Study of variation in ultrasonic propagation parameters of bone, in vitro, by X-ray diffraction technique

Applied Acoustics 26 (1989) 45-55

Study of Variation in Ultrasonic Propagation Parameters of Bone, in Vitro, by X-Ray Diffraction Technique

S a n j a y Y a d a v , S e e m a Singhal, V. R. Singh & K. C. N a g p a l National Physical Laboratory, New Delhi 110012, India (Received 6 June 1988; accepted 29 June 1988)

ABSTRACT Ultrasonic properties of animal bones, in vitro, are studied. A large variation in the results is.found which is due to variations of bone parameters and chemical constituents, such as co'stalliniO'. In order to correlate the crvstallini O' and ultrasonic parameters of a bone, an X-ray diffraction technique is used. It is.found that co'stallinio' of hone samples improves for higher values of ultrasonic velociO'. The presence of a-quartz is .found in particular anbnal bones.

1 INTRODUCTION The ultrasonic propagation properties o f bone have been studied in the recent past t - 6 with respect to anatomical structure, 7- 8 physical behavior 9 and chemical constituents of bone, for example, mineral and ash, t°'1 t using various conventional techniques. 1-~1 F u r t h e r studies on ultrasonic properties of animal bones in vitro are, however, made for the different states, viz. fresh, wet and dry, to investigate possible causes o f a large variation in the results. An X-ray diffraction technique is used to correlate the crystallinity of bone with its ultrasonic velocity. 45 Applied Acoustics 0003-682X/89/$03.50 ,~i~ 1989 Elsevier Science Publishers Lid, England. Printed in Great Britain

46

Sanjay Yadav, Seema Smghal, V. R. Singh, K. (7. Nagpa/

Fig. 1,

Experimental bone specimens used in the present investigation.

2 MATERIALS AND METHODS

2.1 Specimen preparation The experimental animal bone specimens, in vitro, were cleaned first by mechanical and then by chemical means. The samples were shaped from the mid-diaphysis of fresh animal bones by using a hexablade, and running water was used as a coolant during its cutting. Some of the samples were dried and some kept in saline solution for a period of 10 days. The shapes of dry and wet bone samples are shown in Fig. 1. The animal bones (obtained from a butcher's shop) were crushed into powder by using an electric bone cutter (this one used by a craftsman (Fig. 2)). The powder thus obtained was

Fig. 2.

Electric bone cutter for specimen preparation.

Variation in ultrasonic propagation parameters of bone

47

finely ground with the help of a dry ball milling machine for about 24 h, and was then sieved in Jayant Test Sieves of Mesh no. 400, i.e. 37 microns size. This powder was then compressed into discs of regular shapes by using polyvinyl acetate as a binder. 2.2 Ultrasonic velocity measurement The experimental set-up used in the present study is shown in Fig. 3. The ultrasonic velocity was measured in bone specimens by using an ultrasonicdouble-probe-through-transmission technique.l 2,14,1 s A pulser-receiver (in

Fig. 3. Photograph of the experimental set-up for ultrasonic velocity measurement in bones.

this case Panametrics model 5052 PR) was used both for exciting the transmitting transducer and for receiving a signal from the receiving transducer. The received signal was displayed on a dual-trace storage oscilloscope (in this case ECIL type OS 768.8). The ultrasonic velocity in bone was then determined by using the following relationship: D t where D is the depth of the sample and t the time measured at the cathoderay oscilloscope.

48

Sanja.v Yadav, Seema Singhal, V. R. Singh, K. C. Nagpa/

j0

Poth diff, M O + O N = d S i n e + d

Sine

=2dSin e F o r c o n s t . I n t f . 2 d S in O = n x

Fig. 4.

X-ray diffraction principle.

2.3 X-ray diffraction technique With the X-ray diffraction technique, a beam of X-rays falls on a substance of regular periodic arrangement of atoms and the relative absorption of Xrays by the substance becomes a function of its average density or average atomic number of constituents. The diffracted beam then results in particular direction. Figure 4 illustrates the basic principle of X-ray diffraction from the crystals of a bone specimen. All the atoms are situated in rows separated by a distance d. When two parallel waves strike a set of crystal planes at an angle and are scattered in different directions, the angle of incidence is equal to angle of reflection. 13 Reinforcements occur when the path difference in the path lengths of two rays is equal to a whole number of wavelengths. Hence, by Bragg's law, n2 = 2dsin 0 where 2dsin 0 is the path difference (Fig. 4). The schematic diagram of an X-ray diffractometer used in the present study is shown in Fig. 5. The bone crystal diffracts X-rays of known wavelength. The value of wavelength was fixed such that different values o f d are recorded at different angles of reflection 0. The intensity of the diffracted beam was measured directly with the help of an electronic counter, which was driven manually or electrically at a constant angular velocity about the axis of the diffractometer to obtain a required angular position. The X-rays diffracted by bone crystalline phase were detected automatically for known wavelength. The angle 0 was measured directly with the calculation of d.

Variation in ultrasonic propagation parameters of bone

49

.o/ .,..; \ ZO~

1toO

20

Fig. 5. Working principle of X-ray diffractometer. C = powder specimen; F = focus slit; G = counter; K = graduated scale; O = diffractometer axis; S = X-ray source; T = target of X-ray tube; A and B are special slits which define and collimate the incident and diffracted beams; E and H are mechanically coupled.

3 RESULTS A N D DISCUSSION Table 1 shows the ultrasonic parameters at 3 MHz for dry as well as wet states of adult and infant bone samples. The density of bone samples both in infant and adult is found to increase with the increase in dryness of bone sample, though the density of infant bone is lower than that of the adult one. The average ultrasonic propagation velocity in the adult and infant bone specimens is found to be 3300ms-1 and 2500ms-1 respectively, while the values of the acoustic impedance (Z = pv) is higher than that of air, water and soft tissues. TABLE 1 Ultrasonic Parameters of the Animal Bone at 3 MHz Serial no.

I 2 3

4 5 6

S a m p l e spec(h'cation

Adult (dry, after 5'months) Infant (wet, after 20 days) Adult (dry, after 2.5 months) Adult [dry, after 3 months} Adult [fresh, after 15 days) Infant [dry, after 2 months)

Density p ( k g m - 5)

V e l o c i t y z' (m s - 1)

Acoustic impedance Z ( tO 6 k g m - 2 s - 1)

Crystallinity t~f the bone s p e c i m e n

1 631 1 764

3 126 2413

5.09 4.03

Poorly crystalline Poorly crystalline

1 871

3066

5.73

1910

3118

5.85

Carbonate apatite is in slightly bcuer crystallinity form Crystallinity improves

I 956

3 364

6.58

1 784

2 560

4-56

Gradual improvement in crystallinity Poorly crystalline

Sanjay Yadav, Seema Singhal, V. R. Singh, K. C. Nagpal

50

The air pockets between the transducer and the bone sample produce a large reflection factor, which curbs the entry of energy into the sample. Due to the porous nature of the bone, air stays in the pores and detection of ultrasonic wave is difficult. A large variation in the values of acoustic impedance has been further studied and correlated with the crystalline behaviour of bone. The X-ray beam diffracted by a bone crystal gives information on parameters like crystallinity and nature of crystalline phases in bone layers. The crystalline phase detected in the bone specimen used in the present case is carbonate apatite (Dahllite), i.e. (Ca, Mg, Na, H3) 5 (P,C)3012(OH, C1, F). Calcium carbonate is present in poorly crystalline form. Figure 6(a) represents the intensity pattern of the diffracted beam from fresh adult bone sample after 15 days under atmospheric conditions. (a) ~oo 90 80 70 ~

60

~

50

0

~

4O 50 20 ~0

0 60

515

410

415

510

Angle

l

315

~0

I 25

1

20

(deg)

(b)

60

20

I0 7O

65

6O

55

50

45 Angle

40

35

; 30

I 25

20

(deg)

Fig. 6. Diffractionpatterns for bone specimens from various types of bone. (a) adult bone (dry, after 5 months);(b) infant bone (wet, after 20 days);(c) adult bone (dry, after 2.5 months); (d) adult bone (dry, after 3 months); (e) adult bone (fresh, after 15 days).

Variation in ultrasonic propagation parameters of bone

5!

(c) 90 8C 70 6C 5C 4C c

30

10 0

I 50

51

60

•;

,o

315

3tO

215

2o'

i5'

Angle (deg)

(d)

=

2¢

"1~

i 65

I ao

I 55

I ~50

I ,15

Angle

I 4o

i 35

l 30

I 2~

l 20

t 15

(deg)

(e) IG ?0

~ 4o 20 JO

060

$1

50

415

410

I 35 Angle (¢leg)

310

Fig. 6.--contd.

2~

20

II5

io

--

--

3'068(8) 2.797(46) 2.718(32) 2.644(/0) 2.508(2) . 2.252(1 l) --

--

3.427(7)

--

.

4.27(3) 4'058(3) 3-867(2) 3'44(19) 3"351(44) 3'! 1(17) 2"797(32) 2-718(58) --. 2.2595(20) -2"146(3) 2-049(3)

in fan t (wet, after 20 days)

Adult (dry, after 5 months)

-4-00(21

2

l

. . 4.031 (4) 3.857(5) 3.427(•5) 3-345(4/) 3-058(•5) 2.797(88) 2.718(68) 2-629(20) 2.527(6) . . 2.251 5(24) 2.206(5) 2.141(6) 2.040 5(3)

Adult (dr)', after 2"5 months)

3

4

2 ' 0 4 0 5(3)

2.718(76) 2-636(16) 2.543(3) . 2.254(25) --

2"797(100)

. 4-058(3) 3.857(6) 3-427(19) -3"058(2•)

.

Adult (dry, after 3 months)

Serial no.

2

2.265(•9) --2.040 5(3)

-3"85(5) 3.427(•4) -3-099(13) 2-797(70) 2-7 ! 8(55) 2-644(20) 2-508(5) 2'25(•8) --2'053(4)

-3.867(5) 3-427(23) -3-078(•2) 2.797(78) 2-718(46) 2-644(16) 2-501(2)

Infan t (dr)' after 2 months)

6

Diffraction Patterns

Adult (.fresh after 15 days

5

from X-Ray

T A B L E

Data for d Values Measured

2.27(30) --2"05(10)

3"096(30) 2-811(100) 2-731(80) 2.627(20) 2.533(10)

--

3.342(100) -----2.457(8) -2.237(4) 2-127(6) --

-4-09(10) 3.897(20) 3.446(30)

Dahllite (Ca, Mg, Na. H3) 5 (P, C)3012 4.257(22) ----

:t-Quartz SiO 2

2

2

.

1'361(3)

. 1-299(2)

--

. --

.

.

.

.

.

.

The

.

.

in parentheses

.

.

.

1"237(3)

.

--

written

1.404 2(2)

--

values

--

--

.

.

.

.

!450

.

.

1-450 8(4)

-

-

1-534 8(3)

-

-

1-582 6(3)

1.605 2(3)

-

1.642(2)

--

-

1.639(2)

1-683(2)

--

indicate

.

.

.

1-424(2)

.

.

.

.

.

1-434 8(3)

6(2)

1.676 4(2)

1.724 6(5)

. . 1-718 6(5)

--

1-82(2)

1-7906(/3)

1838(9)

. 1-838(8)

.

1"886(4)

1'884(4)

.

. . 1.724 6(7)

.

1-940(12)

.

. 1.941(11}

1.790(6)

-

. 1838(7)

-

.

1.7906(7)

-

-

. 1-937(9)

.

.

.

--

.

--

.

--

--

--

.

.

.

.

.

peaks.

1-721(5)

1.7906(15)

1-80(4)

. !-831(8)

the intensity

.

.

.

.

.

1"888(5)

. 1"941(/2)

.

.

.

.

.

.

--

--

--

--

--

.

1.752(3) !-724 6(6)

1.781(4)

1-797(5)

1"838(5)

1"895(4)

1"939(10)

. --

--

--

--

--

.

1-754(7) 1.72(7)

--

--

!'838(10)

!'884(5)

1"939(/3)

1-1804(3)

!-1978(1)

1"999(2)

1 . 2 2 8 5(•)

1.255 8(2)

1.371 8(8) 1.288(2)

1'3820(6)

1-418 9(4)

1"453 6(1)

1.541 8(9)

1-608(4)

1 . 6 5 9 1(2)

1.671 9(4)

---

--

1-802(4)

1"8179(14)

--

1-979(4) -!-947(30)

--

--

--

--

--

---

--

--

--

--

--

--

--

1.757(10) 1.723(10)

1.785(10)

i.808(10)

--

1878(/0)

1"893(10)

e~

54

Sanjay Yadav, Seema Singhal, V. R. Singh, K. C. Nagpal

The intensity pattern of the diffracted beam from wet infant bone after hydrating for 20 days in saline solution is shown in Figure 6(b) and the intensity patterns for a dry adult bone after 2-5 months, 3 months and 5 months are shown in Fig. 6(c), (d) and (e), respectively. The data has been analysed for values of d and results are shown in Table 2. The difference in the crystallinity of different bone samples is easily seen from these patterns. In the case of infant bone in wet state, the crystallinity which corresponds to the sharpness of X-ray diffraction peaks is of the same order as that of a dry adult bone after 2"5 months. It is also observed that the crystallinity of the bone improves with the increase in ultrasonic velocity (Table 1). In addition to the above chemical constituent, c<-quartz has also been observed for the first time, with a sharp peak in Fig. 7, in some of the solid bone samples and in a powder made from different bones. It supports the fact that bone is a piezoelectric material. IOO

gO 80 70

6O ~o c 40

3O 20

j

I0~ 1 55

Fig. 7.

I 30

I 25

I 20 Angle (deg)

I 15

I I0

Diffraction pattern showing sharp peak of c<-quartz in bone.

4 CONCLUSIONS Ultrasonic parameters of bone have been measured and are found to vary with its crystallinity. The ultrasonic velocity has been found to increase with improvement in the crystallinity. The presence of 0<-quartz in the solid animal bone and its powder has been found for the first time. This property may lead to the development of a piezoelectric transducer element using bone material.

Variation in ultrasonic propagation parameters of bone

55

A C K N O W L E D G E M ENTS The authors are indebted to Prof. S. K. Joshi, Director, National Physical Laboratory, New Delhi, for his deep interest during this investigation. One o f the authors, M r Sanjay Yadav, is grateful to the Director, Bureau o f Police Research and Development, Ministry of H o m e Affairs, G o v e r n m e n t of India, New Delhi, for the award of a Fellowship for this investigation. REFERENCES 1. Abendchien, W. & Hyatt, G. W., Ultrasonics and selected physical properties of bone, Clin. Orthop., 49 (1970) 294. 2. Yoon, H. S. & Katz, J. L., Ultrasonic Tissue Characterisation II. Ed. L. M. Linger, National Bureau of Standards Spec., 1979, p. 525. 3. Lang, S. B., Ultrasonic method for measuring elastic coetticient of bone and results on fresh and dried bovine bones. IEEE Trans. Bio. Med. Engg, BME-17 (1970) 101. 4. Yoon, H. S. & Katz, J. L., Ultrasonic wave propagation in human cortical bone. I. Theoretical considerations for hexagonal symmetry. J. Biomechanics, 9 (1976) 407. 5. Yoon, H. S. & Katz, J. L., Ultrasonic wave propagation in human cortical bone. II. Measurements of elastic properties and micro-hardness. J. Biomechanics, 9 (1976) 413. 6. Ambardar, A. & Ferris, C. D., A simple technique for measuring certain elastic moduli in bone. Biomedical Sci. Instrum., 12 (1976) 23. 7. Katz, J. L. & Yoon, H. S., The structure and anisotropic mechanical properties of bone. IEEE Trans. Bio. Med. Engg, BME-31, 12 (1984) 878. 8. Lakes, R., Yoon, H. S. & Katz, J. L., Ultrasonic wave propagation and attenuation in wet bone. J. Biomedical Engg, 8 (1985) 143. 9. Pal, S., Saha, S. & Reddy, G. N., Frequency dependence of ultrasonic characteristics of cancellous bone. Proc. Third Southern Biomed. Engg Conference. Ed. L. C. Sheppard, Pergamon Press, New York, 1984. 10. Currey, J. D., Mechanical properties of bone tissue with greatly differing functions. J. Biomechanics, 12 (1979) 313. I I. Currey, J. D., Change in impact energy absorption of bone with age. J. Biomechanics, 12 (1979) 313. 12. Singh, V. R., Yadav, S., Ahmed, A. & Bindal, V. N., Ultrasonic propagation parameters of in vitro animal bones. Presented at workshop-cum-conferenceon ultrasonics, instrumentation, Mathematical modelling and applications. Shimla, June 4-6 1987. 13. Yadav, S., Singhal, S., Singh, V. R., Nagpal, K. C. & Bindal, V. N., Variation of ultrasonic propagation velocity and X-ray diffraction study in bones, in vitro. Presented at workshop-cum-conference on ultrasonics, instrumentation, Mathematical modelling and applications, Shimla, June 4-6 1987. 14. Singh, V. R., Yadav, S. & Ahmed, A., Journal of Acoustical Society of America (1988), submitted for publication. 15. Yadav, S., Darshan, B., Ahmed, A. & Singh, V. R., Modelling of ultrasonic properties of bone. Proc. Comp.-Tech. 90s, New Delhi (1987) 9.