are set as 1, and W 2 = [wk j ] is k by 2 matrix. Step 3: Compute the output of pattern node Gk by the Gaussian function
K (Ψi − wk i )2 Gk = exp − , i= 1, 2 (14) 2σk2 k =1
where [ψ1 (k), ψ2 (k)] = [ψL , ψV ], σ1 = · · · = σk = · · · = σK = σ, the optimal value can be obtained by using the optimization methods. Step 4: Compute the outputs of node ΔDOS by K K ΔDOS(ΨL , ΨV ) = wk j Gk Gk . (15) k =1
In (14), adjusting parameter σ refines the accuracy of prediction model. The optimal parameter σ is intended to minimize the mean squared error function (MSEF). The objective function is defined as MSEF =
Fig. 7.
Flowchart of particle swarm optimization algorithm.
k =1
K 1 [T (k) − ΔDOS(ΨL , ΨV )]2 K
(16)
k =1
where T(k) is the desired ΔDOS for the kth training pattern. However, (16) is a nonlinear function and its partial differential equation is difficult to obtain using the gradient/steepest descent method. In this study, the SIA [13]–[15] is an evolutionary optimization technique to solve optimization problems. It is suitable for processing nondifferentiable objective functions, as in (16). It also uses probabilistic transition rules that can find the global best solution by adjusting the trajectory of each individual particle toward its own best location and toward the best particle of the entire swarm. A particle swarm optimization (PSO) algorithm is used to solve this problem. Let σgp be the current position of the gth agent at iteration number p, agent g = 1, 2, 3, . . . , G, where G is the population size. Multiple particles form a population and are represented by p ]. The a G-dimensional vector, as δ p = [σ1p , σ2p , . . . , σgp , . . . , σG p modification of position σg can be represented by velocity p ]. The flowchart Δσgp , Δδ p = [Δσ1p , Δσ2p , . . . , Δσgp , . . . , ΔσG is shown in Fig. 7 and mathematical representation is given by [13]–[15] Velocity : Δσgp+1 = Δσgp + c1 rand1 (σbestg − σgp ) + c2 rand2 σbest − σgp (17) Position : σgp+1 = σgp + Δσgp+1
(18)
where σbest is the global best in the group, and σbestg is the individual best. Parameters c1 and c2 are the positive “acceleration parameters” that pull each particle toward the best positions, and rand1 and rand2 are the uniformly random numbers between 0 and 1. For efficient convergence to the global optimal solution, a PSO algorithm with time-varying acceleration coefficients (TVAC) [15] is used to improve the performance, as c1 = (b1 − a1 )
p p + a1 , c2 = (b2 − a2 ) + a2 (19) pm ax pm ax
where the first term is the “cognitive component,” the second term is the “social component,” a1 , b1 , a2 , and b2 are constant values, of which the experienced values are c1 from 2.5 to 0.5 and c2 from 0.5 to 2.5, respectively, and pm ax is the maximum number of allowable iterations. With a large cognitive component and small social component, multiple particles are allowed to move around the search space [15], [21], as roughly adjust the searching points. By monotonously reducing the cognitive component and increasing the social component, a small cognitive component and a large social component allow the particles to converge to a global optimal solution, as keep fine-tuning at the end of the search. The term, p/pm ax , is used to control the changes of cognitive component and social component at each search stage. There are two convergent conditions for stopping the PSO algorithm: 1) the objective function MSEF is less than the prespecified value and 2) the number of iterations achieves the maximum allowable number pm ax .
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Two group records of ΔDOS versus index Ψ in V sites and loop sites.
IV. EXPERIMENTAL RESULTS AND DISCUSSION The proposed estimation method with feature extraction and GRNN was developed on a PC AMD Athlon II × 2 245 2.91 GHz with 1.75-GB RAM and MATLAB software. To demonstrate the effectiveness of the proposed estimation model, 42 subjects were tested (NCKUH, IRB, under contract number: ER-99-186). Auscultation records were performed with a digital stethoscope at two measurement sites, including the V-site and L-site. In experimental statistics, there were two group records of ΔDOS versus index Ψ in the V sites and Loop sites, as shown in Fig. 8. Preliminary diagnosis results confirmed the specific degrees by ultrasonic images and angiogram examination, as well as observation by clinical physicians. Feasibility tests and case studies after PTA were used to validate the proposed method.
Fig. 9. (a) Position and velocity of each agent. (b) Mean squared error of each generation versus the number of iteration. (c) Optimal parameter versus the number of iteration. (d) Mean squared error of optimal solution versus the number of iteration.
A. Screening System Modeling In this study, GRNN was used to model a screening system for residual stenosis estimation of AVG. The GRNN structure can be immediately determined using the presentation of input– output pair training patterns. According to the input–output pairs of training data, as shown in Fig. 8, we have two input nodes (ψ L , ψ V ) in the input layer, 42 pattern nodes in the pattern layer as the number of pattern nodes being equal to the number of training data, two nodes in the summation layer, and one node in the output layer. Forty-two pairs of training patterns ([ψL (k), ψV (k)] → ΔDOS(k), k = 1, 2, 3, . . . , 42) are used to create weights between the input layer and pattern layer, and between the pattern layer and summation layer. Updating of the network parameters is performed by a PSO algorithm. In PSO optimization research, it is possible to find a good solution using two control factors, such as the maximum number of iterations and population size. The PSO with TVAC is given by population size G = 20 for each iteration, acceleration coefficients a1 = 2.5 and b1 = 0.5 for the cognitive component, acceleration coefficients a2 = 0.5 and b2 = 2.5 for the social component [15], and the maximum allowable number pm ax = 50. Particle swarm is used to optimize the objective function (15). Each agent has its position and velocity in 2-D space.
Fig. 10.
GRNN-based prediction model.
Each agent knows its best parameter σbestg , and its position, or the so-called “personal experiences.” Then, each agent knows the best parameter in the group, σbest, among σbestg . Therefore, each agent tends to modify its position using the (16) and (17), as shown in Fig. 9(a). After a few iterations, computing, velocity, and position gradually decrease. Fig. 9(b) shows the mean squared error of each generation versus the number of iterations. The optimal parameters of each generation are shown in Fig. 9(c). Fig. 9(d) shows that the PSO algorithm reaches the convergent condition, MESF < 0.2. It can converge after less than 50 training iterations to fit a nonlinear function using 42 pairs of training patterns. The promising optimal parameter σbest = 0.0193 minimizes the MSEF with G = 20 and pm ax = 50. The GRNN-based screening model is shown in Fig. 10. When only using one group of training data, the singlechannel input-based GRNN, 1-42-2-1 topology, does not fit
DU et al.: RESIDUAL STENOSIS ESTIMATION OF AVGS USING A DUAL-CHANNEL PCG
Fig. 12.
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Estimation results versus single and double based screening model.
0.1106 Ψ + 0.10, R2 = 0.5747. It has an average error of 12.34 ± 9.42%. The overall results of the regularization method are shown in Fig. 11. It shows that GRNN has “good generalization” along with a gradual decrease of the convergent condition to reduce the mean squared error. When reducing the convergent condition adequately, it can be seen that GRNN with the optimal parameter, σ best = 0.0193, and can avoid overfitting and reduce the generalization errors. Some advantages of the proposed screening system are summarized as follows: 1) The structure of GRNN can be easily determined using the presentation of input–output pair training patterns. 2) The proposed screening model uses the regularization method to obtain the optimal network parameter and to enhance the estimation accuracy. 3) The flexible approximation curve can tolerate fluctuation in the experimental data. B. Experimental Results-Case Studies after PTA Fig. 11. (a) Average errors versus the convergent condition. (b) Number of the iteration versus the convergent condition.
an adequate curve through the overall spread data, especially for the training data of the loop site. In Fig. 8, the blue-dash line clearly fails to fit the experimental data (open circle). On the other hand, GRNN with training data of the V site overfits the experimental data (open triangle) and generally has poor predictive performance, due to the exaggerated minor fluctuation in the data. With the same convergent condition, MESF < 0.2, it has an average error of 12.07 ± 8.02%, as shown in Fig. 11(a). According to previous experiences [26], [27], early stopping of the method, the regularization method, a larger network, and optimal network parameters could solve this problem. In this paper, the network, 2-42-2-1 topology, generalizes with the dual-channel inputs to achieve a flexible approximation curve between the ΔDOS and the indexes ΨL and ΨV , as shown in Fig. 10. In addition, a linear mapping method was also used to perform a least-squares curve fit, which minimizes the sum of the squares of the deviations of the data from the prediction model. The correlation between ΔDOS and Ψ is ΔDOS =
In the case studies, we used 54 datasets (patient record), 42 sets for training data, and 12 sets for testing data. In order to demonstrate the effectiveness of the proposed method, 12 testing patients were randomly selected to verify the residual stenosis estimation. These subjects had a high degree of DOS (> 0.80) before PTA [8]. PTA treatment or surgical revision was used to dilate the stenotic lesion and to enlarge the focal site with a balloon. The dual channel GRNN-based screening model has a high confidence level for the estimation of the ΔDOS, as shown in Table I, with an average error of 6.95%. A comparison of residual stenosis estimation between the single and doublebased screening models is shown in Fig. 12. It is observed that the 12 estimation values approach the actual values when using a double-channel model with MESF < 0.2. Thus, the proposed screening system has high confidences and a noninvasive and automatic means of measurement for deciding the degree of residual stenosis. Some estimation results show slightly high errors (10.0– 15.0%), because of the multiple stenosis sites and quantification errors. This could affect the efficiency of the proposed model. However, most test results show that the estimated values approach the actual values, as shown in Fig. 12, with an average
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TABLE I RESULTS OF RESIDUAL STENOSIS ESTIMATION Patient No.
Index ΨL
Index ΨV
D (cm)
d (cm)
Actual Value Δ DOS
Estimation Value Δ DOS
Error (%)
1 2 3 4 5 6 7 8 9 10 11 12
3.66 4.36 5.27 4.66 4.86 4.96 4.99 5.16 5.16 5.28 5.30 5.34
1.36 2.89 3.41 3.98 4.74 4.86 4.95 5.13 5.17 5.24 5.29 5.36
0.3249 0.2400 0.2176 0.2320 0.1712 0.2112 0.2312 0.1917 0.2445 0.1954 0.2213 0.2349
0.0693 0.0785 0.0351 0.0607 0.0561 0.0993 0.0557 0.0606 0.0470 0.0351 0.0875 0.0652
0.24 0.31 0.42 0.55 0.70 0.83 0.75 0.62 0.88 0.74 0.72 0.79
0.2400 0.3014 0.4355 0.5424 0.6990 0.7107 0.6829 0.6067 0.7945 0.7126 0.6612 0.7061
0.00 2.77 3.69 1.38 0.14 14.37 8.94 2.14 9.71 3.70 8.16 10.62
TABLE II RESULTS OF THE DIAMETER OF GRAFT ACCESS ESTIMATION Actual Value
Estimation Value
Patient No.
D (cm)
d r e f (cm)
Δ DOS
d a c t (cm)
Δ DOS
d e s t (cm)
1 2 3 4 5 6 7 8 9 10 11 12
0.3249 0.2400 0.2176 0.2320 0.1712 0.2112 0.2312 0.1917 0.2445 0.1954 0.2213 0.2349
0.0693 0.0785 0.0351 0.0607 0.0561 0.0993 0.0557 0.0606 0.0470 0.0351 0.0875 0.0652
0.24 0.31 0.42 0.55 0.70 0.83 0.75 0.62 0.88 0.74 0.72 0.79
0.1781 0.1556 0.1384 0.1875 0.1550 0.1781 0.2192 0.1732 0.2342 0.1814 0.1941 0.2133
0.2400 0.3014 0.4355 0.5424 0.6990 0.7107 0.6829 0.6067 0.7945 0.7126 0.6612 0.7061
0.1736 0.1533 0.1478 0.1813 0.1537 0.2038 0.1990 0.1611 0.2229 0.1686 0.2000 0.2078
Error (%)
2.52 1.43 -6.81 3.29 0.816 -14.47 9.20 7.12 4.80 7.03 -3.08 2.54
d 2 −d 2 Note [18]: ±Δ DOS e s t = ±(DOS p r e − DOS p o s t ) = e s t D 2 r e f ⇒ d e s t = d 2r e f ± D 2 Δ DOS e s t where D is the diameter of the normal graft in the direction of blood flow, d r e f is the diameter of the previous measurement, before PTA or in the previous monthly examination, and d a c t is the actual diameter of the graft access.
error of 5.47%. The proposed double-channel screening system can be further applied to estimate the diameter of the graft access. The estimated diameter of the graft access dest and the accuracy are shown in Table II, with an average error of 5.25%. The test results show that the estimated diameter increases after PTA and approaches the actual diameter. This confirms that the proposed screening model provides good estimation of the diameter of the graft access. In clinical applications, it can also provide an early detection technique for estimating diameter. If there is more than one decreasing trend in a monthly examination, the patient must receive PTA treatment and surgical revision. In addition, intragraft blood flow, or arterial or venous segment static pressure ratio examinations can also be used to monitor the graft condition. This provides a noninvasive, simple, and clinically applicable technique.
V. CONCLUSION For long-term use of AVG, it is vital that the volume of the flow is maintained in hemodialysis therapy. Stenosis and subsequent thrombosis usually occur at the site of the graft-to-vein anastomosis in a PTFE graft. A dual-channel screening sys-
tem for the estimation of residual stenosis is proposed as an early detection tool. This system combines feature extraction and GRNN. The Burg AR method is used to smooth the frequency spectra to estimate the characteristic frequencies. The fractional-order-based feature is then used to quantify/scale the degree of residual stenosis in a specific region [0, 6]. A dualchannel model is constructed to estimate the ΔDOS at the loop site and V site. A case study of residual stenosis estimation is used to verify the feasibility of the proposed screening model. The results show that the average error in the estimation of ΔDOS is 6.95%, and that the average error in the estimation of the diameter of the AVG access is 5.25%. Between the V site and the loop site, the dual-channel screening system uses the regularization method to obtain the optimal parameter and enhances estimation accuracy. To overcome the overfitting problem, a flexible curve can tolerate fluctuation in the testing data. The auscultation technique also offers a noninvasive, low cost, and easily used screening method that provides a promising way for detecting multisite stenosis in a graft access. This method offers potential as an automatic screening tool, and can be further integrated in portable or wearable systems for telemedicine or home healthcare applications.
DU et al.: RESIDUAL STENOSIS ESTIMATION OF AVGS USING A DUAL-CHANNEL PCG
REFERENCES [1] D. E. Finlay, D. G. Longley, M. C. Fosbager, and J. G. Letourneau, “Duplex and color Doppler sonography of hemodialysis arteriovenous fistulas and grafts,” RadioGraphics, vol. 13, no. 5, Sep. 1993, pp. 983– 999. [2] M. Haimov, “Construction of vascular access using vascular substitutes,” in Vascular Access: A Practical Guide, M. Haimov, Ed. Mt. Kisco, NY, USA: Futura, 1987, pp. 59–86. [3] M. Haimov, “The peripheral subcutaneous arteriovenous fistulas,” in Vascular Access: A Practical Guide, M. Haimov, Ed. Mt. Kisco, NY, USA: Futura, 1987, pp. 41–58. [4] W. D. Middleton, D. D. Picus, M. V. Marx, and G. L. Melson, “Color Doppler sonography of hemodialysis vascular access: Comparison with angiography,” Amer. J. Roentogenol., vol. 152, pp. 633–639, 1989. [5] V. Dousset, N. Grenier, C. Douws, P. Senuita, G. Sassouste, L. Ada, and L. Potaux, “Hemodialysis grafts: Color Doppler flow imaging correlated with digital subtraction angiography and functional status,” Radiology, vol. 181, pp. 89–94, 1991. [6] A. Asif, F. N. Gadalean, D. Merrill, G. Cherla, C. D. Cipleu, D. L. Epstein, and D. Roth, “Inflow stenosis in arteriovenous fistulas and grafts: A multicenter, prospective study,” Kidney Int., vol. 67, pp. 1986–1992, 2005. [7] W. L. Chen, C. H. Lin, T. S. Chen, P. J. Chen, and C. D. Kan, “Stenosis detection algorithm using the Burg method of autoregressive model for hemodialysis patients: Evaluation of arteriovenous shunt stenosis,” J. Med. Biol. Eng., vol. 33, no. 4, pp. 356–362, Sep. 2013. [8] W.-L. Chen, T. Chen, C.-H. Lin, P.-J. Chen, and C.-D. Kan, “Phonoangiography with a fractional order chaotic system—A novel and simple algorithm in analyzing residual arteriovenous access stenosis,” Med. Biol. Eng. Comput., vol. 51, no. 9, pp. 1011–1019, Sep. 2013. [9] Y. M. Akay, M. Akay, W. Welkowitz, S. Lewkowicz, and J. L. Semmlow, “Non-invasive acoustical detection of coronary artery disease: A comparative study of signal processing methods,” IEEE Trans. Biomed. Eng., vol. 40, no. 6, pp. 571–578, Jun. 1993. [10] O. P. Vasquez, M. M. Munguia, and B. Mandersson, “Arteriovenous fistula stenosis detection using wavelets and support vector machines,” in Proc. IEEE Eng. Med. Biol. Soc. Conf., Mineapolis, MN, USA, Sep. 2–6, 2009, pp. 1298–1301. [11] H. Wendland, “Piecewise, polynomials, positive definite and compactly supported radial basis functions of minimal degree,” Adv. Comput. Math., vol. 4, pp. 389–396, 1995. [12] T. L. Seng, M. Khalid, and R. Tusof, “Adaptive GRNN for the modeling of dynamic plants,” in Proc. IEEE Int. Symp. Intell. Control Vancouver, Canada, 2002, pp. 217–222. [13] E. Bonabeau, M. Dorigo, and G. Theraulaz, Swarm Intelligence: From Natural to Artificial Systems. London, U.K: Oxford Press, 1999. [14] Y.-L. Lin, W.-D. Chang, and J.-G. Hsieh, “A particle swarm optimization approach to nonlinear rational filter modeling,” Expert Syst. Appl., vol. 34, pp. 1194–1199, 2008. [15] A. Ratnaweera, S. K. Halgamuge, and H. C. Watson, “Self-organizing hierarchical particle swarm optimizer with time-varying acceleration coefficients,” IEEE Trans. Evolutionary Comput., vol. 8, no. 3, pp. 240–255, Jun. 2004. [16] K. Roth, I. Kauppinen, P. A. A. Esquef, and V. Valimaki, “Frequency warped Burg’s method for AR-modeling,” in Proc. IEEE Workshop Appl. Signal Process. Audio Acoustics, Oct. 19–22, 2003, pp. 5–8. [17] C. Collomb, “Linear prediction and Levinson-Durbin algorithm,” 2009, [Online]. Available: http://ccollomb.free.fr/technotes/ [18] W.-L. Chen, C.-D. Kan, C.-H. Lin, and T. Chen, “A rule-based decisionmaking diagnosis system to evaluate arteriovenous shunt stenosis for hemodialysis treatment of patients using fuzzy petri nets,” IEEE J. Biomed. Health Inform., vol. 18, no. 2, pp. 703–713, Mar. 2014. [19] J.-H. Chen, “Controlling chaos and chaotification in the Chen-Lee system by multiple time delays,” Chaos, Solitons Fractals, vol. 36, no. 4, pp. 843–852, 2008. [20] L.-J. Sheu, L.-M. Tam, H.-K. Chen, and S.-K. Lao, “Alternative implementation of the chaotic Chen-Lee system,” Chaos, Solitons Fractals, vol. 41, no. 4, pp. 1923–1929, 2009. [21] C.-H. Huang, C.-H. Lin, and C.-L. Kuo, “Chaos synchronization based detector for power quality disturbances classification in a power system,” IEEE Trans. Power Del., vol. 26, no. 2, pp. 944–953, Apr. 2011. [22] K. S. Killer and B. Ross, An Introduction to the Fractional Calculus and Fractional Differential Equations, New York, NY, USA: Wiley, 1993, ch. 6.
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[23] C. Ma and Yoichi Hori, “Fractional-order control: Theory and applications in motion control,” IEEE Ind. Electron. Mag., vol. 1, no. 4, pp. 6–16, Winter 2007. [24] C.-M. Li, Y.-C. Du, J.-X. Wu, C.-H. Lin, Y.-R. Ho, Y.-J. Lin, and T. Chen, “Synchronizing chaotification with support vector machine and wolf pack search algorithm for estimation of peripheral vascular occlusion in diabetes mellitus,” Biomed. Signal Process. Control, vol. 9, no. 2014, pp. 45–55, Jan. 2014. [25] J. Van Der Linden, J. H. M. Smits, J. H. Assink, D. W. Wolterbeek, J. J. Zijlstra, G. H. De Jong, M. A. Van Den Dorpel, and P. J. Blankestijn, “Short- and long-term functional effects of percutaneous transluminal angioplasty in hemodialysis vascular access,” J. Amer. Soc. Nephrol., vol. 13, pp. 715–720, 2002. [26] R. Meir and T. Zhang, “Generalization error bounds for Bayesian mixture algorithms,” J. Mach. Learning Res., vol. 4, pp. 839–860, 2003. [27] E. Alpaydin, Introduction to Machine Learning. Cambridge, MA, USA: MIT Press, 2004, pp. 79–80.
Yi-Chun Du was born in 1978. He received the B.A. and M.S. degrees in biomedical engineering from Chung Yuan Christian University, Taoyuan, Taiwan, in 2003, and the Ph.D. degree in biomedical engineering from National Cheng Kung University, Tainan, Taiwan, in 2008. He is currently an Assistant Professor with the Department of Electrical Engineering, Southern Taiwan University of Science and Technology, Tainan, Taiwan, where he has been since 2013. His research interests include medical device development, biomedical signal processing, and patient care monitoring.
Wei-Ling Chen was born in 1970. She received the B.S. and M.S. degrees in mechanical engineering from the National Cheng Kung University, Tainan, Taiwan, in 1994 and 1996, respectively, where she has been working toward the Ph.D. degree with the Department of Biomedical Engineering since 2010. She is also currently working in the Department of Engineering and Maintenance, Kaohsiung Veterans General Hospital, Kaohsiung, Taiwan, where she has been since 2013. Her research interests include biomedical signal processing, numerical analysis, and medical device design.
Chia-Hung Lin was born in 1974. He received the B.S. degree in electrical engineering from the Tatung Institute of Technology, Taipei, Taiwan, in 1998, the M.S. degree in electrical engineering from the National Sun Yat-Sen University, Kaohsiung, Taiwan, in 2000, and the Ph.D. degree in electrical engineering from National Sun Yat-Sen University in 2004. He is currently a Professor with the Department of Electrical Engineering, Kao-Yuan University, Kaohsiung, Taiwan, where he has been since 2013. His research interests include neural network computing and its applications, biomedical signal processing, and pattern recognition.
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Chung-Dann Kan received the M.D. degree from Kaohsiung Medical College, Kaohsiung, Taiwan, in 1993, and the Ph.D. degree from National Cheng Kung University, Tainan, Taiwan, in 2010. He completed the Residency and Fellowship training in cardiovascular surgery at National Cheng Kung University Hospital, Tainan, Taiwan. He is currently an Attending Physician of the Department of Surgery, National Cheng Kung University Hospital, and Institute of Clinical and Cardiovascular Research Center, Medical College, Tainan, Taiwan. He is also an Assistant Professor at National Cheng Kung University. His research interests include cardiac regeneration and aortic stent graft.
Ming-Jui Wu was born in 1971. He received the B.M. degree in medicine science from the National Yang-Ming University, Taipei, Taiwan, in 1996, and the M.S. degree in biomedical engineering from National Cheng Kung University, Tainan, Taiwan, in 2006. He is currently an attending Physician with the Department of Internal Medicine, Kaohsiung Veterans General Hospital Tainan Branch, Tainan. He is also the Chief of the Department of Internal Medicine, Kaohsiung Veterans General Hospital Tainan Branch, Tainan, Taiwan. His research interests include internal medicine, nephrology, hemodialysis and its application.
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Residual Stenosis Estimation of Arteriovenous Grafts Using a Dual-Channel Phonoangiography With Fractional-Order Features Yi-Chun Du, Wei-Ling Chen, Chia-Hung Lin, Chung-Dann Kan, and Ming-Jui Wu
Abstract—The residual stenosis estimation of an arteriovenous shunt is a valuable for evaluating outcomes of percutaneous transluminal angioplasty (PTA) treatment and surgical revision. This paper proposes a dual-channel phonoangiography (PCG) with fractional-order features to estimate the residual of stenosis estimation of arteriovenous shunt. The auscultation technique provides a noninvasive tool to monitor the degrees of arteriovenous grafts (AVGs). Then, support methods, such as the Burg autoregressive (AR) method and self-synchronization error formulation (SSEF), are used to extract fractional-order features between the loop site (L-site) and venous anastomosis site (V-site). Using 2-D patterns (nonlinear mapping), a generalized regression neural network (GRNN) is designed as a nonlinear estimate model to indicate the outcome of surgical revision or AVG stenosis upon routine monthly examinations. For 42 long-term follow-up patients, the results of examination show the proposed GRNN-based screening model efficiently estimates residual stenosis. Index Terms—Arteriovenous graft (AVG), fractional-order feature, generalized regression neural network (GRNN), phonoangiography (PCG).
I. INTRODUCTION RTERIOVENOUS shunts (AVS) are vital for end-stage renal disease (ESRD) for patients receiving hemodialysis therapy. The bridge accesses of AVS are anastomosed between arteries and veins, including Brescia-Cimino arteriovenous fistulas (AVFs) or synthetic loop grafts (AVGs) made of politetrafluoroethylene (PTFE) for hemodialysis [1], [2]. Due to repeat puncturing of the accesses or long-term use, AVS stenosis and dysfunction are caused by inadequate arterial inflow, venous
A
Manuscript received October 3, 2013; revised April 14, 2014; accepted March 11, 2014. Date of publication June 5, 2014; date of current version March 2, 2015. This work was supported in part by the National Science Council of Taiwan under contracts NSC 102-2218-E-218-006 and NSC 101-2221-E244-001. The Institutional Review Board (IRB) of the National Cheng-Kung University Hospital approved this study under contract ER-99-186. Y.-C. Du is with the Department of Electrical Engineering, Southern Taiwan University of Science and Technology, Tainan 71005, Taiwan (e-mail: terrydu@ mail.stust.edu.tw). W.-L. Chen is with the Department of Biomedical Engineering, National Cheng Kung University, Tainan 70101, Taiwan, and also with the Department of Engineering and Maintenance, Kaohsiung Veterans General Hospital, Kaohsiung 81362, Taiwan (e-mail: [email protected]). C.-H. Lin is with the Department of Electrical Engineering, Kao-Yuan University, Kaohsiung 82151, Taiwan (e-mail: [email protected]). C.-D. Kan is with Department of Surgery, National Cheng Kung University Hospital, Tainan 70101, Taiwan (e-mail: [email protected]). M.-J. Wu is with the Department of Internal Medicine, Yong-Kang Veterans Hospital, Tainan 71051, Taiwan (e-mail: [email protected]). Color versions of one or more of the figures in this paper are available online at http://ieeexplore.ieee.org. Digital Object Identifier 10.1109/JBHI.2014.2328346
outflow occlusion, or total occlusion [2], [3]. In clinical examinations, the traditional imaging method of angiography, along with duplex and Doppler sonography offer promising methods for evaluating dysfunction hemodialysis accesses. Under normal conditions, blood flow in the supply arteries and through the graft are monophasic, peak systolic velocities range from 1.0 to 4.0 m/s, with end-diastolic velocities of 0.6–2.0 m/s, and the draining veins have arterial pulsations with peak velocities of 0.3–1.0 m/s [4], [5]. Compared with the adjacent normal segment, increasing velocities could be shown by duplex and color Doppler sonography in the region of a focal site. Then, PTA treatment or placement of venous stents has been used to repair the intimal hyperplasia, aneurysmal deformability, and thrombosed accesses. However, operational principles must be taken into account, and extra learning about the limitations by the patients themselves is necessary in homecare applications. According to a previous study [6], inflow stenosis occurs in 29% (36/122) of graft cases (total 122 patients), all of whom have a coexisting stenosis on the venous side and that inflow stenosis accounts for 40% (41/101) of fistula cases (total 101 patients), 54% (22/41) of whom have a coexisting dysfunction on the venous side. This shows that the venous side is a site worth measuring to evaluate the conditions of AVS. The findings of other studies [7], [8] also indicate that the V side is a usual site for monitoring AVS function. According to these promising results, the phonography technique is used to estimate the degree of stenosis (DOS). However, the changes in frequency and amplitude are dependent on the stenosis sites, monitoring sites, and severity degree. Only one monitoring site shows slight variations between the frequency features and the DOSs. Therefore, a dual-channel phonoangiography (PCG)-based auscultation method is proposed to enable efficient and accurate estimation of AVS stenosis, as shown in Fig. 1. According to previous promising results [7]–[10], frequencybased features and fractional-order self-synchronization error formulations (SSEF) are used to calculate dynamic errors with changes depending on the DOS. Thus, we propose a highdimensional mapping mechanism, such as generalized regression neural network (GRNN) [11], [12], to model the relationship between ΔDOS and 2-D fractional-order features. The proposed method automates the procedure of complex nonlinear system design in real-time applications, and provides a prediction model-based on flexible curve approximation using a swarm-intelligence algorithm (SIA) [13]–[15] to update the GRNN’s parameters in a dynamic modeling environment.
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DU et al.: RESIDUAL STENOSIS ESTIMATION OF AVGS USING A DUAL-CHANNEL PCG
Fig. 1.
Auscultation method and dual-channel stethoscope placement.
A synthetic tube is implanted under the skin of the forearm/upper arm. The same tube can be used repeatedly when changing needle placement. However, it presents problems than do AVFs in clinical usages, such as clots, infection, and frequent replacement. The patency rate, infection rate, and thrombosis rate of AVGs are higher than those of AVFs, so patients with AVGs are assessed to validate the proposed method. For long-term follow-up patients, the results show that the proposed method is more efficient for residual stenosis estimation. II. TECHNOLOGICALLY SUPPORT Technologically support for feature extraction and SSEF is described below. A. Feature Extraction The PCG signals were acquired using two medical use of electronic stethoscopes (3M Littmann, Model 4100, K051790, MN, USA) in this study. It can detect sounds between 1 Hz to 2 kHz from the heart, vessels, lungs, and other body sounds with the use of a selective frequency undergoing a physical assessment. The stethoscopes offer amplification (18 times the amplification, 25 dB), processing, filtering, and recording functions, as well wireless (infrared transmission) data transfers to compatible PC and tablet PC for further analysis. It has three operation modes: bell (20–500 Hz), diaphragm (20–700 Hz), and extended range (1–20 kHz) modes. Therefore, high-pitch stenosis murmurs between 25 Hz and 2.5 kHz [7], [10] can be acquired with a sampling rate of 4 kHz (Nyquist Theorem). In order to remove the unwanted ambient noises, the filter provides extended frequency response mode for auscultation. Auscultations were performed with dual-channel electronic stethoscopes at the loop site (L-site) and venous anastomosis site (V-site), as shown in Fig. 1.
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On a tablet PC, Hilbert transform and a 5-Hz low-pass digital filter smoothed PCG signals were then used to obtain the peaks of the envelope of the periodic PCG signal. Tracking the peak values, the segmentation process was used to find the minimum value before and after the detected peaks [7], [8]. A reliable acquisition window can be obtained to acquire PCG signals in the segmentation process stage. For analyzing each PCG signal, a 25–200 Hz band-pass filter was implemented to remove the baseline wander and could maintain the main characteristic frequencies in the signal preprocessing stage. Then, the wellknown Burg autoregressive (AR) method [16], [17] was used to estimate the frequency spectra by fitting an autoregressive model of a given specific order. Referring to previous studies [7], [8], [18], an AR model parameters and model order can be determined by the Levinson– Durbin recursion [17]. It is based on minimizing the total sum of the forward and backward prediction errors using the final prediction error criterion. We suggest the AR model order 8 for constructing the Burg AR model with prediction coefficients. This model was used to smooth the frequency spectra and it tends to favor peaky spectra. Thus, the spectral peaks of frequency spectra, the region of 25–800 Hz, can be identified by the Burg AR method. Depending on frequency-based features, it provides key information for residual stenosis estimation. B. Self-Synchronization Error System Chaotic systems (CSs) are widely used in nonlinear physical applications and physical informatics [19], [20]. Generally, an original CS consists of a master system (MS) and a slave system (SS), which can be described as Master System : X˙ = AX + f (X) Slave System : Y˙ = AY + f (Y ) + U
(1) (2)
where X ∈ RN and Y ∈ RN denote the state vector, A is a N × N system matrix, f(X) and f(Y) are the nonlinear vector functions, and term U can be designed as a nonlinear controller to approach the MS for nonlinear control applications [19], [20]. In order to implement nominal plant, dimension N = 3 for a nonlinear CS was chosen for signal processing applications [21]. Consider the nominal Chen-Lee CS, X ࢠ R3 , Y = R3 , where X = [x1 , x2 , x3 ]T , Y = [y1 , y2 , y3 ]T , U = [u1 , u2 , u3 ]T , and matrices, Am or As , is a 3 × 3 system, denoted by the subscripts m and s for MS and SS as ⎡ ⎤ a −x3 0 ⎢x b 0⎥ 3 ⎥ Am = AX + f (X) = ⎢ ⎣ ⎦ 1 x2 0 c 3 ⎤ ⎡ a −y3 0 ⎢y b 0⎥ 3 ⎥ (3) As = AY + f (Y ) = ⎢ ⎦ ⎣ 1 y2 0 c 3
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This results in coupling variables for tracking the dynamic responses between the MS and SS. This system offers good symmetrical behavior and is used in this study [20], [21]. In order to track self-synchronization errors, the control term u1 = u2 = u3 = 0 is used, and we hypothesize that x1 x2 − y1 y2 ≈ (x1 − y1 )(x2 − y2 ), x1 x3 − y1 y3 ≈ (x1 − y1 )(x3 − y3 ), and x2 x3 − y2 y3 ≈ (x2 − y2 )(x3 − y3 ). After defining the error states e = [e1 , e2 , e3 ]T as e1 = (x1 − y1 ), e2 = (x2 − y2 ), and e3 = (x3 − y3 ), subtract (2) from (1), and (x1 − y1 )(x2 − y2 ) = e1 e2 , (x1 − y1 )(x3 − y3 ) = e1 e3 , and (x2 − y2 )(x3 − y3 ) = e2 e3 , the error system can be expressed by ⎡
e˙ 1 ⎣ e˙ 2 e˙ 3
⎤ a −e3 0 ⎡ ⎤ e1 ⎢ b 0⎥ ⎥ ⎣ e2 ⎦ ⎦ = ⎢ e3 ⎦ ⎣ 1 e3 e2 0 c 3 ⎡ ⎤ ⎡ ⎤ ⎡ −e e ⎤ 3 2 a 0 0 e1 ⎥ ⎢ = ⎣ 0 b 0 ⎦ ⎣ e2 ⎦ + ⎣ e1 e3 ⎦ 1 e3 0 0 c e1 e2 3 ⎤
⎡
(4)
According to previous studies, system (4) acts as a chaotic attractor that must satisfy the parameters a, b, and c, under the following specific condition [19], [20]: a > 0, b < 0, c < 0, and 0 0, b = < 0, Γ(2 + α) Γ(2 + α)
c =
cΓ(2) 0.50, Class II: 0.30–0.50, and Class I: < 0.30, after PTA [8]. We monitored three possible anatomy sites, including the A site, loop site (L site), and V site, as shown in Fig. 3. The electronic stethoscope acquired the time-domain PCG signals at the measurement site, as shown in Fig. 4(a). Each segment of PCG signals can be determined between adjacent two minimum values before and after the detected peaks (red-circle symbol), as shown in Fig. 4(b). In Fig. 4, the dynamic errors, Φ1 [i], Φ2 [i], and Φ3 [i], i = 1, 2, 3, . . . , n − 2 (n = 800), can be calculated using (9). When the fractional order q = 0.98 (α = 0.02), the dynamic errors are identified using the system parameters a = 1.983(a = 2), b = −3.966(b = −4), and c = −2.9745(c = −3). Figs. 4(c) and (f) shows the norm of (Φ1 , Φ2 , Φ3 ), index Ψ, on the V site and L site. Referring to a previous study [8], there is no statistical significance in A-sites using statistics analysis (p > 0.05). In this study, we chose dual-channel stethoscopes to measure PCG signals. Fig. 5 shows the average indexes Ψ with three classes on the L and V sites, respectively. The combination patterns of two indexes, ΨL and ΨV , can be separated into three classes, which are denoted by the subscripts L and V for L and V sites. Based on the aim of this research, we select two parameters to estimate the ΔDOS.
III. DUAL-CHANNEL PHONOANIGIOGRAPHY-BASED SCREENING SYSTEM A. Experimental Setup Long-term hemodialysis treatment of patients was chosen for clinical investigation at the Department of Surgery, National Cheng Kung University Hospital, Tainan, Taiwan. The research study was also approved by the hospital research ethics committee and the Institutional Review Board (IRB): ER-99-186. There were 23 females and 19 males with a mean age of 63 ± 10.2 years (52–74 years). The participants’ mean duration of long-term hemodialysis therapy was 48 ± 31 months. Preliminary diagnosis results confirmed the specific degrees by ultrasonic image examination and observation by clinical physicians. In clinical research, the degree of narrowing of the normal vessel is an index for the degree of arteriovenous access. Examination results have confirmed the specific degrees from X-ray images or angiographic images, which are defined as in [7], [8], [18], [25]
d2 (11) DOS = 1 − 2 D where D is the diameter of the normal graft or vessel in the direction of blood flow, d is the diameter of the stenosis lesion. For the surgical results among 42 patients, the overall DOS of
B. Screening System Implementation According to the correlation between ΔDOS and index Ψ, we can utilize “linear” or “exponential” regression to model the relationship between ΔDOS and index Ψ. However, it is not difficult to approximate the scatter data to a function under high dimensionality and nonlinearity. For high-dimensional mapping
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Fig. 4. (a) Phonoangiography (PCG) signal in the time domain. (b) PCG segmentation process, (c), (d), and (e) Frequency spectra, dynamic errors Φ 1 , Φ 2 , and Φ 3 (fractional order q = 0.98), and the index, Ψ, on V site; (f), (g), and (h) Frequency spectra, dynamic errors Φ 1 , Φ 2 , and Φ 3 , and the index, Ψ, on loop site.
Fig. 5.
Average indexes Ψ with three classes on L and V sites.
applications, a “GRNN” is used to model the relationship between ΔDOS and indexes ΨL and ΨV, as shown in Fig. 6. This method has been shown to be effective in a great variety of difficult function mapping and prediction applications [11], [12]. It gives a sufficient number of pattern nodes in the pattern layer and can approximate a nonlinear function. Corresponding pattern nodes allow keep on growing with addition or deletion. The GRNN requires more pattern nodes than a tradition feedforward backpropagation network, but it can be designed in a fraction of the time to train or retrain the network when many training data are available. A continuous learning model can be designed an adaptive mechanism using the optimization algorithms. The feedforward multilayer network consists of four layers, including the input layer, pattern layer, summation layer, and output layer. The curve approximation algorithm of GRNN is summarized as follows:
Fig. 6.
Structure of the GRNN.
Step 1: For each training pattern ψ(k) = [ψL (k), ψV (k)] fork = 1, 2, 3, . . . , K, and create weights wk i , i = 1, 2, between the input layer and pattern layer by
ΨL (k) ΨV (k) , [wk 1 , wk 2 ] = ΨL m ax ΨV m ax T
T (12)
DU et al.: RESIDUAL STENOSIS ESTIMATION OF AVGS USING A DUAL-CHANNEL PCG
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where W 1 = [wk i ] is a K by 2 matrix. It can be extended to work in high-dimensional feature space formed with nonlinear mapping of 2-D input to K-dimensional pattern feature. Step 2: Create weights wk j , j = 1, 2, between pattern layer and summation layer by [wk j ] = [ΔDOS(k), 1]
(13)
where the values of wk 1 are the predicted ΔDOS(k) associated with the pattern [ψ L (k); ψ(k)]. Connection weights from the overall pattern nodes to another summation nodes are set as 1, and W 2 = [wk j ] is k by 2 matrix. Step 3: Compute the output of pattern node Gk by the Gaussian function
K (Ψi − wk i )2 Gk = exp − , i= 1, 2 (14) 2σk2 k =1
where [ψ1 (k), ψ2 (k)] = [ψL , ψV ], σ1 = · · · = σk = · · · = σK = σ, the optimal value can be obtained by using the optimization methods. Step 4: Compute the outputs of node ΔDOS by K K ΔDOS(ΨL , ΨV ) = wk j Gk Gk . (15) k =1
In (14), adjusting parameter σ refines the accuracy of prediction model. The optimal parameter σ is intended to minimize the mean squared error function (MSEF). The objective function is defined as MSEF =
Fig. 7.
Flowchart of particle swarm optimization algorithm.
k =1
K 1 [T (k) − ΔDOS(ΨL , ΨV )]2 K
(16)
k =1
where T(k) is the desired ΔDOS for the kth training pattern. However, (16) is a nonlinear function and its partial differential equation is difficult to obtain using the gradient/steepest descent method. In this study, the SIA [13]–[15] is an evolutionary optimization technique to solve optimization problems. It is suitable for processing nondifferentiable objective functions, as in (16). It also uses probabilistic transition rules that can find the global best solution by adjusting the trajectory of each individual particle toward its own best location and toward the best particle of the entire swarm. A particle swarm optimization (PSO) algorithm is used to solve this problem. Let σgp be the current position of the gth agent at iteration number p, agent g = 1, 2, 3, . . . , G, where G is the population size. Multiple particles form a population and are represented by p ]. The a G-dimensional vector, as δ p = [σ1p , σ2p , . . . , σgp , . . . , σG p modification of position σg can be represented by velocity p ]. The flowchart Δσgp , Δδ p = [Δσ1p , Δσ2p , . . . , Δσgp , . . . , ΔσG is shown in Fig. 7 and mathematical representation is given by [13]–[15] Velocity : Δσgp+1 = Δσgp + c1 rand1 (σbestg − σgp ) + c2 rand2 σbest − σgp (17) Position : σgp+1 = σgp + Δσgp+1
(18)
where σbest is the global best in the group, and σbestg is the individual best. Parameters c1 and c2 are the positive “acceleration parameters” that pull each particle toward the best positions, and rand1 and rand2 are the uniformly random numbers between 0 and 1. For efficient convergence to the global optimal solution, a PSO algorithm with time-varying acceleration coefficients (TVAC) [15] is used to improve the performance, as c1 = (b1 − a1 )
p p + a1 , c2 = (b2 − a2 ) + a2 (19) pm ax pm ax
where the first term is the “cognitive component,” the second term is the “social component,” a1 , b1 , a2 , and b2 are constant values, of which the experienced values are c1 from 2.5 to 0.5 and c2 from 0.5 to 2.5, respectively, and pm ax is the maximum number of allowable iterations. With a large cognitive component and small social component, multiple particles are allowed to move around the search space [15], [21], as roughly adjust the searching points. By monotonously reducing the cognitive component and increasing the social component, a small cognitive component and a large social component allow the particles to converge to a global optimal solution, as keep fine-tuning at the end of the search. The term, p/pm ax , is used to control the changes of cognitive component and social component at each search stage. There are two convergent conditions for stopping the PSO algorithm: 1) the objective function MSEF is less than the prespecified value and 2) the number of iterations achieves the maximum allowable number pm ax .
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Fig. 8.
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Two group records of ΔDOS versus index Ψ in V sites and loop sites.
IV. EXPERIMENTAL RESULTS AND DISCUSSION The proposed estimation method with feature extraction and GRNN was developed on a PC AMD Athlon II × 2 245 2.91 GHz with 1.75-GB RAM and MATLAB software. To demonstrate the effectiveness of the proposed estimation model, 42 subjects were tested (NCKUH, IRB, under contract number: ER-99-186). Auscultation records were performed with a digital stethoscope at two measurement sites, including the V-site and L-site. In experimental statistics, there were two group records of ΔDOS versus index Ψ in the V sites and Loop sites, as shown in Fig. 8. Preliminary diagnosis results confirmed the specific degrees by ultrasonic images and angiogram examination, as well as observation by clinical physicians. Feasibility tests and case studies after PTA were used to validate the proposed method.
Fig. 9. (a) Position and velocity of each agent. (b) Mean squared error of each generation versus the number of iteration. (c) Optimal parameter versus the number of iteration. (d) Mean squared error of optimal solution versus the number of iteration.
A. Screening System Modeling In this study, GRNN was used to model a screening system for residual stenosis estimation of AVG. The GRNN structure can be immediately determined using the presentation of input– output pair training patterns. According to the input–output pairs of training data, as shown in Fig. 8, we have two input nodes (ψ L , ψ V ) in the input layer, 42 pattern nodes in the pattern layer as the number of pattern nodes being equal to the number of training data, two nodes in the summation layer, and one node in the output layer. Forty-two pairs of training patterns ([ψL (k), ψV (k)] → ΔDOS(k), k = 1, 2, 3, . . . , 42) are used to create weights between the input layer and pattern layer, and between the pattern layer and summation layer. Updating of the network parameters is performed by a PSO algorithm. In PSO optimization research, it is possible to find a good solution using two control factors, such as the maximum number of iterations and population size. The PSO with TVAC is given by population size G = 20 for each iteration, acceleration coefficients a1 = 2.5 and b1 = 0.5 for the cognitive component, acceleration coefficients a2 = 0.5 and b2 = 2.5 for the social component [15], and the maximum allowable number pm ax = 50. Particle swarm is used to optimize the objective function (15). Each agent has its position and velocity in 2-D space.
Fig. 10.
GRNN-based prediction model.
Each agent knows its best parameter σbestg , and its position, or the so-called “personal experiences.” Then, each agent knows the best parameter in the group, σbest, among σbestg . Therefore, each agent tends to modify its position using the (16) and (17), as shown in Fig. 9(a). After a few iterations, computing, velocity, and position gradually decrease. Fig. 9(b) shows the mean squared error of each generation versus the number of iterations. The optimal parameters of each generation are shown in Fig. 9(c). Fig. 9(d) shows that the PSO algorithm reaches the convergent condition, MESF < 0.2. It can converge after less than 50 training iterations to fit a nonlinear function using 42 pairs of training patterns. The promising optimal parameter σbest = 0.0193 minimizes the MSEF with G = 20 and pm ax = 50. The GRNN-based screening model is shown in Fig. 10. When only using one group of training data, the singlechannel input-based GRNN, 1-42-2-1 topology, does not fit
DU et al.: RESIDUAL STENOSIS ESTIMATION OF AVGS USING A DUAL-CHANNEL PCG
Fig. 12.
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Estimation results versus single and double based screening model.
0.1106 Ψ + 0.10, R2 = 0.5747. It has an average error of 12.34 ± 9.42%. The overall results of the regularization method are shown in Fig. 11. It shows that GRNN has “good generalization” along with a gradual decrease of the convergent condition to reduce the mean squared error. When reducing the convergent condition adequately, it can be seen that GRNN with the optimal parameter, σ best = 0.0193, and can avoid overfitting and reduce the generalization errors. Some advantages of the proposed screening system are summarized as follows: 1) The structure of GRNN can be easily determined using the presentation of input–output pair training patterns. 2) The proposed screening model uses the regularization method to obtain the optimal network parameter and to enhance the estimation accuracy. 3) The flexible approximation curve can tolerate fluctuation in the experimental data. B. Experimental Results-Case Studies after PTA Fig. 11. (a) Average errors versus the convergent condition. (b) Number of the iteration versus the convergent condition.
an adequate curve through the overall spread data, especially for the training data of the loop site. In Fig. 8, the blue-dash line clearly fails to fit the experimental data (open circle). On the other hand, GRNN with training data of the V site overfits the experimental data (open triangle) and generally has poor predictive performance, due to the exaggerated minor fluctuation in the data. With the same convergent condition, MESF < 0.2, it has an average error of 12.07 ± 8.02%, as shown in Fig. 11(a). According to previous experiences [26], [27], early stopping of the method, the regularization method, a larger network, and optimal network parameters could solve this problem. In this paper, the network, 2-42-2-1 topology, generalizes with the dual-channel inputs to achieve a flexible approximation curve between the ΔDOS and the indexes ΨL and ΨV , as shown in Fig. 10. In addition, a linear mapping method was also used to perform a least-squares curve fit, which minimizes the sum of the squares of the deviations of the data from the prediction model. The correlation between ΔDOS and Ψ is ΔDOS =
In the case studies, we used 54 datasets (patient record), 42 sets for training data, and 12 sets for testing data. In order to demonstrate the effectiveness of the proposed method, 12 testing patients were randomly selected to verify the residual stenosis estimation. These subjects had a high degree of DOS (> 0.80) before PTA [8]. PTA treatment or surgical revision was used to dilate the stenotic lesion and to enlarge the focal site with a balloon. The dual channel GRNN-based screening model has a high confidence level for the estimation of the ΔDOS, as shown in Table I, with an average error of 6.95%. A comparison of residual stenosis estimation between the single and doublebased screening models is shown in Fig. 12. It is observed that the 12 estimation values approach the actual values when using a double-channel model with MESF < 0.2. Thus, the proposed screening system has high confidences and a noninvasive and automatic means of measurement for deciding the degree of residual stenosis. Some estimation results show slightly high errors (10.0– 15.0%), because of the multiple stenosis sites and quantification errors. This could affect the efficiency of the proposed model. However, most test results show that the estimated values approach the actual values, as shown in Fig. 12, with an average
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TABLE I RESULTS OF RESIDUAL STENOSIS ESTIMATION Patient No.
Index ΨL
Index ΨV
D (cm)
d (cm)
Actual Value Δ DOS
Estimation Value Δ DOS
Error (%)
1 2 3 4 5 6 7 8 9 10 11 12
3.66 4.36 5.27 4.66 4.86 4.96 4.99 5.16 5.16 5.28 5.30 5.34
1.36 2.89 3.41 3.98 4.74 4.86 4.95 5.13 5.17 5.24 5.29 5.36
0.3249 0.2400 0.2176 0.2320 0.1712 0.2112 0.2312 0.1917 0.2445 0.1954 0.2213 0.2349
0.0693 0.0785 0.0351 0.0607 0.0561 0.0993 0.0557 0.0606 0.0470 0.0351 0.0875 0.0652
0.24 0.31 0.42 0.55 0.70 0.83 0.75 0.62 0.88 0.74 0.72 0.79
0.2400 0.3014 0.4355 0.5424 0.6990 0.7107 0.6829 0.6067 0.7945 0.7126 0.6612 0.7061
0.00 2.77 3.69 1.38 0.14 14.37 8.94 2.14 9.71 3.70 8.16 10.62
TABLE II RESULTS OF THE DIAMETER OF GRAFT ACCESS ESTIMATION Actual Value
Estimation Value
Patient No.
D (cm)
d r e f (cm)
Δ DOS
d a c t (cm)
Δ DOS
d e s t (cm)
1 2 3 4 5 6 7 8 9 10 11 12
0.3249 0.2400 0.2176 0.2320 0.1712 0.2112 0.2312 0.1917 0.2445 0.1954 0.2213 0.2349
0.0693 0.0785 0.0351 0.0607 0.0561 0.0993 0.0557 0.0606 0.0470 0.0351 0.0875 0.0652
0.24 0.31 0.42 0.55 0.70 0.83 0.75 0.62 0.88 0.74 0.72 0.79
0.1781 0.1556 0.1384 0.1875 0.1550 0.1781 0.2192 0.1732 0.2342 0.1814 0.1941 0.2133
0.2400 0.3014 0.4355 0.5424 0.6990 0.7107 0.6829 0.6067 0.7945 0.7126 0.6612 0.7061
0.1736 0.1533 0.1478 0.1813 0.1537 0.2038 0.1990 0.1611 0.2229 0.1686 0.2000 0.2078
Error (%)
2.52 1.43 -6.81 3.29 0.816 -14.47 9.20 7.12 4.80 7.03 -3.08 2.54
d 2 −d 2 Note [18]: ±Δ DOS e s t = ±(DOS p r e − DOS p o s t ) = e s t D 2 r e f ⇒ d e s t = d 2r e f ± D 2 Δ DOS e s t where D is the diameter of the normal graft in the direction of blood flow, d r e f is the diameter of the previous measurement, before PTA or in the previous monthly examination, and d a c t is the actual diameter of the graft access.
error of 5.47%. The proposed double-channel screening system can be further applied to estimate the diameter of the graft access. The estimated diameter of the graft access dest and the accuracy are shown in Table II, with an average error of 5.25%. The test results show that the estimated diameter increases after PTA and approaches the actual diameter. This confirms that the proposed screening model provides good estimation of the diameter of the graft access. In clinical applications, it can also provide an early detection technique for estimating diameter. If there is more than one decreasing trend in a monthly examination, the patient must receive PTA treatment and surgical revision. In addition, intragraft blood flow, or arterial or venous segment static pressure ratio examinations can also be used to monitor the graft condition. This provides a noninvasive, simple, and clinically applicable technique.
V. CONCLUSION For long-term use of AVG, it is vital that the volume of the flow is maintained in hemodialysis therapy. Stenosis and subsequent thrombosis usually occur at the site of the graft-to-vein anastomosis in a PTFE graft. A dual-channel screening sys-
tem for the estimation of residual stenosis is proposed as an early detection tool. This system combines feature extraction and GRNN. The Burg AR method is used to smooth the frequency spectra to estimate the characteristic frequencies. The fractional-order-based feature is then used to quantify/scale the degree of residual stenosis in a specific region [0, 6]. A dualchannel model is constructed to estimate the ΔDOS at the loop site and V site. A case study of residual stenosis estimation is used to verify the feasibility of the proposed screening model. The results show that the average error in the estimation of ΔDOS is 6.95%, and that the average error in the estimation of the diameter of the AVG access is 5.25%. Between the V site and the loop site, the dual-channel screening system uses the regularization method to obtain the optimal parameter and enhances estimation accuracy. To overcome the overfitting problem, a flexible curve can tolerate fluctuation in the testing data. The auscultation technique also offers a noninvasive, low cost, and easily used screening method that provides a promising way for detecting multisite stenosis in a graft access. This method offers potential as an automatic screening tool, and can be further integrated in portable or wearable systems for telemedicine or home healthcare applications.
DU et al.: RESIDUAL STENOSIS ESTIMATION OF AVGS USING A DUAL-CHANNEL PCG
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Yi-Chun Du was born in 1978. He received the B.A. and M.S. degrees in biomedical engineering from Chung Yuan Christian University, Taoyuan, Taiwan, in 2003, and the Ph.D. degree in biomedical engineering from National Cheng Kung University, Tainan, Taiwan, in 2008. He is currently an Assistant Professor with the Department of Electrical Engineering, Southern Taiwan University of Science and Technology, Tainan, Taiwan, where he has been since 2013. His research interests include medical device development, biomedical signal processing, and patient care monitoring.
Wei-Ling Chen was born in 1970. She received the B.S. and M.S. degrees in mechanical engineering from the National Cheng Kung University, Tainan, Taiwan, in 1994 and 1996, respectively, where she has been working toward the Ph.D. degree with the Department of Biomedical Engineering since 2010. She is also currently working in the Department of Engineering and Maintenance, Kaohsiung Veterans General Hospital, Kaohsiung, Taiwan, where she has been since 2013. Her research interests include biomedical signal processing, numerical analysis, and medical device design.
Chia-Hung Lin was born in 1974. He received the B.S. degree in electrical engineering from the Tatung Institute of Technology, Taipei, Taiwan, in 1998, the M.S. degree in electrical engineering from the National Sun Yat-Sen University, Kaohsiung, Taiwan, in 2000, and the Ph.D. degree in electrical engineering from National Sun Yat-Sen University in 2004. He is currently a Professor with the Department of Electrical Engineering, Kao-Yuan University, Kaohsiung, Taiwan, where he has been since 2013. His research interests include neural network computing and its applications, biomedical signal processing, and pattern recognition.
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Chung-Dann Kan received the M.D. degree from Kaohsiung Medical College, Kaohsiung, Taiwan, in 1993, and the Ph.D. degree from National Cheng Kung University, Tainan, Taiwan, in 2010. He completed the Residency and Fellowship training in cardiovascular surgery at National Cheng Kung University Hospital, Tainan, Taiwan. He is currently an Attending Physician of the Department of Surgery, National Cheng Kung University Hospital, and Institute of Clinical and Cardiovascular Research Center, Medical College, Tainan, Taiwan. He is also an Assistant Professor at National Cheng Kung University. His research interests include cardiac regeneration and aortic stent graft.
Ming-Jui Wu was born in 1971. He received the B.M. degree in medicine science from the National Yang-Ming University, Taipei, Taiwan, in 1996, and the M.S. degree in biomedical engineering from National Cheng Kung University, Tainan, Taiwan, in 2006. He is currently an attending Physician with the Department of Internal Medicine, Kaohsiung Veterans General Hospital Tainan Branch, Tainan. He is also the Chief of the Department of Internal Medicine, Kaohsiung Veterans General Hospital Tainan Branch, Tainan, Taiwan. His research interests include internal medicine, nephrology, hemodialysis and its application.
