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Computation of local directivity, speed of sound and attenuation from ultrasonic reflection tomography data
ULTRASONIC IMAGING 10, 110-120
COMPUTATION OF LOCAL DIRECTIVITY, SPEED OF SOUND AND ATTENUATION FROM ULTRASONIC REFLECTION TOMOGRAPHY DATA H . Bartelt Siemens AG, Corporate Research Center ZFE TPH 41 D-8520 Erlangen, Federal Republic of Germany
Ultrasound reflection tomography based on the compound scan principle, allows one to produce reflectivity images with high quality and reproducibility . In this paper, methods are discussed on how to extract additional physical parameters from the same set of reflection data. for medical applications . Experimental results from a phantom object and in-vivo measurements illustrate the capabilities of such tomographic reflection systems . m 1558 Aeaaemlc Press, In . Key words : Medical imaging ; parameter extraction ; reflection tomography . 1 . INTRODUCTION Tomographic ultrasound reflection systems for medical imaging based on the conpound scan principle, have the potential to give a great amount of information about an object structure which goes well beyond that of conventional reflectivity imaging [1-4] . It is important, however, to make full use of the measured data and to represent the obtained information in a suitable way. For improved diagnostic interpretation and especially for application in tissue characterization procedures, it would be useful to have several, independent physical parameters available for the same object structure . In this paper, methods are discussed to calculate three different parameters, namely directivity, speed of sound and attenuation from tomographic reflectivity measurements . Several alternative methods have been discussed in the literature, especially to obtain speed of sound or attenuation data [5-9! . The methods described here were developed with the intention to use the same data set for the computation of different parameters without the need of additional and independent measuring procedures . In the following, the tomographie reflection system used for the experimental measurenients will be described briefly. 'Then the parameter computation from reflection data will be discussed separately for each parameter with results from experimental measurements for illustration . 2 . EXPERIMENTAL SYSTEM The experimental system used for our measurements is based on a linear compound scan principle (Fig . I) . It. consists of six linear transducer arrays mounted on a ring over an angle of 60 degrees . Additionally, the transducer ring can he rotated by an arbitrary angle . The center frequency of the transducer arrays is 3 .5 MHz . The objects to be measured are placed in a water bath as coupling medium . The reflected, 0161-7346/88 $3 .00 Copyright © 1988 by Academic Press, Inc . All rights of reproduction in any form reserved.
110
COMPUTATION OF DIRECTIVITY, SOUND SPEED AND ATTENUATION
image monitor
n
waterbath with transducer arrays
ultrasound control electronic
n angle position
control
I
computer POP 1 1 /73
L
with data storage
CAMAC - signal processing
Fig . I Experimental system for ultrasonic reflection tomography measurements based on the compound scan principle .
demodulated signals are processed off-line to give the final superposition image . In the case of the reconstruction of a tomographic reflectivity image, the measured B-scans are superimposed by addition . These images will be here referred to as tomographic iniages, although no inverse scattering algorithms have been applied 10,11] . An example of such a reconstructed summation image is shown in figure 2 . The object was a phantom structure containing several regions that differ in their physical properties . Such tomographic compound scans show improved resolution and better signal-to-noise ratio as compared to conventional B-scans . In this reflectivity image, obtained from a superposition by addition, any information concerning the difference of B-scans measured from different directions is lost . The methods for parameter extraction discussed in the following make positive use of this fact . 3 . DIRECTIVITY The strength of a backscattered signal from a boundary depends on the insmsofica4ion angle . An example for such a variation at an specific point on the phantom object is shown in figure 3 . The directivity of the backscattered signal may be defined as the slope near the reflection peak . The value of this parameter can be therefore obtained by comparing adjacent B-scans : d(a, y) -
with
d"
dp
at s
d : directivity s : reflection signal pp : insonofication angle 111
(1)
H.
BARTELT
a
Fig, 2 Phantom object used for ultrasonic reflection tomography measurements . (a) Compovents of the phantom object . (b) Superimposed reflectivity image from 36 B-scans .
-- pastiotube matencl - nylon tissue Oatonal
Fig . 3 Variation of direct reflection with insonofication angle for two specific positions of different material in the phantom object (the shown values arc averaged over 20 degrees in angle) .
1 12
COMPUTATION OF DIRECTIVITY, SOUND SPEED AND ATTENUATION
Fig. 4 Directivity image of the phar tout object .
A mirror-like structure, for example, will show a strong directivity whereas a scattering surface will give a low directivity. Hence, this parameter can display angle dependent information without the need to make true scattering measurements and can serve for characterization of boundary properties . A result for the phantom object is shown in figure 4 . The directivity representation differentiates clearly between the woven nylon tissue (strong scattering) and the plastic tube material (flat surface) .
4 . SPEED OF SOUND Speed of sound images are usually reconstructed from transmission measurements [5,6] . From reflection measurements, the speed of sound can be obtained from the analysis of A-scans measured from opposite scan directions (Fig . 5) . In the reflectivity image, the position for each scatterer is reconstructed from the measured data under the assumption of a known and constant speed of sound . A variable speed of sound, however, may result in double structures for every single scatterer in the superimposed reflectivity image . This effect is obvious for the boundary of the salt solution in figure 2 .
transducer2
transducer i
• actual position
e • o
e
{
-J
reconstructed positions
Fig . 5 Effect of varying speed of sound on scans measured from opposite directions .
1 13
H.
BARTELT
The reconstructed positions for a single scatterer x directions can he described as : x1 - (cot, )/
2 = co JO
r
and x i for opposite measuring
°
(2) xz=xd - (cotz)/2=xd with
o
4l dx
t,, t 2 : time of flight for opposite measuring directions x o : actual position of scatterer a d : distance of opposite transducers cs : assumed speed of sound
The difference of these positions is directly related to the average inverse speed of sound along the measuring direction and is independent of the actual scatterer position : xz - xi = xd - cord
<
ats7
>
(3)
where < . . > means average over po ion x . Mathematically, this distance of the reconstructed scatterer positions is obtained by a correlation operation . Sufficient overlapping of opposite A-scans is therefore necessary for this method . With the average inverse speed of sound known for different lines and different directions, the local inverse speed of sound can be calculated using methods of computed tomography, e .g ., the filtered backprojection method [12,13] . If necessary, one may further transform the local inverse speed of sound to give directly the speed of sound image . A result for the phantom object calculated from 216 different B-scans is shown in figure 6 . The region with the 20 percent salt solution which differs in speed of sound by about 8 percent from the surrounding water is clearly visible . Resolution is, however, lower compared to the reflectivity image due to the true computer tontographic reconstruction method . For this result, 216 different B-scans with an angle increment of 1 .7
Fig . 6 Inverse speed of sound image for the phantom object measured from 216 B-scans .
1 14
COMPUTATION OF DIRECTIVITY, SOUND SPEED AND ATTENUATION
Fig . 7 In-vivo measurement of a lmmail forearm . (a) Reflectivity image from 36 B-scans . (b) Inverse speed of sound image from 108 B-scans .
degree have been used . A problem will occur in practical applications if areas with strong attenuation are present in the object and no overlapping A-scans are obtained . This problem occurs, for example, in the experimental result of a human forearm in figure 7 (calculated from 108 different B-scans) . The shift measurement is more critical here because of shadow effects caused by the bones . But it is possible to differentiate in the reconstruction between fat tissue and muscle tissue . The speed itself is a valuable parameter . But it is also possible to use this information (or directly the correlation data) for correction of the double structure artifacts in the reflectivity representation . Examples are shown in figure 8 . For the phantom object, the double structures of the tube with the salt solution have vanished . In the in-vivo measurement, one can also identify several double structures whichh have been removed by the correction operation . .5 . ATTENUATION Attenuation includes all processes with energy loss such as reflection, scattering and absorption . Usually, attenuation images are obtained either by frequency analysis of reflection data or from transmission measurements [5,7,8,9] .
115
H . BARTELT
Fig . 8 Reflectivity images corrected for speed of sound variations from the calculated correlation data . (a) Phantom object (compare with figure 2b) . (b) In-vivo measurement of a human forearm (compare with figure 7a) .
From tornographic reflection measurements, information concerning attenuation can be obtained by calculating the average amplitude difference of opposite A-scans . This difference gives a measure of average attenuation along a single line . From the data of different lines and orientations, a qualitative image of local attenuation can be obtained by computed tomography . This computation of local attenuation requires a speed of sound correction as mentioned in the previous section . For simplicity, the method and its assumptions will be explained first for an object structure with constant attenuation . In this case, the ultrasonic signal will decay with penetration depth for the signals a, (z) and a,(x) measured from opposite directions : linear model : a,(x) = ao - ax a2(x) = ao - a(xo - x) exponential model : a,(x) = a oexp(-ax) a2(x) = aoexp - a(xo - x)] 1 16
(4)
COMPUTATION OF DIRECTIVITY, SOUND SPEED AND ATTENUATION
with a,, : constant a : attenuation coefficient xo : transducer distance x : actual position The average modulus of the difference of both opposite measuring directions (or its logarithm for the exponential model) gives : linear model : fo° I a,( .x) - a2(x) ( dx = axa/2 exponential model : fo° ln[a,(x)]
-ln[a2 (x)]
I-axo/2
(5)
The result is, in both cases, directly proportional to the attenuation coefficient a . In the general case, with variable attenuation coefficient a(x), a result can be obtained which is approximately proportional to the average attenuation coefficient a for small variations of a, e .g ., in the exponential model : signals :
a,(x)=aoexp[-fo a(x')dr'] a2(x) = aoexp[-fx ° a(x' )dx ' ]
modulus of the difference : ln[a,(x)] - ln[a2 (x)] I=1 -
(6)
f„ a(x')dx' - fy° a(x')dx'
-1 ax - a(x o - x) I
integration over all positions x : fu ° I a ;re - n(x o - x,) I da = kn
for small variations of a(r)
with k : proportionality constant
Fig . 9 Attenuation image for the phantom object calculated from 216 B-scans . 1 17
H.
BARTELT
Fig . 10 In-viva measurement of a human forearm . (a) Reflectivity image . (b) Attenuation image (linear model) from 216 Bscans .
Algorithms of computed tomography are then applied to these data to produce an image of local attenuation . Since we have to assume small variations of a, this method is not suitable to obtain quantitative values . It is useful, however, to give a qualitative image of the attenuation distribution . A result for the phantom object from 216 measuring directions is shown in figure 9 . The area of the castor oil ( with absorption of 0 .95 dB/am at 1 MHz [5] ) and the surface of the tube with the salt solution are represented with high attenuation . In an experimental iu-vivo measurement of a human forearm, the skin surface and the bones are reconstructed with high attenuation (Fig . 10) . These images of local attenuation can be also interpreted to display the causes of shadowing effects in the original B-scans . Shadows are an important diagnostic element in the analysis of conventional B-scans . In the superimposed tomographic reflectivity image, however, this information is averaged out and therefore not available for diagnosis . The information is, of course, contained in the original data set and can be extracted as attenuation in the described way .
1 18
COMPUTATION OF DIRECTIVITY, SOUND SPEED AND ATTENUATION
6 . CONCI,?XSIONS The methods for parameter extraction discussed here Were supposed to demonstrate the capabilities of a tomographic reflection compound scan s ystem . t t has been shown that the same set of data call be used to reconstr,sct several local parameters . Besides the improved quality of reflectivity images, this fact could be another advantage for a tomographic systern and may compensate partially for the missing real-time capability . With the knowledge of different physical parameters for the same object, further processing of the data also becomes interesting . For parameters like speed of sound and attenuation with relatively low spatial resolution, it . makes sense to combine its representation with the reflectivity image . One possibility of such a combined representation is the use of a color display system . The reflectivity as a first parameter can be coded, for example, as intensity and the second parameter (e .g. attenuation) as color saturation .
The different parameters could be also useful as a data base for further tissue characterization procedures . A combination of the data of the different parameters would allow a more complex analysis of the object structure and could improve the diagnostic value of a medical ultrasound system . ACKNOWLEDGEMENT The author would like to thank very much K .Newerla for his assistance in making measurements with the tomographic ultrasound system .
REFERENCES [1~ Robinson, B .S . and Greenleaf, J .F ., Computerized Ultrasound Tomography, in Three-Dimensional Biomedical Imaging, Vol-11, R .A .Robb, ed ., pp 58-78 (CRCPress, Boca Raton, 1985) . [2' Dines,K .A . and Goss, S .A ., Computed ultrasonic reflection tomography, IEEE Trans . UFFC-34, 309-318 (1987) .
X31 Hiller, D . and Ennert, H ., System analysis of ultrasound reflection mode computerized tomography, IEEE Trans . Sonics Uitrrasonics SU-31, 240-2 .50 (J984) . ., Hondt, F . and Maderlechner, U 4] Frie(Irid ., NT ., Europ . J . Radial . 26, 764-758 (,1982) . 5] Wells, P .N .T ., Biomedical tillcosonics (Academic Press, New York, 1977) . f6] Ophir, J ., Estimation of the speed of sound propagation in biological tissue : a beam tracking method, IEEE Tmns . Ultrasonics, Ferroelectrics Freq, Control UFFC-33, 359-368 (1986) . 17] He, P . and Greenleaf, J ., Attenuation estimation on phantoms - a stability test, Ultrasonic Imaging 8, 1245-1272 (1986) .
1 19
H.
BARTELT
[81 Parker, K .J . and Waag, R .C ., Measurement of ultrasonic attenuation within regions selected from B-scan images, IEEE Trans . Biomedical Eng . BME-30, 431-437 (1983) . [91 Duerinckx, A .J ., Ferrari, L .A ., Hoefs, J .C ., Sankar, P .V ., Fleming, D . and ColeBueglet, C ., Estimation of acoustic attenuation in liver using one megabyte of data . and the zero-crossing technique, Ultrasonics 24, 32.5-332 (1986) . [I01 Greenleaf, J .F ., Computerized tomography with ultrasound, Proc . IEEE fl, 330337 (1971) . llJ Kaveh, M . and Soumekh, M ., Computer-Assisted Diffraction Tomography, in Image Recovery : Theory and Application, pp . 369-413 (Academic Press, New York, 1987) . 11211 Devaney, A .J ., A fast filtered backpropagation algorithm for ultrasound toinography, IEEE Trans . Ultrasonics, Ferroelectrics Freq . Control UFFC-34, 330-340 (1987) . `131 Kak, A .C ., Computerized tomography with x-ray, emission andd ultrasound sources, Proc . IEEE St7, 1245-1272 (1979) .
120
COMPUTATION OF LOCAL DIRECTIVITY, SPEED OF SOUND AND ATTENUATION FROM ULTRASONIC REFLECTION TOMOGRAPHY DATA H . Bartelt Siemens AG, Corporate Research Center ZFE TPH 41 D-8520 Erlangen, Federal Republic of Germany
Ultrasound reflection tomography based on the compound scan principle, allows one to produce reflectivity images with high quality and reproducibility . In this paper, methods are discussed on how to extract additional physical parameters from the same set of reflection data. for medical applications . Experimental results from a phantom object and in-vivo measurements illustrate the capabilities of such tomographic reflection systems . m 1558 Aeaaemlc Press, In . Key words : Medical imaging ; parameter extraction ; reflection tomography . 1 . INTRODUCTION Tomographic ultrasound reflection systems for medical imaging based on the conpound scan principle, have the potential to give a great amount of information about an object structure which goes well beyond that of conventional reflectivity imaging [1-4] . It is important, however, to make full use of the measured data and to represent the obtained information in a suitable way. For improved diagnostic interpretation and especially for application in tissue characterization procedures, it would be useful to have several, independent physical parameters available for the same object structure . In this paper, methods are discussed to calculate three different parameters, namely directivity, speed of sound and attenuation from tomographic reflectivity measurements . Several alternative methods have been discussed in the literature, especially to obtain speed of sound or attenuation data [5-9! . The methods described here were developed with the intention to use the same data set for the computation of different parameters without the need of additional and independent measuring procedures . In the following, the tomographie reflection system used for the experimental measurenients will be described briefly. 'Then the parameter computation from reflection data will be discussed separately for each parameter with results from experimental measurements for illustration . 2 . EXPERIMENTAL SYSTEM The experimental system used for our measurements is based on a linear compound scan principle (Fig . I) . It. consists of six linear transducer arrays mounted on a ring over an angle of 60 degrees . Additionally, the transducer ring can he rotated by an arbitrary angle . The center frequency of the transducer arrays is 3 .5 MHz . The objects to be measured are placed in a water bath as coupling medium . The reflected, 0161-7346/88 $3 .00 Copyright © 1988 by Academic Press, Inc . All rights of reproduction in any form reserved.
110
COMPUTATION OF DIRECTIVITY, SOUND SPEED AND ATTENUATION
image monitor
n
waterbath with transducer arrays
ultrasound control electronic
n angle position
control
I
computer POP 1 1 /73
L
with data storage
CAMAC - signal processing
Fig . I Experimental system for ultrasonic reflection tomography measurements based on the compound scan principle .
demodulated signals are processed off-line to give the final superposition image . In the case of the reconstruction of a tomographic reflectivity image, the measured B-scans are superimposed by addition . These images will be here referred to as tomographic iniages, although no inverse scattering algorithms have been applied 10,11] . An example of such a reconstructed summation image is shown in figure 2 . The object was a phantom structure containing several regions that differ in their physical properties . Such tomographic compound scans show improved resolution and better signal-to-noise ratio as compared to conventional B-scans . In this reflectivity image, obtained from a superposition by addition, any information concerning the difference of B-scans measured from different directions is lost . The methods for parameter extraction discussed in the following make positive use of this fact . 3 . DIRECTIVITY The strength of a backscattered signal from a boundary depends on the insmsofica4ion angle . An example for such a variation at an specific point on the phantom object is shown in figure 3 . The directivity of the backscattered signal may be defined as the slope near the reflection peak . The value of this parameter can be therefore obtained by comparing adjacent B-scans : d(a, y) -
with
d"
dp
at s
d : directivity s : reflection signal pp : insonofication angle 111
(1)
H.
BARTELT
a
Fig, 2 Phantom object used for ultrasonic reflection tomography measurements . (a) Compovents of the phantom object . (b) Superimposed reflectivity image from 36 B-scans .
-- pastiotube matencl - nylon tissue Oatonal
Fig . 3 Variation of direct reflection with insonofication angle for two specific positions of different material in the phantom object (the shown values arc averaged over 20 degrees in angle) .
1 12
COMPUTATION OF DIRECTIVITY, SOUND SPEED AND ATTENUATION
Fig. 4 Directivity image of the phar tout object .
A mirror-like structure, for example, will show a strong directivity whereas a scattering surface will give a low directivity. Hence, this parameter can display angle dependent information without the need to make true scattering measurements and can serve for characterization of boundary properties . A result for the phantom object is shown in figure 4 . The directivity representation differentiates clearly between the woven nylon tissue (strong scattering) and the plastic tube material (flat surface) .
4 . SPEED OF SOUND Speed of sound images are usually reconstructed from transmission measurements [5,6] . From reflection measurements, the speed of sound can be obtained from the analysis of A-scans measured from opposite scan directions (Fig . 5) . In the reflectivity image, the position for each scatterer is reconstructed from the measured data under the assumption of a known and constant speed of sound . A variable speed of sound, however, may result in double structures for every single scatterer in the superimposed reflectivity image . This effect is obvious for the boundary of the salt solution in figure 2 .
transducer2
transducer i
• actual position
e • o
e
{
-J
reconstructed positions
Fig . 5 Effect of varying speed of sound on scans measured from opposite directions .
1 13
H.
BARTELT
The reconstructed positions for a single scatterer x directions can he described as : x1 - (cot, )/
2 = co JO
r
and x i for opposite measuring
°
(2) xz=xd - (cotz)/2=xd with
o
4l dx
t,, t 2 : time of flight for opposite measuring directions x o : actual position of scatterer a d : distance of opposite transducers cs : assumed speed of sound
The difference of these positions is directly related to the average inverse speed of sound along the measuring direction and is independent of the actual scatterer position : xz - xi = xd - cord
<
ats7
>
(3)
where < . . > means average over po ion x . Mathematically, this distance of the reconstructed scatterer positions is obtained by a correlation operation . Sufficient overlapping of opposite A-scans is therefore necessary for this method . With the average inverse speed of sound known for different lines and different directions, the local inverse speed of sound can be calculated using methods of computed tomography, e .g ., the filtered backprojection method [12,13] . If necessary, one may further transform the local inverse speed of sound to give directly the speed of sound image . A result for the phantom object calculated from 216 different B-scans is shown in figure 6 . The region with the 20 percent salt solution which differs in speed of sound by about 8 percent from the surrounding water is clearly visible . Resolution is, however, lower compared to the reflectivity image due to the true computer tontographic reconstruction method . For this result, 216 different B-scans with an angle increment of 1 .7
Fig . 6 Inverse speed of sound image for the phantom object measured from 216 B-scans .
1 14
COMPUTATION OF DIRECTIVITY, SOUND SPEED AND ATTENUATION
Fig . 7 In-vivo measurement of a lmmail forearm . (a) Reflectivity image from 36 B-scans . (b) Inverse speed of sound image from 108 B-scans .
degree have been used . A problem will occur in practical applications if areas with strong attenuation are present in the object and no overlapping A-scans are obtained . This problem occurs, for example, in the experimental result of a human forearm in figure 7 (calculated from 108 different B-scans) . The shift measurement is more critical here because of shadow effects caused by the bones . But it is possible to differentiate in the reconstruction between fat tissue and muscle tissue . The speed itself is a valuable parameter . But it is also possible to use this information (or directly the correlation data) for correction of the double structure artifacts in the reflectivity representation . Examples are shown in figure 8 . For the phantom object, the double structures of the tube with the salt solution have vanished . In the in-vivo measurement, one can also identify several double structures whichh have been removed by the correction operation . .5 . ATTENUATION Attenuation includes all processes with energy loss such as reflection, scattering and absorption . Usually, attenuation images are obtained either by frequency analysis of reflection data or from transmission measurements [5,7,8,9] .
115
H . BARTELT
Fig . 8 Reflectivity images corrected for speed of sound variations from the calculated correlation data . (a) Phantom object (compare with figure 2b) . (b) In-vivo measurement of a human forearm (compare with figure 7a) .
From tornographic reflection measurements, information concerning attenuation can be obtained by calculating the average amplitude difference of opposite A-scans . This difference gives a measure of average attenuation along a single line . From the data of different lines and orientations, a qualitative image of local attenuation can be obtained by computed tomography . This computation of local attenuation requires a speed of sound correction as mentioned in the previous section . For simplicity, the method and its assumptions will be explained first for an object structure with constant attenuation . In this case, the ultrasonic signal will decay with penetration depth for the signals a, (z) and a,(x) measured from opposite directions : linear model : a,(x) = ao - ax a2(x) = ao - a(xo - x) exponential model : a,(x) = a oexp(-ax) a2(x) = aoexp - a(xo - x)] 1 16
(4)
COMPUTATION OF DIRECTIVITY, SOUND SPEED AND ATTENUATION
with a,, : constant a : attenuation coefficient xo : transducer distance x : actual position The average modulus of the difference of both opposite measuring directions (or its logarithm for the exponential model) gives : linear model : fo° I a,( .x) - a2(x) ( dx = axa/2 exponential model : fo° ln[a,(x)]
-ln[a2 (x)]
I-axo/2
(5)
The result is, in both cases, directly proportional to the attenuation coefficient a . In the general case, with variable attenuation coefficient a(x), a result can be obtained which is approximately proportional to the average attenuation coefficient a for small variations of a, e .g ., in the exponential model : signals :
a,(x)=aoexp[-fo a(x')dr'] a2(x) = aoexp[-fx ° a(x' )dx ' ]
modulus of the difference : ln[a,(x)] - ln[a2 (x)] I=1 -
(6)
f„ a(x')dx' - fy° a(x')dx'
-1 ax - a(x o - x) I
integration over all positions x : fu ° I a ;re - n(x o - x,) I da = kn
for small variations of a(r)
with k : proportionality constant
Fig . 9 Attenuation image for the phantom object calculated from 216 B-scans . 1 17
H.
BARTELT
Fig . 10 In-viva measurement of a human forearm . (a) Reflectivity image . (b) Attenuation image (linear model) from 216 Bscans .
Algorithms of computed tomography are then applied to these data to produce an image of local attenuation . Since we have to assume small variations of a, this method is not suitable to obtain quantitative values . It is useful, however, to give a qualitative image of the attenuation distribution . A result for the phantom object from 216 measuring directions is shown in figure 9 . The area of the castor oil ( with absorption of 0 .95 dB/am at 1 MHz [5] ) and the surface of the tube with the salt solution are represented with high attenuation . In an experimental iu-vivo measurement of a human forearm, the skin surface and the bones are reconstructed with high attenuation (Fig . 10) . These images of local attenuation can be also interpreted to display the causes of shadowing effects in the original B-scans . Shadows are an important diagnostic element in the analysis of conventional B-scans . In the superimposed tomographic reflectivity image, however, this information is averaged out and therefore not available for diagnosis . The information is, of course, contained in the original data set and can be extracted as attenuation in the described way .
1 18
COMPUTATION OF DIRECTIVITY, SOUND SPEED AND ATTENUATION
6 . CONCI,?XSIONS The methods for parameter extraction discussed here Were supposed to demonstrate the capabilities of a tomographic reflection compound scan s ystem . t t has been shown that the same set of data call be used to reconstr,sct several local parameters . Besides the improved quality of reflectivity images, this fact could be another advantage for a tomographic systern and may compensate partially for the missing real-time capability . With the knowledge of different physical parameters for the same object, further processing of the data also becomes interesting . For parameters like speed of sound and attenuation with relatively low spatial resolution, it . makes sense to combine its representation with the reflectivity image . One possibility of such a combined representation is the use of a color display system . The reflectivity as a first parameter can be coded, for example, as intensity and the second parameter (e .g. attenuation) as color saturation .
The different parameters could be also useful as a data base for further tissue characterization procedures . A combination of the data of the different parameters would allow a more complex analysis of the object structure and could improve the diagnostic value of a medical ultrasound system . ACKNOWLEDGEMENT The author would like to thank very much K .Newerla for his assistance in making measurements with the tomographic ultrasound system .
REFERENCES [1~ Robinson, B .S . and Greenleaf, J .F ., Computerized Ultrasound Tomography, in Three-Dimensional Biomedical Imaging, Vol-11, R .A .Robb, ed ., pp 58-78 (CRCPress, Boca Raton, 1985) . [2' Dines,K .A . and Goss, S .A ., Computed ultrasonic reflection tomography, IEEE Trans . UFFC-34, 309-318 (1987) .
X31 Hiller, D . and Ennert, H ., System analysis of ultrasound reflection mode computerized tomography, IEEE Trans . Sonics Uitrrasonics SU-31, 240-2 .50 (J984) . ., Hondt, F . and Maderlechner, U 4] Frie(Irid ., NT ., Europ . J . Radial . 26, 764-758 (,1982) . 5] Wells, P .N .T ., Biomedical tillcosonics (Academic Press, New York, 1977) . f6] Ophir, J ., Estimation of the speed of sound propagation in biological tissue : a beam tracking method, IEEE Tmns . Ultrasonics, Ferroelectrics Freq, Control UFFC-33, 359-368 (1986) . 17] He, P . and Greenleaf, J ., Attenuation estimation on phantoms - a stability test, Ultrasonic Imaging 8, 1245-1272 (1986) .
1 19
H.
BARTELT
[81 Parker, K .J . and Waag, R .C ., Measurement of ultrasonic attenuation within regions selected from B-scan images, IEEE Trans . Biomedical Eng . BME-30, 431-437 (1983) . [91 Duerinckx, A .J ., Ferrari, L .A ., Hoefs, J .C ., Sankar, P .V ., Fleming, D . and ColeBueglet, C ., Estimation of acoustic attenuation in liver using one megabyte of data . and the zero-crossing technique, Ultrasonics 24, 32.5-332 (1986) . [I01 Greenleaf, J .F ., Computerized tomography with ultrasound, Proc . IEEE fl, 330337 (1971) . llJ Kaveh, M . and Soumekh, M ., Computer-Assisted Diffraction Tomography, in Image Recovery : Theory and Application, pp . 369-413 (Academic Press, New York, 1987) . 11211 Devaney, A .J ., A fast filtered backpropagation algorithm for ultrasound toinography, IEEE Trans . Ultrasonics, Ferroelectrics Freq . Control UFFC-34, 330-340 (1987) . `131 Kak, A .C ., Computerized tomography with x-ray, emission andd ultrasound sources, Proc . IEEE St7, 1245-1272 (1979) .
120