ABSTRACT
One transducer emits a broadband pulse and the other one acts as a receiver. The two transducers are placed on opposite sides of the bone to be measured. While the calcaneus (heel bone) is the skeletal site, for which most experimental and clinical data exist, the principle has also been applied to measure the œnger phalanges [2-4], the distal radius at the forearm, and the proximal femur at the hip [5,6]. By moving sender and receiver simultaneously in the scan plane perpendicular to the sound beam axis, acoustic images can be generated (Figure 13.2a). For each scan position, the received signal is digitized. The speed of sound c is calculated using a substitution method [7,8]:
c x x
c d
d c TOF f
( , ) ( )
,1 2 = ⋅
− Δ
(13.1)
where d is the thickness of the heel cf is the sound velocity in the coupling ¢uid (water) ΔTOF is the difference of the pulse travel times with and without the sample in the propagation path
13.1 In Vivo Characterization of Bone with Low Frequencies .................................................... 723 13.1.1 Transverse Transmission........................................................................................... 723 13.1.2 Axial Transmission ................................................................................................... 725
13.2 Acoustic Microscopy of Hard Tissues .................................................................................. 726 13.2.1 Wave Interference Contrast ...................................................................................... 729 13.2.2 Confocal Amplitude Contrast ................................................................................... 730 13.2.3 Time-Resolved Techniques ....................................................................................... 731 13.2.4 Tooth Enamel and Dentin ......................................................................................... 733 13.2.5 Bone .......................................................................................................................... 735
13.3 Conclusions ........................................................................................................................... 740 References ...................................................................................................................................... 741
The frequency-dependent attenuation α(x1, x2, f) is found from the ratio of the magnitude spectrum A(x1, x2, f) of the signal transmitted through the heel and a reference spectrum Ar(x1, x2, f) of a signal transmitted through water:
α( , , ) log
( , , ) ( , , )
.x x f A x x f
A x x fr 1 2 10
20= (13.2)
In cancellous bone, the attenuation is nearly linearly increasing with frequency (Figure 13.2c). The slope of the attenuation or broadband ultrasonic attenuation (BUA) is found by a linear regression of α(x1, x2, f) within the usable bandwidth of the transducers.
