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Session topic: Biomedical Ultrasonics Paper No.: MoPpm2-07

Date: 2005-07-13

Study on ultrasonic backscattering microstructural feature of human

kidney by cepstrum based on wavelets decompositions method

Sheng-ju Wu a,* , De-an Ta b

a Applied Acoustics Institute, Shaanxi Normal University, Xian,710062, P.R.China

b

Department of Electronic Engineering, Fudan University, Shanghai,200433, P.R.China

Abstract

This paper presenta novel signal processing methodology for ultrasonic scattered signals based on wavelets

decomposition using cepstrum method, which is WD cepstrum. Ultrasonic backscattering microstructural feature

and MSS of human kidney with normal and renal adenoma in vitro is analyzed by means of WD cepstrum, and

the results are compared with wavelets transform and AR cepstrum. The results of WD cepstrum showed that for

normal human kidney the MSS is 1.02 0.08mm, for renal adenoma the MSS is 1.66 0.10mm. It is found that

WD cepstrum method is better than that of MSS estimation with wavelets transform and AR cepstrum. The

results of normal and renal adenoma human kidney demonstrate that the two tissues MSS have a distinct

difference. Pathological change of tissue will results in variation of MSS. So the results of kidneys MSS

provides an effective information for clinical diagnose of pathological changes.

Keywords: Ultrasonic backscattering; Wavelets transform; WD cepstrum; Kidney tissue; Scatterer spacing.

1. Introduction

As the most common forms of benign, solid kidney tumor and renal adenomas are typically small and low-

grade growths. And the Mean Scatterer Spacing (MSS) estimation of biologic tissue is expected to be an

____________

* Corresponding author. Tel.: +86-29-5303775. E-mail address: wushju@yahoo.com.cn(Sheng-ju Wu).1

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effective means for tissue characterization using ultrasound and clinical diagnosis of such pathological changes.

The present estimation means of MSS include methods of the power spectrum, autoregressive (AR)

cepstrum, the complex cepstrum [1], spectral auto-correlation, the catastrophe point detection method based on

the backscattered signals [2], wavelets transform [3], and so on. The power spectrum and AR cepstrum are so

sensitive to noise at low frequency that some spectrum peaks may be submerged. When intensively random

diffusive scatter exists in tissue, the performance of the AR cepstrum will deteriorate and many peaks emerged in

AR cepstrum diagram. Hence, MSS is difficult to be estimated. Based on catastrophe point detection with

wavelets transformation method, the undetectable signals characteristics can be unveiled and analyzed the signal

in different zoomed frequency band [2,3]. But its resolution is not very high in MSS estimation.

A novel signal processing methodology for ultrasonic scattered signals based on wavelets decomposition

using cepstrum method (WD cepstrum for short) is presented in the paper. Meanwhile, ultrasonic

backscattering microstructural feature and MSS of human kidney with normal and pathological (renal adenoma)

in vitro is analyzed by means of WD cepstrum. In order to obtain the correct characteristics of biologic tissue and

examine performance of WD cepstrum, AR cepstrum and catastrophe point detection with wavelets transform

methods are used to contrast its results, and the analytical results are discussed.

2. Material and methods

2.1 Principle of WD cepstrum and MSS estimation

Cubic central B-spline is adopted in the paper as wavelet basic function. Forrandom scattered signal )(tx ,

its power spectrum can be defined as

fffPfSf

x =

/),(lim)(0

(1)

wherePis power and f is wavelet bandwidth (or frequency interval of analysis) on scale a ,

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Taf /4)/1(= . Normalized power is defined as )(2 tx

ftxfSx = /)()(2

(2)

The wavelets transform of signal can be regard as passing through a filter whose transfer function is

)(2/1 aa , a is scaled factor, and function )(, tba is called wavelet. And shift factor siTtb = , sT is

sampling interval. The output of time domain is the time domain result of wavelets transform ),( six TtaWT .

Then the instantaneous and average powers delivered by the filter are

),()( 2 sixi TtaWTfS = (3)

and =

=N

i

sixa TtaWTN

fS1

2),(

1)( (4)

where Nis the sample numbers. Under the circumstances of a certain bandwidth, each a corresponds to an

average power. Therefore, for discrete wavelets transform, the power spectrum of output signal corresponding to

a certain frequency is

2

1

1( ) ( ) / (2 , ) /

N

m

a x i s

i

S f S f f WT t T f N

=

= = (5)

The different values ofa

mean different frequency band for estimating signal spectrum. The less varies of

a , the more accurate of estimation.

To estimate tissues MSS,the following principle is available for WD cepstrum. The cepstrum is calculated

by performing logarithm on the power spectrum of Eq.(5), and then doing an Inverse Fast Fourier Transform

(IFFT)

))((log)( fSIFFTts = (6)

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Forbiologic tissue scatterers with regular distribution, their backscattering signals )(tx would have

harmonic components in power spectrum, so there also have harmonic components in frequency spectrum

apparently. Consequently some apparent peaks would emerge in cepstrum and MSS can be obtained[4]. Usually,

the abscissa denotes time. However, in order to be convenient for mean spacing determination, the time axis is

converted into distance axis. If the position of primary maximum is max , for reflection mode imaging the

corresponding distance is converted by the following equation

2/maxcd = (7)

where dis the mean scatterer spacing (MSS) and c representsultrasonicvelocity in tissue.

2.2 Experimental system and method

A schematic diagram of the ultrasonic system is shown in Fig.1. MF-6 Impulse Signal Source with pulse

width 0.1s is available. The center frequency ofbroadband focused transducer is8MHz.

The experimental specimens were immersed in a tank (1.00.60.5 m3) filled with physiological saline

solution at about 36C. The ultrasonic beam orientation is perpendicular to the cortical surface of tissue and renal

tubules orientation. The specimens were perfused with saline and laid quietly in tank for one hour before

measurement. Displacement in ,x y and zdirections was controlled by stepper motors. The echoes were

received by the same transducer, then amplified, filtered, and sent into digital storage oscilloscope (HP54601A).

The sampling rate was MHzfs 40= over 256 averages. The signal was analyzed off-line on a PC.

Seven male (age ranging from 41 to 65 years) kidneys were used for the experiment, which were taken

from First Attached Hospital of Xian Medical University, each of which has normal and pathological parts. The

pathological specimens used in this experiment were all renal adenomas, which were benign tumors of kidney

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originated from renal tubules in cortex, near the surface of kidney. The tumor cells were large, hard and abundant

in granules, with a regular size and figure relatively.

In order to decrease errors come from observation noise and random echoes from irresolvable tissue

microstructure, five regions-of-interest (ROI) were recorded for every specimen and ten times for every ROI.

Then all the results of measurement for every part were averaged by statistics.

3. Results and discussion

During computing WD cepstrum of ultrasonic echo signals of kidney, we consider that there are powerful

observation noises in lower order scales of wavelets decomposition. Furthermore, as long as binary wavelets

decomposition scale 6M , the information for quasi-periodic of microstructure will be lost. Therefore, the

wavelets decomposition on six scales is dealt with for the ultrasonic backscattering signals. The abundant results

indicate that observation noise has been eliminated on the third scale, while on first and second scales random

diffusive scatter and observation noise still exist.Moreover, on fourth, fifth and sixth scales some useful signals

also have been eliminated which make the transform signals smooth. Therefore, the cepstrum on the third scale

was selected as last result. The results are shown in Fig.2, where Fig.2 (a) and (b) are WD cepstrum of a

wavelets transform on the third scale of echo signal of the normal human kidney and renal adenoma tissue,

respectively.

From Fig.2(a), it can be discovered that there is distinct harmonic component. For scattering signal of tissue

scatterer there is primary maximum in WD cepstrum whose depth is the position of scatterer. According to the

position, MSS is estimated. The result is 1.01 0.06mm for the statistical average of normal kidney. It is evident

that 1.01 0.06mm is just the position of the primary maximum.

It was discovered that theultrasonic scatter of kidney has an apparent anisotropy [5-7] which is caused by

complex structure of kidney cortex. Because of the complexity of the kidney microstructure, it presents a poor

homogeneity in acoustics, which makes the scatterers distribute densely and have a smaller spacing. In

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processing the experimental data, we findthat the kidney scatterers spacing is unequal. Perhaps it is caused by

the half-ordered microstructure cortical radiation of cortex, which results in the anisotropy. Insana et al. [8,9] and

Hall et al [10] suggested that the dominant backscattering structure is the glomerulus (approximately 200 m in

diameter in adults) when frequency is below about 5MHz. Once the frequency is above 5MHz, the dominant

sources of backscattering are renal tubules and cortical radiation. In our experiment, the frequency is 8MHz, so

the renal tubules and cortical radiation play an important role.Glomerulusis strong scatterers and they distribute

sparsely. When the incidence beam is parallel to the nephron structure, backscattering from the small structures

(renal tubules and blood vessels) is less. Therefore, below 5MHz, sparse structures are more apparent and the

signal-to-noise (SNR) is low. The smaller scatterers begin to dominate backscattering while SNR increasing with

frequency [11]. However, when the incidence beam is perpendicular to cortical radiation, even at low frequency,

more cortical radiations, renal tubules and the blood vessels contribute to the backscattering. Consequently, the

SNR remains invariability at all frequencies.

From the Fig.2(b), it can be seen that the renal adenoma tissues MSS is 1.66 0.08mm. It is accord with the

position of the primary maximum. Compared with the normal kidney,there is a noticeable increment in MSS of

renal adenoma tissue, which just results from the change in microstructure of kidney. According to pathology,

owing to various carcinogenic factors, the tumor becomes excessively hyperplastic and then the hyperplastic

cells form plumps. The tumor cells of renal adenoma have regular size and figure relatively. Compared with

normal tissue, the hyperplasia of renal tubules makes the numbers of scatterers in certain volume decrease so that

the density of scatterers distribution becomes sparser. The experimental result is in good agreement with the

pathologic characteristics.

In order to check up the advantage of WD cepstrum, we have also used AR cepstrum and wavelets

transform to processing the backscattered signals of normal human kidney and renal adenoma tissue.

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Fig.3(a) and Fig.3(b) display the high-order AR cepstrum of normal and renal adenoma tissues

backscattered signal, respectively. As for AR model parameter, Burg method and Akaike Information Theory

Criterion are adopted, the order is settled finally at 105=p . From Fig.3 (a), it can be seen that the MSS is 1.02

0.10mm (mean mean deviation) for normal human kidney and for renal adenoma tissue, the MSS is 1.67

0.13mm as showed in Fig.3(b). Compared Fig.3(a) with Fig.2(a), and Fig.3(b) with Fig.2(b), The results of AR

cepstrum is in agreement with WD cepstrum and the pathologic characteristics. However, due to the existence of

the diffusive scatter and disturbing noise, several peaks appear in AR cepstrum diagrams, which make the

performance of AR cepstrum worse. Therefore, the correct estimation of MSS becomes difficult.

A cubic central B-spline function of compact support has been used as the wavelets throughout this paper.

Fig.4 is waveform of the normal human kidneys backscattering signal, along with those of the wavelets

transformed on the 3rd~6th scales. Fig.5 is waveform of renal adenoma tissues backscattering signal, along with

those of the wavelets transformed on the 3rd~6th scales. From the 5th scale in Fig.4,it can be seen that there are

five scatterers in the tissue and the statistical mean spacing is 1.02 0.07mm. The statistical mean spacing is 1.66

0.10mm for renal adenoma tissue shown in Fig.5.

From above three methods, we can see that those methods are in good agreement with each other and with

the pathologic characteristics. Furthermore, WD cepstrum method ismore effective to reflect the microstructural

feature of biologic tissue and characterization of tissue scatterers.

4. Conclusion

This paper presenta novel signal processing methodology for ultrasonic scattered signals based on wavelets

decomposition using cepstrum method (WD cepstrum for short). Using this method, together with AR cepstrum

and wavelets transform, the backscattered signals of normal and renal adenoma human kidney in vitro were

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processed, and the Mean Scatterer Spacing (MSS) was estimated.

The results show that the WD cepstrum method is insensitive to noisesand avoids the presence of many

peaks. Furthermore, it improves the resolution of catastrophe point detection with wavelets transform method for

estimation of MSS. This gives preliminary evidence that WD cepstrum method is reliable for estimation of

scattered signal of heterogeneity tissue. The processing results of the three methods are shown in Table 1, which

gives the results of statistical average for seven male kidneys. From the table 1, it can be seen that the results

obtained by WD cepstrum technique are in good agreement with those estimated by other two approaches.

The analysis results of normal and renal adenoma human kidney demonstrate that the two tissues MSS

have a distinct difference.Pathological change of tissue results in variation in MSS. So the estimation results of

kidneys MSS provides an effective information for clinical diagnose of pathological changes.

Acknowledgments

This work was sponsored by National Natural Science Foundation of China (No.10304003).

Reference

[1] R.S. Mia, M.H. Loew, K.A. Wear, R.F. Wagner. Mean scatterer spacing estimation using the complex

cepstrum. Proc. SPIE-Int. Soc. Opt. Eng. (USA), 3049(Pt1-2), 1997.

[2] J.P. Xu, L. Li, Y.J. Wu, J.Z.Cheng,Q.M.Chen. A new method on mean scatter spacing of biologic

tissue. Biophysics Trans., 12 (1996) 653- 662.

[3] X. Y. Tang, U. R. Abeyratne. Wavelet transforms in estimating scatter spacing from ultrasound echose.

Ultrasonics, 38 (2000) 688-692.

[4] K.A. Wear, R.G. Wagner, M.F. Insana T.J.Hall. Application of autoregressive spectral analysis to

cepstral estimation of mean scatterer spacing. IEEE Trans. On UFFC, 40 (1993) 50-58.

[5] D.Y. Fei, K.K. Shung. Ultrasonic backscatter from mammaliant tissue. J. Acoust. Soc. Am., 78 (1985)

871-878.

[6] M.F. Insana, T.J. Hall, J.L. Fishback. Identifying acoustic scattering sources in normal renal

parenchyma from the anisotropy in acoustic properties. Ultras. Med. Biol., 12 (1991) 623-631.

[7] M.F. Insana. Modeling acoustic backscatter from kidney microstructure using an anisotropic

8

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correlation function. J. Acoust. Soc. Am., 97 (1995) 649-655.

[8] M.F. Insana, J.G. Wood, T.J. Hall. Identifying acoustic scattering sources in normal renal parenchyma

in vivo by varying arterial and ureteral pressures. Ultras. Med. Biol., 18 (1992) 587-599.

[9] M.F. Insana, J.G. Wood, T.J. Hall. Effects of endothelin-1 on renal micro -vasculature measured using

quantitative ultrasound. Ultras. med. Biol., 21 (1995) 1143-1151.

[10]T.J. Hall, M.F. Insana, L.A. Harrison, G.G.Cox. Ultrasonic measurement of glomerular diameters in

normal adult humans. Ultras. Med. Biol., 22 (1996) 987-997.

[11]K.A. Wear, R.F. Wagner, D.G. Brown, M.F. Insana. Statistical properties of estimates of signal-to-

noise ratio and number of scatterers per resolution cell. J. Acoust. Soc. Am., 102 (1997) 635-641.

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Table 1. MSS of normal part and renal adenoma part for all seven male kidneys

(mean mean deviation)(unit: mm)

Figure captions

1. FIG.1 Scheme of the experimental system

2. FIG.2 WD cepstrum of wavelets decomposition at 3rd scale for backscattered signals of

normal kidney and renal adenoma tissue

(a) normal kidney; (b) renal adenoma tissue

3 FIG.3 AR cepstrum for backscattered signals of normal human kidney and renal adenoma

tissue. (a) normal kidney; (b) renal adenoma tissue

4. FIG.4 Waveform of normal human kidneys scattering signals and wavelets transform on the

3rd~6th scale

5. FIG.5 Waveform of renal adenoma tissues scattering signals and wavelets transform on the

3rh~6th scale

FIG.1

mothodstissues

ARcepstrum

Waveletstransform

WDcepstrum

Normal kidney 1.02 0.15 1.02 0.10 1.02 0.08Renal adenoma 1.68 0.19 1.66 0.12 1.66 0.10

10

ProbeComputerRange

gatingGate widthmodulator

Digitaloscilloscope

Impulse

source

Switching

gate

wide-bandamplifier

Band-passfilter

y x

z

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FIG.2 FIG.3

FIG.4 FIG.5

11

(a) Normal kidney

0.0

0.2

0.4

0.6

0.8

3.53.02.52.01.51.00.50.0

Amplitude

Depth(mm)

(b) Renal adenoma tissue

0.0

0.2

0.4

0.6

0.8

3.53.02.52.01.51.00.0 0.5

Amplitude

Depth(mm)

(a) Normal kidney

(b) Renal adenoma tissue

0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.50.0

0.1

0.2

0.3

0.4

0.5

0.6

Amplitude

Depth(mm)

0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.50.0

0.1

0.2

0.3

0.4

0.5

0.6

Amplitude

Depth(mm)

f(d)

W(23,d)

W(24,d)

W(25,d)

W(26

,d)

0 1 2 3 4 5

Depth(mm)

f(d)

W(23,d)

W(24,d)

W(25,d)

W(26,d)

0 2 4 6 8

Depth(mm)