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Ultrasonics 48 (2008) 35–39

Fractal dimension of 40 MHz intravascular ultrasound radiofrequency signals

E. Santos Filho a,*, Y. Saijo a, A. Tanaka b, T. Yambe a, M. Yoshizawa c

a Department of Medical Engineering and Cardiology, Institute of Development, Aging, and Cancer,

Tohoku University, 4-1 Seiryomachi, Aoba-ku, Sendai 980-8575, Japanb Faculty of Symbiotic Systems Science, Fukushima University, Japan

c Information Synergy Center, Tohoku University, Japan

Received 18 April 2007; received in revised form 24 August 2007; accepted 24 August 2007Available online 7 November 2007

Abstract

Objective: Fully automatic tissue characterization in intravascular ultrasound systems is still a challenge for the researchers. The pres-ent work aims to evaluate the feasibility of using the Higuchi fractal dimension of intravascular ultrasound radio frequency signals as afeature for tissue characterization.

Methods: Fractal dimension images are generated based on the radio frequency signals obtained using mechanically rotating 40 MHzintravascular ultrasound catheter (Atlantis SR Plus, Boston Scientific, USA) and compared with the corresponding correlation images.

Conclusion: An inverse relation between the fractal dimension images and the correlation images was revealed indicating that the hardor slow moving tissues in the correlation image usually have low fractal dimension and vice-versa. Thus, the present study suggests thatfractal dimension images may be used as a feature for intravascular ultrasound tissue characterization and present better resolution thenthe correlation images.� 2007 Elsevier B.V. All rights reserved.

PACS: 87.62; 87.59.M; 47.53.+n

Keywords: Intravascular ultrasound; Tissue characterization; Fractal dimension; Radio frequency signal; Coronary artery

1. Introduction

Intravascular ultrasound (IVUS) has been clinicallyapplied since early 1990s. The tomographic orientation ofultrasound enables visualization of the entire circumferenceof the vessel wall and provide information about tissuesbeneath the luminal border. However, visual analysis ofIVUS images by experts is usually accompanied by limita-tions associated with interpersonal variations, errors due tofatigue, environmental distractions, etc. Computer-aidedtissue characterization of IVUS images has a potential toadd objective strength to the interpretation of the expert

0041-624X/$ - see front matter � 2007 Elsevier B.V. All rights reserved.

doi:10.1016/j.ultras.2007.08.006

* Corresponding author. Tel.: +81 22 717 8517; fax: +81 22 717 8518.E-mail address: esmeraldo@ieee.org (E.S. Filho).

becoming an important tool for coronary diseases diagno-sis. Analysis of IVUS radio frequency (RF) signal haspotential to provide powerful features for tissue character-ization because it is the original source of information fromthe backscattered ultrasound beam.

Nair et al. [1] successfully used spectral analysis of back-scattered IVUS RF signals to classify plaque compositionby constructing classification trees. However, for test data,in spite of presenting accuracy of 100% for calcified-necro-sis, the accuracies for fibrolipid and collagen were 83% and69%, respectively, showing that improvements and new sig-nal processing techniques are still necessary for a full tissuecharacterization in IVUS imaging.

Signal processing based on estimating fractal dimensionin a time series has been successfully applied in a number of

36 E.S. Filho et al. / Ultrasonics 48 (2008) 35–39

medical applications due to its capability of expressing sig-nal irregularity [1–5].

Alacam et al. [6] showed that the features obtained bystatistical modeling of RF echo can be used as decision cri-terion for tissue characterization in breast cancer diagnosis.They proposed the fractional differencing auto regressivemoving average (FARMA) model which captures the frac-tal and long term correlated nature of the backscatteredspeckle texture. Using a linear classifier their method pre-sented an area of 0.87 under the receiver operating charac-teristic (ROC) curve.

Moradi et al. [7] have presented an innovative approachfor detection of prostate cancer based on the fractal analy-sis of RF ultrasound echo signals. They used Higuchi’s [8]method to calculate the fractal dimension over a region ofinterest (ROI) and used it as feature to detect the prostatecancer through a Bayesian classifier [9]. Their algorithmpresented accuracy of 86% indicating the feasibility of theirapproach.

Saijo et al. [10,11], have developed a method for tissuecharacterization based on two-dimensional correlationbetween two consecutive frames of an IVUS sequence. Thistechnique was shown capable of distinguishing regions offast moving fluid like blood or surrounding tissue fromregion of slow moving or stable like the vessel wall.

In this work, we investigate the feasibility of using theHiguchi’s fractal dimension as a feature for tissue charac-terization in IVUS through comparison with correlationimages.

2. Materials and methods

IVUS data were acquired with an IVUS console ClearView Ultra (Boston Scientific Inc., Natick-MA, USA)and 40 MHz mechanically rotating IVUS catheter Atlan-tis SR Plus (Boston Scientific Inc., Natick-MA, USA)and the pulse repetition rate was 7680 Hz. RF data weredigitized and stored in a personal computer (PC) (Dell8250, Pentium 4, 2.4 GHz, 1.50 GB RAM, Dell Inc.,Round Rock, TX, USA) using an A/D board GAGECompuscope 8500 (500 Msamples/s, with 8 bits of resolu-tion, Gage Applied Inc., Montreal, Quebec, Canada) foroff-line analysis. The algorithms were developed usingMATLAB (The Mathworks Inc., Natick, MA, USA).A single frame of the IVUS system consisted of 256 linesso that 7680 pulses made 30 frames per second (f/s). RFsignal data were acquired in vivo from 14 human leftanterior descending (LAD) coronary arteries during per-cutaneous transluminal coronary angioplasty (PTCA).The patients average age was 72 ± 12 years and six ofthem presented detected calcification regions and onedetected soft plaque in their IVUS images. This processwas approved by a local investigation review boardand was performed in accordance with the ethicalprinciples for medical research involving human subjects.We obtained written informed consent from all thesubjects.

2.1. Fractal dimension image

The concept of fractal dimension is based on the prop-erty of self-similarity. In spite of not being self-similar overall the scales, the IVUS RF signals usually present somelevel of self-similarity within some range and thus the Hig-uchi fractal dimension can be used as an efficient method toexpress the irregularity of the RF signals in the ROIs ofappropriate size.

Higuchi’s algorithm [8] is proven to be a stable methodto estimate the fractal dimension of a time series and, moreimportantly, works well for time series with few samples.The algorithm, computes mean length of the signal at dif-ferent scales, plots a log–log graph of length versus scaleand measures the slope of the linear fit of this graph asthe fractal dimension.

Thus, for generation of the fractal dimension images thefollowing algorithm was used.

Algorithm. For each ROI defined by the position of a 100points wide sliding window, the following steps were used:

1. Extract the signal envelop through the calculation of theabsolute value of the Hilbert transform.

2. Normalize the envelop by dividing it by its maximumvalue in that sample.

3. Calculate the fractal dimension of the normalized signalusing the Higuchi method.

4. The sliding window is shifted of 25 points and the abovesteps are repeated for all RF lines that comprise theIVUS image.

2.2. Correlation image

Conventional B-mode IVUS images were generatedfrom RF signals by software developed by our group[10]. Then the IVUS image was divided into 64 · 64 squareshape ROIs. Template matching method was applied forcalculation of correlation and displacement of the ROIsbetween the consecutive two frames. Template matchingis the process of determining the presence and the locationof a reference image or an object inside a scene image underanalysis by a spatial cross-correlation process. Fig. 1 showsthe schematic illustration of template matching method. Ifthe coordinates of the center of the ROI in the first frame(a) are defined as p(0, 0) and the most similar patternedROI in the next frame (b) is q(k, l), the correlation is givenby:

Rfgðk; lÞ ¼Pn2�1

i¼0 fi � �f i

� �gi � �gið ÞffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiPn2�1

i¼0 fi � �f i

� �2Pn2�1i¼0 gi � �gið Þ2

q ð1Þ

where fi and gi are pixels inside the ROI in consecutiveframes, �f i and �gi are the corresponding mean gray level val-ues of each ROI, and n is the length of the side of thesquare shaped ROI.

Fig. 1. Schematic illustration of template matching method. The coordi-nates of the center of the ROI in the first frame (A) is defined as p(0, 0) andthe most similar ROI in the next frame (B) is q(k, l).

E.S. Filho et al. / Ultrasonics 48 (2008) 35–39 37

Based on our tests, we could observe that the movingregions such as blood and surrounding tissues presentedcorrelation values below 0.5 and the regions of vessel wallpresented correlation values above 0.75. The vessel wallwas assumed stable during 1/30 s.

3. Results

In Fig. 2, we can see an example of two samples of IVUSRF signal extracted from the region of blood and theregion of vessel wall. It can be seen that the sampleextracted from the blood region presents a more irregular

Fig. 2. Example of RF signal ROIs extracted from lumen region (A) and vesposition from where the ROIs were extracted. They are 100 samples length ROrespective envelop (in blue). (C) and (F) are graphs of the normalized envelop

shape than the sample from the region of vessel. As thefractal dimension can be regarded as a measure of irregu-larity, we used the fractal dimension as a feature for tissuecharacterization.

In Fig. 3C and F, we can see two examples of fractaldimension images. They are images whose pixel colors rep-resent the fractal dimension of a 100 points wide slidingwindow centered at the corresponding position in the RFline. In spite of being quite noisy, we can observe thatthe regions of lumen present fractal dimension valueshigher (light blue and green) than the vessel wall region(dark blue). More homogeneous regions, like calcificationregions for example, present a lower fractal dimensionvalue (dark blue).

Also, in Fig. 3B and E, we can compare the fractalimages with the correlation images, which are imageswhose pixel value represents the correlation index calcu-lated through Eq. (1). The correlation image shows its low-est level in the regions of blood (light blue), which is themost dynamic region. This fact is also detected throughthe fractal dimension image.

In Fig. 3A, we can observe clearly the boundary lumen/vessel that is confirmed in Fig. 3B, where the lumen regionpresents correlation values usually below 0.5, representedby light green or light blue, due to the fast moving blood.The red region is the static or slow moving vessel wall. Inthe fractal dimension image (Fig. 3C) we can observe that

sel wall region (D). The small regions in red in (A) and (D) indicate theIs. (B) and (E) are the graphs of the RF signals ROIs (in green) and theirs.

Fig. 3. Comparison between correlation image and fractal dimension image. (A) and (D) are the original images. (B) and (E) are examples of correlationimages. (C) and (F) are example of fractal dimension images.

38 E.S. Filho et al. / Ultrasonics 48 (2008) 35–39

the lumen region is light blue whereas the vessel wall regionis dark blue. This means that the fractal dimension in thelumen region, usually between 1.25 and 1.5, is higher thanthe fractal dimension in the vessel wall region that is usu-ally below 1.20. This suggests that the irregularity level ofthe RF signal expressed by Higuchi fractal dimension canbe used, to some extent, to characterize the moving tissues.The region outside the vessel in Fig. 3C is quite yellow andred, with fractal dimension values around 1.7, mainlybecause this is a region of high noise level. The correspond-ing area in Fig. 3B present low correlation level indicatingfast moving connecting tissues. Additionally, we canobserve in Fig. 3E and F that the region of calcium is alsoa region of high correlation value and low fractal dimen-sion. It can also be observed that the fractal dimensionimages present better resolution than the correlationimages.

4. Discussion

The examples in Fig. 2 showed that, besides the differ-ences in amplitude, the irregularity of the envelop is fairlydifferent in these both regions suggesting that a measure ofsignal irregularity could be a useful discriminator forregions of vessel wall and lumen. Saijo et al. [10] haveobserved similar results through the two-dimensional cor-relation analysis. Their results were validated by compari-sons with histology data.

Accordingly to our tests, RF signal samples shorterthen 60 points did not provide acceptable results becausethe images generated using a window of this width did

not present clear contrast between the lumen and thevessel wall. The highest contrast is achieved for slidingwindow with width of around 100 points. Sliding win-dows wider than 100 points did not present visibleimprovements.

As reported in [8], the Higuchi method presented morestable results when compared with other methods basedon power spectrum. In tests performed with IVUS RF sig-nals the power spectrum based fractal dimension did notprovide satisfactory results, probably, due to the largeamount of noise, suggesting the robustness of Higuchimethod.

Using the PC described in Section 2, the average pro-cessing time needed to generate the fractal dimensionimages was 128 s. This suggests that the proposed algo-rithm may be used in real time if more powerful hardwareis used and the program is optimized.

The fractal dimension images presented an average con-trast-to-noise ratio (CNR) of 3.73 whereas the correlationimage presented 3.05. However, together with lowerCNR, the correlation images present lower resolution.Thus the fractal images with a CNR of 3.05 seen to presenta satisfactory trade-off between noise and resolutionbecause the resultant fractal dimension images presentedless distortion of the lumen contour than the correlationimages as can be seen in Fig. 3.

Comparing images from different patients, for exam-ple, patients with calcification and patients without calci-fication, we could observe that the fractal dimensionvalues in the calcification regions is similar to levels pre-sented in the vessel wall region, as shown in Fig. 3. This

E.S. Filho et al. / Ultrasonics 48 (2008) 35–39 39

suggests that the fractal dimension images may not beuseful in calcification detection. In tests with image con-taining soft plaque, the resulting fractal dimension imagedid not present clear contrast between the soft plaque andblood. Thus, this method does not seem likely to be agood discriminator for plaques. However, it may be use-ful as a pre-processing stage toward luminal contourdetection.

5. Conclusion

A comparison between correlation images and fractaldimension images was presented and we could observethat, in general, the regions of high correlation valuesin the correlation image correspond to the regions oflow fractal dimension in the corresponding fractal dimen-sion image and vice-versa. This fact suggests that thefractal dimension, as measure of irregularity of the RFecho signal, can be also an indicator of the moving char-acteristic of the interrogated tissue as well as the correla-tion image. However, the fractal dimension image has theadvantage of presenting more clearly the fine details ofthe luminal contour when compared to the correlationimages.

Acknowledgement

This study was supported by the Grants-in-Aid from theMinistry of Health, Labor and Welfare of Japan (H17-nano-001).

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