Ultrasound in Med. & Biol., Vol. 35, No. 3, pp. 382–394, 2009
Copyright © 2009 World Federation for Ultrasound in Medicine & Biology
Printed in the USA. All rights reserved
0301-5629/09/$–see front matterdoi:10.1016/j.ultrasmedbio.2008.09.022● Original Contribution
IMAGING OF GAPS IN DIGITAL JOINTS BY MEASUREMENT OFULTRASOUND TRANSMISSION USING A LINEAR ARRAYHIDEYUKI HASEGAWA,#,* MICHIKO MATSUURA,† HIROSHI SATO,† TERUKO YAMAMOTO†
and HIROSHI KANAIⴱ,##

Graduate School of Biomedical Engineering; *Graduate School of Engineering; and †Graduate School of Dentistry,
Tohoku University, Sendai, Japan(Received 14 December 2007; revised 18 August 2008; in final form 15 September 2008)

Abstract—In orthodontic dentistry for young subjects, it is important to assess the degree of growth of the jaw
bones to determine the optimum time for treatment. The structure of the digital joint changes with age, with suchchanges correlating to the degree of bone growth (including jaw bones). There are two gaps in the digital jointof a young subject, one of which disappears with aging. In the present study, a method for noninvasive assessmentof such change in the structure of a digital joint was examined, in which continuous-wave ultrasound is radiatedto a digital joint by a single-element ultrasonic transducer. This continuous ultrasound, which passes through thedigital joint, is received by a linear array ultrasonic probe situated opposite the transducer. The probe
simultaneously realizes pulse– echo imaging and imaging of transmission ultrasound, which passes through thejoint. Using this experimental apparatus, the existence and position of a gap can be detected clearly by imaging
the transmission ultrasound on a pulse– echo image. In basic experiments, continuous-wave ultrasound generated
by a planar or focused transducer was radiated to a gap between two acrylic bars, which simulated that in adigital joint; transmission ultrasound, which passed through the gap, was measured with a linear array probe.
The basic experimental results showed that a gap with a width >0.4 mm is detectable and that the width at half
maximum of the amplitude profile of the received transmission ultrasound that passed through the gap correlatedwith the width of the gap. Furthermore, in the preliminary in vivo experiments, transmission ultrasound thatpassed through two gaps in the case of a child was clearly imaged by the proposed method, and that which passed
through only one gap in the case of an adult was also imaged. These results show the possibility for the use of
the proposed method to noninvasively assess the change in the structure of a joint as a result of aging. (E-mail:hasegawa@ecei.tohoku.ac.jp) © 2009 World Federation for Ultrasound in Medicine & Biology.
Key Words: Bone age, Digital joint, Continuous-wave ultrasound, Ultrasound transmission, Linear array.

that assessed by hand radiography. This method would
be useful because the cervical spine is always seen on thelateral cephalometric radiograph. Although these methods give an accurate estimate of bone age, exposure ofhealthy subjects to x-rays is inevitable.
Because ultrasound is useful for noninvasive diagnosis of bone, many studies on ultrasonic measurementof bone have been conducted. Wells (1975) reported the
speed of sound and ultrasonic absorption in bone,whereas Williams (1991) predicted the propagation ofslow and fast waves propagating through bone by Biot’s
theory (Biot 1962) and also experimentally measured
these waves. Otani and colleagues extensively investigated slow and fast waves (Hosokawa and Otani 1997,
1998; Hosokawa et al. 1997; Otani 2005), which propagate in bone marrow and the contained hard structure,
respectively. Therefore, the amplitude of a slow-wave

INTRODUCTION
In orthodontic dentistry for young subjects, it is important to assess the degree of growth of the jaw bones todetermine the optimum time for treatment. The ossification of bones in a hand is often used for assessment ofbone age, such ossification being evaluated by x-ray
imaging of a hand and wrist (Tanner et al. 1975; Rucci etal. 1995; Wit et al. 2005; Jones and Ma 2005). In addition, Khal et al. (2008) have recently proposed a methodby which the degree of bone growth is assessed based on
the maturation of the cervical spine. The bone maturity
assessed by this method was found to correlate well with

Address correspondence to: Hideyuki Hasegawa, Department of
Biomedical Engineering, Graduate School of Biomedical Engineering,Tohoku University, 6-6-05 Aramaki-aza-Aoba, Aoba-ku, Sendai 9808579, Japan. E-mail: hasegawa@ecei.tohoku.ac.jp382

Imaging of gaps in digital joints ● H. HASEGAWA et al.

383

Fig. 1. X-ray image of the second joint of the middle finger. (a) 5-year-old male. The arrowhead indicates the gap thatdisappears with aging. (b) 26-year-old female.

Fig. 2. (a) Ultrasonic B-mode image of the second joint of the
middle finger of a 33-year-old male. (b) Illustration of regions
imaged by pulse– echo imaging.

propagating through the cancellous or trabecular boneincreases as the hard structure decreases, whereas that ofa fast wave decreases. The hard structure in trabecularbone decreases because of osteoporosis and, thus, amethod has recently been developed to quantitatively
estimate bone density and quality by measuring the amplitude change of these waves that cannot be obtained
only from the attenuation coefficient of bone (Otani
2005). Speed-of-sound and attenuation of ultrasound inbone is used widely for characterization of bone (Asai etal. 1996; Wear 2000, 2001a; Bossy et al. 2004). However, the structure of bone is complex, and the measured
sound velocity shows a significant dispersion. Many
studies have been conducted to identify the sources ofthis dispersion (Droin et al. 1998; Wear 2000, 2001b),
and Häat et al. (2006) have attempted to generalize themeasurement of sound velocity in bone. Furthermore,methods for estimating attenuation and spacing of cancellous bone structures by analyzing backscattered ultrasound have been developed (Wear 2003; Pereira et al.
2004) because the aforementioned methods require measurement of transmission ultrasound through the bone,
and it is difficult to apply such methods to bone deep
inside the body. All of these methods measure speed-ofsound and attenuation of ultrasound propagating through,or backscattered from, a large bone to estimate the bonedensity for diagnosis of osteoporosis in elderly subjects,
the quality of bone being the main focus.
The present study was focused on the structure of a
joint. As shown by a method using x-ray imaging (Tanner et al. 1975; Rucci et al. 1995; Wit et al. 2005; Jonesand Ma 2005), the structure of a joint of a young subjectchanges because of aging. In the case of a digital joint ofa young subject, there are two gaps, one of which disappears with aging. The present study investigated an

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Fig. 3. (a) Measurement apparatus to realize pulse– echo imaging and ultrasound transmission imaging simultaneously. (b)Schematic diagram of experimental setup. Both planar andfocused transducers were used for ultrasound transmission.

Volume 35, Number 3, 2009

ultrasonic-based method to noninvasively assess suchchange in the structure of a digital joint by using ultrasound transmission through a joint. Weigel et al. (1982)
conducted ultrasound transmission imaging using sacrificed dogs seven to eight weeks of age. They usedcollimated ultrasound (plane wave) for transmission, thetransmitted ultrasound being focused by an acoustic lenssystem. Their system achieved a spatial resolution of
approximately 1 mm at an ultrasonic frequency of 2MHz. In the present study, higher-frequency ultrasoundwas used for ultrasound transmission through a digital
joint, the gap of such joint usually being ⬍1 mm. Furthermore, focused and unfocused ultrasound were usedbecause the latter may be better for transmission througha narrow gap. Ultrasound transmitted through a gap was
measured by a linear array ultrasonic probe. This experimental setup enables simultaneous pulse– echo imaging
and ultrasound transmission imaging. The feasibility ofthis method was investigated by basic experiments using
acrylic bars. Furthermore, initial in vivo imaging was
conducted for child and adult subjects.
Current methods for assessment of the bone maturity using x-rays are accurate and exposure to radiation isrelatively low. However, ultrasonic methods would supplement x-ray methods because of their absolute noninvasiveness and potential for use in a wide range of
medical institutions, because the cost of ultrasonic equipment is lower than that of x-ray equipment. Unfortunately, no equipment for imaging ultrasound transmission is now commercially available, and thus a newexperimental system was used in this study to examine
the basic concepts of the proposed method.
MATERIALS AND METHODS
Growth of bone in digital joints
Figure 1a and b show x-ray images of the second
joints of middle fingers of a 5-year-old male and 26-year-

Fig. 4. (a) Imaged pattern and (b) amplitude profile along the red line in (a) of transmission ultrasound: (1) planar, 5MHz; (2) focused, 7 MHz.

Imaging of gaps in digital joints ● H. HASEGAWA et al.
0.25
0.125
0
0.25
normalized amplitude

old female, respectively. The gap indicated by the whitearrow in Fig. 1a disappears because of aging. Therefore,a joint with developing bone can be differentiated fromthat with mature bone by identifying whether there are
two gaps. In addition, the width of the gap indicated by
the white arrow in Fig. 1a can be used for evaluation ofbone age. This study was approved by the Ethics Committee on Clinical Investigation, Graduate School of
Dentistry, Tohoku University, and was performed inaccordance with the policy of the Declaration of Helsinki; all subjects gave informed consent.

385

0.125
0
0.25
0.125
0
0.25
0.125
0
0.25
0.125
0

10 mm
10 mm

(a)

10 mm

10 mm
(k)
width at half maximumof amplitude profile [mm]Conceptual overview
Ultrasonic B-mode imaging is useful for morphologic diagnosis of organs. Figure 2a shows a B-mode

4

3

2

1

0
0

[dB]
0
(b)

−20

−40

normalized
amplitude

(c)

0.25

(d)

0.125
0
10 mm

Fig. 5. Example of analysis in basic experiments (diameters ofbars: 10 mm; width of gap: 0.6 mm; planar transducer for
ultrasound transmission): B-mode images (a) with and (b)without exposure of transmission ultrasound, respectively. The
transmitting transducer was placed on the bottom and the linear
array probe was placed at the top. (c) Subtraction image obtained from (a) and (b). (d) Amplitude profile along the red linein (c).

12

3
4
width of gap [mm]Fig. 6. Amplitude profiles at different widths of the gap (planartransducer, diameter of bars: 10 mm): (a) 0 mm, (b) 0.4 mm, (c)0.8 mm, (d) 1.2 mm, (e) 1.6 mm, (f) 2 mm, (g) 2.4 mm, (h) 2.8mm, (i) 3.2 mm and (j) 3.6 mm. (k) Width at half maximum of
the amplitude profile plotted as a function of the gap width(diameter of bars: 10 mm). Planar transducer was used, andwidths at half maximum were obtained from 10 image frames
at each gap width d.

image of the second joint of the middle finger of a33-year-old male. A gap in the joint can be recognized in
the B-mode image shown in Fig. 2a. However, the tissue
structure in the joint is poorly imaged because the incident ultrasound is almost perfectly reflected by the nearsurfaces of bones and the pulse– echo imaging can only
assess the shape of the near surfaces (illustrated by thesolid curves in Fig. 2b). In addition, the exact position ofa gap is somewhat unclear because the image pattern ina gap is inhomogeneous, as shown in Fig. 2a, similar tothat of the surrounding soft tissue. The reason is that the
acoustic impedance of cartilage (of course, there is soft
tissue in a joint) is much closer to that of soft tissuecompared with that of bone (Töyräs et al. 2003), andthere is no distinct echo from a gap.
To overcome this drawback, in this study transmission of continuous ultrasound through a gap in a joint
was imaged in combination with pulse– echo imaging toclearly assess the existence of gaps and their positions. A
linear array ultrasonic probe was positioned, as shown in
Fig. 3a, for pulse– echo imaging of a gap. A singleelement ultrasonic transducer opposite the linear array

Ultrasound in Medicine and Biology
0.5
0.25

normalized amplitude

0
0.5
0.25
0
0.5
0.25
0
0.5
0.25
0
0.5
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0
10 mm

10 mm

width at half maximumof amplitude profile [mm]

(k)
4

3

2

1

0

0

1

2

3
4
width of gap [mm]Fig. 7. Amplitude profiles at different widths of the gap (focused transducer, diameter of bars: 10 mm): (a) 0 mm, (b) 0.4mm, (c) 0.8 mm, (d) 1.2 mm, (e) 1.6 mm, (f) 2 mm, (g) 2.4 mm,(h) 2.8 mm, (i) 3.2 mm and (j) 3.6 mm. (k) Width at half
maximum of the amplitude profile plotted as a function of the
gap width (diameter of bars: 10 mm). Focused transducer wasused, and widths at half maximum were obtained from 10
image frames at each gap width d.

was used for irradiation of continuous-wave ultrasoundfor transmission through the gap. Transmission ultrasound that passed through the gap was received by thelinear array. Ultrasound for transmission was irradiatedcontinuously, and transmission ultrasound that passed
through the gap was imaged together with the pulse-echo
image. Imaged transmission ultrasound clearly showed
the existence of a gap, and the transmission patternprovided information on the width of the gap.
Experimental setup
As shown in Fig. 3b, two acrylic bars were placed
between a 10-MHz linear array probe (UST-5545, Aloka
Co., Ltd., Tokyo, Japan) for imaging and a transducer for
generation of continuous-wave ultrasound to penetrate a
gap with width d between the two acrylic bars. The gap
simulated that between bones in a joint. Transmission
ultrasound that passed through the gap was measured by
the linear array probe. Planar (5Z10I-C, Tokimec Co.,
Ltd., Tokyo, Japan) and focused (7Z10I-PF30-C-K445,
Tokimec Co., Ltd.) transducers, driven by 5-MHz and
7-MHz continuous signals, respectively, were used forVolume 35, Number 3, 2009

generation of transmission ultrasound. The distance between the surface of the transducer and the lower edgesof the acrylic bars was set at 30 mm, which corresponds
to the focal distance of the focused transducer. The
distance between the surface of the linear array probe andthe upper edges of the acrylic bars was set at 20 mm,
which corresponds to the elevational focal distance(fixed focus using acoustic lens). Using this apparatus,
the ultrasound transmitted through the gap could be
imaged together with the object (acrylic bars). RF signals, which contain both continuous-wave and pulsed
ultrasound produced by the transducer and array probe,
respectively, and are received by the array probe, were
sampled at 40 MHz.
As described previously, it is essential for evaluation of bone age of a young subject to investigate
whether one or two gaps exist between the bones in ajoint. Furthermore, it is desirable that the width of thegap be assessed from the measured pattern of transmission ultrasound. In basic experiments, transmission ultrasound was measured by changing the gap width dfrom 0 – 4 mm, with increments of 0.2 mm to investigate
how a small gap can be detected and whether the width

10 mm

10 mm

(a)

width at half maximumof amplitude profile [mm]386

leading
descending

4
3
2
1
0

(b)
0

1

2

3
4
width of gap [mm]Fig. 8. (a) Example of measurement of an amplitude profile atthe leading edge (indicated by red line) of the echo from theupper surface of the bar (diameter of bars: 10 mm). (b) Widths
at half maxima of amplitude profiles obtained at the leading anddescending edges of the echo from the upper surface of the bar.

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387

Table 1. Widths at half maxima ⌬w of the amplitude profilesof transmission ultrasound measured for different distances
between the focused transducer for transmitting ultrasoundand the lower surface of the acrylic bar (10 mm in diameter)

Fig. 9. Illustration of measurement of sound field emitted froma gap.

of such a gap can be evaluated using the measured
transmission ultrasound.
Difference between imaged patterns of transmission ultrasound produced by planar and focused transducers
Figure 4(1-a) and (2-a) show the imaged transmission ultrasound produced by the planar and focused

Width of gap
d (mm)

Distance between focusedtransducer and lower
surface of bar (mm)Width at half
maximum⌬w (mm)

0.6
0.6
2.0
2.0

30
40
30
40

0.8
0.7
1.8
1.8

transducers for transmission, respectively. In these figures, gap width d was set at about 5 mm and 9 mm,
respectively, i.e., ⬎4 mm (maximum gap width in basic
experiments), to visualize the imaged pattern of transmission ultrasound in a wider area. Figure 4(1-b) and(2-b) show the profiles of the amplitudes of ultrasoundsignals received by the linear array probe along the redlines in Fig. 4(1-a) and (2-a). The imaged radiation
pattern of the focused transducer (Fig. 4[2-a]) was rather
complex compared with that of the planar transducer(Fig. 4[1-a]), the latter being suitable for imaging a wider
gap. However, as the measured transmission ultrasoundproduced by the focused transducer showed a high in-

Fig. 10. Sound fields measured by a hydrophone when a focused transducer for ultrasound transmission was placed (1)30 mm and (2) 40 mm away from the lower surface of the bar (diameter of bars: 10 mm). (a) Continuous and (b) pulsed
ultrasound were emitted from a focused transducer.

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tensity within a narrow area (width at half maximum: 2mm), it would be useful for penetration of cartilage andtissue in a joint because the attenuation in such tissue ismuch greater than that in water. Thus, the focused transducer was used in the following preliminary in vivo
imaging, whereas both the planar and focused transducers were used in the basic experiments.
BASIC EXPERIMENTAL RESULTS
Measurements with the planar transducer
Figure 5a and b show B-mode images with andwithout exposure of transmission ultrasound producedby the 5-MHz planar transducer. The width of the gap in
Fig. 5 was 0.6 mm. Ultrasound transmitted through the
gap was clearly imaged. In the basic experiments, theobject was stationary. Therefore, as shown in Fig. 5c,
only transmission ultrasound that passed through the gap
could be imaged by subtracting the RF signals without
exposure from those with exposure, which were received

Volume 35, Number 3, 2009by the linear array probe. Figure 5d shows the profile ofthe echo amplitude along the red line shown in Fig. 5c.
Using the same procedure, the amplitude profiles atthe same depth, shown by the red line in Fig. 5c, wereobtained for other widths d of gaps. Figure 6a–j show theamplitude profiles at various gap widths d from 0 –3.6
mm. The amplitude profile was obtained at the descending edge of the echo from the upper surface of the bars,
as indicated by the red lines in Fig. 5. As can be seen in
Fig. 6b, transmission ultrasound was detected at a gap
width d larger than 0.4 mm. In Fig. 6a–j, the red lines
show the width at half maximum ⌬w of each amplitude
profile. Figure 6k shows the width at half maximum ⌬wplotted as a function of gap width d. In Fig. 6k, widths at
half maximum ⌬w obtained from 10 image frames areplotted at each gap width d. As shown in Fig. 6k, there isa correlation between the width ⌬w of the amplitude
profile and the gap width (correlation coefficient between
the actual and measured gap widths: 0.93 [overall], 0.60

Fig. 11. Imaged transmission ultrasound in B-mode images (diameter of acrylic bars: 10 mm). Gap widths d were set
at (1) 0.6 mm and (2) 2.0 mm. The elevational positions y of the bars were set at (a) 0 mm, (b) 2.5 mm and (c) 5 mm.

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389

Fig. 12. Imaged transmission ultrasound in B-mode images (diameter of acrylic bars: 6 mm). Gap widths d were set at(1) 0.6 mm and (2) 2.0 mm. The elevational positions y of the bars were set at (a) 0 mm, (b) 1 mm, (c) 2 mm and (d)3 mm.

[d ⫽ 0.4 to 2 mm], 0.98 [d ⫽ 2 to 4 mm]). These results
show the possibility of using the proposed method tomeasure gap width d. However, the correlation is weakin the range of gap width d ⬍2 mm in the case of theplanar transducer.
Measurements with the focused transducer
Figure 7a–j show the amplitude profiles measured
with the focused transducer. As in the case of the planartransducer, ultrasound transmitted through the gap can bedetected at a gap width d ⬎0.4 mm. However, theamplitude profile does not change so much in the rangeof gap width d ⬎2 mm because the width at half maximum of the amplitude profile of the original radiation
pattern of the focused transducer was 2 mm, as shown in
Fig. 4(2-b). However, the amplitude of the received
transmission ultrasound was two times larger than that ofthe planar transducer, which is a great advantage forpenetrating the cartilage and tissue in a joint. Figure 7k
shows the width at half maximum ⌬w of an amplitude

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Table 2. Widths at half maxima ⌬w of the amplitude profilesof transmission ultrasound measured for different elevational
positions y of the bars (10 mm in diameter)
Gap widthd (mm)

Elevational positiony (mm)

Width at half maximum⌬w (mm)

0.6
0.6
0.6
2.0
2.0
2.0

0
2.5
5
0
2.5
5

0.8
0.9
1.0
1.8
1.8
1.6

profile plotted as a function of gap width d. In Fig. 7k,
widths at half maximum ⌬w obtained from 10 image
frames are plotted at each gap width d. There is nocorrelation between the width at half maximum ⌬w and
gap width d in the range of gap width ⬎2 mm, whichcorresponds to the fact that the amplitude profile does notchange in that range, as shown in Fig. 7a–j. However,there is a strong correlation at a gap width d ⬍2 mm(correlation coefficient between the actual and measured
gap widths: 0.7 [overall], 0.94 [d ⫽ 0.4 to 2 mm] and⫺0.94 [d ⫽ 2 to 4 mm]). Therefore, a focused transducer
is useful, especially for imaging a narrow gap in a digital
joint. As shown in Fig. 1, the typical width of a gap in adigital joint is ⬍2 mm. Therefore, the focused transducer
was used in the subsequent experiments.
Widths at half maxima shown in Fig. 7k were
measured at depth positions assigned by referring to thedescending edge of the echo from the upper surface of
the acrylic bar. Figure 8 shows the widths at half maxima
measured at the leading edge of the echo from the uppersurface; the measured widths ⌬w in Fig. 8 are similar to
those in Fig. 7k. In this study, widths at half maxima ⌬w
were measured at the descending edge in the subsequent
experiments because stable measurements of ⌬w can beachieved as long as measurement is done at the leadingor descending edge of the echo from the upper surface ofthe bars.
The sound pressure distribution measured with ahydrophone, which scans the sound field in the horizontal direction x (the longitudinal axis of the bar), as shownin Fig. 9, was shown in Figure 10(1-a). Gap width d was
set to be 0.6 mm, and the distance between the lower
surface of the bar and the transmitting transducer was set
at 30 mm. To more clearly observe how the ultrasoundwave propagated, pulsed ultrasound was irradiated fromthe transmitting transducer as shown in Fig. 10(1-b),
which shows that a spherical wave was emitted from thegap. The distance between the hydrophone and thesource of the spherical wave, which was estimated fromthe time delay (p ⫽ 0.07 ␮s, as shown in Fig. 10[1-b])
between signals received at two different horizontal po-

Volume 35, Number 3, 2009

sitions x, was 19 mm. Therefore, the source was estimated to be located at the gap on the level of the uppersurface of the bar. In the diagnostic ultrasound equipment used, dynamic focusing was applied to the signals
received by the array elements. In this case, the width of
the ultrasound beam becomes the narrowest at the position of the source of the spherical wave.
Figure 10(2) shows the sound field measured when
the distance l between the lower surface of the bar andthe transmitting transducer was set at 40 mm, and Table
1 shows a comparison of the widths at half maxima ⌬wmeasured at l ⫽ 30 and 40 mm. The wave pattern was
similar to that in Fig. 10(1), and the width at half maximum ⌬w measured at l ⫽ 40 mm was similar to that atl ⫽ 30 mm. However, the amplitude of transmission
ultrasound that passed through the gap decreased 50%, asshown in Fig. 10(2). It is considered that more energy
can enter a gap when the beam width is narrower at theentrance of a gap. These results indicate that it is betterto locate the focal point of a transmitting transducer at
the lower surface of the bar.
Measurements of gaps between bars with different diameters
Acrylic bars 10 mm and 6 mm in diameter wereused to create gaps, as shown in Fig. 3b. Transmission
ultrasound that passed through gaps with different widths
d of 0.6 and 2.0 mm were measured for the different
positions, y, of the acrylic bars in the elevational direction to investigate the influence of the alignment of thebars.
Figures 11 and 12 show the B-mode images andTables 2 and 3 show the widths at half maxima ⌬w of theamplitude profiles of transmission ultrasound measured
at each setting of gap width d and elevational position y.
As shown in Tables 2 and 3, the measured width at half
maximum ⌬w does not change when the elevational
position y is less than half the radius of the bar, and thedifference between widths at half maxima of the ampli-

Table 3. Widths at half maxima ⌬w of the amplitude profilesof transmission ultrasound measured for different elevational
positions y of the bars (6 mm in diameter)
Gap widthd (mm)

Elevational positiony (mm)

Width at half maximum⌬w (mm)

0.6
0.6
0.6
0.6
2.0
2.0
2.0
2.0

0
1
2
3
0
1
2
3

0.7
0.7
0.6
0.7
1.7
1.7
1.4
1.9

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391

Fig. 13. Imaged transmission ultrasound through the gap (width d: 0.6 mm) at different angles of incident ␪ of (a) 0degree, (b) 2.5 degrees, (c) 5 degrees and (d) 7.5 degrees. Diameter of bars was 10 mm.

tude profiles obtained for 6-mm and 10-mm acrylic bars
was 0.1 mm when y ⫽ 0.
Measurements at different angles of incidence between
ultrasound and the gap
The amplitude profile of transmission ultrasoundwould be influenced by the angle of incidence between
the ultrasound beam radiated by the focused transducer
and the gap. In the previous section, the widths at half
maxima measured for the acrylic bars with different
diameters were similar when the elevational position y
was zero. Therefore, the influence of the angle of incidence was investigated using acrylic bars 10 mm indiameter by setting the elevational position y at zero. The
gap width d was set at 0.6 mm. Figure 13 shows imagesof transmission ultrasound through the gap at different
angles of incidence ␪ ⫽ 0, 2.5, 5 and 7.5 degrees. Table
4 shows the width at half maximum ⌬w measured atthese angles of incidence ␪. As shown in Fig. 13, although the change in the alignment was obvious, evenwhen the angle of incidence was 2.5 degrees, the measured widths at half maxima were similar, as shown in
Table 4.
Preliminary in vivo imaging
Figure 14(1-a) and (2-a) show x-ray images of thehands of a 5-year-old male and a 26-year-old female,respectively, and Fig. 14(1-b) and (2-b) are enlarged
views of the second joints of their middle fingers. One of
the two gaps found in the child subject indicated by thewhite arrow in Fig. 14(1-b) is not found in the joint of the
26-year-old female shown in Fig. 14(2-b).
Figure 14(1-c) shows an ultrasound B-mode image
with exposure of transmission ultrasound (focused, 7MHz) for the 5-year-old male, and Fig. 14(2-c) showsthat of the 26-year-old female. The widths of gaps ofthese two subjects are from 1–2 mm, and the focusedtransducer was used with consideration of the results ofthe basic experiments. In Fig. 14(1-c), transmission ultrasound that passed through the two regions in the joint
can be clearly recognized in the case of the 5-year-old
male. On the other hand, in the B-mode image of the
26-year-old female (Fig. 14[2-c]), applied focused ultrasound passed through only one region. These results
Table 4. Widths at half maxima ⌬w of the amplitude profilesof transmission ultrasound measured at different angles ofincidence ␪ (diameter of bars: 10 mm)
Angle of incidence ␪ (deg.)

Width at half maximum ⌬w (mm)

0
2.5
5
7.5

0.7
0.7
0.7
0.8

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(a)

30 mm

10 mm

Volume 35, Number 3, 2009

(a)

30 mm

10 mm
(b)

(b)

(c)

(c)

10 mm

10 mm

bone
bone

bone

bone

(1)

(2)

Fig. 14. In vivo imaging of transmission ultrasound through the second joint of the middle finger. (1) 5-year-old male.
(2) 26-year-old female. (a) X-ray image. (b) Enlarged x-ray image of the second joint. (c) Ultrasound B-mode imageof the second joint, with exposure of transmission ultrasound (focused, 7 MHz).

correspond well to the structures of the joints shown by
x-ray images and indicate that the proposed method has
potential for noninvasive assessment of the change instructure of a joint because of aging.
DISCUSSIONAs shown in Fig. 4, depending on the type of atransducer (planar or focused), transmission ultrasound received by a linear array probe showed different patterns in the B-mode image. The lateral variationin the amplitude of transmission ultrasound depends
on the type of transducer (planar or focused). However, variation in the direction of depth should notoccur because continuous-wave ultrasound was used
to penetrate a gap in cases of both the planar andfocused transducers. However, there are variations in

the direction of depth, especially in the case of the
focused transducer. Such a variation in the direction of
depth is considered to depend on the receiving focusof the linear array probe. Although dynamic focusing
was applied to the received signals in the used diagnostic equipment, the relationship between the receiving focus setting and the imaged pattern of transmission ultrasound should be further investigated in the
future to reduce the spatial inhomogeneity in the original imaged radiation pattern shown in Fig. 4.
It was found that a focused transducer should be
used for transmitting ultrasound through a gap with awidth ⬍2 mm, which corresponds to the typical width ofa gap in a digital joint. Through basic experiments using
acrylic bars, it was found that the width at half maximum⌬w of the amplitude profile of transmission ultrasoundImaging of gaps in digital joints ● H. HASEGAWA et al.

correlated well with actual gap width d under the following conditions:(1) The focal point of a transmitting transducer is located at the lower surface of the bar.
(2) The elevational positions y of the bars are set to beless than half of the radius of the bar.
(3) The width at half maxima ⌬w is measured at theleading or descending edge of the echo from theupper surface of the bar.
To realize stable in vivo measurements, in future
work it will be important to develop a measurement
system in which the above conditions are maintained.
To apply this method to other larger joints, the separation between a transducer for ultrasound transmission and
an imaging probe needs to be increased. To keep the focal
position of a transducer as it was in the present study, adifferent transducer and different probe must be used toincrease the separation. The frequency of ultrasound mayneed to be changed because of the increase of the distance
between the skin surface and a joint. In addition, the type oftransducer (planar or focused) may need to be considered toimage a wider gap in a larger joint. Therefore, the optimum
frequency of transmission ultrasound and the type of transducers (planar or focused) should be more thoroughly investigated because the frequency of ultrasound significantly
influences the spatial resolution. In this preliminary study,
different frequencies were used for the planar and focusedtransducers. A set consisting of planar and focused transducers operated at the same frequency would be required toinvestigate the difference between these transducers, andsets of transducers at different frequencies would be required to investigate the optimum frequency.
Although there are many things to be investigatedfurther as described here, the proposed method would enable the tomographic imaging of a digital joint. The combination of pulse– echo imaging and tomographic imaging
should be useful for diagnosis of joint structures.
CONCLUSION
The structure of a digital joint changes with aging.
There are two gaps in a digital joint of a young subject,
one that disappears with aging. To noninvasively assess
such change in a digital joint, in this study continuouswave ultrasound was radiated through a gap between two
acrylic bars, which simulated the gap in the digital joint.
Transmission ultrasound was measured with a linear
array probe for imaging. The basic experimental results
showed that a gap with a width ⬎0.4 mm can be imaged.
In the case of a planar transducer, the width at half
maximum of the amplitude profile of received transmission ultrasound that passed through the gap correlatedwith the width of the gap when the gap was ⬎2.0 mm.

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On the other hand, the width at half maximum obtainedusing a focused transducer correlated with the gap width
when the gap was ⬍2.0 mm. From these results, afocused transducer is considered to be preferable for themeasurement of a gap in a digital joint whose width istypically ⬍2 mm. Furthermore, in the preliminary in vivo
experiments, transmission ultrasound that passed throughtwo gaps was clearly imaged by the proposed method in
the case of a child subject, whereas transmission ultrasound that passed through only one gap was imaged in
the case of an adult subject. These results show thepossibility of using the proposed method to noninvasively assess the change in the structure of a joint because of aging.
REFERENCES
Asai H, Kanai H, Chubachi N. Noninvasive method for measuring
velocity of leaky surface skimming compressional wave propagating on bone surface. Electron Lett 1996;32:2290 –2291.
Biot MA. Generalized theory of acoustic propagation in porous dissipative media. J Acoust Soc Am 1962;34:1254 –1264.
Bossy E, Talmant M, Defontaine M, Patat F, Laugier P. Bidirectional
axial transmission can improve accuracy and precision of ultrasonicvelocity measurement in cortical bone: A validation on test materials. IEEE Trans Ultrason Ferroelectr Freq Control 2004;51:71–79.
Droin P, Berger G, Laugier P. Velocity dispersion of acoustic waves incancellous bone. IEEE Trans Ultrason Ferroelectr Freq Control 1998;
45:581–592.
Häat G, Padilla F, Cleveland RO, Laugier P. Effects of frequency-dependent attenuation and velocity dispersion on in vitro ultrasound velocity
measurements in intact human femur specimens. IEEE Trans Ultrason
Ferroelectr Freq Contr 2006;53:39 –51.
Hosokawa A, Otani T. Ultrasonic wave propagation in bovine cancellous bone. J Acoust Soc Am 1997;101:558 –562.
Hosokawa A, Otani T, Suzaki T, Kubo Y, Takai S. Influences oftrabecular structure on ultrasonic wave propagation in bovine cancellous bone. Jpn J Appl Phys 1997;36:3233–3237.
Hosokawa A, Otani T. Acoustic anisotropy in bovine cancellous bone.
J Acoust Soc Am 1998;103:2718 –2722.
Jones G, Ma D. Skeletal age deviation assessed by the Tanner-Whitehouse 2 method is associated with bone mass and fracture risk inchildren. Bone 2005;36:352–357.
Khal HAA, Wong WK, Rabie ABM. Elimination of the hand-wrist
radiographs for maturity assessment in children needing orthodontic therapy. Skeletal Radiol 2008;37:195–200.
Otani T. Quantitative estimation of bone density and bone quality using
acoustic parameters of cancellous bone for fast and slow waves. Jpn
J Appl Phys 2005;44:4578 – 4582.
Pereira WCA, Bridal SL, Coron A, Laugier P. Singular spectrum
analysis applied to backscattered ultrasound signals from in vitro
human cancellous bone specimens. IEEE Trans Ultrason Ferroelectr Freq Control 2004;51:302–312.
Rucci R, Coppini G, Nicoletti I, Cheli D, Valli G. Automatic analysisof hand radiographs for the assessment of skeletal age: A subsymbolic approach. Comput Biomed Res 1995;28:239 –256.
Tanner J, Whitehouse R. Assessment of Skeletal Maturity and Prediction of Adult Height (TW2 method). New York: Academic Press,
1975.
Töyräs J, Laasanen MS, Saarakkala S, Lammi MJ, Rieppo J, Kurkuärvi
J, Lappalainen R, Jurvelin JS. Speed of sound in normal anddegenerated bovine articular cartilage. Ultrasound Med Biol 2003;
29:447– 454.
Wear KA. The effects of frequency-dependent attenuation and dispersion on sound speed measurements: Applications in human trabec-

394

Ultrasound in Medicine and Biology

ular bone. IEEE Trans Ultrason Ferroelectr Freq Control 2000;
47:265–273.
Wear KA. Ultrasonic attenuation in human calcaneus from 0.2 to 1.7
MHz. IEEE Trans Ultrason Ferroelectr Freq Control 2001a;48:602–
608.
Wear KA. A stratified model to predict dispersion in trabecular bone.
IEEE Trans Ultrason Ferroelectr Freq Control 2001b;48:1079 –1083.
Wear KA. Characterization of trabecular bone using the backscatteredspectral centroid shift. IEEE Trans Ultrason Ferroelectr Freq Control 2003;50:402– 407.
Weigel JP, Cartee RE, Marich KW. Preliminary study on the use ofVolume 35, Number 3, 2009
ultrasonic transmission imaging to evaluate the hip joint in theimmature dog. Ultrasound Med Biol 1983;9:371–378.
Wells PNT. Absorption and dispersion of ultrasound in biologicaltissue. Ultrasound Med Biol 1975;1:369 –376.
Williams JL. Ultrasonic wave propagation in cancellous and corticalbone: Prediction of some experimental results by Biot’s theory. J
Acoust Soc Am 1992;91:1106 –1112.
Wit JM, Rekers-Mombarg LT, Cutler GB, Crowe B, Beck TJ, Roberts
K, Gill A, Chaussain JL, Frisch H, Yturriaga R, Attanasio AF.
Growth hormone (GH) treatment to final height in children with
idiopathic short stature: Evidence for a dose effect. J Pediatr 2005;
146:45–53.