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Tissue Characterization Using Fractal Dimension

of High Frequency Ultrasound RF Time Series

Mehdi Moradi1, Parvin Mousavi1, and Purang Abolmaesumi1,2

1School of Computing, Queen’s University, Kingston, Canada

2Department of Electrical and Computer Engineering, Queen’s University

{moradi,pmousavi,purang}@cs.queensu.ca

Abstract. This paper is the first report on the analysis of ultrasound

RF echo time series acquired using high frequency ultrasound. We show

that variations in the intensity of one sample of RF echo over time is

correlated with tissue microstructure. To form the RF time series, a

high frequency probe and a tissue sample were fixed in position and

RF signals backscattered from the tissue were continuously recorded.

The fractal dimension of RF time series was used as a feature for tissue

classification. Feature values acquired from different areas of one tissue

type were statistically similar. For animal tissues with different cellular

microstructure, we successfully used the fractal dimension of RF time

series to distinguish segments as small as 20 microns with accuracies as

high as 98%. The results of this study demonstrate that the analysis of

RF time series is a promising approach for distinguishing tissue types

with different cellular microstructure.

1Introduction

Ultrasound-based tissue characterization techniques rely on different scatter-

ing patterns of ultrasound in tissues with dissimilar cellular microstructures.

Although the exact physical mechanisms that govern these patterns are not

well understood [1], microstructure-induced differences in ultrasound-tissue in-

teraction are documented both at clinical (2-10 MHz) frequencies [2] and at

higher frequencies [1,3]. In other words, ultrasound Radio-Frequency (RF) echoes

contain information about tissue characteristics. However, it is challenging to dis-

entangle this information from the variations in the signal caused by the system-

dependent effects, such as mechanical and electrical properties of the transducer

and diffraction effects due to the finite aperture of the transducer. This funda-

mental restriction of ultrasound-based tissue characterization techniques limit

their sensitivity and specificity in diagnosis of cancer lesions [4,5].

In a new approach to analysis of RF echoes for tissue characterization, we have

recently proposed that if a specific location in tissue undergoes continuous inter-

actions with ultrasound, the time series of the RF echo signals (see Figure 1) from

that location carries “tissue characterizing” information [6,7]. In other words, al-

though variations in the intensity of one sample of RF echo over time are partly

due to the electronic noise of the ultrasound machine or the errors caused during

N. Ayache, S. Ourselin, A. Maeder (Eds.): MICCAI 2007, Part II, LNCS 4792, pp. 900–908, 2007.

c ? Springer-Verlag Berlin Heidelberg 2007

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Tissue Characterization Using Fractal Dimension901

Fig.1. RF time series: Sequential echoes received from one location of tissue

the beam-forming process [8], they depend on the tissue type as well. Specifically,

the fractal dimension (FD) of the RF time series was successfully used to detect

cancerous lesions in prostate tissue [7], as well as to distinguish different animal

tissues [6].

These tissue characteristic variations might be due to the vibrations in the

microstructural level induced by the continuous emission of ultrasound beams.

However, more studies on the origin of this phenomenon are necessary. Specifi-

cally, in the current paper we report the results of our new research that addresses

three fundamental questions about the RF time series: 1) Are the results of tissue

classification based on the RF time series, correlated with the microstructure of

the tissue? In other words, is this approach more successful in separating tissue

types with significantly different microstructures? 2) What is the effect of utiliz-

ing high frequency ultrasound on the outcome of the method? It is a well-known

fact that at very high frequencies the scattering of ultrasound is primarily caused

by the cellular microstructure [1] as opposed to tissue macrostructure. Therefore,

the dependence of the FD of RF time series on cellular microstructure should be

more evident in high frequency data. 3) Are the tissue characterizing properties

of RF time series emphasized in A-mode? Some of the system related alter-

ations in the RF time series acquired in B-mode, including the beam-forming,

are absent in A-mode imaging.

To answer these questions, we analyzed RF echo time series acquired using

high frequency ultrasound A-mode probes. Based on microscopic studies, we

showed that at these frequencies, the separability of tissues based on FD of RF

time series is closely related to differences in tissue microstructures. We used FD

of the RF times series to successfully distinguish segments as small as 20 microns

of animal tissues of dissimilar microstructures with accuracies as high as 98%.

Furthermore, the FD values calculated from the RF time series of different tissues

showed statistically significant differences, far beyond the variations in FD values

in one tissue type. These experiments suggest the presence of microstructure-

related information in the RF time series. Some of the pathologic conditions,

including cancer, are characterized by a dramatic change in the microstructure

of the affected tissue. Therefore, the proposed tissue characterization approach

could lead to an effective method for diagnosis of certain types of cancer [7].

The rest of this paper is organized as follows: Section 2 introduces the data

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902M. Moradi, P. Mousavi, and P. Abolmaesumi

collection method, feature extraction and classification approaches, Section 3

presents our results and discussions, and Section 4 provides a summary and the

conclusions.

2Methods

To study the tissue characterizing capabilities of RF echo time series acquired

at higher frequencies, we used four different tissue types: bovine liver, pig liver,

bovine muscle, and chicken breast. As illustrated in Figure 2, the cellular struc-

ture of both bovine and pig liver are characterized by hepatocyte cells (of slightly

different shape and density), whereas bovine muscle and chicken breast both have

fibrous structures formed by sarcomeres.

The high frequency ultrasound RF time series in this study were collected

using a Vevo 770 high resolution ultrasound system (VisualSonics Inc., Toronto,

Canada) with RMV706 and RMV711 scanheads (see Table 1 for the specifica-

tions). The depth of scanning was about 1mm which corresponded to 512 signal

samples. While the tissue and the probe were fixed in place, we continually ac-

quired 500 ultrasound A-lines (frame rate: 60 fps) from one spot of the tissue.

In other words, we formed a time series of length 500 from each sample of the

ultrasound A-line. With each probe type, we acquired two separate lines of RF

time series from two different areas of each tissue type.

Table 1. Specifications of the high frequency ultrasound scanheads

Model

RMV711

RMV706

Broadband frequency Center frequency Axial resolution

Up to 82.5 MHz55 MHz

Up to 60 MHz 40 MHz

30 μ

40 μ

2.1 Feature Extraction

In this study, tissue types were characterized by the average of FDs computed

for all the RF time series in a Region of Interest (ROI). Our high frequency data

was acquired in A-mode. Therefore, ROIs were simply segments of RF lines (each

signal sample covered a depth of almost 2 microns).

FD of time series originating from natural processes has been extensively

studied as a parameter that quantifies nonlinear internal dynamics of complex

systems [9,10]. In such systems, the mechanisms of interaction that give rise to

the output time series are not well understood. FD has been shown to have

low sensitivity to the noise-induced variations [11]. In RF time series analysis,

the microstructural information is received along with noise-related variations.

Therefore, we chose FD to characterize the RF time series. We used Higuchi’s al-

gorithm [12] for computation of the FD of time series which can be summarized as

follows: Each sample of the RF data forms a time series {X(1),X(2),...,X(N)}

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Tissue Characterization Using Fractal Dimension903

(a) Bovine liver(b) Pig liver

(c) Chicken breast(d) Bovine muscle

Fig.2. Images of the cellular structure of tissue types used in this study at 200X mag-

nification (acquired from H&E stained slides with a Zeiss AxioImager M1 microscope)

over sequential ultrasound frames, where N = 500 for our high frequency RF

data. From this time series, we first construct k new time series of form:

Xm

k: {X(m),X(m + k),X(m + 2k)...,X(m + [N − m

k

].k)}

(1)

where k is the sampling time interval (which determines the scale, k < N) and

m = 1,2,...,k − 1. Both m and k are integers. The length of each time series,

Lm(k), is defined as:

N − 1

[N−m

k

i=1

Lm(k) = 1/k × (

].k) ×

[N−m

k

?

]

|X(m + ik) − X(m + (i − 1).k)|

(2)

The average value of Lm(k) over k sets, L(k), is the so-called length of the time

series at scale k. This procedure is repeated for each k ranging from 1 to kmax.

A line is fitted to values of ln(L(k)) versus ln(1/k) and the slope of this line is

considered as the FD. The number of the samples, N, and the nature of the time

series determine the optimal value of the parameter kmax. For the current study,

the value of kmax was optimized based on the average classification accuracy

acquired. We examined kmax values between 4 and 56. Feature extraction for

each A-line involved computation of FD of 512 time series of length 500. We call

the output of this process an FD vector.

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904M. Moradi, P. Mousavi, and P. Abolmaesumi

2.2Classification

All classification results reported in the current paper were acquired with a

Bayesian approach. If ω1 and ω2 represent ROIs from two categories of tissue

involved in one of our classification experiments, and x represents the feature

value of a given ROI (which its category is unknown), Bayes’ rule states that

the classification can be performed based on the following inequalities:

P(x|ω1)P(ω1) ≷ P(x|ω2)P(ω2)(3)

P(ω1) and P(ω2) are a priori probabilities (which can be simply calculated as

the ratio of the number of ROIs in each category to the total number of ROIs in

the two categories). P(x|ω1) and P(x|ω2) are the probability density functions

(pdf) of feature values in categories 1 and 2 respectively. We fit a Gaussian pdf

to the distribution of the feature in each category.

We followed a leave-10%-out approach to validate the classification procedure.

In other words, we randomly partitioned the data in each category to 10 folds.

We evaluated the pdfs on 90% of the data samples, classified the remaining 10%

based on the evaluated pdfs, and repeated the procedure for all 10 portions of

the data. We repeated the whole leave-10%-out process 200 times (each time

with a random partitioning of the ROIs to 10 folds). The mean accuracies and

standard deviations reported in our results were recorded over these 200 trials.

3Results and Discussions

FD vectors from the same tissue types: The first step in our analysis was

to perform one-way ANalysis Of VAriance (ANOVA) tests on pairs of FD vec-

tors from the same tissue types. ANOVA is a statistical test in which the null

hypothesis is the equality of means in samples from two different populations.

As Table 2 illustrates, when two FD vectors from the same tissue type were

compared, the p-values in ANOVA tests were relatively large, also the sam-

ples from two lines could not be distinguished (classification accuracies close

to 50%). The ROI size used for classification was 20 microns (10 samples)

and Kmax= 16.

Table 2. Comparison of two FD vectors from two RF lines of one tissue type

Tissue typeANOVA p-value accuracy in separating ROIs from the two lines

RMV711results on RMV711 - mean (STD)

0.47

0.007

0.0001

0.68

Bovine liver

Pig liver

chicken breast

Bovine muscle

52% (3.7)

47% (3.9)

59% (3.1)

53% (4.3)

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Tissue Characterization Using Fractal Dimension905

Table 3. Comparison and classification of data from different tissue types

ANOVA

p-value

(RMV711) (RMV711)

0

0

0

0

0

mean (STD) mean (STD) mean(STD)

Res: 2μ

Res: 20μ

(RMV711)

81.1% (2.5) 92.2% (5.8) 96.9% (3.5)

84.1% (2.3) 95.5% (4.0) 93.7% (5.3)

84.6% (2.3) 96.0% (4.2) 92.3% (5.3)

89.2% (2.1) 98.2% (3.1) 90.0% (6.4)

73.7% (3.0) 83.7% (7.1) 65.1% (7.9)

Tissue types

Res: 20μ

(RMV706)

Bovine liver - chicken breast

Bovine liver - bovine muscle

Chicken breast - pig liver

Pig liver - bovine muscle

Bovine liver - pig liver

Chicken breast - bovine muscle 5.7 × 10−1364.1% (3.1) 72.2% (8.9) 63.1% (8.1)

Average79.5%

89.6%

83.2%

FD vectors from different tissue types (Kmax= 16): We performed the

ANOVA tests on FD vectors of different tissue types (Table 3). The p-values

were all virtually zero and showed that the vectors were statistically different

in all six pairs. Two separate FD vectors from each tissue type, computed from

the data acquired on RMV711 scanhead, were available. We combined the two

vectors of each tissue type to acquire a single vector of length 1000 and used

the Bayesian approach described in the previous section to perform pairwise

classifications. The results for these classification trials which were in single RF

sample resolution, are reported in column 3 of Table 3. It is interesting to note

that even at this resolution, we were successful in classification when the two

involved tissue types were from different microstructural categories (rows 1-4);

however, when pig liver was compared with bovine liver (row 5) or the two

fibrous tissue types were compared (row 6), the classification at this extremely

high resolution produced low accuracies.

Furthermore, we examined the performance of our approach at a lower reso-

lution. We averaged 10 samples of each FD vector to acquire vectors of length

50 (100 after combining the two lines from RMV711). Each element of these

vectors represented an ROI of size 20 microns. The results of pairwise classifica-

tion experiments at this level of resolution are presented in column 4, Table 3.

In general, the classification accuracy is significantly higher in this lower resolu-

tion (overall accuracy of 89.6% on RMV711). The mean accuracy for tissues in

different microstructural categories was around 95% (rows 1-4) and for tissues

with similar microstructures was around 80% (rows 5-6).

For validation purposes, the classification process (at 20 micron resolution)

was repeated on a similar dataset that was acquired on scanhead RMV706 (which

operates at a lower frequency and axial resolution). The results are reported in

column 5, Table 3. In general, the overall outcome declined in comparison with

RMV711 data (average over all: 83.2%). However, the same pattern of perfor-

mance (excellent on different microstructures, moderate on similar microstruc-

tures) was observed. The overall decrease in the classification results can be

explained by the lower axial resolution of RMV706.

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906M. Moradi, P. Mousavi, and P. Abolmaesumi

10203040 50

65

70

75

80

85

90

Kmax

(a)

average accuracy (%)

05 101520

78

80

82

84

86

88

90

average accuracy (%)

ROI size

(b)

Fig.3. (a) The average of classification accuracy over six pairs of tissue for different

values of Kmax (at resolution of 10 samples). (b) The average of classification accuracy

over six pairs of tissue for different number of samples in an ROI (Kmax = 16).

Optimal Kmax value: We examined different possible values for Kmax (or

maximum scaling level of the signal) in Higuchi’s algorithm. In Figure 3-a, the

average accuracy of tissue classification over six pairs of tissue types is plotted

against the values of Kmaxbetween 4 and 56. Values between 10 and 32 resulted

in very similar outcomes. The Higuchi algorithm becomes increasingly computa-

tionally expensive for large values of Kmax. We chose Kmax= 16 as a reasonably

small number that also resulted in maximum accuracy. This is also in agreement

with previous findings about the optimal Kmaxvalue on RF time series acquired

from human prostate specimens [7].

Optimal ROI size: As Figure 3-b illustrates, the classification accuracy in-

creased when ROIs of larger size were used. However, we were limited by the

size of the dataset. Increasing the size of the ROI to over 10 samples meant that

the Gaussian PDFs were estimated on less than 100 data points and tested on

less than 10 points in our leave-10%-out classification approach. It appears that

this low number of samples was not sufficient for training and testing of the

classifiers and therefore, we witnessed an unexpected and irregular decrease in

the accuracy of classification for ROIs of sizes larger than 10 samples.

Comparison with results at 6.6 MHz: As previously reported, even at fre-

quencies normally utilized on clinical machines (2-10MHz), the RF time series

contain tissue characterizinginformation [7,6]. However, the maximum resolution

is much lower. For comparison, we used a Sonix RP (Ultrasonix Inc., Vancouver,

Canada) ultrasound machine to collect RF time series at 6.6 MHz from the same

specimens that we had scanned at high frequencies. The temporal length of time

series (number of frames taken from each cross-section) was 255 and the data

was collected with a BPSL9-5/55/10 probe at the rate of 22 frames per second.

ROIs of size 8 × 44 RF samples (equivalent to 0.03cm2) of the tissue were used

in classification; 150 ROIs from each tissue type were available. Results reported

in Table 4 show an overall accuracy of around 76.5%.

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Tissue Characterization Using Fractal Dimension 907

Table 4. Results of applying the proposed tissue classification approach to the data

acquired on a clinical ultrasound machine (probe center frequency: 6.6 MHz)

Tissue types classification accuracy (STD)

82.9% (6.4)

80.7% (6.8)

71.4% (6.7)

74.8% (7.5)

69.3% (5.3)

79.6% (5.9)

76.5%

Bovine liver - chicken breast

Bovine liver - bovine muscle

Chicken breast - pig liver

Pig liver - bovine muscle

Bovine liver - pig liver

Chicken breast - bovine muscle

Average over all six tissue pairs

4Conclusions

In this paper we reported the exploitation of high-frequency RF time series for

tissue characterization. We used fractal dimension of RF echo time series ac-

quired on ultrasound probes operating at center frequencies of 55 MHz and 40

MHz to successfully characterize tissue types of different microstructure at the

resolution of only 20 microns. The correlation of variations in RF time series

with tissue microstructure was evident. FD vectors acquired from different areas

of one tissue type were very similar (Bayesian approach resulted in only around

50% successful separation of ROIs from two areas of one tissue type). For two

different tissue types which were from a similar category of microstructure (both

mammalian liver or both fibrous muscles), the ROIs could be separated with ac-

curacies around 80%. For tissue types from different microstructural categories,

the classification of ROIs based on the Gaussian approach was nearly perfect

(up to 98% accuracy). The same approach was also applied to data acquired

on a clinical ultrasound machine and an average accuracy of around 77% was

observed at the resolution of 0.03cm2.

These findings strongly suggest that the microstructure of the tissue has an

effect on the variations of the RF time series. This concept can potentially be

used in ultrasound-based detection of pathologic conditions such as cancer.

Acknowledgement. The authors would like to thank Mr. G. Leney from Vi-

sualSonics Inc. and Mr. R. Watering for their help in data collection. This work

was supported by Natural Sciences and Engineering Research Council of Canada

(NSERC), and Institute of Robotics and Intelligent Systems (IRIS).

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