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A spectral approach to ultrasonic scattering from human tissue: methods, objectives and backscattering measurements
This content has been downloaded from IOPscience. Please scroll down to see the full text. 1975 Phys. Med. Biol. 20 799 (http://iopscience.iop.org/0031-9155/20/5/009) View the table of contents for this issue, or go to the journal homepage for more
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PHYS. MED. BIOL.,
1975, VOL.20,
NO.
5, 799-815. 0 1975
A Spectral Approach to Ultrasonic Scattering from Human Tissue: Methods, Objectives and Backscattering Measurements R.
c.
c. CHIVERS,
PH.D.,M.1NST.P.) A.F.1.M.A.t and R. HILL, PH.D.,F.INST.P., M.I.E.E.
Physics Division, Institute of Cancer Research, Sutton, Surrey, U.K. Received 9 December 1974, in final form 24 March 1975
ABSTRACT.The dearth of information on the physical processes involved in the propagation of ultrasound in tissue and the growing need for such information are discussed. Thephysical nature of the ultrasonicdiagnostic process is considered in terms of a wave phenomenon and the limitations and advantages of frequency spectral analysis as a means of obtaining information are briefly analysed. A description is given of an experimental measuring system using a time-gate to select echoes scattered from a particular volume a t a depth insoft tissues. The influence of attenuation by overlying tissue and the choice of the duration of the acceptance gate on the frequency spectra obtained are considered. The paper reports some backscattering measurements on formalin-fixed samples of human fat, liver and spleen in the frequency range 0 . 5 4 0 MHz. The results suggest that theapproach may have diagnostic value in a clinical situation, in the characterization of structure in specific volumes of soft human tissue.
1. Introduction
Hithertothe development of medical pulse-echotechniques has been strongly conditioned by the implicit use of a theoretical ray model for the ultrasonic beam, in which the scale of acoustic discontinuities of interest is both discussion and considered t o be greater than the wavelength. Thus in instrumental implementation, specular reflective processes have been almost exclusively considered. It was clear, however, even from the early scans of Wild and Reid (1952)) that appreciable echoes may arise from relatively small scale tissue structure, and the recent successful demonstration of ‘grey-scale echography’ for the visualization of the fine structure of tissues (Kossoff 1974, Hill and Carpenter 1975) reinforces this conclusion. This shift in viewpoint, from the strictly ray approach one to in which interest is centred on the interaction of acoustic waves with tissue structure, may have significant implications,not only in termsof tissue visualization techniques,but also in leading to quantitative approaches to specific characterization of the tissue structure itself. Consistent qualitative comments have been made on the use of the amplitude and number of the echoes arising from a volume of one type of tissue in diagnosis ( H o m y 1965, Donald 1966, Kelly, Okuyama and Fry 1968, Damascelli, Fossata, Livraghi and Severini 1969, Deland 1969), but ~~
t Present address: Physics Department, University of Surrey, Guildford, Surrey.
800
R. C. Chivers and C . R.Hill
to date theonly quantitative approach has been the analysis of the statistical parameters of a relevant portionof the A-scan envelope (Wells,RlcCarthy, Ross and Read 1969, Mountford and Wells 1972a, b). The growing awareness of the importance of the low-level echoes in diagnosis has been reflected in instrumental developments in three ways. Firstly, the introduction of gated depth rectilinear scanning (the C-scan) and gated spiralscanning (Hill and Carpenter 1975) presupposes some useful interpretation of the information obtained. Secondly, the use of compression amplifiers to utilize fully the dynamic range of the display unit (grey-scale echography) effectively reduces the overwhelming significance of strong interfaceechoes in the B-scan and, thirdly, theuse of computers for the storage and processing of serial A- or B-scans (Fry, Leichner, Okuyama, Fry and Fry 1968, Milan 1972, Erickson and Brill 1974) is of particular value when the scans contain a large amountof information and when that information can be interpreted most efficiently in terms of biological structure and function. It is the purpose of this paper to discuss some of the theoretical and practical problems that are involved in obtaining an understanding of the physics of the interaction of acoustic waves with tissue. I n particular it considers the uses and limitations of spectral analysis for obtaining diagnostically useful information on tissue structure. 2. Thenature of the problem
Thefundamental principleunderlying pulse-echo techniquesis that of obtaininginformation a t acertaindepthin asoft-tissuestructure.If the acoustic pulse that is sent into the tissue is very short, it might be reasonable to suppose that every peak in the echo train would correspond to a reflection from adiscontinuity or t o amultiple reflection betweentwo or more discontinuities. Few commercially available diagnostic machines can offer a pulse that even approaches this ideal, the best being a t least two cycles long. Not only does this finite length introduce uncertainty as to the depthcalibration of a given signal, but it also permits the occurrence of interference phenomena between echoes from closely spaceddiscontinuities. I n principle,computing techniques should permit the shape of the pulse to be deconvoluted out of the A-scan to produce an apparently ideal train of discontinuities. To achieve this, two corrections would be necessary : firstly, a suitable time-varied gain function would be required and secondly, the shape of the pulse to be deconvoluted out of the A-scan would have to change withdepthtoaccount for dispersive absorption.Eventhen,the realpossibility of interference effects occurring would prohibitauniquesolution and thus severelylimit thefundamental nature of the information provided. The degree of refinement of the information that it may be possible to obtain from a volume of tissue cannot yet be discussed in rigorous theoretical terms because the microscopic ultrasonic physics of biological tissue in the frequency range of interest is an unwritten book. The variationof density or bulk modulus across one or more cells is unknown so that an appreciation of the size of biological structures that will be acoustically significant over regions comparable
Ultrasonic Scattering
from Tissue
801
with or smaller than thewavelength remains to be discovered. Direct measurements aredifficult because of the immense practical problems of making physical measurements on a microscopic scale, and to some extent they may be largely irrelevant when the wavelengths to be used are very much greater than the diameter of a cell. Even the gross acoustical properties of tissue that are of immediate use in diagnosis, such asthe variation of attenuation withfrequency, are very poorly catalogued (Chivers and Hill 1978). The fact remains that the signal referred to above has been observed t o originate from a volume of tissue lacking gross interfaces and thus may be considered to arise from some sort of scattering process within the tissue (Hill and Chivers 1972). Whether it is considered t o arise from a complex array of a conceptual matter whose interfaces or fromdiscretescatteringcentresis essence is that its use in diagnosis has been based on the average effect it produces on a cathode ray tube display. Its apparently random nature, which a t present is analysed visually, emphasizes its stochastic origin. The most useful quantitative approach appears to be that of measuring the scattering and then solving the inverse scattering problem (that is to say, finding the parameters of a distribution of scatterers that will give rise to a measured scattered signal). Again this will not give a unique solution but itwill provide empirical information that may be used in a diagnostic situation, even though its origin is not clearly understood (Chivers, Hill and Nicholas 1974). 3. Pulse techniquesandtimegating
Fixedfrequencycontinuous wave techniques suffer from the basic disadvantage of allowing no selection of the volume from which scattering isbeing measured.Pulsedcontinuous waves do permitthis, but arerestrictedfor in vitro work by the size of the tissue specimens that can be obtained. The depth of t'he region of scattering will be uncertain by an amount equal to the length of the pulse, so that the shorter the pulse that is used, the better the volume is defined and thesmaller the volume that can be sampled. The natural inclination is thus towards the use of the very short pulses used in pulse-echo diagnostic machines, for not only do they representt'he common source of diagnostic ultrasound, but also offer the advantages of good volume resolution so that the information obtained per and have a broad frequency spectrum pulse should be greater. I n addition t o this, a successful quantitative approach to scattering phenomena islikely to require implementation with the minimum modification of existing equipment. There is an area of some conceptual difficulty here. The shortness of the pulse is instrumental in defining the volume considered; however, its transformation into a broad frequency spectrum requires that the component pure sinusoids are of infinite extent in the time domain. The (incomplete) experimental evidence for the scattering of pulses from a single body (Hickling 1962, 1964, Chivers 1973) suggests that the process may be considered either in the time domain, or as involving a continuous distribution of pure sinusoids of infinite duration (producingacontinuousdistribution of thesteady-state sinusoidal scattering solutions).
802
R.C. Chivers and C. R.Hill
The infinite duration of sinusoids for a single body can obviously be relaxed in its rigorous sense provided that the steady stateconditions are reached and measured for all the frequencies in the range of interest. The criterion that should be adopted for steady conditions in tissue is harderto define because of the scattering that may take place on the pathbetween the transducer and the tissue volume of interest, and because of the likelihood of multiple scattering effects occurring. It is suggested that the following physical approachbe adopted until sufficient evidence is available to improve it. The volume of tissue to be considered is defined by thegeometry of the beam (i.e. the transducer) and by the delay and duration of an acceptance gate. The depth of the volume from which scattering is said to occur will then be uncertain by an amountcT where T is the pulse duration and c the wave group velocity in tissue (c is assumed to be constant and independent of frequency in the first approximation). The spectral representation of the pulse will be considered valid, subject to the proviso that the limitation on the duration of pure sinusoids is the duration of the gate, r . Thus, provided the time for which the gateis open is much longer than theperiod of the frequencies concerned, the conditions may be considered similar to those for continuous waves. As the period of the lowest frequency components approachesr , the significance of any spectral analysis that can be performed a t these frequencies becomes severely limited. Kharkevich (1960) suggests that a limitation of At on a signal may lead to an uncertainty in the frequency Af given by
Af At
0.048
where the equalityindicates the optimum choice of functions. One of the present authors (Chivers 1973) has estimated the resolution Af that can be associated with a gate length r when considering broad spectra to be given by
provided that the lowest frequency of interest fo is such that
r
l/fo.
4. Transducer response
The importance of the transducer in the measurements is not restricted to the simple idea that its diameter defines the volume from which scattering is measured. For steadystate conditions, theshape of the volume defined depends on whether the acceptance gate lies in thenear-field or the far-field of the transducer. The distinction between these two regions is by no means as clear for short pulses as it is for continuous wave excitation, since the interference phenomena which combine to produce the near-field distribution may be prevented bythe shortness of the pulse. Even if the differing suggestions for the position of the start of the far-field were resolved, the position would still depend on frequency. For a short pulse, with a broad frequency spectrum, its position will become uncertain, unless an approach like that of Robinson, Lees and Bess (1975) is followed, whereby it is placed as for the classical theory with a frequency of 1/2T, where T is the pulse duration (Chivers 1973).
Ultrasonic Scattering
from Tissue
803
Since the radiation pattern of a transducer is dependent on frequency, it is likely that the spectrum of radiation emitted by a pulsed transducer will vary with position in the radiation field. Christie (1962) provides evidence for this by showing that the pulse shape varies from one point to another in the field. Fig. 1 shows the spectrum of a short acoustic pulse reflected from a plane flat
:,:h
Vertical lOdB scate +IO
Angle ofo rotation
-30
2.0
4.0
6.0 Frequency [MHz)
2.0
4.0
6.0 Frequency (MHz)
- 60
-804
, , , , , ,
4.0 2.0
-30
40
, , , 6.0 Frequency(MHz1
3
P o
-70
2.0
4.0
6.0 Frequency (MHz)
Fig. 1. Spectra of the echo from a plane reflector rotated in front’of a ‘4 MHz’ transducer, about an axis in the planeof the transducer face.
target that has been rotated in front of a 4 MHz transducer, about an axis of symmetry in the circular transducer face. The spectral radiation pattern of a pulsed transducer is difficult to measure since the use of another transducer, as in Christie’s work, involves the directionality and frequency response of the monitoring probe, while the use of a small target such as a small sphere is complicated by the fact that it may well not be an omnidirectional reflector at all frequencies (Chivers 1973). 5. Angular scatter and backscatter
One geometrical arrangement that can be used with a plane parallel-sided specimen is shown in fig. 2. The section of the wavefront that sets out from the centre of the transmitting transducer, and as a result of the scattering process
R.C.Chivers and C. R.Hill
804
arrives at the centre of the receiving transducer, takes a time ( x + r ) / c (where c is the velocity of sound, x the distance along the receiver axis to the point of scattering and r the distance from the scattering centre t o the centre of the Tissue
Tissue
U
I cm
Fig. 2. Time-gated angular scattering geometry with z = 4 cm, r = 4 cm, e = 10 and 40”. (C = 1500 m s-l.)
T
=8
PS
and
receiving transducer). If the acceptance gate is timed to open as this wavelet the scattering arrives, the delay will be ( z + r ) / c . To afirstapproximation centres for the wavelets that arrive as the gate opens lie on an ellipsoid whose axis of symmetry is theline joining its foci, the centres of the two transducers. The length of its semi-axes are given by
a’
= fr(z + r )
and b‘
= [+?x(
1 -COS
e)]*.
Allowing the signals an extra timer , equal t o the gate duration, to arrive gives, as a locus for the scattering centres of the last scattered signals t o be included in the gate, anellipsoid confocal with the first having semi-axes
a” = fr(z + r + C T ) = a’ + frcr and = fr[czTz =
( $c2 T 2
+ 2rz(1- cos e) + 2CT(Y + z)l+ + CTa‘ + b”)’.
The major axes of these ellipsoids (a’ and a”)are independent of the scattering angle. This has been achieved by stipulating that the gateshould open after a time ( r + z ) / c . If it opens a t any other time, the loci of initial and final signals received will still be given by two confocal ellipsoids, but the ‘direct path’ of fig. 2 will not necessarily be included in them.
Ultrasonic Scattering
from Tissue
805
For a scattering event to contribute to the gated signal, it is only necessary for its time of travel to be between ( r + .)/c and ( T + .)/c + T ; it does not matter where the points of emission and reception are on the two transducers. The relevant ellipsoids for the twogiven pointswill have the same semi-axesas those given above, but the foci will be at thepoints of emission and reception on the transducer faces. The quality of the approximation of taking the ellipsoids focused at the centres of the transducers increases as their diameters decrease compared t'o (T + z ) . Fig. 2 shows that there is a limit on the angularresolution that can be obtained imposed by thegeometry of the scattering situation. This can beestimatedby drawingorcalculation.(Multiplescattering events, whereby a wavelet is scattered a t two points in the tissue before reaching the receiving transducer within theopening time of the gate, are assumed to provide a negligible contribution in this discussion. That this is a reasonable assumption is suggested by thelow overall scattered amplitudesbut itis a questionthat will require further attention.) Measurement of angular scatter using two transducers is thus seen to be difficult t o achieve in practice since it requires a detailed knowledge of the transducer radiation patt'erns, refract'ion effects, and a measurement over an awkwardly shaped volume. Theawkw7ardness of the shapeof this volume can be partly removed using a symmetrical transducer arrangement as in fig. 3, and Tissue
'ed gate
Tissue
Fig. 3. Symmetrical transducer arrangement for angular scattering, with f? = 40' and T = 2 and 8 p . (c = l500 m S-l.)
2
= r = 4 cm,
relyingontime-gating to specify the scatteringangle.The poor angular resolution and signal-to-noise ratio obtainable with this arrangement, unless thin specimens and wide angle transducers are used (bringing with them their own problems), militate against its implementation.
R.C. Chivers and C. R.Hill
806
If only one transducer is used (i.e. e = 180" in figs 2 and 3), the ellipsoids become concentric spherical shells separated by a distance BCT, as shown in fig. 4. For any element included in this volume, the backscattered spectrum, S(f),is in principle given by
S(f)= E S (f)exp ( 2 x H ( f ) ) Ro(f 1 where
S , is the measured backscattered spectrum, R, is the loop frequency response of the transducer, x is the depth of the element in the tissue, H is the attenuation per unit length of the tissue and E
is a correction for transmission across the boundary.
The total backscattered spectrum will be the sum of these elements over the volume defined by the transducer and the acceptance gate. The effect of these factors in a practical situation is discussed in the following sections.
Tissue
Icm
Fig. 4. Backscattering geometry (0 = 180') for z = r = 4 cm,
T
=8
p.
(c = 1500 m s-l.)
6. Experimentalarrangement
The details of the experimental arrangement used for our investigations have been discussed elsewhere (Chivers 1973, Chivers et al. 1974). Its essential componentswere:a pulse-echo A-scope, atime-gate t o select the signal originating from a chosen depth in the tissue sample and a spectrum analyser. The volume from which the scattering may be considered t o have arisen is determined by thegeometry of the transducerbeam and thedelay and duration of the gate. For the results reported, the transducerswere found t o produce a constant spectral output over the face of a flat reflecting target (of any size greater thanthat of the transducerface).Thevariationmeasured was i 0.5 dB for distances ranging from1 to 8 cm in frontof the transducer, andfor a broad range of frequencies for each transducer. Table 1 gives the nominal frequencies, diameters andspectral ranges of the transducers used, all of which were probes bought for use with a commercial B-scan equipment.
Ultrasonic Scattering
from Tissue
807
On the basis of these measurements, and others takenon the variation of the spectral response of the transducer as the targetwas rotated out of the beam, thetransducer beams were assumed to be well collimated, an assumption Table 1. Nominal frequency, diameter and bandwidth of transducers
I
l
I
I
Effective bandwidth (MHz)
(MHz)
0.6-1.4 1.0-2.5 1.6-2.8 3.0-6.0
20 15 15
1.5 2.0
4.0
%
40 43 27 33 I
I
I
I
consistentwith the fact that allmeasurements were madewithinwhat is traditionallytakento be the near-field of thetransducers.Theaveraging involved in the scattering measurements (arising from the finite diameterof the transducer and the finite duration of the acceptance gate) is not disadvantageous in that the signal being analysed is essentially stochastic, and some form of averaging is necessary to define relevant parameters. The use of an averaging system that iscapable of immediateapplicationin a clinical situation has obvious merit. The practical implications of the time-gating on the spectral analysis are discussed later (section 7 ) . Fig. 5 illustrates the derivation of the required spectrum. An electrical input E , to the transducer produces a corresponding acousticaloutput A,. Similarly Tissue
Plane
reflector
Transducer
rL -
Gate delay
Fig. 5 . Scattering signal geometry.
an acoustical input A , to the transducer produces a corresponding electrical output E,, but thespectral transfei functionsfor emission and reception are not necessarily identical. The reflection from a plane reflecting target provides a measure of the loop spectral response of the transducer, provided that the reflection is assumed to be anharmonic and that a correction is made to the level of signal returned to take account of imperfect reflection by the target (the attenuation in water is assumed to be negligible). The polished Perspex targets used for these experiments produce an echo that is 8.7 dB below that from a perfect reflector (Wells 1969). The E, and A , are spectral functions,the
R.C. Chivers and C. R.Hill
808
latter being spatialfunctionsas well, although the method of defining the useable bandwidths of the transducers described above and summarizedin table 1 has removed this dependence as a practical consideration. The signal acceptedby a gate set a distance ct inside a tissue specimen (where c is the group velocity of sound in the tissue) and of duration T will, in a first approximation, give rise to an acoustical signal at thetransducer of amplitude A,
s(f)
= C 2 ( t f& T ) 2H z(!)T2Al(f)
(1)
where
H (f ) is the attenuation per unit distance travelled in the tissue,
T is the transmission coefficient at the water tissue boundary, S(f)is the signal scattered from the shaded volume of fig. 1, A , ( f ) is the amplitude of the interrogating signal emitted by the transducer, and f is the frequency.
If there is no tissue present, thesigna'l from the reflector only isAT(!) = A,( f )R where R is the reflection coefficient of the target (assuming the attenuation in the water bath at 18 'c t o be negligible). Taking the ratio of the gated signal and thereference signal A,( f ), we obtain the measured scattering function
For most tissues, T 2 - 0.1 dB and is negligible, but this is not the case for the attenuation term H 2 ( f ) . Good attenuation measurements are thus seen to be a prerequisite for analysing scattering measurements. 7. The effect of the time-gate
The existence of the selection gate canmanifest itself in the measured spectra in three ways. In the first place the existence of a DC pedestal in the gate will affect both the level and form of the spectrum observed, as can be seen in fig. 6 ( a ) . Even when the pedestal represents only 4% of the 2 V peak to peak of the RF pulse, its presence can be detected. As it isincreased to 15%, a markedsinusoidal oscillation withfrequencyisobserved.Thefrequency of these oscillat'ions with frequency (a quantity having the dimension of time for which the name 'ffrequency' has been suggested (Chivers 1973)) is seen to be 12 p , corresponding to the length of the gate. Any periodicity (or the obvious presence of one or more ffrequencies) in the scattering spectra can be immediately related to a distance correlation since, with c constant, distance is proportional t o time. The second effect of the gate on the spectrum can be seen in fig. 6 ( b ) where the duration of the gate has been successively decreased. Initially the effect is negligible, but as the gate rejects more of the energy in the pulse, the peak level of the spectrum decreases. Accompanying this expected amplitudedecrease is a deterioration of the resolution obtained inthe spectrum. In thelimit, where the gate duration represents onlyafraction of a cycle of the mostprominent
Ultrasonic Scattering
from Tissue
809
frequency present in the RF pulse, it is almost impossible to say what that frequency is. The thirdeffect of using a time-gate in this context derives from the natureof the signals being investigated. If the signal of interest is essentially finite in
Fig. 6. Effect of (a)gate pedestal and ( b ) gate length on the spectra obtained with a ‘2 MHz’ transducer. (a)theffequency of the oscillations introduced by the pedestal is seen to be very close to 12 p , the length of the acceptance gate used. No oscillations can be observed onthe main spectral peaks because the totalsignal level was causing the analyser to saturate. ( b ) A s the gate length decreases, the higher ffrequencies disappear and the signal level decreases.
time (e.g. the echo from a plane reflector), and lies entirely within the gate, the length of the gate is irrelevant provided i t is longer than the signal and the signal is entirely within it. However, if the signal is longer than the gate, the gate mustaffect the spectrum obtained. If the scattered signal is s(t) and the gate opens for a time r , the resulting signal out of the gate is s ( t ) g ( t ) where g ( t ) = 1, O < t < T = 0 otherwise. Taking the Fourier transform of this product, we obtain a convolution 2 W17 9(0)* 3 ( ~ = ) Y(w-o,)-Ssin-dw, (3) 01 2
::1
R.C. Chivers and C. R.Hill
810
whence the scattering spectrum displayed can be seen to be implicitly related to the gate length in such a way as to preclude easy calculation of Y ( w ) ,the scatteringfunction, andthe relatedbackscattering cross-section. Although thisputsfundamentalinformationout of reach a t present,comparative empiricalstudiescanbe made, provided that the gate parametersremain constant, and may be of use in a clinical situation. 8. Backscatteringmeasurements
Measurements have been made on pairs of fixed samples of human fat, liver and spleen, and one sample of fresh porcine liver. The gate duration was fixed a t 8 p , the delay being adjusted so that the gate accepted signals returning more than 10 ps after the reflection from the water-tissue interface, thereby allowing time for this last reflection t o die away before the scattered signals were selected. The spectra were recorded on Polaroid film, enlarged and traced before data were taken from them, the total errorsinvolved in these processes were taken over being 5 0.5 dB. With each transducer three measurements different regions within each sample. The IF filter of the analyser was set to a width of 100 kHz for all spectra except those for which the ‘4MHz’ transducer was used, where a filter width of 300 kHz was chosen. Points were read off the tracings a t intervals corresponding to the appropriate filter width. The effect of the IF filter is twofold; not only does it smooth the display, hiding some of the effects of the convolution discussed above, it also affects the level of the signalobservedin the spectrum. Provided that thescanned spectrum is broad comparedto thewidth of the filter (Chivers 1973) the level of the signal is directly proportional to the filter width. For the convoluted scattering spectra, this proportionality is only a crude first approximation. However, for the reference spectra the approximation is much more accurate and account mustbe taken of the filter widths used when comparing two reference spectra or a reference spectrum with a scattered spectrum. Fig. 7 shows the spectrum backscattered from a piece of fat compared to the reference spectrum from a plane target. Of immediate interest is the relative
.-.-c .-
v)
V
b (D
V 0
Frequency (MHz)
Fig. 7. Backscatteringfrom (‘4 MHz’ transducer).
fixed humanfat
compared t o the reference spectrum
Ultrasonic Scattering
from Tissue
81 1
complexity of the scattered spectrum compared to the reference, the direct result of gating a continuous signal. The occurrence of peaks a t approximately 125 kHz suggests the presence of a ffrequency of 8 p , the length of the gate. Fig. 8 shows the actual spectra recorded for the two samples of fixed human liver and the one sample of fresh porcine liver. The difference of almost 20 dB Human liver A
Human liver B
-
+io0-10-
-
-
-30-
S
0-
Y
?
d
-
tio-
-l0:
Porclne llver
-:A I
":-
-:
1
I
l
1
-
1
1
1
I
l
I
1
I
I
-
l
1
I
I
I
3.'0
410
5.0
$ -mm
I
+ io-
0-
I
l
I
I
I
-10-
-
-30I
2.0
I
l
6.0
I
20
I
3.0
I
4 0
l
5.0
1
6.0
I
20
I
3.0
I
4.0
I
5.0
1
6.0
Frequency ( M H z )
Fig. 8. Backscattering spectra fromfixed human and fresh porcine liver. Filter width 300 kHz, gate length 8 p, transducer '4 MHz'.
on the peak level of scattering is very strong and supports the idea of distinguishing gross differences in tissuestructure, anidea that is given more practical credence by the comparison of the spectra from the two fixed liver samples. Their spectral peaks are at approximately the same level, but the occurrence of a peak a t about 2.5 MHz in all the pictures from specimen A and theabsence of a corresponding peak in the spectra from specimen B, although possibly fortuitous, is stronglysuggestive of a difference in composition between the two specimens. The comparison of different types of tissue does not yield such simple criteria fordifferentiation (fig. 9). Thepeak level of scattering for spleen and fat appears to be consistently higher than that from the liver by between 2 and 5 dB. The dual peak structure of the liver spectrum is notso prominent in fat, slightly more high and difficult t o detectin spleen tissue, thelasthaving frequency components than either of the other two tissues. A comparison of this sort is based on the premise that the attenuation function H ( f ) may be considered to be the same for all the tissues being considered. The attenuation coefficients for the samples of tissue have been reported elsewhere (Chivers and Hill 1975) and, to a first approximation, the assumption is valid. Application
R.C. Chivers and C. R.Hill
812
of the individual attenuation coefficients requiresdigitalization and deconvolution of the data presented in these figures, as discussed earlier (section 6). The comparison of spectra from different tissues, while experimentally convenient, lacks therelevance to a clinical situation of the comparison of different samples of the same tissue.
+IO-
0-10-
-
-30-
+io-
t
t
0-10-
-
-30+IO-
0-10-
-
-30-
Fig. 9. Backscattering spectra fromfixed liver, spleen and fat. Filter width 300 kHz, gate length 8 p, transducer '4 MHz'.
Conclusion The discussion presented inthis paper is areview of the complexities involved in the ultrasonic diagnostic process with particular reference to the spectral analysis of scattered energy for use as a diagnostic tool. As such it lays a basis for future work in this difficult but potentially rewarding field, indicating problems to be overcome. Theonly some of thepracticalandconceptual tractable scattering situationis seen to be that in which measurements of backscattering are made. These have the advantage of requiring a minimum of modification of present pulse-echo diagnostic machines forimplementation when the success of the technique has been established. Backscattering measurements from different types of fixed tissue have been reported and compared. The use of such measurements is illustrated in fig. 10. Having located the volume of interest in a patient, the A-scan is gated out, the signal accepted bythegate being Fouriertransformed. Atthisstage two directions of investigation are open. These simple measurements of the spectra of time-gatedscattering,albeit complicated bytheintrusion of thegate duration, may very well provet'o be capable of exploitationindiagnostic 9.
Ultrasonic Scattering
Tissue from
813
situations on an empirical basis (Chivers et al. 1974), although the problems involved in making such comparisons are likely to be severe for work in vivo. Alternatively the spectra may be deconvoluted by computer to obtain the relevantbackscatteringcross-section. These can be compared with less ambiguity in order t o provide an empirical approach to tissue differentiation. B . scan locates volume of
interest
I A - scan gated out at relevant place Gated A - scan i! Fourier transformed
\ \\
Histology
Fig. 10. Uses of backscattering measurements in medical ultrasonics.
The backscattering cross-section has three further uses. In the first place the evaluation of scattering cross-sections and their dependence on frequency should enable assessment to be made of the scale of the structures of acoustic significance in thescattering process, and thushelp t o delineate the fundamental limitations of ultrasonic diagnosis. Secondly, knowledge of the frequency dependence of both the attenuation and the total scattering will permit calculation of the dependence of the absorption on frequency,and thusenable absorption mechanisms to be discussed innumericalterms.Thirdly, and more remotely, the backscattering cross-sections may conceivably, by the mediation of theory, be linked to macroscopic histology. The present paper shows that, although the difficulties of obtaining fundamental information from backscattering are great, there is evidence from a limited number of measurements that a relationship exists between the structure of a tissue and the signal it scatters back t o the transducer; a relationship that may be quantified and one that should be investigated further. Comparison of results will only be possible if the following parameters are included in a discussion of the measurements : the loop spectral response and effective bandwidth of the transducers, the gate duration, the depth in tissue the at which the IF filter setting of the spectrum analyser. gate opens and the One of the authors(R. C. C.) would like t o thank the Royal Marsden Hospital Physics Division of the Institute of Cancer Research, Sutton, Surrey, with the support and encouragement of Professor J. W. Boag. for financial support for this work, which was carried outinthe
814
R.C. Chivers and C. R.Hill RESUME
Approche spectrale L la dispersion ultrasonore des tissus humains: Mhthodes, Objectifs et mesures de dispersion B rebours La penurie d’informationssur les procedes physiques entrant dans lapropagation des ultra-sons dans les tissus, et le besoin croissant pour de telles informations sont discut6s. On considhe la nature physique du procede de diagnostic ultrasonique en termes de phenombne d’ondes et l’on analyse sommairement les limitations et avantages de l’analyse spectrale des frequences comme moyen d’obtention des donnees. I1 parait une description d’un systbme de mesure exp6rimental utilisant un appareil selecteur It temps de comptage pour selectionner les 6chos disperses dans un certain volume de tissus mous It une profondeur donnee. L’influence de l’amortissement par les tissus surja cents et le choix de la duree de la selection sur les spectres de frequences obtenus sont considAr6s. Le memoire rapporte des mesures de dispersion B rebours sur des Achantillons fixes dans le formol de tissus gras humains, tissus defoie et de rate, dansla gamme des frequences de 0,5 B 5 MHz. Les resultats suggbrent que l’approche peut avoir une valeur diagnostique en clinique, dans la caracterisation de lastructure dansdes volumes specifiques de tissus humainsmous.
ZUSAMMENFASSUNG Untersuchungen des Spektrums von Ultraschall-Riickstreuungen in menschlichen Gewebeteilen : Methoden, Ziele und Ergebnisse von Riickstrahlungsmessungen Des mangelnde Wissen iiber die physikalischen Vorgange bei der Ausbreitung von Cltraschall in Gewebeteilen und die steigende h’otwendigkeit diesbeziiglicher Kenntnisse werden besprochen; die physikalischen Aspekte der Ultraschalldiagnose mit Hilfe der Wellenerscheinungen betrachtet, und Grenzen und Vorteile der Analyse des Frequenzspektrums auf der Suche nach verschiedenen Auskiinften kurz analysiert. Ein experimentelles Messsystem mit Zeitintervalltor zur selektiven Wahl des Echos von einem bestimmten Volumen weicher Gewebeteile in bestimmter Tiefe wird beschrieben; der Einfluss der Abschwachung durch dariiberliegende Gewebeteile so wie der Zeitintervalleinstellung des Tores auf das Frequenzspektrum betrachtet ; und einige Widerhallmessungen a n formalinfixierten Proben menschlicher Fett-, Leber- und Milzteile im Frequenzbereich zwischen 0,5 und 5 MHz vorgelegt. Die Ergebnisse lassen auf diagnostische Moglichkeiten in klinischen Fallen durch Charakterisierung der Struktur spezifischer Teile menschlichen Gewebes schliessen.
REFERENCES CHIVERS,R.C., 1973, Ph.D. Thesis, University of London. CHIVERS,R.C., and HILL,C. R.,1975, Ultrasound X e d . Biol., in press. CHIVERS,R. C., HILL,C. R.,a n d NICHOLAS,D., 1974, i n Ultrasonics in Medicine, Ed. de Vlieger et al. (Amsterdam: Excerpta Medica) pp. 300-303. CHRISTIE,D. G., 1962, A p p l . Mat. Res., 1, 86. DAMASCELLI, B., FOSSATA, F., LIVRAGHI,T., a n d SEVERINI,A., 1969, Am. J . Roentg., 105, 428.
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DELAND, F. H., 1969, Am. J . Roentg., 105, 446. DONALD, I., 1966, Ultrasonics, 4, 119. ERICKSON, J. J., and BRILL,A. B., 1970, Radiology, 95, 589. FRY,W. J., LEICHNER, G. H., OKWAMA,D., FRY,F. J., and FRY,E. K., 1968, J . Acoust. Soc. Am., 44, 1324. HICKLING, R. D., 1962, J . Acoust. Soc. Am., 34, 1582. HICKLINO, R. D., 1964, J . ACOUB~. Soc. Am., 36, 1124. HILL, C. R., and CARPENTER,D. A., 1975, B r . J . Radiol, in press. HILL, C. R., and CHIVERS,R. C., 1972, in Ultrasonics in Biology and Medicine, Ed. L. Filipczynski (Warsaw: Polish Scientific Publishers) p. 119-123. HOWRY,D. H., 1965, Radiol. Clins N . Am., 3, 433. KELLY, E., OKUYAMA,D., and FRY,F. J., 1968, in Proc. 6th Int. Conf. on Acoustics, Tokyo, paper "1-1. KHARKEVICH, A. A., 1960, Spectra and Analysis (New York: Consultants Bureau). KOSOFF,G., 1974, Proc. R. Soc. Med., 67, 135. MILAN, J., 1972, B r . J . Radiol., 45, 911. MOUNTFORD,R. A., and WELLS,P. N. T.,1972a, Phys. Med. Biol., 17, 14. MOUNTFORD,R. A., and WELLS,P. N. T.,1972b, Phyla. Med. Biol., 17, 261. ROBINSON, D. E., LEES,S., and BESS,L., 1975, in press. WELLS,P. N. T.,1969, Physical Principles of Ultrasonic Diagnosis (New York: Academic Press). WELLS,P. N. T.,MCCARTHY,C. F., Ross, F. G. M,, and READ,A. E. A., 1969, Br. J . Radiol., 42, 818. WILD,J. J., and REID, J. M., 1952, Am. J. Path., 28, 839.
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A spectral approach to ultrasonic scattering from human tissue: methods, objectives and backscattering measurements
This content has been downloaded from IOPscience. Please scroll down to see the full text. 1975 Phys. Med. Biol. 20 799 (http://iopscience.iop.org/0031-9155/20/5/009) View the table of contents for this issue, or go to the journal homepage for more
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PHYS. MED. BIOL.,
1975, VOL.20,
NO.
5, 799-815. 0 1975
A Spectral Approach to Ultrasonic Scattering from Human Tissue: Methods, Objectives and Backscattering Measurements R.
c.
c. CHIVERS,
PH.D.,M.1NST.P.) A.F.1.M.A.t and R. HILL, PH.D.,F.INST.P., M.I.E.E.
Physics Division, Institute of Cancer Research, Sutton, Surrey, U.K. Received 9 December 1974, in final form 24 March 1975
ABSTRACT.The dearth of information on the physical processes involved in the propagation of ultrasound in tissue and the growing need for such information are discussed. Thephysical nature of the ultrasonicdiagnostic process is considered in terms of a wave phenomenon and the limitations and advantages of frequency spectral analysis as a means of obtaining information are briefly analysed. A description is given of an experimental measuring system using a time-gate to select echoes scattered from a particular volume a t a depth insoft tissues. The influence of attenuation by overlying tissue and the choice of the duration of the acceptance gate on the frequency spectra obtained are considered. The paper reports some backscattering measurements on formalin-fixed samples of human fat, liver and spleen in the frequency range 0 . 5 4 0 MHz. The results suggest that theapproach may have diagnostic value in a clinical situation, in the characterization of structure in specific volumes of soft human tissue.
1. Introduction
Hithertothe development of medical pulse-echotechniques has been strongly conditioned by the implicit use of a theoretical ray model for the ultrasonic beam, in which the scale of acoustic discontinuities of interest is both discussion and considered t o be greater than the wavelength. Thus in instrumental implementation, specular reflective processes have been almost exclusively considered. It was clear, however, even from the early scans of Wild and Reid (1952)) that appreciable echoes may arise from relatively small scale tissue structure, and the recent successful demonstration of ‘grey-scale echography’ for the visualization of the fine structure of tissues (Kossoff 1974, Hill and Carpenter 1975) reinforces this conclusion. This shift in viewpoint, from the strictly ray approach one to in which interest is centred on the interaction of acoustic waves with tissue structure, may have significant implications,not only in termsof tissue visualization techniques,but also in leading to quantitative approaches to specific characterization of the tissue structure itself. Consistent qualitative comments have been made on the use of the amplitude and number of the echoes arising from a volume of one type of tissue in diagnosis ( H o m y 1965, Donald 1966, Kelly, Okuyama and Fry 1968, Damascelli, Fossata, Livraghi and Severini 1969, Deland 1969), but ~~
t Present address: Physics Department, University of Surrey, Guildford, Surrey.
800
R. C. Chivers and C . R.Hill
to date theonly quantitative approach has been the analysis of the statistical parameters of a relevant portionof the A-scan envelope (Wells,RlcCarthy, Ross and Read 1969, Mountford and Wells 1972a, b). The growing awareness of the importance of the low-level echoes in diagnosis has been reflected in instrumental developments in three ways. Firstly, the introduction of gated depth rectilinear scanning (the C-scan) and gated spiralscanning (Hill and Carpenter 1975) presupposes some useful interpretation of the information obtained. Secondly, the use of compression amplifiers to utilize fully the dynamic range of the display unit (grey-scale echography) effectively reduces the overwhelming significance of strong interfaceechoes in the B-scan and, thirdly, theuse of computers for the storage and processing of serial A- or B-scans (Fry, Leichner, Okuyama, Fry and Fry 1968, Milan 1972, Erickson and Brill 1974) is of particular value when the scans contain a large amountof information and when that information can be interpreted most efficiently in terms of biological structure and function. It is the purpose of this paper to discuss some of the theoretical and practical problems that are involved in obtaining an understanding of the physics of the interaction of acoustic waves with tissue. I n particular it considers the uses and limitations of spectral analysis for obtaining diagnostically useful information on tissue structure. 2. Thenature of the problem
Thefundamental principleunderlying pulse-echo techniquesis that of obtaininginformation a t acertaindepthin asoft-tissuestructure.If the acoustic pulse that is sent into the tissue is very short, it might be reasonable to suppose that every peak in the echo train would correspond to a reflection from adiscontinuity or t o amultiple reflection betweentwo or more discontinuities. Few commercially available diagnostic machines can offer a pulse that even approaches this ideal, the best being a t least two cycles long. Not only does this finite length introduce uncertainty as to the depthcalibration of a given signal, but it also permits the occurrence of interference phenomena between echoes from closely spaceddiscontinuities. I n principle,computing techniques should permit the shape of the pulse to be deconvoluted out of the A-scan to produce an apparently ideal train of discontinuities. To achieve this, two corrections would be necessary : firstly, a suitable time-varied gain function would be required and secondly, the shape of the pulse to be deconvoluted out of the A-scan would have to change withdepthtoaccount for dispersive absorption.Eventhen,the realpossibility of interference effects occurring would prohibitauniquesolution and thus severelylimit thefundamental nature of the information provided. The degree of refinement of the information that it may be possible to obtain from a volume of tissue cannot yet be discussed in rigorous theoretical terms because the microscopic ultrasonic physics of biological tissue in the frequency range of interest is an unwritten book. The variationof density or bulk modulus across one or more cells is unknown so that an appreciation of the size of biological structures that will be acoustically significant over regions comparable
Ultrasonic Scattering
from Tissue
801
with or smaller than thewavelength remains to be discovered. Direct measurements aredifficult because of the immense practical problems of making physical measurements on a microscopic scale, and to some extent they may be largely irrelevant when the wavelengths to be used are very much greater than the diameter of a cell. Even the gross acoustical properties of tissue that are of immediate use in diagnosis, such asthe variation of attenuation withfrequency, are very poorly catalogued (Chivers and Hill 1978). The fact remains that the signal referred to above has been observed t o originate from a volume of tissue lacking gross interfaces and thus may be considered to arise from some sort of scattering process within the tissue (Hill and Chivers 1972). Whether it is considered t o arise from a complex array of a conceptual matter whose interfaces or fromdiscretescatteringcentresis essence is that its use in diagnosis has been based on the average effect it produces on a cathode ray tube display. Its apparently random nature, which a t present is analysed visually, emphasizes its stochastic origin. The most useful quantitative approach appears to be that of measuring the scattering and then solving the inverse scattering problem (that is to say, finding the parameters of a distribution of scatterers that will give rise to a measured scattered signal). Again this will not give a unique solution but itwill provide empirical information that may be used in a diagnostic situation, even though its origin is not clearly understood (Chivers, Hill and Nicholas 1974). 3. Pulse techniquesandtimegating
Fixedfrequencycontinuous wave techniques suffer from the basic disadvantage of allowing no selection of the volume from which scattering isbeing measured.Pulsedcontinuous waves do permitthis, but arerestrictedfor in vitro work by the size of the tissue specimens that can be obtained. The depth of t'he region of scattering will be uncertain by an amount equal to the length of the pulse, so that the shorter the pulse that is used, the better the volume is defined and thesmaller the volume that can be sampled. The natural inclination is thus towards the use of the very short pulses used in pulse-echo diagnostic machines, for not only do they representt'he common source of diagnostic ultrasound, but also offer the advantages of good volume resolution so that the information obtained per and have a broad frequency spectrum pulse should be greater. I n addition t o this, a successful quantitative approach to scattering phenomena islikely to require implementation with the minimum modification of existing equipment. There is an area of some conceptual difficulty here. The shortness of the pulse is instrumental in defining the volume considered; however, its transformation into a broad frequency spectrum requires that the component pure sinusoids are of infinite extent in the time domain. The (incomplete) experimental evidence for the scattering of pulses from a single body (Hickling 1962, 1964, Chivers 1973) suggests that the process may be considered either in the time domain, or as involving a continuous distribution of pure sinusoids of infinite duration (producingacontinuousdistribution of thesteady-state sinusoidal scattering solutions).
802
R.C. Chivers and C. R.Hill
The infinite duration of sinusoids for a single body can obviously be relaxed in its rigorous sense provided that the steady stateconditions are reached and measured for all the frequencies in the range of interest. The criterion that should be adopted for steady conditions in tissue is harderto define because of the scattering that may take place on the pathbetween the transducer and the tissue volume of interest, and because of the likelihood of multiple scattering effects occurring. It is suggested that the following physical approachbe adopted until sufficient evidence is available to improve it. The volume of tissue to be considered is defined by thegeometry of the beam (i.e. the transducer) and by the delay and duration of an acceptance gate. The depth of the volume from which scattering is said to occur will then be uncertain by an amountcT where T is the pulse duration and c the wave group velocity in tissue (c is assumed to be constant and independent of frequency in the first approximation). The spectral representation of the pulse will be considered valid, subject to the proviso that the limitation on the duration of pure sinusoids is the duration of the gate, r . Thus, provided the time for which the gateis open is much longer than theperiod of the frequencies concerned, the conditions may be considered similar to those for continuous waves. As the period of the lowest frequency components approachesr , the significance of any spectral analysis that can be performed a t these frequencies becomes severely limited. Kharkevich (1960) suggests that a limitation of At on a signal may lead to an uncertainty in the frequency Af given by
Af At
0.048
where the equalityindicates the optimum choice of functions. One of the present authors (Chivers 1973) has estimated the resolution Af that can be associated with a gate length r when considering broad spectra to be given by
provided that the lowest frequency of interest fo is such that
r
l/fo.
4. Transducer response
The importance of the transducer in the measurements is not restricted to the simple idea that its diameter defines the volume from which scattering is measured. For steadystate conditions, theshape of the volume defined depends on whether the acceptance gate lies in thenear-field or the far-field of the transducer. The distinction between these two regions is by no means as clear for short pulses as it is for continuous wave excitation, since the interference phenomena which combine to produce the near-field distribution may be prevented bythe shortness of the pulse. Even if the differing suggestions for the position of the start of the far-field were resolved, the position would still depend on frequency. For a short pulse, with a broad frequency spectrum, its position will become uncertain, unless an approach like that of Robinson, Lees and Bess (1975) is followed, whereby it is placed as for the classical theory with a frequency of 1/2T, where T is the pulse duration (Chivers 1973).
Ultrasonic Scattering
from Tissue
803
Since the radiation pattern of a transducer is dependent on frequency, it is likely that the spectrum of radiation emitted by a pulsed transducer will vary with position in the radiation field. Christie (1962) provides evidence for this by showing that the pulse shape varies from one point to another in the field. Fig. 1 shows the spectrum of a short acoustic pulse reflected from a plane flat
:,:h
Vertical lOdB scate +IO
Angle ofo rotation
-30
2.0
4.0
6.0 Frequency [MHz)
2.0
4.0
6.0 Frequency (MHz)
- 60
-804
, , , , , ,
4.0 2.0
-30
40
, , , 6.0 Frequency(MHz1
3
P o
-70
2.0
4.0
6.0 Frequency (MHz)
Fig. 1. Spectra of the echo from a plane reflector rotated in front’of a ‘4 MHz’ transducer, about an axis in the planeof the transducer face.
target that has been rotated in front of a 4 MHz transducer, about an axis of symmetry in the circular transducer face. The spectral radiation pattern of a pulsed transducer is difficult to measure since the use of another transducer, as in Christie’s work, involves the directionality and frequency response of the monitoring probe, while the use of a small target such as a small sphere is complicated by the fact that it may well not be an omnidirectional reflector at all frequencies (Chivers 1973). 5. Angular scatter and backscatter
One geometrical arrangement that can be used with a plane parallel-sided specimen is shown in fig. 2. The section of the wavefront that sets out from the centre of the transmitting transducer, and as a result of the scattering process
R.C.Chivers and C. R.Hill
804
arrives at the centre of the receiving transducer, takes a time ( x + r ) / c (where c is the velocity of sound, x the distance along the receiver axis to the point of scattering and r the distance from the scattering centre t o the centre of the Tissue
Tissue
U
I cm
Fig. 2. Time-gated angular scattering geometry with z = 4 cm, r = 4 cm, e = 10 and 40”. (C = 1500 m s-l.)
T
=8
PS
and
receiving transducer). If the acceptance gate is timed to open as this wavelet the scattering arrives, the delay will be ( z + r ) / c . To afirstapproximation centres for the wavelets that arrive as the gate opens lie on an ellipsoid whose axis of symmetry is theline joining its foci, the centres of the two transducers. The length of its semi-axes are given by
a’
= fr(z + r )
and b‘
= [+?x(
1 -COS
e)]*.
Allowing the signals an extra timer , equal t o the gate duration, to arrive gives, as a locus for the scattering centres of the last scattered signals t o be included in the gate, anellipsoid confocal with the first having semi-axes
a” = fr(z + r + C T ) = a’ + frcr and = fr[czTz =
( $c2 T 2
+ 2rz(1- cos e) + 2CT(Y + z)l+ + CTa‘ + b”)’.
The major axes of these ellipsoids (a’ and a”)are independent of the scattering angle. This has been achieved by stipulating that the gateshould open after a time ( r + z ) / c . If it opens a t any other time, the loci of initial and final signals received will still be given by two confocal ellipsoids, but the ‘direct path’ of fig. 2 will not necessarily be included in them.
Ultrasonic Scattering
from Tissue
805
For a scattering event to contribute to the gated signal, it is only necessary for its time of travel to be between ( r + .)/c and ( T + .)/c + T ; it does not matter where the points of emission and reception are on the two transducers. The relevant ellipsoids for the twogiven pointswill have the same semi-axesas those given above, but the foci will be at thepoints of emission and reception on the transducer faces. The quality of the approximation of taking the ellipsoids focused at the centres of the transducers increases as their diameters decrease compared t'o (T + z ) . Fig. 2 shows that there is a limit on the angularresolution that can be obtained imposed by thegeometry of the scattering situation. This can beestimatedby drawingorcalculation.(Multiplescattering events, whereby a wavelet is scattered a t two points in the tissue before reaching the receiving transducer within theopening time of the gate, are assumed to provide a negligible contribution in this discussion. That this is a reasonable assumption is suggested by thelow overall scattered amplitudesbut itis a questionthat will require further attention.) Measurement of angular scatter using two transducers is thus seen to be difficult t o achieve in practice since it requires a detailed knowledge of the transducer radiation patt'erns, refract'ion effects, and a measurement over an awkwardly shaped volume. Theawkw7ardness of the shapeof this volume can be partly removed using a symmetrical transducer arrangement as in fig. 3, and Tissue
'ed gate
Tissue
Fig. 3. Symmetrical transducer arrangement for angular scattering, with f? = 40' and T = 2 and 8 p . (c = l500 m S-l.)
2
= r = 4 cm,
relyingontime-gating to specify the scatteringangle.The poor angular resolution and signal-to-noise ratio obtainable with this arrangement, unless thin specimens and wide angle transducers are used (bringing with them their own problems), militate against its implementation.
R.C. Chivers and C. R.Hill
806
If only one transducer is used (i.e. e = 180" in figs 2 and 3), the ellipsoids become concentric spherical shells separated by a distance BCT, as shown in fig. 4. For any element included in this volume, the backscattered spectrum, S(f),is in principle given by
S(f)= E S (f)exp ( 2 x H ( f ) ) Ro(f 1 where
S , is the measured backscattered spectrum, R, is the loop frequency response of the transducer, x is the depth of the element in the tissue, H is the attenuation per unit length of the tissue and E
is a correction for transmission across the boundary.
The total backscattered spectrum will be the sum of these elements over the volume defined by the transducer and the acceptance gate. The effect of these factors in a practical situation is discussed in the following sections.
Tissue
Icm
Fig. 4. Backscattering geometry (0 = 180') for z = r = 4 cm,
T
=8
p.
(c = 1500 m s-l.)
6. Experimentalarrangement
The details of the experimental arrangement used for our investigations have been discussed elsewhere (Chivers 1973, Chivers et al. 1974). Its essential componentswere:a pulse-echo A-scope, atime-gate t o select the signal originating from a chosen depth in the tissue sample and a spectrum analyser. The volume from which the scattering may be considered t o have arisen is determined by thegeometry of the transducerbeam and thedelay and duration of the gate. For the results reported, the transducerswere found t o produce a constant spectral output over the face of a flat reflecting target (of any size greater thanthat of the transducerface).Thevariationmeasured was i 0.5 dB for distances ranging from1 to 8 cm in frontof the transducer, andfor a broad range of frequencies for each transducer. Table 1 gives the nominal frequencies, diameters andspectral ranges of the transducers used, all of which were probes bought for use with a commercial B-scan equipment.
Ultrasonic Scattering
from Tissue
807
On the basis of these measurements, and others takenon the variation of the spectral response of the transducer as the targetwas rotated out of the beam, thetransducer beams were assumed to be well collimated, an assumption Table 1. Nominal frequency, diameter and bandwidth of transducers
I
l
I
I
Effective bandwidth (MHz)
(MHz)
0.6-1.4 1.0-2.5 1.6-2.8 3.0-6.0
20 15 15
1.5 2.0
4.0
%
40 43 27 33 I
I
I
I
consistentwith the fact that allmeasurements were madewithinwhat is traditionallytakento be the near-field of thetransducers.Theaveraging involved in the scattering measurements (arising from the finite diameterof the transducer and the finite duration of the acceptance gate) is not disadvantageous in that the signal being analysed is essentially stochastic, and some form of averaging is necessary to define relevant parameters. The use of an averaging system that iscapable of immediateapplicationin a clinical situation has obvious merit. The practical implications of the time-gating on the spectral analysis are discussed later (section 7 ) . Fig. 5 illustrates the derivation of the required spectrum. An electrical input E , to the transducer produces a corresponding acousticaloutput A,. Similarly Tissue
Plane
reflector
Transducer
rL -
Gate delay
Fig. 5 . Scattering signal geometry.
an acoustical input A , to the transducer produces a corresponding electrical output E,, but thespectral transfei functionsfor emission and reception are not necessarily identical. The reflection from a plane reflecting target provides a measure of the loop spectral response of the transducer, provided that the reflection is assumed to be anharmonic and that a correction is made to the level of signal returned to take account of imperfect reflection by the target (the attenuation in water is assumed to be negligible). The polished Perspex targets used for these experiments produce an echo that is 8.7 dB below that from a perfect reflector (Wells 1969). The E, and A , are spectral functions,the
R.C. Chivers and C. R.Hill
808
latter being spatialfunctionsas well, although the method of defining the useable bandwidths of the transducers described above and summarizedin table 1 has removed this dependence as a practical consideration. The signal acceptedby a gate set a distance ct inside a tissue specimen (where c is the group velocity of sound in the tissue) and of duration T will, in a first approximation, give rise to an acoustical signal at thetransducer of amplitude A,
s(f)
= C 2 ( t f& T ) 2H z(!)T2Al(f)
(1)
where
H (f ) is the attenuation per unit distance travelled in the tissue,
T is the transmission coefficient at the water tissue boundary, S(f)is the signal scattered from the shaded volume of fig. 1, A , ( f ) is the amplitude of the interrogating signal emitted by the transducer, and f is the frequency.
If there is no tissue present, thesigna'l from the reflector only isAT(!) = A,( f )R where R is the reflection coefficient of the target (assuming the attenuation in the water bath at 18 'c t o be negligible). Taking the ratio of the gated signal and thereference signal A,( f ), we obtain the measured scattering function
For most tissues, T 2 - 0.1 dB and is negligible, but this is not the case for the attenuation term H 2 ( f ) . Good attenuation measurements are thus seen to be a prerequisite for analysing scattering measurements. 7. The effect of the time-gate
The existence of the selection gate canmanifest itself in the measured spectra in three ways. In the first place the existence of a DC pedestal in the gate will affect both the level and form of the spectrum observed, as can be seen in fig. 6 ( a ) . Even when the pedestal represents only 4% of the 2 V peak to peak of the RF pulse, its presence can be detected. As it isincreased to 15%, a markedsinusoidal oscillation withfrequencyisobserved.Thefrequency of these oscillat'ions with frequency (a quantity having the dimension of time for which the name 'ffrequency' has been suggested (Chivers 1973)) is seen to be 12 p , corresponding to the length of the gate. Any periodicity (or the obvious presence of one or more ffrequencies) in the scattering spectra can be immediately related to a distance correlation since, with c constant, distance is proportional t o time. The second effect of the gate on the spectrum can be seen in fig. 6 ( b ) where the duration of the gate has been successively decreased. Initially the effect is negligible, but as the gate rejects more of the energy in the pulse, the peak level of the spectrum decreases. Accompanying this expected amplitudedecrease is a deterioration of the resolution obtained inthe spectrum. In thelimit, where the gate duration represents onlyafraction of a cycle of the mostprominent
Ultrasonic Scattering
from Tissue
809
frequency present in the RF pulse, it is almost impossible to say what that frequency is. The thirdeffect of using a time-gate in this context derives from the natureof the signals being investigated. If the signal of interest is essentially finite in
Fig. 6. Effect of (a)gate pedestal and ( b ) gate length on the spectra obtained with a ‘2 MHz’ transducer. (a)theffequency of the oscillations introduced by the pedestal is seen to be very close to 12 p , the length of the acceptance gate used. No oscillations can be observed onthe main spectral peaks because the totalsignal level was causing the analyser to saturate. ( b ) A s the gate length decreases, the higher ffrequencies disappear and the signal level decreases.
time (e.g. the echo from a plane reflector), and lies entirely within the gate, the length of the gate is irrelevant provided i t is longer than the signal and the signal is entirely within it. However, if the signal is longer than the gate, the gate mustaffect the spectrum obtained. If the scattered signal is s(t) and the gate opens for a time r , the resulting signal out of the gate is s ( t ) g ( t ) where g ( t ) = 1, O < t < T = 0 otherwise. Taking the Fourier transform of this product, we obtain a convolution 2 W17 9(0)* 3 ( ~ = ) Y(w-o,)-Ssin-dw, (3) 01 2
::1
R.C. Chivers and C. R.Hill
810
whence the scattering spectrum displayed can be seen to be implicitly related to the gate length in such a way as to preclude easy calculation of Y ( w ) ,the scatteringfunction, andthe relatedbackscattering cross-section. Although thisputsfundamentalinformationout of reach a t present,comparative empiricalstudiescanbe made, provided that the gate parametersremain constant, and may be of use in a clinical situation. 8. Backscatteringmeasurements
Measurements have been made on pairs of fixed samples of human fat, liver and spleen, and one sample of fresh porcine liver. The gate duration was fixed a t 8 p , the delay being adjusted so that the gate accepted signals returning more than 10 ps after the reflection from the water-tissue interface, thereby allowing time for this last reflection t o die away before the scattered signals were selected. The spectra were recorded on Polaroid film, enlarged and traced before data were taken from them, the total errorsinvolved in these processes were taken over being 5 0.5 dB. With each transducer three measurements different regions within each sample. The IF filter of the analyser was set to a width of 100 kHz for all spectra except those for which the ‘4MHz’ transducer was used, where a filter width of 300 kHz was chosen. Points were read off the tracings a t intervals corresponding to the appropriate filter width. The effect of the IF filter is twofold; not only does it smooth the display, hiding some of the effects of the convolution discussed above, it also affects the level of the signalobservedin the spectrum. Provided that thescanned spectrum is broad comparedto thewidth of the filter (Chivers 1973) the level of the signal is directly proportional to the filter width. For the convoluted scattering spectra, this proportionality is only a crude first approximation. However, for the reference spectra the approximation is much more accurate and account mustbe taken of the filter widths used when comparing two reference spectra or a reference spectrum with a scattered spectrum. Fig. 7 shows the spectrum backscattered from a piece of fat compared to the reference spectrum from a plane target. Of immediate interest is the relative
.-.-c .-
v)
V
b (D
V 0
Frequency (MHz)
Fig. 7. Backscatteringfrom (‘4 MHz’ transducer).
fixed humanfat
compared t o the reference spectrum
Ultrasonic Scattering
from Tissue
81 1
complexity of the scattered spectrum compared to the reference, the direct result of gating a continuous signal. The occurrence of peaks a t approximately 125 kHz suggests the presence of a ffrequency of 8 p , the length of the gate. Fig. 8 shows the actual spectra recorded for the two samples of fixed human liver and the one sample of fresh porcine liver. The difference of almost 20 dB Human liver A
Human liver B
-
+io0-10-
-
-
-30-
S
0-
Y
?
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Fig. 8. Backscattering spectra fromfixed human and fresh porcine liver. Filter width 300 kHz, gate length 8 p, transducer '4 MHz'.
on the peak level of scattering is very strong and supports the idea of distinguishing gross differences in tissuestructure, anidea that is given more practical credence by the comparison of the spectra from the two fixed liver samples. Their spectral peaks are at approximately the same level, but the occurrence of a peak a t about 2.5 MHz in all the pictures from specimen A and theabsence of a corresponding peak in the spectra from specimen B, although possibly fortuitous, is stronglysuggestive of a difference in composition between the two specimens. The comparison of different types of tissue does not yield such simple criteria fordifferentiation (fig. 9). Thepeak level of scattering for spleen and fat appears to be consistently higher than that from the liver by between 2 and 5 dB. The dual peak structure of the liver spectrum is notso prominent in fat, slightly more high and difficult t o detectin spleen tissue, thelasthaving frequency components than either of the other two tissues. A comparison of this sort is based on the premise that the attenuation function H ( f ) may be considered to be the same for all the tissues being considered. The attenuation coefficients for the samples of tissue have been reported elsewhere (Chivers and Hill 1975) and, to a first approximation, the assumption is valid. Application
R.C. Chivers and C. R.Hill
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of the individual attenuation coefficients requiresdigitalization and deconvolution of the data presented in these figures, as discussed earlier (section 6). The comparison of spectra from different tissues, while experimentally convenient, lacks therelevance to a clinical situation of the comparison of different samples of the same tissue.
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Fig. 9. Backscattering spectra fromfixed liver, spleen and fat. Filter width 300 kHz, gate length 8 p, transducer '4 MHz'.
Conclusion The discussion presented inthis paper is areview of the complexities involved in the ultrasonic diagnostic process with particular reference to the spectral analysis of scattered energy for use as a diagnostic tool. As such it lays a basis for future work in this difficult but potentially rewarding field, indicating problems to be overcome. Theonly some of thepracticalandconceptual tractable scattering situationis seen to be that in which measurements of backscattering are made. These have the advantage of requiring a minimum of modification of present pulse-echo diagnostic machines forimplementation when the success of the technique has been established. Backscattering measurements from different types of fixed tissue have been reported and compared. The use of such measurements is illustrated in fig. 10. Having located the volume of interest in a patient, the A-scan is gated out, the signal accepted bythegate being Fouriertransformed. Atthisstage two directions of investigation are open. These simple measurements of the spectra of time-gatedscattering,albeit complicated bytheintrusion of thegate duration, may very well provet'o be capable of exploitationindiagnostic 9.
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situations on an empirical basis (Chivers et al. 1974), although the problems involved in making such comparisons are likely to be severe for work in vivo. Alternatively the spectra may be deconvoluted by computer to obtain the relevantbackscatteringcross-section. These can be compared with less ambiguity in order t o provide an empirical approach to tissue differentiation. B . scan locates volume of
interest
I A - scan gated out at relevant place Gated A - scan i! Fourier transformed
\ \\
Histology
Fig. 10. Uses of backscattering measurements in medical ultrasonics.
The backscattering cross-section has three further uses. In the first place the evaluation of scattering cross-sections and their dependence on frequency should enable assessment to be made of the scale of the structures of acoustic significance in thescattering process, and thushelp t o delineate the fundamental limitations of ultrasonic diagnosis. Secondly, knowledge of the frequency dependence of both the attenuation and the total scattering will permit calculation of the dependence of the absorption on frequency,and thusenable absorption mechanisms to be discussed innumericalterms.Thirdly, and more remotely, the backscattering cross-sections may conceivably, by the mediation of theory, be linked to macroscopic histology. The present paper shows that, although the difficulties of obtaining fundamental information from backscattering are great, there is evidence from a limited number of measurements that a relationship exists between the structure of a tissue and the signal it scatters back t o the transducer; a relationship that may be quantified and one that should be investigated further. Comparison of results will only be possible if the following parameters are included in a discussion of the measurements : the loop spectral response and effective bandwidth of the transducers, the gate duration, the depth in tissue the at which the IF filter setting of the spectrum analyser. gate opens and the One of the authors(R. C. C.) would like t o thank the Royal Marsden Hospital Physics Division of the Institute of Cancer Research, Sutton, Surrey, with the support and encouragement of Professor J. W. Boag. for financial support for this work, which was carried outinthe
814
R.C. Chivers and C. R.Hill RESUME
Approche spectrale L la dispersion ultrasonore des tissus humains: Mhthodes, Objectifs et mesures de dispersion B rebours La penurie d’informationssur les procedes physiques entrant dans lapropagation des ultra-sons dans les tissus, et le besoin croissant pour de telles informations sont discut6s. On considhe la nature physique du procede de diagnostic ultrasonique en termes de phenombne d’ondes et l’on analyse sommairement les limitations et avantages de l’analyse spectrale des frequences comme moyen d’obtention des donnees. I1 parait une description d’un systbme de mesure exp6rimental utilisant un appareil selecteur It temps de comptage pour selectionner les 6chos disperses dans un certain volume de tissus mous It une profondeur donnee. L’influence de l’amortissement par les tissus surja cents et le choix de la duree de la selection sur les spectres de frequences obtenus sont considAr6s. Le memoire rapporte des mesures de dispersion B rebours sur des Achantillons fixes dans le formol de tissus gras humains, tissus defoie et de rate, dansla gamme des frequences de 0,5 B 5 MHz. Les resultats suggbrent que l’approche peut avoir une valeur diagnostique en clinique, dans la caracterisation de lastructure dansdes volumes specifiques de tissus humainsmous.
ZUSAMMENFASSUNG Untersuchungen des Spektrums von Ultraschall-Riickstreuungen in menschlichen Gewebeteilen : Methoden, Ziele und Ergebnisse von Riickstrahlungsmessungen Des mangelnde Wissen iiber die physikalischen Vorgange bei der Ausbreitung von Cltraschall in Gewebeteilen und die steigende h’otwendigkeit diesbeziiglicher Kenntnisse werden besprochen; die physikalischen Aspekte der Ultraschalldiagnose mit Hilfe der Wellenerscheinungen betrachtet, und Grenzen und Vorteile der Analyse des Frequenzspektrums auf der Suche nach verschiedenen Auskiinften kurz analysiert. Ein experimentelles Messsystem mit Zeitintervalltor zur selektiven Wahl des Echos von einem bestimmten Volumen weicher Gewebeteile in bestimmter Tiefe wird beschrieben; der Einfluss der Abschwachung durch dariiberliegende Gewebeteile so wie der Zeitintervalleinstellung des Tores auf das Frequenzspektrum betrachtet ; und einige Widerhallmessungen a n formalinfixierten Proben menschlicher Fett-, Leber- und Milzteile im Frequenzbereich zwischen 0,5 und 5 MHz vorgelegt. Die Ergebnisse lassen auf diagnostische Moglichkeiten in klinischen Fallen durch Charakterisierung der Struktur spezifischer Teile menschlichen Gewebes schliessen.
REFERENCES CHIVERS,R.C., 1973, Ph.D. Thesis, University of London. CHIVERS,R.C., and HILL,C. R.,1975, Ultrasound X e d . Biol., in press. CHIVERS,R. C., HILL,C. R.,a n d NICHOLAS,D., 1974, i n Ultrasonics in Medicine, Ed. de Vlieger et al. (Amsterdam: Excerpta Medica) pp. 300-303. CHRISTIE,D. G., 1962, A p p l . Mat. Res., 1, 86. DAMASCELLI, B., FOSSATA, F., LIVRAGHI,T., a n d SEVERINI,A., 1969, Am. J . Roentg., 105, 428.
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DELAND, F. H., 1969, Am. J . Roentg., 105, 446. DONALD, I., 1966, Ultrasonics, 4, 119. ERICKSON, J. J., and BRILL,A. B., 1970, Radiology, 95, 589. FRY,W. J., LEICHNER, G. H., OKWAMA,D., FRY,F. J., and FRY,E. K., 1968, J . Acoust. Soc. Am., 44, 1324. HICKLING, R. D., 1962, J . Acoust. Soc. Am., 34, 1582. HICKLINO, R. D., 1964, J . ACOUB~. Soc. Am., 36, 1124. HILL, C. R., and CARPENTER,D. A., 1975, B r . J . Radiol, in press. HILL, C. R., and CHIVERS,R. C., 1972, in Ultrasonics in Biology and Medicine, Ed. L. Filipczynski (Warsaw: Polish Scientific Publishers) p. 119-123. HOWRY,D. H., 1965, Radiol. Clins N . Am., 3, 433. KELLY, E., OKUYAMA,D., and FRY,F. J., 1968, in Proc. 6th Int. Conf. on Acoustics, Tokyo, paper "1-1. KHARKEVICH, A. A., 1960, Spectra and Analysis (New York: Consultants Bureau). KOSOFF,G., 1974, Proc. R. Soc. Med., 67, 135. MILAN, J., 1972, B r . J . Radiol., 45, 911. MOUNTFORD,R. A., and WELLS,P. N. T.,1972a, Phys. Med. Biol., 17, 14. MOUNTFORD,R. A., and WELLS,P. N. T.,1972b, Phyla. Med. Biol., 17, 261. ROBINSON, D. E., LEES,S., and BESS,L., 1975, in press. WELLS,P. N. T.,1969, Physical Principles of Ultrasonic Diagnosis (New York: Academic Press). WELLS,P. N. T.,MCCARTHY,C. F., Ross, F. G. M,, and READ,A. E. A., 1969, Br. J . Radiol., 42, 818. WILD,J. J., and REID, J. M., 1952, Am. J. Path., 28, 839.
