coronary plaque characterization considering continuity of ... · , which are cut off randomly from...

IJBSCHS Biomedical Soft Computing and Human Sciences, Vol.x,No.x,pp.000-000) [Original article] Copyright©1995 Biomedical Fuzzy Systems Association

(Accepted on 20xx.xx.xx)

1

Coronary Plaque Characterization Considering Continuity of

Tissue by Sparse Modeling of 2D IVUS Signal

Shota FURUKAWA*, Eiji UCHINO*, **, Tadahiro AZETSU*** and Noriaki SUETAKE*

*Graduate School of Science and Engineering, Yamaguchi University, Japan **Fuzzy Logic Systems Institute, Japan

*** Yamaguchi Prefectural University, Japan

Abstract: A major cause of Acute Coronary Syndrome (ACS) is a blood clot generated by a rupture of plaque in the coronary artery. For a diagnosis of ACS, it becomes important to characterize accu-rately the tissue of coronary plaque. Several methods to characterize the tissue of coronary plaque have been proposed so far. They are not however always useful due to the limitation of the perfor-mance of the features selected. In this study, we propose a new method to use sparse modeling of the 2D ultrasound signal reflected from the target tissue of plaque. The effectiveness of the proposed method has been verified by comparing the characterization results by the proposed method to those by the conventional methods for the real intravascular ultrasound data obtained from the human coronary arteries. Keywords Sparse modeling, Tissue characterization, Coronary plaque, Radio frequency signal,

Intravascular ultrasound.

1. Introduction

The main cause of Acute Coronary Syndrome (ACS) is a thrombus caused by a rupture of plaque formed in a coronary artery. A plaque is classified into two types by its composition. One is a stable plaque which has a thick fibrous cap and a small lipid core under it. The other is an unstable plaque which has a thin fibrous cap and a large lipid core under it. The fibrous cap of unstable plaque easily ruptures and causes a thrombus which blocks the flow of blood. Therefore, the tissue characteri-zation of plaque is very important for a diagnosis of ACS.

The Intravascular Ultrasound (IVUS) method is one of the tomographic imaging techniques. It is used for the visualization of the inside of the coronary artery. In the IVUS method, a catheter with an ultrasound probe at-tached to its end is inserted into the arterial lumen. The

ultrasound signal is emitted from the probe, and its re-flected signal from the vessel wall and the tissue of plaque is again received by the probe. This ultrasound signal is called a Radio Frequency (RF) signal.

In the IVUS method, the amplitude of the RF signal is transformed into intensity to form a cross-sectional im-age of a blood vessel. This cross-sectional image is called a brightness or B-mode image [1].

In general, a medical doctor observes this B-mode image to diagnose the plaque. It is however very difficult to characterize the plaque just by observing this B-mode image. For these reasons, many methods have been pro-posed for the characterization of the tissue of the coronary plaque.

There are two major methods to classify (character-ize) the tissue of plaque. One is an Integrated Backscatter (IB) method [2], [3], and the other is a method which is based on the frequency analysis of RF signal [4]. In the IB method, it cannot classify accurately the tissue of plaque, because the IB value changes according to the distance between the probe and the plaque. The position of the

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23

IJBSCHS

［Original Article］Biomedical Soft Computing and Human Sciences, Vol.20, No.2, pp.23-29

CopyrightⒸ1995 Biomedical Fuzzy Systems Association(Accepted on 2016.1.14)

Biomedical Soft Computing and Human Sciences, Vol.x, No.x, (20xx)

2

probe in the coronary artery cannot be controlled. On the other hand, concerning the method based on the frequency analysis, the classification accuracy is not enough neither, because the frequency characteristics of the tissue are not so clearly split among tissues.

In this study, we propose a novel method to improve the accuracy of plaque tissue characterization by using the sparse modeling [5], [6]. The sparse modeling is a method to represent the signal by a linear combination of a few basis functions. So, the expansion coefficients of the basis functions obtained by a sparse modeling are thus sparse, which means that a few of the coefficients have only some significant values, and many other coefficients have very small values.

In the proposed method, the patterns of the coeffi-cients are employed as the feature vectors to classify the plaque tissue. The number of the significant patterns of coefficient is small because of the sparseness of the coef-ficients.

Experiments are performed for the classification of the tissues of plaque into the fibrous and lipid tissues using the RF signal obtained from human coronary arteries. The effectiveness of the proposed method has been verified by comparing the classification results by the proposed method to those by the frequency analysis based conven-tional method.

2. Conventional Tissue Characterization Method

2.1. IVUS Method

The IVUS method is one of the medical imaging techniques. In the IVUS method, the catheter with the ul-trasound probe attached to its end is inserted into the cor-onary artery and then rotated (Fig. 1 (a)). The output power of the ultrasound probe is 0.033 mW. The ultra-sound signal is transmitted from the ultrasound probe, and its reflected signal from the vessel wall and the tissue is received also by the probe. This reflected ultrasound sig-nal is called a Radio Frequency (RF) signal. The transmit-ting frequency of the ultrasound signal is 40 MHz, and the RF signal is sampled at 400 MHz.

An IVUS B-mode image is constructed by analyz-ing the received RF signal (Fig. 1 (b)) [7]. This IVUS B-mode image expresses a tomographic image of the cross-section of the coronary artery. This image is constructed with 2,048 points in depth, and 256 lines in radial direc-tion. In an ideal condition, the resolution of IVUS B-mode image is about 40 μm in depth, and about 80 μm in radial direction. 2.2. IB Analysis

The IB analysis focuses on the energy of the RF sig-nal, i.e., the IB value of the RF signal in each local area.

(a) (b)

Fig. 1. (a) An ultrasound probe attached to the distal end of a catheter. The ultrasound signal istransmitted from the probe and its reflected signal from the vessel wall and the plaque tissue isreceived again by the probe. (b) An example of the B-mode image by the IVUS method. This is areal time ultrasound cross-sectional image of a blood vessel where a catheter probe is currentlyrotating.

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Biomedical Soft Computing and Human Sciences, Vol.20, No.2, 2016

S. FURUKAWA, E. UCHINO, T. AZETSU and N. SUETAKE: Coronary Plaque Characterization by Sparse Modeling

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The IB value is calculated by integrating the local RF sig-nal [2].

In the IB analysis, the thresholds of the IB values for the characterization of the tissue are decided experi-mentally so that the learning signals are most precisely classified. The IB analysis is simple, and indeed is effective in a restricted case. However, it cannot always accurately classify the tissues of plaque, because some types of tis-sues have similar IB values with each other, and the IB value depends on a distance between the probe and the tis-sue. The position of the probe in the coronary artery can-not be controlled nor measured. This is a fatal defect of the IB analysis. 2.3. Frequency Analysis-Based Method The frequency analysis-based method [8], [9] is an-other approach for the tissue characterization. In this method, the normalized power spectrum of the local RF signal is used as the feature vector. However, since the fre-quency characteristics of some tissues are similar to others, a precise tissue characterization is not yet achieved.

3. Tissue Characterization Method by Sparse Modeling

3.1. Sparse Modeling

The sparse modeling is a method to represent the signal by a linear combination of the basis functions with a few significant coefficients, which imitates a perceptual system of the mammalian visual cortex.

The sparse modeling (coding) was first proposed by B. A. Olshausen and D. J. Field [5]. The algorithm for learning the overcomplete sparse codes is described in ref-erence [6]. It is closely related to the Independent Compo-nent Analysis (ICA) [10], [11], which is well known as a statistical method to estimate the underlying features of the observed signal.

We use the excellent feature extraction ability of sparse modeling (coding) for the tissue characterization of plaque. In the proposed method, the RF signal is treated as a two dimensional signal with the depth and radial di-rections. The sparse code patterns for the RF signal are employed as the feature vectors. 3.1.1. Representation of RF Signal

A local RF signal � in a short time interval is ex-pressed as a linear combination of the basis functions �� as follows:

� ��

��, (1)

where �� are the expansion coefficients for each basis function ��, and � is the number of the basis functions. � and �� are given by: � � ��,� , ��, (2)�� ,� , ��, (3)

where � is a dimension of � and � is a transpose oper-ation. 3.1.2. Cost Function of Sparse Modeling The basis functions �� and the coefficients �� are statistically determined from a set of the local RF signals �, which are cut off randomly from the learning RF sig-nals. In the sparse modeling, the following cost function is introduced to determine �� and �� [5], [6]:

� � ��

��

��

�

��, (4)

where ⟨∙⟩ is an averaging operator, and � is a positive constant. � is a scaling constant, for which the standard deviation of the learning signals is employed. �� is an arbitrary nonlinear function.

The first term of Eq. (4) is the sum of the squared error between the input signal � and the reconstructed signal by a linear combination of ��. This indicates the signal reconstruction performance. The second term is the evaluation of the sparseness of the expansion coefficients ��. The function of log�� , ��, or |�| can be used as ��. In this study, log�� is used. 3.1.3. Learning Algorithm of Sparse Modeling

Eq. (4) is minimized with respect to �� and �� . The updating rule of �� is then given as follows [5], [6]:

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S. FURUKAWA, et al.: Coronary Plaque Characterization Considering Continuity of Tissue by Sparse Modeling of 2D IVUS Signal


4

��

�

�� , (5)

with

��

��, (6)

��

��, (7)

where �� are updated values of �� , and �� is the first derivative of ��. The updating rule of �� is given as follows:

��

�� , (8)

where � is a learning rate. �� are updated according to Eq. (5) every time when each input signal is applied, and �� are updated after 250 input signals are applied. In this paper, we use the code patterns �� as the feature vectors of the RF sig-nal for the tissue characterization. 3.1.4. Classification

The proposed method classifies the tissues by using the sparse code patterns ��. The basis functions for the

sparse modeling are first constructed by the learning sig-nals which contain both fibrous and lipid tissues. The learning local RF signals are then represented by the above basis functions to get the sparse code patterns ��. The target local RF signal, reflected from the un-known tissue, is represented by the basis functions con-structed by the learning RF signals, and then the sparse code patterns �� for the unknown tissue to be classified are obtained. Finally the unknown tissue is classified by the k-NN algorithm using the code patterns ��. Fig. 2 shows the average of the absolute values of the sparse code patterns for fibrous and lipid tissues. It is confirmed that the ignited bases for each tissue are differ-ent. Using these different code patterns the tissue charac-terization is performed. 3.2. k-Nearest Neighbor Method In the proposed method, the k-Nearest Neighbor (k -NN) algorithm is used [12]. The k-NN makes a statistical classification based on the training prototype neighbor-hood vectors in a feature space (Fig.3). The algorithm is briefly described in the following. Suppose that the feature vectors �� ,�,� ,�� are given, and let the class label �� of each feature vector be known. The feature vectors are used as the training pro-totype vectors. When the input vector �, whose class label is un-known, is given to k-NN, the class label of the input vector is determined by:

(a) (b)Fig. 2. Average of the absolute values of the sparse code patterns. (a) Fibrous tissue. (b) Lipid tissue.


4

3.1.3. Learning Algorithm of Sparse Modeling

Eq. (4) is minimized with respect to �� and ��. The updating rule of �� is then given as follows [5], [6]:

��

�

�� , (5)

with

��

��, (6)

��

��, (7)

where �� are updated values of �� , and �� is the first derivative of ��. The updating rule of �� is given as follows:

��

�� , (8)

where � is a learning rate. �� are updated according to Eq. (5) every time when each input signal is applied, and �� are updat-

ed after 250 input signals are applied. In this paper, we use the code patterns �� as the feature vectors of the RF signal for the tissue characterization. 3.1.4. Classification

The proposed method classifies the tissues by using the sparse code patterns ��. The basis functions for the sparse modeling are first constructed by the learning signals which contain both fibrous and lipid tissues. The learning local RF signals are then repre-sented by the above basis functions to get the sparse code patterns ��. The target local RF signal, reflected from the unknown tissue, is represented by the basis functions constructed by the learning RF signals, and then the sparse code patterns �� for the unknown tissue to be classified are obtained. Finally the unknown tissue is classified by the k-NN algorithm using the code pat-terns ��. Fig. 2 shows the average of the absolute values of the sparse code patterns for fibrous and lipid tissues. It is confirmed that the ignited bases for each tissue are different. Using these different code patterns the tissue characterization is performed. 3.2. k-Nearest Neighbor Method In the proposed method, the k-Nearest Neighbor (k -NN) algorithm is used [12]. The k-NN makes a statistical classification based on the training prototype neighborhood vectors in a feature space (Fig.3). The

(a) (b)Fig. 2. Average of the absolute values of the sparse code patterns. (a) Fibrous tissue. (b) Lipid tissue.

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5

� � �r��

∑ �� ,�� (9)

�� 1 if‖�� ‖ � ��,0 otherwise, (10)

where �� represents the Euclidean distance between the input vector � and the k-th nearest prototype vector. In determining the class label for the input vector, the prototype vectors within the k-th nearest neighbor are selected according to the distance of Eq. (10). After that, the class label of the input vector is determined by a ma-jority vote for the class labels of the k nearest neighbor prototype vectors by Eq. (9).

4. Experiments 4.1. Experimental Methods In the experiments, the typical three cross-sections observed in the coronary artery of one patient are classi-fied. In the classification, the tissues of coronary plaque are classified into two types of fibrous and lipid tissues. The classification performance of the proposed method is compared to that of the frequency analysis based conven-tional method. In the proposed method and also in the frequency analysis based method, the local RF signals are considered

in two dimensions of depth and radial direction. The win-dow size of the area is 32 points in depth and 4 lines in radial direction. This is to grasp the tissue in 2-dimension and thus to reflect the continuity of tissue in classification.

In the sparse modeling, the parameters � and � are set to 0.75 and 256, respectively. The number of itera-tions for learning is 1,000. And in the k-NN, the number of neighbors k is set to 9.

In the frequency analysis based method, the normal-ized power spectrums of the local RF signals obtained by 2-dimensional Fourier transform are used as the feature vectors. These feature vectors are classified by k-NN in the same way as the proposed method.

The classification rate (CR) is given by:

�� , (11)

� � ��erof�i�e�s��e��s��, (12)� � ��erof�i�e�s��e��s��, (13)

where TP (True Positive) means correct identification, and FN (False Negative) means incorrect rejection. Each pixel of B-mode image is judged whether it is correctly identi-fied (TP) or incorrectly rejected (FN).

The correct tissue labels are assigned pixel by pixel pathologically in advance according to the medical doc-tor’s findings, which were found out by observing with a microscope the dyed tissues of the plaque in the corre-sponding B-mode image. This is accomplished by an ex-pert medical doctor. 4.2. Experimental Results Table 1 shows the classification rates by each method. It is observed that the proposed method has good performance in both cases for fibrous and lipid tissues.

In the cross-sectional image 3, the classification rates of the lipid tissue by each method are lower than the

Fig. 3. Overview of the k-NN method.

Table 1. Classification rates.

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other two cross-sectional images. The reason is under in-vestigation, but it is probably that this lipid tissue itself was a special one hard to classify. The proposed method however gives a better classification result, a slight im-provement though, than the frequency analysis based con-ventional method. Fig. 4 shows the classification results for the fibrous and lipid tissues by each method. The yellow and green areas correspond to the fibrous and lipid tissues, respec-tively. Using the same classifier, the proposed method gives better results than the frequency analysis based con-ventional method. This shows that the feature vectors ob-tained by the sparse modeling are more effective than those obtained by the frequency analysis based method.

5. Conclusions This paper proposed a novel method for the tissue characterization of coronary plaque using sparse feature vectors considering the continuity of the tissue. In the pro-posed method, the RF signal was expanded by the learned basis functions, and the code patterns of the expansion co-efficients of the basis functions were used as the feature vectors for classification. The effectiveness of the proposed method was ver-ified by comparing it to the frequency analysis based con-ventional method. Experimental results show that the fea-ture vectors obtained sparse modeling are more effective for the tissue characterization of coronary plaque than

Fig. 4. Coronary plaque tissue classification results. (a) - (c) Medical doctor's findings for cross-sec-tional images 1, 2 and 3, respectively. The yellow and green areas correspond to the fibrous and lipid tissues, respectively. (d) - (f) Tissue classification results by the frequency analysis based conventionalmethod for cross-sectional images 1, 2 and 3. (g) - (i) Tissue classification results by the proposed method for cross-sectional images 1, 2 and 3.

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those obtained by the frequency analysis based conven-tional method. Future work is to further improve the classification rate by developing the classifier specialized for the sparse features.

Acknowledgements This work was supported by JSPS KAKENHI, Grant Numbers 23300086 and 15J06889.

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Kunishima, A., Arai, M., Nishigaki, K., Takemura, G., Morita, N., Minatoguchi, S., Fujiwara, H.: “Noninvasive Quantitative Tissue Characterization and Two-Dimensional Color-Coded Map of Human Atherosclerotic Lesions Using Ultrasound Integrated Backscatter: Comparison between Histology and In-tegrated Backscatter Images,” J. of the American Col-lege of Cardiology, Vol.38, No.2, pp.486–492, 2001.

[3] Kawasaki, M., Takatsu, H., Noda, T., Sano, K., Ito, Y., Hayakawa, K., Tsuchiya, K., Arai, M., Nishigaki, K., Takemura, G., Minatoguchi, S., Fujiwara, T., Fu-jiwara, H.: “In Vivo Quantitative Tissue Characteri-zation of Human Coronary Arterial Plaques by Use of Integrated Backscatter Intravascular Ultrasound and Comparison with Angioscopic Findings,” Circulation, Vol.105, No.21, pp.2487–2492, 2002.

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[5] Olshausen, A. B., Field, J. D.: “Emergence of Simple-Cell Receptive Field Properties by Learning a Sparse Code for Natural Images,” Nature, Vol.381, pp.607–609, 1996.

[6] Olshausen, A. B., Field, J. D.: “Sparse Coding with an Overcomplete Basis Set: A Strategy Employed by V1?,” Vision Research, Vol.37, No.23, pp.3311–3325, 1997.

[7] Potkin, N. B., Bartorelli, L. A., Gessert, M. J., Neville, F. R., Almagor, Y., Roberts, C. W., Leon, B. M.: “Coronary Artery Imaging with Intravascular High-Frequency Ultrasound,” Circulation, Vol.81, No.5, pp.1575–1585, 1990.

[8] Linker, T. D., Kleven, A., Grønningsæther, Å., Yock, G. P., Angelsen, J. A. Bj.: “Tissue Characterization with Intra-arterial Ultrasound: Special Promise and Problems,” Int. J. of Cardiac Imaging, Vol.16, pp.255–263, 1991.

[9] Moore, P. M., Spencer, T., Salter, M. D., Kearney, P. P., Shaw, D. R. T., Starkey, R. I., Fitzgerald, J. P., Er-bel, R., Lange, A., McDicken, W. N., Sutherland, R. G., Fox, A. A. K.: “Characterisation of Coronary Ath-erosclerotic Morphology by Spectral Analysis of Ra-diofrequency Signal: in vitro Intravascular Ultra-sound Study with Histological and Radiological Val-idation,” Heart, Vol.79, pp.459–467, 1998.

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[11] Hyvärinen, A., Hoyer, O. P.: “Emergence of Phase and Shift-Invariant Features by Decomposition of Natural Images into Independent Feature Subspaces,” Neural Computation, Vol.12, No.7, pp.1705–1720, 2000.

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Shota FURUKAWA

He is a Ph.D. candidate at the Grad. School

of Science and Engineering of Yamaguchi

Univ., Japan. His research interests include

digital signal processing, image processing

and intelligent systems. He is a Member of

the Institute of Electronics, Information and

Communication Engineers (IEICE).

Eiji UCHINO, for a photograph and biography, see p.59 of the May

2014 issue of this Journal.

Tadahiro AZETSU

He is presently an Assoc. Prof. of the Office

for Information and Technology, Yamagu-

chi Prefectural Univ., Japan. His research

interests include speech signal processing

and image processing. He is a Member of

the Institute of Electronics, Information and

Communication Engineers (IEICE).

Noriaki SUETAKE, for a photograph and biography, see p.59 of the

May 2014 issue of this Journal.

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