SOME

DESIGN

PROBLEMS

A. I. Drozhzhin, Yu. D. Safonov,

OF A. and

A. V.

TRANSDUCERS

ULTRASONIC

UDC 616-073.432.19-71

Tyumin, A. Vasil'ev

The m e a s u r e m e n t of blood flow velocity and the observation and r e c o r d i n g of heart valve movement by means of u l t r a s o n i c s which a r e based on the use of the Doppler effect have disclosed new possibilities in diagnosing c a r d i o - v a s c u l a r d i s e a s e s . This method was f i r s t employed f o r diagnostic purposes by Yoshida in Japan [9, 10], and l a t e r in our c o u n t r y [ i i , 12]. The g r e a t i n t e r e s t in the devices has led to a study of design problems f o r the m o s t important unit, the ultrasonic t r a n s d u c e r . In medical t r a n s d u c e r s piezoelectric elements made of b a r i u m titanate and lead z i r c o n a t e - t i t a n a t e (LZT) c e r a m i c s have been widely employed. Quartz finds p r a c t i c a l l y no use as a m a t e r i a l in p r a c t i c e except for high-frequency ranges (15 MHz and above). When designing diagnostic t r a n s d u c e r s a n u m b e r of c h a r a c t e r i s t i c s m u s t be kept in mind. The f i r s t of these is that the operating condition depends On the purpose of the apparatus. Thus, for continuous radiation two s e p a r a t e t r a n s d u c e r s a r e employed and t h e r e f o r e it is possible to investigate s e p a r a t e l y the receiving and radiating conditions together with the special c h a r a c t e r i s t i c s f o r them. The second c h a r a c t e r i s t i c is that the working medium has a low acoustic impedance (pC)* with r e spect to the pC of the piezoelectric element itself which runs f r o m 22 • 105 to 30 • 105 g / c m 2 • s e c . This has a g r e a t influence on the choice of t r a n s d u c e r operating conditions, and in some c a s e s (if special m e a s u r e s a r e not taken) it is a v e r y r e s t r i c t i v e f a c t o r in achieving the p a r a m e t e r s specified for apparatus. According to the data of V. B a i e r [4] and also of I. E, t~l'piner [5, 6] the pC of soft human t i s s u e s v a r i e s f r o m 1.34 • 105 to 1.7 • 105g/cm 2 • sec including fatty and m u s c u l a r t i s s u e s and bone m a r r o w . Bony tissue has a pC = 6.2 • 105 g / c m 2 • s e c . It is t h e r e f o r e seen that the objects being examined are situated a d m i s t t i s s u e s with n e a r l y the s a m e pC so that the reflected signals a r e v e r y low and a v e r y sensitive r e c e i v e r is required to detect them. The p r i m a r y c h a r a c t e r i s t i c s of an ultrasonic t r a n s d u c e r a r e the operating conditions of the r a d i a t o r , the intensity of the radiation, the voltage on the t r a n s d u c e r , the m a t e r i a l , the t r a n s d u c e r dimensions, the s t r u c t u r a l f e a t u r e s , the sensitivity of the receiving piezoelectric element, and the operating frequency (the frequency of the ultrasonic vibrations). The universal c h a r a c t e r i s t i c f o r piezoelectric t r a n s d u c e r s in the radiation mode is in the intensity of the ultrasound in the medium being examined. The m a x i m u m intensity of the radiation is limited to 0.2 W / c m 2, and the minimum by the threshold of sensitivity f o r the amplifier, which is d e t e r m i n e d by its noise f a c t o r . Starting f r o m the m a x i m u m radiation intensity p e r m i s s i b l e in tissue we will determine the m a x i m u m voltage that can be supplied to the piezoelectric element [2]: ueff

=

~

e33

(1)

• The notation is explained at the end of the a r t i c l e . Voronezh Polytechnic Institute and Voronezh Medical Institute. T r a n s l a t e d f r o m Meditsinskaya Tekhnika, No. 5, pp. 8-13, S e p t e m b e r - O c t o b e r , 1968. Original a r t i c l e submitted D e c e m b e r 12, 1967.

251

To provide a radiation intensity that does not exceed the tolerable value a low voltage (several volts) is needed to d r i v e a piezoelectric radiating element made f r o m L Z T c e r a m i c . This is completely safe f o r the staff personnel and requires no special m e a s u r e s to insulate the c u r r e n t - c a r r y i n g w i r e s . T r a n s d u c e r s in the receiving mode are c h a r a c t e r i z e d by their sensitivity which d e t e r m i n e s (all other things being equal) either the nviewing" depth or the gain needed in the receiving portion of the apparatus. The design of t r a n s d u c e r s in the receiving mode involves both electric and acoustic matching. Acoustic matching makes it possible to i n c r e a s e the sensitivity and to b r o a d e n the frequency r e sponse of the piezoelectric element in the neighborhood of the operating frequency. In o r d e r to m a t c h the piezoelectric element with the medium being examined, use is made of a m a t c h ing l a y e r having a thickness in multiples of a q u a r t e r wavelength (k/4) which is made of a m a t e r i a l with a pC lower than the pC of the piezoelectric element and higher than the pC of the medium being examined. F o r even multiples of X/4 the quality f a c t o r of the t r a n s d u c e r is i n c r e a s e d and the pass band is narrowed. F o r odd multiples the pass band is broadened, thus promoting the undistorted t r a n s m i s s i o n of a pulse. The matching l a y e r is fabricated f r o m epoxy r e s i n s , organic g l a s s , and polystyrene which have a low pC and are good s t r u c t u r a l m a t e r i a l s . Curves a r e given in the l i t e r a t u r e [1-3] for the acoustic t r a n s m i s s i o n and reflection coefficients as a function of the pC of the medium and also as a function of the matching layer thickness with various m a terials. If, in o r d e r to broaden the frequency band, the piezoelectric element is loaded with a damping medium that has a f a i r l y high pC, then with a m i s m a t c h between the piezoelectric element and the tissue (or water) a large part of the radiated power is taken up by the damping medium. When the piezoelectric element is half a wavelength in thickness, the radiated powers are related by: N1 PICI ~V~ -PzC2'

(2)

If p2C2 > PlCi, as is usually the c a s e , then N 2 > N i. The lower the pC of the medium into which the piezoelectric element is radiating, the higher is its quality f a c t o r , the m o r e the pulse is prolonged, and the lower is the p r e s s u r e developed in the medium being examined. It is well known that [8] the quality f a c t o r of a piezoelectric element can be determined f r o m the formula:

Q=

4 V

4(1 +~z~z)~--(~z+~z)~(2+~) (a~+~),

'

(3)

where z._..L

p1Cx

~ z ~ Zo --poCo;

z~

p~Cs

~ z ~ Zo --poCo"

When the radiation is on one side Z0

[~z=0andQ-- 2 zl According to the data presented above for the quantities z 0 and z 1 the quality f a c t o r of a p i e z o e l e c tric element radiating in one direction into tissue or water will be approximately equal to 25. When a damping medium is p r e s e n t (flz >> a z ) , the quality f a c t o r will be entirely determined by this medium: for instance, when flz = 0.3, Q = 5. The c h a r a c t e r i s t i c which is m o s t commonly considered in the calculation and design of t r a n s d u c e r s is the g e o m e t r i c shape of the radiating surface. The t r a n s d u c e r dimensions and the shape of the radiating

252

.g

~

/

[~°m°z ,

~mQ~TL[7~ j

qmQx •.~

R~

~°'~111~% ~ ~ o

A 2

/

3

~

~

!~---~

O[E

[~!

5

2

, 3

!//

IIIDmmax

m" . Inmln i~I $ I

Operating frequency fo (in MHz) Operating frequency jeo (in MHz) Fig. 1. A r e a s r e c o m m e n d e d f o r choosing the p i e z o e l e c t r i c e l e m e n t dimensions of a t r a n s d u c e r f o r c a r d i a c diagnosis. (A) R e gion of choice for the dimensions of p i e z o e l e c t r i c e l e m e n t s in the shape of h a l f - d i s k s : Rmin) m i n i m u m radius of the h a l f - d i s k p i e z o e l e c t r i c e l e m e n t s , Rmax) m a x i m u m radius of the h a l f - d i s k p i e z o e l e c t r i c e l e m e n t s ; (B) region of choice f o r the dimensions of a p i e z o e l e c t r i c r a d i a t o r disk: Damin) m i n i m u m d i a m e t e r of the p i e z o e l e c t r i c r a d i a t o r disk; Da max ) m a x i m u m d i a m e t e r of the p i e z o e l e c t r i c r a d i a t o r disk; (C) region of choice f o r the d i m e n sions of a ring p i e z o e l e c t r i c r e c e i v e r : Dinmin ) m i n i m u m inner d i a m e t e r of the ring; Dinmax) m a x i m u m inner d i a m e t e r of the ring; Domin ) m i n i m u m outer d i a m e t e r of the ring; D o m a x ) m a x i m u m outer d i a m e t e r of the ring; Hmin) m i n i m u m width of the ring. and r e c e i v i n g p i e z o e l e c t r i c e l e m e n t s play an i m p o r t a n t p a r t in t r a n s d u c e r s f o r diagnostic a p p a r a t u s : t h e y d e t e r m i n e the directional p a t t e r n t h a t c h a r a c t e r i z e s the s e l e c t i v e p r o p e r t i e s of a t r a n s d u c e r and the nviewing" depth of the objects being examined. The l a r g e r the d i a m e t e r of the r a d i a t o r , the s m a l l e r the angle of d i v e r g e n c e of the u l t r a s o n i c b e a m at a specified f r e q u e n c y , i.e., the s e l e c t i v i t y of the t r a n s d u c e r is i m p r o v e d and the "viewing" depth is i n c r e a s e d . The e x t e r n a l d i a m e t e r of a t r a n s d u c e r for the diagnosis of c a r d i o - v a s c u l a r activity is limited by the i n t e r c o s t a l spacing which v a r i e s f r o m 8 to 15 ram. When it is c o n s i d e r e d that the radiation and r e c e p t i o n functions should be s e p a r a t e d for a continuous radiation condition and that the t r a n s d u c e r dimensions a r e r e s t r i c t e d , the t r a n s d u c e r m a y be f a b r i c a t e d in the f o r m of a s p l i t - c o m b i n a t i o n s t r u c t u r e and the p i e z o e l e c t r i c e l e m e n t s in the f o r m of h a l f - d i s k s or a diskin a ring. The d i m e n s i o n s of the h a l f - d i s k s , of the radiating disk, and of the r e c e i v i n g ring p i e z o e l e c t r i c e l e m e n t s a r e chosen in a c c o r d with the c u r v e s of Fig. 1. The a r r a n g e m e n t of a combination t r a n s d u c e r w h e r e b y the radiating disk is enveloped by the r i n g receiving p i e z o e l e c t r i c e l e m e n t m a k e s it p o s s i b l e to achieve a good effect in the radiation mode with limited t r a n s d u c e r dimensions (on account of t h e b e t t e r m a t c h to the e l e c t r i c oscillation g e n e r a t o r ) . In addition, t h e r e is l e s s need to orient the t r a n s d u c e r with r e s p e c t to angle although the directional c h a r a c t e r i s t i c s of the p i e z o e l e c t r i c e l e m e n t a r e s o m e w h a t i m p a i r e d . According to the data of L. B e r g m a n [2] and I. M a t a u s h e k a [1], within the distance r2

R0 = T f°

(4)

the r a d i a t e d power is c o n c e n t r a t e d p r i m a r i l y inside the confines of a cylindrical b e a m having a c r o s s - s e c tional a r e a equal to the active zone a r e a of the p i e z o e l e c t r i c e l e m e n t (Fig. 2).

253

J°r

~ MHz

~ii

40

yO

MHz

d'MHz 2 MHz

/0

I

I

I

2

4,

0

[

8

8

D (in mm)

Distance to Diam. of the valve the valve (in mm) (in mm)

Pulmonary Aortic Tricuspid _ Mitral

46

_

5-Y - 6 0

2Y - JY

£0

20 - 3Y

- 80

.gY - 80

YY - 40

80 - 100

dY - 60

I

I

p

2

4

~

I

8 D(in ram)

F i g . 3, A p p a r a t u s a n g l e of the ultrasonic beam.

F i g . 2. N e a r zone of the r a d i a t o r .

Valves

MHz MHz :/o * MHz f l , 5 MHz

At g r e a t e r d i s t a n c e s ( s e e F i g . 2) t h e b e a m d i v e r g e s a n d b e c o m e s c o n e s h a p e d . The a n g l e b e t w e e n t h e g e n e r a t r i x e s of t h e c o n e ( F i g . 3) i s :

c cp~ arc sin 1.22 ~-~-.

(5)

y~

io

¢o I

o

l

20

I

I

~o

I

I

6"0

I

I

80

I

I

IOO

Z (in mm)

F i g . 4. D i a m e t e r of a s u r f a c e b e i n g s o u n d e d (D) a s a f u n c t i o n of t h e d i s t a n c e to t h e o b j e c t b e i n g e x a m i n e d (L) when t h e d i a m e t e r of t h e r a d i a t o r i s 4 m m a n d i t s o p e r a t i n g f r e q u e n c y is 3 MHz.

In o r d e r to a c h i e v e s e l e c t i v e l o c a t i o n of the o b j e c t s b e i n g e x a m i n e d w i t h a s e t of r a d i a t o r d i m e n s i o n s it is n e c e s s a r y to know t h e s i z e of t h e s u r f a c e b e i n g s o u n d e d . A g r a p h i c a l m e t h o d c a n b e u s e d to c a l c u l a t e t h i s s u r f a c e . The g i s t of it i s a s f o l l o w s : A f t e r c h o o s ing t h e o p e r a t i n g f r e q u e n c y and t h e d i m e n s i o n s of t h e radiating piezoelectric element from the curves given in F i g . 1 the l e n g t h of t h e n e a r z o n e R 0 i s d e t e r m i n e d ( f r o m t h e c u r v e s s h o w n in F i g . 2). T h i s v a l u e is p l o t t e d on the g r a p h p r e s e n t e d in F i g . 4.

At p o i n t A c o r r e s p o n d i n g to t h e end of t h e n e a r z o n e c o n s t r u c t t h e a n g l e ~ o b t a i n e d f r o m the c u r v e s shown in F i g . 3, and a t the d i s t a n c e of t h e o b j e c t b e i n g e x a m i n e d , t h e d i a m e t e r of the s u r f a c e b e i n g s o u n d e d is found. A s s o c i a t e d w i t h t h e g e o m e t r i c a l s h a p e and d i m e n s i o n s of t h e r a d i a t o r is a p a r a m e t e r l i k e the o p e r a t ing f r e q u e n c y t h a t is i n c l u d e d when t h e d i r e c t i o n a l c h a r a c t e r i s t i c s of t h e r a d i a t o r a r e b e i n g e v a l u a t e d . The o b j e c t s b e i n g c h a r t e d in t h i s c a s e a r e v a l v e s o r m u s c l e s w h i c h a r e m o v i n g a t a n e g l i g i b l e v e l o c i t y c o m p a r e d w i t h t h e p r o p a g a t i o n v e l o c i t y of u l t r a s o u n d in t i s s u e s . T h e r e f o r e t h e D o p p l e r f r e q u e n c y c a n b e found f r o m t h e f o r m u l a : 2V Fa = f0 "L'-cos a.

(6)

The D o p p l e r f r e q u e n c i e s c o m p u t e d b y m e a n s of Eq. (6) f o r h e a r t m u s c l e and v a l v e s w i t h an u l t r a s o n i c b e a m at n o r m a l i n c i d e n c e c a n b e put in t h e f o r m of a g r a p h ( F i g . 5). I t is s e e n f r o m t h i s g r a p h t h a t a s the o p e r a t i n g f r e q u e n c y of t h e r a d i a t i o n i s i n c r e a s e d , t h e b a n d of t h e D o p p l e r f r e q u e n c i e s A F d o b t a i n e d a s a r e s u l t of m o t i o n in t h e h e a r t m u s c l e a n d v a l v e s i s i n c r e a s e d and it b e c o m e s e a s i e r to s e l e c t . The f o l l o w i n g i n f o r m a t i o n i s u s e d to c h o o s e t h e o p e r a t i n g f r e q u e n c y of a t r a n s d u c e r : A s the o p e r a t i n g f r e q u e n c y i s i n c r e a s e d t h e u l t r a s o n i c a b s o r p t i o n i n c r e a s e s , a n d in o r d e r to r e c e i v e r e f l e c t e d s i g n a l s a r r i v i n g f r o m c o n s i d e r a b l e d e p t h it i s n e c e s s a r y to i n c r e a s e t h e s e n s i t i v i t y of t h e r e c e i v e r , w h i c h i s n o i s e

254

limited; for the s a m e dimensions of the r a d i a t o r its directional c h a r a c t e r i s t i c s a r e improved so that the energy can be c o n c e n t r a t e d into a n a r r o w b e a m ; t h e r e is an i n c r e a s e in the Doppler frequency, which is c a r r y i n g the information about the object being examined. With a reduction of the operating frequency the a b s o r p tion in the medium is reduced and the sounding depth is i n c r e a s e d .

Y

V

A reduction of the Doppler frequency is undesirable because it leads to complexity of the apparatus; it is m o r e difficult to filter the lower frequencies received f r o m heart muscle o r blood v e s s e l walls.

2

It follows from this discussion that it is better to choose a higher operating frequency, but the i n c r e a s e d ultrasonic absorption and the reduced sounding depth at high frequencies f o r c e s a c o m p r o m i s e solution. 2 d 4 ~Operating frequency fo (in MHz) Fig. 5. Graph of the Doppler f r e quencies for valves and walls of the heart. Fdvmax) maximum Doppler frequency for h e a r t valves; Fdvrnin ) minimum Doppler frequency for h e a r t valves; F d m m a x ) m a x i m u m Doppler frequency for h e a r t muscle; Fdmmin) minimum Doppler f r e quency for h e a r t m u s c l e ; AFdmin)

Experimental data shows that a radiation frequency in the range f r o m 2 to 5 MHz can be r e c o m m e n d e d . In addition, it is n e c e s s a r y to take into c o n s i d e r a t i o n the ability of the human ear (its frequency c h a r a c t e r i s t i c s ) to hear the band of the Doppler frequencies. Other t r a n s d u c e r p a r a m e t e r s - the radiation r e s i s t a n c e , the capacity of the piezoelectric element, and also the e l e c t r o m e c h a n ical coupling c o e f f i c i e n t - m e r e l y determine the r e q u i r e m e n t s for the electric oscillation g e n e r a t o r . Specifically, when matching the g e n e r a t o r with the piezoelectric element it is n e c e s s a r y to take into account the electric input impedance of the latter which depends on the acoustic impedance of the media that are loading the piezoelectric element.

minimum band of the Doppler f r e quencies; A F d m a x ) m a x i m u m band

Notation: Pi is the density of the medium; C is the ultrasonic velocity in the medium; z 1 = plC~ is the acoustic r e s i s t a n c e of the medium being examined; z 0 = PoCo is the acoustic r e s i s t a n c e of the of the Doppler f r e q u e n c i e s . piezoelectric element; t 2 = P2C2 is the acoustic r e s i s t a n c e of the damping medium; z m = PmCrn is the acoustic r e s i s t a n c e of the matching l a y e r ; I is the intensity of the radiation; N 1 is the power radiated into the medium being e x a m ined; N 2 is the power radiated into the damping medium; f o is the operating frequency; r is the radius of the r a d i a t o r ; V is the velocity of the movement in the object being c h a r t e d ; a is the angle between the plane of the object being examined and the axis of the r a d i a t o r (the angle of incidence); d o is the thickness of the piezoelectric element; 133 is the p i e z o e l e c t r i c modulus.

LITERATURE i. 2. 3. 4. 5. 6. 7. 8. 9. i0. ii. 12.

CITED

I. Mataushek, Ultrasonic Engineering [in Russian], Moscow (1962). L: Bergman, Ultrasonics and Its Use in Science and Engineering [in Russian], Moscow (1957). O.I. Babikov, Ultrasonic Methods of Physico-Chemical Analysis [in Russian], Moscow (1962). V. Baler and ]~. Derner, Ultrasonics in Biology and Medicine [in Russian], Leningrad (1958). I.E. I~l'piner, Ultrasonics. Phvsieo-Chemical Action [in Russian], Moscow (1963). L.D. Rosenberg and I. E. ]~l'piner, in: Electronics in Medicine [in Russian], Moscow (1960), p. 260. M.D. Gurevich, in: Electronics in Medicine [inRusslan], Moscow (1960), p. 268. H.B. Huntington and Y. W. Hughes, Franklin Inst., 245, Pt. i, 1 (1948). S. Satomura et al., J. Aeoust. Soc. Am., 29, 1181 (1957). Yoshida, Cited in M. N. Turnanovskii, et al. M.N. Tumanovskii et al., in: Electronics and Chemistry in Cardiology [in Russian], No. 2, Voronezh (1965), p. 13. V.M. Lub~ eta[., in: Electronics and Chemistry in Cardiology [in Russian], No. 3, Voronezh (1966), p.5.

255