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© 2002 by the American Institute of Ultrasound in Medicine
J Ultrasound Med 21:783-788 • 0278-4297

Technical Advance

A New Method for Attenuation Coefficient Measurement in the Liver

Comparison With the Spectral Shift Central Frequency Method

Yasutomo Fujii, MD, Nobuyuki Taniguchi, MD, PhD, Kouichi Itoh, MD, PhD, Kouichiro Shigeta, MD, Yi Wang, MD, PhD, Jing-Wen Tsao, PhD, Kenji Kumasaki and Takashi Itoh, PhD

Department of Clinical Laboratory Medicine, Jichi Medical School, Tochigi, Japan (Y.F., N.T., K.I., K.S.); and Aloka Co, Ltd, Tokyo, Japan (J.-W.T., K.K., T.I.).

Address correspondence and reprint requests to Yasutomo Fujii, MD, Department of Clinical Laboratory Medicine, Jichi Medical School, Minami Kawachi-machi, Kawachi-gun, Tochigi 329-0498, Japan.


   Abstract
Top
 Abstract
Introduction
 Materials and Methods
 Results
 Discussion
 References
 
Objective. To assess the feasibility of a new method of measuring the attenuation coefficient in the liver, which offers less variability of results than the conventional method. Methods. The attenuation coefficient was evaluated on the basis of the following equation with sound field correction:



In our system, the attenuation coefficient was also evaluated by the spectral shift central frequency method at the same time. We used 44 cases of normal liver, 40 cases of fatty liver, and 20 cases of cirrhotic liver in the system. Results. With this new method, attenuation coefficient values were 0.59 ± 0.10 dB • cm-1 • MHz-1 in normal livers, 0.80 ± 0.12 dB • cm-1 • MHz-1 in fatty livers, and 0.62 ± 0.09 dB • cm-1 • MHz-1 in cirrhotic livers. In both methods we recorded a statistically significant difference between normal and fatty livers and between fatty and cirrhotic livers (P < .0001). Only in the fatty liver was any significant difference (P < .0001) found between attenuation coefficients in the new method and those in the spectral shift central frequency method (0.70 ± 0.05 dB • cm-1 • MHz-1). Conclusions. This new method, which was more sensitive in detecting fatty infiltration than the spectral shift central frequency method, was considered usable for evaluating the attenuation coefficient of the liver in vivo.

Key Words: attenuation coefficient • cirrhotic liver • fatty liver • tissue characterization • ultrasonography

Abbreviations: RF, radio frequency • RMI, Radiation Measurements, Inc • ROI, region of interest • SS method, spectral shift central frequency method


   Introduction
Top
 Abstract
 Introduction
Materials and Methods
 Results
 Discussion
 References
 
Current methods for in vivo measurement of attenuation can be placed in 2 main categories: (1) measurements of the difference in peak or total energy between the signal received from 2 depths (the power method) and (2) measurements of the downshift in the center frequency of the signal received at the 2 depths.

Many investigators, including ourselves, have reported the results of determining the attenuation coefficient using the spectral shift zero-crossing method,1–3 the spectral difference method,4,5 or the spectral shift central frequency method (SS method)6,7 in a diseased liver. These methods, however, all involve some problems. Results obtained thus far by the SS method or the zero-crossing method show a relatively high degree of stochastic variability.8 The spectral difference method is rather accurate, but it requires many signals, especially indicating direction and depth, for the calculation of accurate results.

We have developed a system for evaluating the attenuation coefficient by using a hybrid of the 2 conventional categories introduced above, which is equivalent to the un-normalized moment method.9 In the un-normalized moment method, stochastic variation of the attenuation coefficient is reduced because only zero-order and first-order moments are used in attenuation coefficient calculation.10 The purpose of this study was to assess the feasibility of this new system for measuring the attenuation coefficient of the liver. To clarify the advantages of the new method, we compared the results obtained by it with those of the SS method.


   Materials and Methods
Top
 Abstract
 Introduction
 Materials and Methods
Results
 Discussion
 References
 
Theory
In the SS method, the attenuation coefficient is calculated according to the following equation1,6,7:



(1)
where ß1 is the attenuation coefficient, fc is the central frequency, and {sigma}(z) is the SD of the spectrum of the ultrasonic pulse.

In our new method, the attenuation coefficient is determined as explained below. In a homogenous medium, the power spectral density of a received signal O(z,f) is expressed by the following formula:



where I(z,f) is the power spectral density of the transmitted signal, and f is frequency.

If this formula is simplified to be independent of z in I(z,f), we obtain the following equations:



where Mn(z) is the short-term power in the nth moment:





(2)


(3)
where the central frequency of the echo is defined by:



In both our method and the un-normalized moment method, the attenuation coefficient is evaluated by using Equations 2 and 3GoGo, respectively. These equations appear in theory to be equivalent, and the new method shows lower variability in the attenuation coefficient.

Sound Field Correction
The attenuation coefficients given by Equations 1 and 2GoGo, however, include the diffraction effect in the sound field: it is corrected by adjusting fc(z) and M0(z). The corrected attenuation coefficients, {alpha} values, are determined with the following equations:





With a commercially available Radiation Measurements, Inc (RMI) phantom (Gammex RMI, Middleton, WI; attenuation coefficient, 0.50 dB • cm-1 • MHz-1), the diffraction correction factors {varepsilon}(z) and {tau}(z) are experimentally determined as the difference between the measured and estimated shifts in central frequency and as that between the measured and estimated shifts in the short-term power, respectively. This method of correction is based on the blind restoration technique.1,11,12 The field near the transducer is saturated with strong backscattered radio frequency (RF) signals, whereas the far field exhibits much noise. These effects must be avoided in the proper determination of the attenuation coefficient. Therefore, the depth range of the 3.75-MHz sector array scanner was set between 16 and 125 mm with the focus depth of 106 mm for the purpose of sound field correction.

Data Acquisition and Calculation
In this study, the attenuation coefficient was measured with a 3.75-MHz sector array scanner (SSD-5500; Aloka Co, Ltd, Tokyo, Japan) equipped to use 2 attenuation coefficient measurement systems: the SS method6,7 and a new method, which is a hybrid form of the power and SS methods.9 Preparation of the system involved programming an offline computer to obtain and analyze RF signals. The computer software (RF signal filing tool 3.2.2, Aloka; and MATLAB, The MathWorks, Natick, MA) was used for obtaining RF signals and for analysis of the RF signal.

By slightly tilting the scanner manually, we were able to obtain 10 frames of RF signals from all cases. Two amplitude values are independent if the probe is translated by about half its width between the measurements.13 Thus, to reduce the statistical dependency of the amplitude from frame to frame, the probe was tilted as quickly as possible.

In both systems, the received power spectral density in a region of interest (ROI) using RF signals for 10 frames was evaluated in the following process. In each A-line in 1 frame, the power spectral density was evaluated by fast Fourier transform analysis with a Hamming window of 48 points ({approx}2.5 mm), which was arrayed at a shift interval of 4 points ({approx}0.20 mm) in the direction for depth. The power density of each Hamming window located at the same depth from the scanner was averaged in each of the A-lines and the 10 frames. The resulting average was considered the relevant power spectral density versus depth of the ROI in each case.

On the basis of the B-mode image, an ROI was selected manually to cover as large an area of the liver parenchyma as possible, excluding relatively large vessels in all cases (Fig. 1Go). The values of the attenuation coefficient using the SS method and our proposed method were calculated in an ROI at the same time. It took approximately 5 minutes to calculate the attenuation coefficient values using this computer system.



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  		Figure 1. Conventional B-mode image showing ROI location in a fatty liver.

 
The following 3 operations were carried out by the attenuation coefficient calculator. The diffraction effect was corrected by subtracting {varepsilon}(z) and {tau}(z) from the observed fc(z) and the observed M0(z); the time derivatives in the equations were evaluated from the slope of a line fitted to the corrected fc(z) and M0(z); and each {alpha} was calculated (Figs. 2 and 3GoGo).



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  		Figure 2. Attenuation slope obtained with the new method in the same case as in Figure 1Go. The attenuation coefficient value appears at the top right. In this case, it was 0.82.

 


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  		Figure 3. Attenuation slope obtained with the SS method in the same case as in Figure 1Go. The attenuation coefficient value appears at the top right. In this case, it was 0.73.

 
Phantom Study
To verify the accuracy of the new method, we performed a phantom study using a commercially available RMI phantom (Gammex RMI; attenuation coefficient, 0.70 dB • cm-1 • MHz-1). A square ROI (3 x 3 cm) containing 64 A-lines was determined at a depth of 3 cm from the phantom. The attenuation coefficient of each A-line was evaluated with the system described above.

Clinical Study
The attenuation coefficients of the livers of 44 subjects (16 male and 28 female; age range, 13–77 years) without liver disease were studied. Forty patients with fatty liver (18 male and 22 female; age range, 14–77 years) and 20 with liver cirrhosis (13 male and 7 female; age range, 47–86 years) were also studied, and the values obtained were compared with those from the healthy subjects. In all cases, the diagnoses were confirmed by 1 or more of the following: laboratory test results, computed tomography, and histopathologic findings.

The paired or unpaired t test was used in the statistical analysis. P < .05 indicated a statistically significant difference.


   Results
Top
 Abstract
 Introduction
 Materials and Methods
 Results
Discussion
 References
 
Phantom Study
In the phantom, the attenuation coefficient values of each A-line were 0.68 ± 0.15 dB • cm-1 • MHz-1 with the new method and 0.61 ± 0.65 dB • cm-1 • MHz-1 with the SS method.

Clinical Study
The attenuation coefficient value of normal liver averaged 0.59 ± 0.10 dB • cm-1 • MHz-1 with the new method and 0.59 ± 0.07 dB • cm-1 • MHz-1 with the SS method. In the new method, patients with fatty liver had a wide variation in their attenuation coefficients, which ranged from 0.58 to 1.20 dB • cm-1 • MHz-1; the mean attenuation value was 0.80 ± 0.12 dB • cm-1 • MHz-1 and did not vary widely, ranging from 0.57 to 0.83 dB • cm-1 • MHz-1; the mean attenuation value was 0.70 ± 0.05 dB • cm-1 • MHz-1 with the SS method. In both methods, attenuation coefficient values in the cirrhotic liver group varied less, ranging from 0.34 to 0.86 dB • cm-1 • MHz-1, whereas with the new method, the mean attenuation value was 0.61 ± 0.12 dB • cm-1 • MHz-1, and with the SS method, it was 0.62 ± 0.09 dB • cm-1 • MHz-1. In both methods, there were statistically significant differences between normal and fatty livers (P < .0001) and between fatty and cirrhotic livers (P < .0001; Figs. 4 and 5GoGo). Attenuation coefficient values obtained with the new method were significantly greater than those obtained with the SS method in fatty liver (P < .0001), although no significant differences were found between the new and the SS methods in either normal (P = .79) or cirrhotic (P = .96) liver.



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  		Figure 4. Attenuation coefficients of normal and fatty livers and fatty and cirrhotic livers (P < .05) obtained by using the new method. LC indicates cirrhotic liver.

 


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  		Figure 5. Attenuation coefficients of normal and fatty livers and fatty and cirrhotic livers (P < .05) obtained by using the SS method. LC indicates cirrhotic liver.

 

   Discussion
Top
 Abstract
 Introduction
 Materials and Methods
 Results
 Discussion
References
 
The results of the phantom study supported the superiority of the stochastic stability of this new method because of the lower SD of the estimates. The new method may permit us to determine the attenuation coefficients of organs much smaller than the liver, such as the thyroid.

In our clinical study, we found that the attenuation coefficients of fatty and cirrhotic liver were both elevated beyond the normal range, and the attenuation coefficient of fatty liver was higher than that of cirrhotic liver in both methods. On this issue, other workers have reported similar results.1,4,14–16 The attenuation coefficients of normal liver in this study were 0.59 ± 0.07 dB • cm-1 • MHz-1 with the spectral-shift method and 0.59 ± 0.10 dB • cm-1 • MHz-1 with our method. These data differed from those of Kuc and Schwartz4 (0.44 ± 0.04) and Suzuki et al17 (0.49), which were lower, but were on a par with those of Itoh et al1 (0.55 ± 0.05), Ophir et al14 (0.52 ± 0.03), Garra et al15 (0.627 ± 0.126), Lu et al16 (0.55 ± 0.07), and Wilson et al18 (0.53 ± 0.1).

Conversely, the attenuation coefficient values obtained with our method were significantly greater than those obtained with the SS method in fatty livers, but no significant differences were seen in normal and cirrhotic livers. This result suggests that the new method is more sensitive than the SS method in detecting fatty infiltration of the liver. We speculated that a nonlinear factor, n, was the cause of this finding. Although many reports19–23 indicate that a power law function of the type {alpha}(f) = {alpha}0fn describes the frequency dependence rather well, most reports have considered only linear cases, that is n = 1.1–8,11 In this study, a linear frequency dependence of attenuation was also assumed. Conversely, fatty liver has a higher nonlinear factor than normal or cirrhotic liver.14

In conclusion, the new method appears capable of making a useful contribution to the evaluation of the attenuation coefficient of the liver in vivo. We are considering using the method for determining the attenuation coefficients of small organs such as the thyroid and the mammary glands.


   Footnotes
 
Received December 10, 2001, from the Department of Clinical Laboratory Medicine, Jichi Medical School, Tochigi, Japan (Y.F., N.T., K.I., K.S.); and Aloka Co, Ltd, Tokyo, Japan (J.-W.T., K.K., T.I.).


   References
Top
 Abstract
 Introduction
 Materials and Methods
 Results
 Discussion
 References
 

  1. Itoh K, Yasuda Y, Suzuki O, et al. Studies on frequency-dependent attenuation in the normal liver and spleen and in liver diseases, using the spectral-shift-zero crossing method. J Clin Ultrasound 1988; 16:553–562.[Medline]
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  3. Ophir J, Ghouse MA, Ferrari LA. Attenuation estimation with the zero-crossing technique: phantom studies. Ultrason Imaging 1985; 7:122–132.[Medline]
  4. Kuc R, Schwartz M. Estimating the acoustic attenuation coefficient slope for liver from reflected ultrasound signals. IEEE Ultrason Symp Proc 1978; 26:353–362.
  5. Kuc R. Clinical applications of an ultrasound attenuation coefficient estimation technique for liver pathology characterization. IEEE Trans Biomed Eng 1980; 27:312–319.[Medline]
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  7. Fink M, Cardoso JF. Diffraction effects in pulse-echo measurement. IEEE Ultrason Symp Proc 1984; 31:313–329.
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  9. Tsao JW, Morimura T, Itoh T, Konishi T. A comparison of methods derived for attenuation (FDA) measurement from pulse-echo signals [abstract in Japanese]. Proc Jpn Soc Ultrason Med 1986; 48:659–660.
  10. Suzuki A, Yagi S, Nakayama K. Ultrasonic echo spectral moment tomography: advanced method of attenuation tomography [abstract in Japanese]. Proc Jpn Soc Ultrason Med 1984; 45:711–712.
  11. Tsao JW, Itoh H, Itoh K, Konishi T. Diffraction correction for ultrasonic attenuation (FDA) measurements [abstract in Japanese]. Proc Jpn Soc Ultrason Med 1985; 47:317–318.
  12. Pratt WK. Specialized spatial image restoration techniques. In: Pratt WK (ed). Digital Image Processing. New York, NY: John Wiley & Sons, 1978:433–437.
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  18. Wilson LS, Robinson DE, Doutst BD. Frequency domain processing for ultrasonic attenuation measurement in the liver. Ultrason Imaging 1984; 6:278–292.[Medline]
  19. Ophir J, McWhirt RE, Maklad NF, Jaeger PM. A narrowband pulse-echo technique for in vivo ultrasonic attenuation estimation. IEEE Trans Biomed Eng 1985; 32:205–212.[Medline]
  20. Goss SA, Frizzell LA, Dunn F. Ultrasonic absorption and attenuation in mammalian tissues. Ultrasound Med Biol 1979; 5:181–186.[Medline]
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