Ultrasound in Med.& Biol.. Vol. 5, pp. 321-331 Pergamon Press Ltd.. 1979. Printedin Great Britain

A N E W M E T H O D OF O B T A I N I N G AN ACOUSTIC I M P E D A N C E P R O F I L E FOR C H A R A C T E R I Z A T I O N OF T I S S U E STRUCTURES* A. HERMENTt, P. PERONNEAU* and M. VAYSSE Centre National de la Recherche Scientifique, Hopitai Broussais, 96 Rue Didot, 75674 Paris Cedex 14, France (First received 24 October 1978; and in final form 3 April 1979)

AbstraetmA special method of processing an echographic signal is described. This method is used to estimate the reflected impulse response of the media examined, without employing conventional deconvolution techniques. Under certain conditions, this impulse response can he used to obtain quantitative results concerning the acoustic impedance of different structures. Measurements have been made, leading to definition of the possibilities of the method: dynamic impedance range is now only limited by the technology of the equipment used, and the influence of noise on impedance profile quality is very low. Nevertheless. depth definition appears insufacient. The initial application of the method related to an excised canine aorta. Key words: Ultrasound, Pulse echo technique, Impulse response, Tissue characterization, Impedance profiling, Correlation function.

1. INTRODUCTION

Ultrasonic diagnostic techniques are currently making substantial progress, this being largely due to their atraumatic nature. In the field of echography in particular, technical progress in the form of fast imaging, use of grey scales and improved image contours provide the physician with increasingly detailed information. Nevertheless, irrespective of the results obtained, echography is limited by its principle to the provision of cartographic data concerning the geometry of the media observed. While detection of the echo envelope, on which this technique is based, makes it possible to show up the separating surface between two media or discontinuities within the same medium, it cannot actually characterize a tissue. New techniques have appeared, as Impediography (Jones 1973) and Raylography (Beretsky 1972) which can be used to establish acoustic impedance profiles, similar in their presentation to A-mode echograms. On these profiles, the acoustic impedance characterizing the nature of the media observed is displayed according to observation depth. In due course, these techniques should make it possible to achieve a

*Work carried out by E.R.A., C.N.R.S. n°785 "Instrumentation et Dynamique cardiovasculaire", at the H6pitai Broussais, Paris, France. l"Attach~ de Recherches at INSERM. CMahre de Recherches at INSERM. 321

classification of tissues, providing important information concerning their possible pathological state. These techniques lead to the elaboration of an impedance profile, using the principles of echography but with much more comprehens i v e exploitation of the signal received. Various calculation methods have been proposed. These involve processing of the echographic signal, using procedures which are relatively delicate in" their application. We propose a different approach to the problem, whereby the desired impedance profile is established by much simpler processing of the echoes. 2. PRINCIPLES OF OBTAINING AN IMPEDANCE PROFILE

The different points in the procedure used •to convert the echographic signal to an acoustic impedance profile form, should be identified. It has been demonstrated that it is relatively simple, taking certain hypotheses relating to the nature and geometry of the media examined, to establish a mathematical connection between the reflected impulse response of these media, h(t), when interrogated by an ultrasonic wave, and the acoustic impedance profile plotted against time, Z(~). However, it is not always simple, in practice, to make the conversions required to determine the desired impulse response h(t), from the echographic signal e(t). Such a process requires the following three steps, to

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pass from the physical properties of the medium concerned, to the impedance profile for the latter: (a) Acquisition of echographic signal e(t), meeting the validity hypotheses for the equation linking reflected impulse response of the medium h(t) to acoustic impedance profile

z(o; (b) Processing of signal e(t), to obtain desired impulse response h(t); (c) Determination of impedance profile Z(O, from this impulse response. We will examine these three aspects of the method in succession.

2.1. Constraints on the echographic signal The simplified equation normally used to pass from h(t) to Z(O, is demonstrated taking the following hypotheses: • The structure comprises flat, parallel terfaces, and reflections are specular, • Orientation of the ultrasonic beam close to the normal to these interfaces, • Variations in acoustic impedance change of medium are small, • Attenuation of the ultrasonic wave the different media is negligible, • Multiple reflections can be ignored.

in-

Attenuation of ultrasonic signals in the living medium cannot be ignored, except at very shallow observation depth. It is therefore necessary to apply compensation, either electronically during the reception of the analog waveforms or computationally during the processing of the digitized signals. This attenuation is normally taken t o be exponential with distance, for a given tissue. Since these exponential coefficients are roughly the same from one tissue to another and since the impedance discontinuities are small, the attenuation can be corrected, at least to first order, using a single exponential equivalent to the average attenuation value for the tissues examined. Finally, multiple reflections can be ignored since they are small and because the attenuation of the ultrasonic signals in tissues and the imperfect parallelism of successive interfaces contribute to their substantial reduction.

is on in

The hypotheses concerning the geometry of the structures studied: and the orientation of the ultrasonic beam, are not as restrictive as they appear at first glance. If we have a sufficiently fine ultrasonic beam, surfaces presenting a large radius at the point examined, with respect to the lateral dimensions of the beam, can be considered as fiat. With respect to the perpendicularity of the ultrasonic beam to the interfaces and the parallelism of the latter, it is possible, provided access can be obtained to the medium under examination at different angles of incidence, if not to obtain precise perpendicularity of the beam with respect to all interfaces, at least to apply the requisite corrections to the result, using information extracted from measurements taken at different angles of incidence. Data obtained from relevant literature indicates that the hypothesis Lconcerning slight discontinuities of impedance is relatively realistic. As a result, the greater part of the energy is transmitted as each interface is passed. Pulmonary and bone tissues are two obvious exceptions.

2.2. Determination of the reflected impulse response of the medium With an echographic signal meeting the above hypotheses, we now have to deduce the reflected impulse response of the medium examined, h(t), or at least obtain a good estimation of this response, h'(t). The echographic signal is obtained by driving the transmitting transducer with a very short electric pulse which can be considered as a Dirac impulse (75 ns). The wave transmitted by this transducer therefore corresponds to its transmission impulse response, Ct(t). The ultrasonic signal is then modified by medium impulse response h(t). The reflected signal is modified in turn by the receiver transducer, the reception impulse response of which is designated C2(t). As a result, reception signal e(t) takes the following form, to the nearest time shift e(t) = C1(t) * h(t) * C2(t)

(I)

For the sake of convenience in the following text, we will call C(t) the convolution product of C~(t) and C2(t). C(t) is the impulse response of the transducers for transmission/reception. Equation 1 can now be written

e(t) = C(t) * h(t).

(2)

Strict solution of this equation, to extract

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A new method of obtaining an acoustic impedance profile h(t), normally calls for the use of deconvolution techniques. Two observations are relevant at this point: (a) C(t) is the signal obtained on reception, when the transmitted signal is reflected by a flat acoustic mirror, perpendicular to the ultrasonic beam, for which impulse response is of the Dirac" impulse type. (b) If C(t) is very close to a Dirac impulse, then its Fourier transform, C(to), will be nonzero over a wide frequency band, and irapulse response h(t) will be known, via the transducer, for a wide range of frequencies. Under these conditions, the. convolution equation can be solved simply. The transducers normally used for echographic purposes, generally have an oscillating response C(t), and the Fourier transform of this response, C(to), only exists for a relatively narrow frequency band. In this case, h(t) is only known for a more restricted range of frequencies, and solution of the convolution equation becomes a difficult matter.

I .=--Zo

I z,

z2

Z3 D

e(t) 2 ~OECONVtX.UTK)N.

A

h(t) t

V

'

"2~)INTEGRATION.

,~o~[ / 2E

Fig. 1. Sequence of operations used to convert the echographic signal e(t) into impedance profile form. In order: the set of different media examined, characterized by their acoustic impedance values, echographic signal e(t), reflected impulse response of the media h(t), and logarithmic impedance profile Ln (Z(OIZo). pulse response of the media h(t), and finally logarithmic impedance profile Ln(Z(~)/Zo). 3. S'rA~ or w o k m THISmnZLD

Various work is described in the relevant literature, concerning the establishment of the relation used to pass from h(t) to Z(~:), and the 2.3. Conversion from reflected impulse res- method employed for solution of the convolution equation. ponse to acoustic impedance profile form Jones (1973, 1974, 1976) and Kak and Fry Within the framework of the hypotheses in(1976) concerned themselves with these two dicated above, we can easily relate the aspects of the problem, and their work was acoustic impedance profile according to relatively similar. As regards the first point, transit time Z(~) (calculated from transand adopting the hypotheses already desmission instant ~ = 0) to impulse response cribed, these authors break down the medium h(t) of the medium. We only need to know acoustic impedance Z0 for the first medium artificially into a series of interfaces, each encountered by the ultrasonic beam. This having the same coefficient of reflection. relation has been demonstrated in various Then going to the limit, and integrating the different ways. We will restrict ourselves result, they obtain the relation already dishere to giving the final equation, which is cussed. They then extend their results to third order multiple echoes, although noting written that in this case a single solution is obtained only in special circumstances. Ln Z(~) = 2 f02~ h(t) dt (3) The work of these authors appears to differ z0 with respect to appfication of the method, where ~ is the time of flight of the ultrasonic and the deconvolution procedure used. wave between transducer and interfaces, t Jones employed a deconvolution procethe time of echoes reception with respect to dure, involving the use of transmitter and emission. This relation clearly leads to im- receiver transducers of special type, which pedance profile Z(~). In Fig. 1, we have do not appear directly applicable in this form summarized the sequence of normal opera- for echographic diagnosis purposes. He contions, used to convert the echographic signal ducted the first experimental test of this into impedance profile form. We show, in method using simple test objects as well as order: the set of different media examined, samples of biological tissues (brain and eyes). characterized by their acoustic impedance Kak and Fry used a method for solving the values, echographic signal e(t), reflected ira- convolution equation, assuming prior knowUM~ v'oL 5, No. ,4.~-B

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A. H ~ l c r

ledge of the echo waveform. The purpose of this procedure was to reduce the noise sensitivity of the deconvolution process. They obtained accurate results, on glass and lucite models and apply their "method to the characterization of brain tissue behind skull. Lefebvre (1978) was only concerned with the relation used to pass from h(t) to Z(O. He used the same hypotheses as already discussed, with the exception of that relating to the absence of multiple reflections. After proposing a model of the medium, for which he obtains the ultrasonic wave propagation equation, he then converts this equation into a form equivalent to the Schr6dinger equation. He can then use existing algorithms for the inverse problem of diffraction in quantum mechanics, to solve the equation in this form He obtains relation (3) on the first iteration. Higher order iterations provide expressions for the acoustic impedance in which multiple reflections are taken into account. Leeman (1978) suggested a mathematical formulation of the relation between h(t) and Z(~) taking in account the ultrasonic beam profile and the spatial distribution of reflecting elements. In addition, he proposed a theoretical solution of the problem of multiple order echoes. Beretsky (1977), and Papoulis and Beretsky (1977) devoted their attention to the problem of deconvolution alone. They used a single transducer for transmission and reception, and developed an iterative procedure for deconvolution involving filtration and estimation of h(t). The complexity of the procedure is directly linked with the oscillating behaviour of the echo signals processed. These authors have published interesting results applying their digital model to an excised aortic wall. If we accept the hypotheses developed above, it emerges from the foregoing that the delicate point in the establishment of an acoustic impedance profile, concerns the obtaining of a good estimation, h'(t), of the reflective impulse response of the medium. All techniques so far proposed for the solution of this problem present the common advantage of improving depth definition by comparison with conventional echography. On the other hand the procedures for processing the signals are co/nplex, in certain cases requiring the use of extensive computation resources. Furthermore, deconvolut/on techniques become delicate where signals affected by noise have to be

et al.

processed as is likely to be the case with in vivo applications for these methods. 4. V~SCaWnONOF~ PaOmSED~n'UOV As we have seen, certain hypotheses are necessary to obtain an acoustic impedance profile. Whatever the hypotheses used, we have to pass from the echographic signal to an estimation of h(t). Our study relates to this latter point, and has led to elaboration of a method derived from the following observations. Theoretically, the reflected impulse response of the medium corresponds to a series of Dirac impulses. The interface generating each pulse is characterized by the moment of arrival, polarity and surface of the pulse. The moment of return of the reflected pulse characterizes the position of the interface, its polarity gives the sign of the coefficient of reflection, and the surface of the pulse indicates the ampfitude of the coefficient of reflection. Deconvolution of the echographic signal results in association of a spike with each e(t) echo, this spike being as close as possible to the theoretical Dirac impulse, which characterizes the interface generating the reflected pulse in the same way. We have attempted to associate a similar spike with each echo, grouping these three characteristics but without using a deconvolution procedure, employing for this purpose the cross-correlation function between e(t) and C(t), which is written

C,~(¢) = f+_~e(t). C(t - ~) dt. The absolute extrema of this function give us the exact position of the echoes, and their sign. Information concerning the area of the surface subtended by the spike, is extracted e/ther from signal e(t) itself or from C,~(¢). We will now examine each of these points in detail Nevertheless it has to be mentioned that, if composite echoes are superimposed inadequate resuRs could be obtained due to inaccurate detection of C,~(~) extrema. That particular point will be further developed (§6.2.4).

(a) Position of h'(t) spires. This information is provided very accurately by the temporal position of the absolute extrema for each echo of function C,~(~').

A new method of obtaining an acoustic impedance profile

h'(t) spikes. It should be recalled that the hypotheses covering flat interfaces, perpendicular to the ultrasonic beam, involved the use of real coefficients of reflection. In other words, any echo generated by an interface will be homothetic with C(t). As C(t) is generated by a coefficient of reflection with a value of 1, any echo with a positive similarity factor corresponds to a positive coefficient of reflection, and conversely, any echo obtained from, C(t) by a negative similarity factor, corresponds to a negative coefficient of reflection. Consequently, an absolute maximum of C,~0") corresponds to a positive coefficient of reflection and an absolute minimum of C~(T) corresponds to a negative coefficient of reflection. To illustrate these two paragraphs, Fig. 2a shows -eference echo C(t), and Fig. 2b shows cross-correlation function C~(~), corresponding to an isolated echo generated by a water/perspex interface (amplitudes have been standardized between + 1 and - 1). The position of the absolute extremum of C~(~') is clearly determined. This extremum is a maximum, indicating a positive coefficient reflection. This is obviously the case for the interface examined.

325

(b) Sign of

(c) Surface under

h'(t) spikes. The h'(t) spikes are obtained by rectifying either e(t) or C,~(r), taking account of sign and position data previously extracted from C,~(r). In Fig. 3, traces a and b correspond to rectification of curves 2a and 2b; rectification is positive, taking account of the sign of the C~0") extremum. The choice of e(t) or C,c(~') is dictated by two factors: desired depth definition, and the possibility of obtaining correct results in the presence of interference. As is demonstrated later in this paper good depth definition requires the use of e(t), but accurate results

~l

c(t)

11

c,.~r)

Fig. 2. (a) reference echo C(t). Co) cross-correlation function C,~(v) between an isolated echo generated by a water/perspex interface and the reference echo.

Fig. 3. Reflected impulse response of an isolated waterlperspex interface: (a) h'(t) obtained from e(t); CO) h'(t) obtained from C~(r).

in the presence of noise involve the processing of C~O'). It now remains to demonstrate that the surface subtended by a spike obtained from e(t), and that subtended by a spike obtained from C,~(~) both have areas which can be related to the corresponding coefficient of reflection by a multiplier constant. If we take any echo eat), starting at t = ti, with reference echo C(t) starting at t = 0, the corresponding similarity factor will naturally be ri, the coefficient of reflection. These observations are summarized by the following relation

e,(t) = r~C(t - t,). As rectification has no effect on amplitude, we obtain le,(t)[ = [rjC(t - tO[ = Iril[C(t - t O[. If the duration of C(t) is T, the surface subtended by IC(t)[ is a constant, which can be written K, =

I:

[C(t)[ dr.

(4)

Under the same conditions, the surface subtended by e~(t), after rectification, is written

ft::r,r,,,C(t - t,) I dt = lr, lti ft::rlC(t- t,)l dt = K,Ir~l

(5)

The surface subtended by each h'(t) spike, obtained from e(t), accurately characterizes the modulus of the coefficient of reflection which generated the pulse. We can also demonstrate that the area under each h'(t) spike, obtained from C,~0"), is proportional to the coefficient of reflection. Using the same notations as above for isolated echo es(t) C,~(~) = f_~ ei(t). C(t - ~) dt

_ f tl+T --

Jti

r~'(t - t~)C(t - ~)dt.

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A. HERMENT et al.

Rectification gives

[

I ttl +T

[C~c(r)[ = [ri[ [Jt~

1

C(t - ti)C(t - r) d t .

SA~°t E

The area of the surface subtended by [Ce~c(r)[ is written

~

- '

Fig. 4. Block diagram of the equipment.

t,,÷r

J,,_r Ir, I

C(t - ti) •

C(t

-

I

r) dt dr =

putation operations required to obtain Z(O. A general block diagram of this equipment is l'tl + r I f t i + r shown in Fig. 4. dr Ir,lJ,,_rlJ,, C(t-tO.C(t-r) The analog part is similar in design to devices encountered in the field of echo(6) = Ir, lgz graphy. For transmission, the transducer is as the double integral representing the area of driven by a very short electric signal (75 ns the surface subtended by the rectified cor- pulse). On reception, the signal is first amrelation ruction of the reference echo, is a plified and then sent to a multiplier, the latter constant, which we can write compensating for attenuation of the ultrasonic signal in the tissue, according to distance. It should be remembered that this Kz= r C(t). C ( t - r ) d t dl". (7) compensation should strictly be exponential, although experience has shown that parabolic The surface subtended by each h'(t) spike correction, which is easier to achieve, is obtained from C,c(~'), therefore characterizes adequate for initial approximation. The effective signal is then sampled and the coefficient of reflection generating the converted into 8-bit word form; it is loaded in spike. To conclude, we propose the following a buffer storage with a capacity of 2 k bytes. procedure for conversion from e(t) to h'(t): We use sampling rates of 50 and 100 MHz. (a) Calculation of cross-correlation func- These frequencies, together with storage tions C~(r), between echographic signal e(t) dimension, set the length of the observation window, at 3 cm and 1.5 cm respectively. The and reference echo C(t); (b) Extraction of position and sign data for position of this window, with respect to the transducer, is determined with the aid of a the different echoes, from C~(r); (c) Rectification of the different echoes of digital delay, initiated at the moment of transe(t)lK1 or C~(r)IK~, taking account of the mission. The microprocessor transfers data from data obtained by step (b) above, giving h'(t). Before illustrating this method by measure- buffer storage to its own storage, and chains ment results, we must describe the manner in the computation operations required to obtain the acoustic impedance profile. Futhermore, which the latter were obtained. this microprocessor drives the display system $. E X ~ A L DEVICE (oscilloscope or X - Y plotter) used to present The measurement and processing system the result of all intermediate calculations, and the impedance profile. used comprises:

dt'[

f*lf/

I

• Water tank in which the samples and transducer* are submerged; • Analogue circuits for transmission and reception of ultrasonic signals; • A/D converter;t • Digital processing system,~ organized round a microprocessor, used for all corn*Krautkrfimer H5K transducer. t Biomation 8100. ~Micral N, R2E.

6. MEASUREMENT RESULTS

Firstly we present the results obtained on a laminated sample. These results can be used to demonstrate, step by step, the sequence of the operations converting the echographic signal into impedance profile form. We then examine the limits of this method. Finally, we give results, obtained in vitro, on an excised canine aorta. The signals presented were sampled at 50 MHz in the ease of the animal tissue sample, and 100 MHz in all other cases,

A new method of obtaining an acoustic impedance profile

in order to improve trace definition. Impedance profiles are presented in the form P ( ~ ) = Ln (Z(~)/Zo), making it possible to show up slight variations in Z(O more clearly. Amplitude values for e(t),C,~(r) and h'(t) have been standardized between -1 and + 1. Only the amplitude of P(~) = Ln (Z(O/Zo) has been calibrated according to the different analog and digital gains of the measurement system. 6.1. Execution of a measurement The plots shown in Fig. 5, illustrate processing of the echographic signal corresponding to a sample comprising two silicon plates. The plate nearer the transducer has a thickness of 2 mm, and the other a thickness of 1 mm. The two plates are parallel with respect to each other, and are separated by 1 mm of water. Curve (a) shows the echographic signal after compensation of attenua tion according to depth. Trace (b) corresponds to the result of correlation of this signal with the reference echo. The position and sign of the C,~(~) extrema should be noted. Curve (c) shows h'(t), obtained from e(t). Note the concordance between the polarity of the h'(t) spikes, and the signs of the C,~(¢) extrema. Finally, the logarithmic impedance profile resulting from integration of h'(t) is shown by curve (d). Analog results would have been obtained if h'(t) was extracted from C,~(¢). In this particularly simple example, phase and position of the echoes can be extracted from e(t), without calculation of C~O'). This

327

is not always the case, as for example with a signal heavily impaired by noise. 6.2. Limits of the method We will now detail the performance of the processing procedure which we have developed, comparing, when possible, the results with those given in the relevant literature. The latter is not extensive, and we have therefore limited our comparison to the following three points: depth definition of the measuring system, dynamic impedance range for a given profile, and aptitude of the method for processing signals affected by noise. Subsequently, we will deal with the problem of mixed echoes and sensitivity of our system.

6.2.1. Depth discrimination. Different criteria can be applied for evaluation of the capacity of a procedure, for separation of two variations in impedance, occurring very close to each other in space. These generally consist in first setting the maximum admissible error on exact impedance value, then calculating the minimum distance which must occur between two variations in impedance, to avoid introduction of an error greater than that already set. We adopted the simpler, and at the same time more stringent of these criteria, setting as our resolution limit value, the distance required between two variations of impedance for there to be no error in the impedance values. In simpler terms, this corresponds to recording the time required by the impedance profile to pass from one value to another, then converting this time into a distance, using the propagation speed for ultrasonic waves in the selected tissue, in this case 1500 ms -~. The edges of the impedance profile depend on the method used to obtain h'(t). Firstly we shall study depth definition with h'(t) 1 h' (t) obtained from e(t), and secondly when h'(t) is calculated from C,c(¢). If we look at Fig. 5d described above, we can see that the edges of the impedance profile obtained from e(t) have a duration of al~---s d less than 0.75 ~ s. This duration, converted into a distance Fig. 5. Results for the sample comprising two silicon plates of 2 mm and 1mm thickness separated by I mm of value, corresponds to a depth definition of water. (a) echographic signal after depth compensation e(t); (b) cross-correlation function C,~(¢) between e(t) about 0.55 mm. The same criteria applied to and C(t); (c)impulse response h'(t) obtained from e(t); data extracted from the relevant literature, (d) logarithmicimpedance profile P(O -- Ln(Z(O/Zo). lead to estimated space discrimination values

tj

A. HF.,rMENT et aL

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Table I.

Beretsky method Jones method Proposed method

Bandwith (B)

Depth definition

Product

(-6dB)

(8)

(B.8)

1.6 MHz 1.4 MHz 2.3 MHz

0.15 m m 0.75 m m 0.55 nun

of 0.75 nun for the experimental arrangement described by Jones, and 0.15 mm in the case of Beretsky. Taken at their face value, these results place the capabilities of our equipment between these two values, but are not adequate for comparison of the methods since the experimental devices used are different. A more objective analysis is necessary, obfiging us to take account of the spectral width of the reference echo. Beretsky gives details of this spectrum in his publications. In the case of Jones, we have manually sampled the reference echo which he describes, and calculated the spectrum for this signal using a Fourier analyser. Spectral bandwidth was taken at a value of - 6 dB. Table 1 gives a comparison of the different results. For the same bandwith, the proposed method gives the worst depth discrimination. This was to be expected, as deconvolution normally leads to good results on this point. Where the impedance profile involves rectification of C,~O'), the mathematical properties of the cross-correlation function indicate cross-correlation spikes having a duration twice that of the echoes. This gives impedance profile edges twice as long as before. In practice, we use the result of C,(~) coded on 8 bits, and quantification cancels out the first and last temoral values for the C,~0"), which are very low. Referring to Figs 3(a) and Co), we observe that spike length in the case of correlation is only 1.2 times that of the rectified echoes. In this case, depth definition is close to 0.65 mm in tissues. 6.2.2. Dynamic impedance range. At this point, we wish to demonstrate the ratio between the greatest and smallest variation in acoustic impedance which can be measured in the same impedance profile. The procedure used is as follows: a first echo is recorded, and loaded in computer storage. A second measurement is then taken, moving the transducer away from the sample, and dividing reception amplifier gain b y 50. We thus

0.24 m m . M H z 1.05 m m . M H z 1.15 m m . M H z

obtain a second echo, delayed and at l o w amplitude, which is then added digitally to the first. Figure 6a shows this composite signal. The second sp/ke of C,~0") (Fig. 6b) cannot be used on the trace, due to the limited dynamic range of the plotter. Nevertheless, it is clearly shown, by calculation. This is illustrated in Fig. 6b', where this same cross-correlation spike is plotted, having multiplied the values of C,#0") by 64. For this purpose, we first cancelled the first echo, so as to avoid saturation of the X - Y plotter. Finally, h'(t) and P(O=Ln(Z(~)IZo) are shown in Figs 6(c) and (d). In this case, the relative value of the impedance intervals is 4%. We repeated the identical operations, not presented here as the plots are no longer significant, up to ratio of 1:127 between the two echoes, and the results obtained were very satisfactory in all cases. This limit ratio is set b y the dynamic range for AID conversion on 8 bits, and not by the

m

c

1!

d

Fig. 6. Dynamic impedance range in an impedance profile (a) composite signal e(t); (b) cross-correlation function C=O') between e(t) and C(t); (b') second spike of C,#O') magnified 64 times during the calculation cycle; (c) impulse response h'(t) obtained from e(t); (d) logarithmic impedance profile P(~) = Ln (Z(~)IZo).

A new method of obtaining an acoustic impedance profile

method itself. A more accurate display system, associated with finer sampling, would therefore make it possible to increase the dynamic impedance range, without initial influence from limitations due to the proposed method. If we now turn to the results given in the relevant literature, it appears that Beretsky was not directly concerned with this problem, while Jones ~ndicated the possibility of showing up relative variations of as little as 1% on an impedance profile. 6.2.3. Sensitivity to noise. We will here compare the results obtained with the proposed method, for signals with and without noise. For this purpose, w e take two measurements. Firstly we process a single echo obtained from an isolated water/perspex interface, represented in Figs 7(a-d). We then repeated our measurement, with analog addition of white noise in the 20 Hz-20 MHz band to this same echo, and processed the signals. The different processing operations are presented in Figs 8(a-d). In the present case, the power SIN ratio is 0 cLB. Obviously, h'(t) is obtained from C~(~), (Figs 7c and 8c), and not from e(t). In Fig. 8(b), note the major improvement in SIN ratio on C,~(~'), crosscorrelation having properties similar to those of a bandpass filter. We must also compare the impedance profiles shown in Figs 7(d) and 8(d), which demonstrate both the very low ripple in the profile obtained in the presence of noise, and the independence of these results with respect to the noise, the difference between the two profiles being less than 5%. The limits of the method, which depend on the noise power at the time of the echo, and

1le(t)

+ 1tr'':(t)

b

IY~

c

/~s

Fig. 7. Processing of a single water/perspex echo without noise: (a) echo~'aphic signal after depth compensation e(t); (b) cross-correlation function C,~(~); (c) impulse response h'(t) obtained from C~(e); (d) logarithmic impedance profile P(~) = Ln (Z(~)IZo).

0

'

/~

I

c

329

,

t

~

d

Fig. 8. Processing of a single water/perspex echo ¢lelp'~led by noise (signal to noise ratio=0dB) (a) echographic signal after depth compensation e(t): (b) cross-correlation function C~(~); (c)impulse response h'(t) obtained from C~0"); (d) logarithmic impedance profile P(~) = Ln (Z(~)/Zo).

its spectral distribution, are reached when one of the C~(~') peaks is too badly degraded for extraction of the extremum. At all events, it appears that a value of 0 dB is not critical for white noise. To our knowledge, only Beretsky has considered the influence of noise, studying the problem in the following way: having synthesized an echographic signal digitally, he adds noise of less than 30 dB to this signal, again by calculation. In this example, the results obtained are good.

6. 2. 4. Mixed echoes. In the case of overlap-

ping echoes, theoretical limitations of the method depend on various parameters; mainly the reference echo waveform and the relative phase and ampfitude of mixed echoes. We will explain the main theoretical problems and experimentally quantify the limit of depth resolution, only in the case of two interfering echoes for clarity of explanation. Considering the echographic signal, we have firstly to distinguish ff a simple echo or a composite one has to be processed. For that purpose a simple comparison of the respective lengths of the reference echo and processed signal is convenient, composite echoes being always longer. In the presence of noise, comparison will be done between the durations of C~O-), autocorrelation function of C(t), and C~O'). The next step is the extraction of C~c(~) extrema. Effectively ff the two echoes are very close to each other, only one extremum will be extracted from C~(~) and the two interfering echoes will not be discriminated. If on the contrary, the two extrema can be

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distinguished, location and polarity of corresponding h'(t) spikes can be used to rectify e(t). Nevertheless rectification of the echographic signal according to the previously described procedure induces an error on the value of the areas under h'(t) spikes and subsequent coefficients of reflection, but this error may be fully corrected taking account of C(t) waveform. In order to set an experimental value of the depth discrimination of our arrangement, at least in the case of mixed echoes with the same order of magnitude, the results obtained on a 0.5 ram lucite sample are given in Fig. 9. As before, e(t) is presented in a). In b), absolute extrema of C,c(¢) are distinct and significant. In c), h'(t) has been obtained from e(t) and P(~) is drawn in d). Notice the step in impedance value appearing behind the plate, which is due to the transmission losses at the interfaces and consequent violation of the hypothesis requiring weak discontinuities of impedance. Calculation indicates a 5% error on the plate impedance due to inadequate rectification of the echoes, but as mentioned before this error may be exactly compensated. On the other hand, the weak oscillation at the end of e(t) is due to third order reflection in the plate and not processed here. Finally the delay between C,cO') absolute extrema in b) is 350 ns, which corresponds to a depth discrimination better than 0.3 mm in tissues. This is not a definite limit of our resolution but a realistic one taking account of the degraded shape of C,~O') as the mixed echoes get closer.

Experimental sensitivity of the arrangement. A direct determination of the 6.2.5.

Fig. 9. Processing of a 0.5 mm lucite sample echographic signal (mixed echoes): (a) echographic signal; (b) crosscorrelation function C,c(~'); (c) impulse response h'(t) obtained from e(t); (d) impedance profile P(~:) (without respect to the small impedance discontinuities hypothesis).

maximal sensitivity of our equipment would have needed interfaces with very small calibrated coefficients of reflection. Using a simplified procedure, we simulated a coefficient of reflection " r " , corresponding to an impedance step (AZ(6)IZ(6))= 2r, by a perfect acoustic mirror coupled to the transducer through a medium which provides, neglecting the dispersion effect, an attenuation r-'. From this point of view, it is obvious that the performances of our equipment depends on the depth, but the product of the attenuation by the corresponding minimal measurable relative step in impedance is a constant equal to "2r". In order to get a signal to noise ratio of 0 dB on reception, which is still suffÉcient for convenient processing of echoes, we had to insert between the probe and mirror a lucite sample presenting a global attenuation of 85 dB. In other terms coefficients of reflection as little as -85 dB (impedance variations as small as - 7 9 d B ) may be analyzed by our experimental arrangement. For instance the product value of -79 dB allows one to analyze an impedance step of 1% at about 4 cm of depth in living structures. 6.3. In vitro measurement on excised canine

aorta A fresh excised rectilinear segment of the descending thoracic aorta is submerged in the measurement tank. The ultrasonic beam is focused with an acoustic lens, giving the beam a diameter of approx. 3 mm on the artery. The centre line of the beam traverses the vessel diameter, at a point where the external and internal diameters of the latter are respectively 10.5 and 7.5 ram. As before, in Fig. 10, e(t) corresponds to a), C,c(~') to b), h'(t) to c) and P(~:)= Ln (Z(O/Zo) to d). It should be noted that concerning definition of vascular walls, depth discrimination of the method is extremely satisfactory, although certain fixed structures on the interior of the wall have certainly been ignored. This is probably the origin of the small peak observed in the impedance profile, at the end of the second wall. The Z(~)/Zo of 1.036 for the vascular wall, is comparable with the quantative results obtained by Beretsky for a human aortic wall. 7. CONCLUSION

We propose a special method for processing echographic signals, used to obtain the

A new method of obtaining an acoustic impedance profile "

/2~s

b

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some recent work, the number of hypotheses used must still be reduced, with particular reference to orientation of the beam and the geometry of the interfaces, so as to be able to execute in vivo examinations under good conditions. Acknowledgement--Work supported in part by a grant of the Institut National de la Sant6 et de la Recherche M&licale (No. ATP 83.79.115).

Fig. 10. In vitro measurement on excised segment of canine descending thoracic aorta: (a) echographic siena! after depth compensation e(t); (b)cross-correlation function C,c(~); (c) impulse response obtained from e(t); (d) logarithmic impedance profile P(O ~ Ln (Z(~)/Zo).

reflected impulse response from the media observed, for an ultrasonic beam. The method, involving calculation of the correlation function of the signal with a reference echo, associates with each interface in the medium, a spike characterizing the position, s~gn and value of this coefficient of reflection. This set of spikes gives an estimate of the desired impulse response. Under certain conditions, and as already demonstrated by the work of various authors, this response leads to the acoustic impedance profile of the media examined, this profile providing substantially more information than a single echogram. Results obtained o n an in vitro model, demonstrate that the acoustic dynamic impedance range provided by the method, is now only limited by sampling accuracy. Absolute sensitivity of the experimental arrangement appears convenient for studying biological structures. Furthermore, very satisfactory results have been obtained in cases where the echographic signal to be processed is mixed with noise. On the other hand, depth resolution, limited by the global bandwith of the device can induce erroneous results when a number of echoes are superimposed and has still to be improved. Apart from these problems, which are particular to the proposed method, further progress is still required in the formulation of the relation leading from the reflected impulse response to the impedance profile. In spite of

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