The effect of bone structure on ultrasonic attenuation and velocity M . B . Tavakoli and J.A. Evans Centre for Bone and Body Composition, Academic Unit of Medical Physics, University of Leeds, Leeds General Infirmary, Leeds LS1 3EX, UK
Received 31 July 1991; revised 6 April 1992 The relationship between the structure of bovine cancellous bone, and its ultrasonic propagation parameters is investigated by means of a novel technique involving the application of large static loads, thereby changing the porosity in a controlled manner. The results show that for frequencies in the range 0.4 to 1 MHz, porosity decreases up to 35% are associated with a reduction in attenuation of up to 500%, whereas the velocity increases by roughly 35% for the same changes. The data taken overall suggest that in determining the ultrasonic attenuation coefficient at these frequencies, the amount of material in a given bone section is significantly less important than the distribution of that material.
Keywords: ultrasonic scattering; velocity and attenuation; osteoporosis; bone mineral
Osteoporosis is rapidly becoming a major health problem, particularly for the two major at risk groups, the elderly and post-menopausal women. The disease is identified by a decrease in mass in both cortical and cancellous bone with a more pronounced effect on cancellous bone 1. Currently available non-invasive clinical methods for the detection of osteoporosis include: single photon absorptiometry (SPA) of the cortical bone (usually the forearm), dual photon absorptiometry (DPA) of the spine, and quantitative computed tomography (QCT). All of these methods are associated with ionizing radiation 2. Ultrasonic assessment of bone disease has been introduced more recently. The ultrasonic parameters involved, attenuation and velocity, have been measured in normal and pathological bone, both cortical and cancellous, by a number of workers 3-11. Attempts have been made to relate these properties to bone mineral density (BMD) using DPA 12-15, bone mineral content (BMC) using SPA 14-21 and bone mineral density (BMD) using QCT t6,21-2a. The results obtained have been contradictory and inconsistent. Other workers have attempted to correlate the attenuation or velocity with physical density (PD) 5's'22-24'2~. The acoustic properties of any composite material such as bone depend not only upon the amount of the various constituent materials present, but also on the spatial arrangement of those materials. In bone, the main constituents are hydoxyapatite (HAP), collagen and fat and these three have quite different acoustic properties. It would therefore be predicted that the acoustic 0041-624X/92/060389-07 © 1992 Butterworth-Heinemann Ltd
impedance mismatch found at interfaces involving these constituents would cause significant scattering and hence attenuation. Furthermore, the scattering characteristics are likely to depend upon the local architecture, particularly because the inhomogeneities in question are a small fraction of a wavelength in size. Despite the recognition that the scattering due to structure is an important component of the total ultrasonic attenuation mechanism, the magnitude and nature of this component have not been identified. Theoretical models have also failed so far to elucidate the problem 23. In this study, we have devised a technique to monitor the attenuation and velocity of bone samples during the application of large loads. Under such loads, the trabecular structure begins to fracture giving significant structural change, while at the same time there is a general increase in physical density anda corresponding decrease in porosity. However, the total mass of bone material between the transducers remains constant.
Instrumentation A block diagram of the instrument is shown in Figure 1. The instrument consists of two parts: (a) an electric and electronic system and (b) a sample holder including transducers and press. The electric and electronic system This system consists of a high voltage pulse generator (RPIO0, Vigilant) connected to the transmitting transducer
Ultrasonics 1992 Vol 30 No 6
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Effect of bone structure on attenuation and velocity: M.B. Tavakofi and J.A. Evans
Experimental method
Press
Attenuation
Perspex buffer
IEEE-488
0Peroexbu er° t To synchronous output of pulser 1-Steel cylinder to protect the transducers 2-Aluminium cylinder 3--Backing spring 4--Transmitting transducer 5 - Receiving transducer
-
Press
Ultrasonic waves produced by the transmitting transducer travel along the buffer in contact with the transmitter. In the absence of a sample, the ultrasonic energy is transmitted directly to the buffer in contact with the receiving transducer although some is reflected. When the two buffers are of the same material and provided that no air or foreign bodies are trapped, the reflected signal is negligible. The transmitted signal then travels through the receiving buffer and is detected by the receiving transducer. When a sample is sandwiched between the two buffers, some of the energy is reflected back into the first buffer at the first boundary, thereby attenuating the energy transmitted into the sample. A further reflection takes place at the second boundary and hence there is an additional attenuation of the signal sent into the second buffer. The energy transmitted into the receiving buffer is detected by the receiving transducer, where the electronic signal produced is processed and stored. A correction for
a
Receiver
I
Figure 1 The diagram of the system used for measurement of acoustical properties of bone at different porosities
I
j•A1
I
(f)
Receivingbuffer
and a 100 M Hz sampling rate digital oscilloscope (Philips PM 3350) connected to the receiving transducer. The oscilloscope was also connected to a BBC-computer through an IEEE-488 interface. The synchronous output of the pulser was connected to the trigger input of the oscilloscope. The delay function of the digital oscilloscope was used to bring the desired signal on to the oscilloscope screen, hence removing the necessity for electronic gating. The signal could then be recorded on a floppy disc for later processing.
Sample holder, transducers and press The rest of the system includes the sample holder, transducers and a 40 ton hydraulic press. The diagram of the sample holder is shown in Figure 1. It consists of an aluminium cylinder of diameter 7 cm and two identical perspex buffers which can move inside the cylinder. The thickness of both of the buffers is 2.5 cm and their diameters are 7 cm. Each perspex buffer is in contact on one side with the sample and, on the other side, with the corresponding transducer. The transducers are housed in steel cylinders to protect them when the sample holder is inside the hydraulic press. Alignment of the transducers is achieved by producing a small recess for the steel case on the perspex buffer surfaces facing the transducers. At the rear of each transducer a spring is located to push it against the perspex buffer with constant pressure. Ultrasonic gel is used for coupling. The transducers used were two identical 2.5 cm diameter 0.6 MHz broadband transducers and the hydraulic press (Moores, Birmingham) was capable of applying loads up to 40 000 kg, although it was not used above 20 000 kg in this study.
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Ultrasonics 1992 Vol 30 No 6
Transmitting buffer j~ A0(f)
I
I Transmitter
b
I
Receiver
I
I
I
I
I
I
Transmitter
Figure 2 The diagram shows the ultrasonic propagation in the buffers and sample: (a) with no sample present; (b) with the sample present
Effect of bone structure on attenuation and velocity: M.B. Tavakofi and J.A. Evans the losses due to reflections at the boundaries was performed using the method described below. Further corrections were applied to allow for losses due to diffraction. The whole system was then validated with the use of a standard reference material, polythene. The details of the calculation used are given below. In Figure 2a the signal arriving at the receiver in the absence of a sample can be expressed as:
A l ( f ) = tAo(f)ex p -- (~lbl +
~2b2)
(1)
where Ao(f) and A l ( f ) are the amplitudes of the signal at the surface of the transmitting transducer and at the surface of the receiving transducer respectively when there is no sample between the buffer. ~x and ~2 are the attenuation coefficients of the transmitting and receiving buffers, bl and b2 are the thicknesses of those buffers and t is the amplitude transmission coefficient. When the buffers are identical and the contact between them is good, t h e n b ~ = b 2 = x , 0 q = ~ 2 = % a n d t = l therefore; a 1( f ) = Ao(f)exp( -- 2~pX)
(2)
When the sample is sandwiched between the buffers (Figure 2b) then;
A s ( f ) = Av(f)exp(-0tpx)
(3)
AT(f) = t2A5(f)
(4)
As(f) = A,(f)exp(-cz,d)
(5)
Aa(f) = q A 2 ( f )
(6)
A2(f) = Ao exp(-~XpX)
(7)
where t t and t 2 are the amplitude transmission coefficients at the two boundaries, d is the sample thickness and ~s is the ultrasonic attenuation coefficient in the sample. From the above equations, it can be deduced that: aq(dB c m - 1) =
8.686 I n ( A a ( f ) ~ = 8.686 I n ( A " ( f ) ~ d \T~I(~),/ d \AI(f)] + In(1)
(8)
where A 8( f ) and A 1( f ) are the received signal amplitudes with and without the sample and T is the energy transmission coefficient which could be calculated using the equation;
T-
4Z2Z2 (Zb + Z,) 2
(9)
where Z b = pbcb and Zs = psc~ are the mechanical impedances of buffer and sample, Pb and p~ are the densities and perspex and the sample, and c b and cs are the velocities of ultrasound in Perspex and the sample. The densities were measured using Archimedes' principle as described in the results section, and the velocities in perspex and in the sample were measured directly using a time-of-flight method as detailed below. Thus, by using Equations (8) and (9) one can calculate T a n d cts if the sample thickness d, is known. Alternatively, the total attenuation in the sample can be evaluated as ~sd (dB). The validity of the above method depends upon an appropriate choice of geometry for sample and apparatus. The main constraints are as described below. 1 The buffer and sample thicknesses should be great enough to prevent interference between the reflected
2
and transmitted signals in each case. This is achieved if the pulse duration is short relative to the transit time in question. The Perspex thickness used for the buffer was 2.5 cm and hence the transit time is about 18/~s which is much longer than the pulse duration. The thickness of the bone samples was about 1.6 cm with a corresponding transit time of about 17/~s which was felt to be acceptable. The diameter of the buffer and sample should be large enough to prevent wall effects as a result of diffraction of the ultrasound beam over the frequency range of interest. As the diameter of the transducers was 2.5 cm, the near-field length in the Perspex buffer at 0.4 MHz (the lowest frequency measured in this experiment) is roughly 2.3 cm and the diffraction angle 0 is given by: 0 = sin- 10.61,1. - ~
2o o
(lO)
a
For a sample with 2 cm thickness and a receiving buffer with a 2.5 cm thickness, the diameter of the beam at 6.5 cm is about 6 cm which is still less than the diameter of the buffer and sample in this experiment. A diffraction correction was performed at each frequency using the method of Papadakis zT. This is necessary because the separation of the transducer alters when the sample is introduced between the buffer rods and because the sound velocity differs between the rods and the sample.
Velocity In all cases, the velocity was measured using a time-of-flight method (TOF). The time shift At of the ultrasound pulse with a sample present relative to that without the sample, was measured directly from the oscilloscope screen. The thickness of the sample d was also measured with a micrometer. The velocity e was calculated using the equation e = d/At. For the polyethylene standard, the values obtained for both velocity and attenuation coefficient showed good agreement with those reported in the literature ( Table 1).
Porosity The primary aim of the study was to investigate the relationship between both velocity and attenuation in bone samples and the porosity ~b. This is defined strictly as the volume fraction of the less dense phase, in this case marrow, i.e.
~= Volume occupied by marrow Volume of whole sample If the densities of the sample, mineralized bone fibre and marrow fat are p,, Pm and pf respectively and the corresponding masses in a particular sample are ms, mm Table 1
The results of attenuation and velocity measurements in polyethylene used as the standard material to test the instrument )erformance Attenuation (dB cm -1) Velocity ( m s -1 ) at 0.6 MHz at 1.0MHz Frequency ( M H z ) Measured value Reported value 28
2005 2000
0.6 2.9 -
1.0 4.6 4.75
Ultrasonics 1992 Vol 30 No 6
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Effect of bone structure on attenuation and velocity: M.B. Tavakofi and J.A. Evans and mf, then Volume occupied by marrow fat = sample volume - bone fibre volume i.e. /T/f
-
m s
Pf Ps and then
m m
(11)
length at different pressures using a dial gauge placed between the two sides of the press. The resolution of the dial gauge was 5 #m. The experiment was repeated for both samples. In both cases, the attenuation in the bone decreased dramatically as the pressure increased. The detailed results from one of the samples are shown in Figures 3 and 4 and the
Pm 40
~p : (m_~ mm~(rns~-' Pm/ \Pm,/
:1
minos ms Pm
A F = 0.4 MHz
and if the mass of marrow is small relative to the mass of mineralized bone fibre, then we can say ~b= 1
30
Ps Pv
•
F = 0.6 MHz
o
F = 0.8 MHz
•
BUA
C O_
Sample
preparation
=:
A bovine femur was obtained fresh from a local abattoir. A coring drill of 7 cm inside diameter was used to obtain bone cores from both proximal and distal ends of the bone. The end faces of the cores obtained were made parallel and smooth using a rotary electric saw and a coarse sandpaper. The final cores obtained had thicknesses of 1.8 and 1.2 cm as measured by a micrometer and these were then preserved in phosphate buffer solution for about one month before the start of the experiment. The air bubbles trapped in the samples were removed before the start of the measurement by placing them underwater in a dessicator overnight and vacuum degassing. Measurements
and
results
The sample was placed at room temperature between the two Perspex buffers and the ultrasonic signal received by the receiving transducer, with just enough pressure to obtain good contact, was recorded (ultrasonic gel was used as a coupling material between sample and buffers). To change the porosity and therefore the structural pattern of the bone samples without changing the amount of bony tissue in the ultrasound path, the thickness of the sample was then reduced by increasing the pressure on it. As the bone samples were located in between the two Perspex buffers in the aluminium cylinder, which had the same diameter as the buffers, and the aluminium cylinder itself, the bone tissue could not escape and hence the amount of bone tissue in the ultrasonic path remained constant while the thickness of the sample, and therefore its porosity, decreased. The received ultrasonic signals at different pressures, and therefore different porosities or structural patterns, were recorded and were used in conjunction with the signal received when there was no sample between the two buffers, to calculate the attenuation in the sample. In calculating the attenuation in bone samples, corrections for the two reflections at the Perspex-bone and bone-Perspex boundaries were made as discussed earlier. The densities of the samples at the beginning of the experiment were measured using Archimedes' principle with a submersion technique. The change of density during the experiment as a result of increasing the pressure was measured by noting the change in the sample
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Ultrasonics 1 9 9 2 Vol 3 0 N o 6
20
2600
2600
2400
2200
I 1.2
I 1.4
I
[ 1.6
,
I 1.8
,
I 2.0
= 2.2
Density (g cm -3 ) Figure 6 Ultrasonic velocity (m s -1 ) in bone under pressure as a function of density (g c m - 3 ) . The sample is the same as in Figure 3. Note the apparent discontinuity at a density of around 1.6 g cm 3
The reproducibility of the measurement was also evaluated for the standard by measuring attenuation and velocity three times after removing the sample from its position and putting it back in position. The standard deviation of the reproducibility obtained for attenuation was 0.3 dB for attenuation values less than 10 dB and 0.5 for higher attenuation values. For velocity the standard deviation was 0.3%.
Discussion and conclusion As mentioned earlier, the method used reduces the thickness of the sample (and hence its porosity) while keeping constant the amount of bony material in the ultrasonic path. Thus, in the absence of scatter, although the attenuation coefficient in dB cm-1 will change as a result of increasing the density, it would be anticipated that the total attenuation in the sample would remain unchanged. This facilitates an investigation of the role of structure in determining the acoustical properties of the bone. As the applied load increases, structural changes occur and hence the porosity of the bone alters. As the porosity q~is reduced, the density of the sample approaches that of pure compact mineralized bone fibre (MBF) and the value of ~b can be calculated from a consideration of the density changes. Bone is taken to be a two-component system comprising MBF and fat with densities Pm and pf respectively. In order to obtain a value for Pro, it is necessary to consider its make-up further. MBF can be considered as consisting of roughly 46% collagen and 46% HAP with the remaining 8% water. Assuming a density of 1430kgcm -3 for collagen 3° and 3170kgcm -3 for HAP 61, then the calculated value of Pm is about 2200 kg cm- 3. The porosity can then be calculated from
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Ultrasonics 1992 Vol 30 No 6
(11)
•
where Ps is the sample density. In the above calculation the effect of fat on the porosity calculation is neglected, as its density is assumed to be close to 1 g cm-3 and therefore negligible. The results obtained are tabulated in Table 2. From Figure 3 it is clear that the attenuation in the 1.2cm thick sample under normal conditions with a porosity of 41% is about 18 dB at 0.6 MHz. When the porosity is reduced to 5%, the attenuation decreases to less than 5 dB and almost by the same ratio at other frequencies. The ratio of the attenuation at highest porosity (i.e. normal bone) to that at the lowest porosity achieved, is about 4 for this sample at this frequency which means that, in this sample, the attenuation depends mostly on the structure rather than on the component materials. Similar results were obtained from the other sample (1.8 cm thick). Even at the lowest attenuation shown in the graph the porosity is still not zero. Also, since there are at least two constituent materials even at zero porosity, the density and velocity differences between them ensure that there will still be a scattering component. The size of the individual particles of the constituent materials is very small compared with the wavelength used in this experiment and hence, according to the Mason and McSkimin32 theory for polycrystalline systems with grain sizes much smaller than a wavelength, the scattering depends on 2 -4 . Scattering is more important in this experiment as the sample is not only a polycrystalline material but also a multiphase system, and therefore the absorption in bone must be significantly less than the attenuation value at zero porosity. A potential source of error in all measurements of this type on heterogeneous materials is that due to phase cancellation artefacts. It might be argued that the observed reduction in attenuation with decreasing porosity should be attributed in part to the increase in homogeneity of the sample associated with the porosity change. However, recent evidence from Robins et al. 33 suggests that this is not significant in the specific case of ultrasonic bone measurements. The change of velocity as a result of reducing porosity while keeping the amount of material constant, shows much less change than the attenuation, as is shown in Fi#ures 5 and 6 and Table 2. The ratios of the minimum to the maximum of the attenuation obtained at 0.6 MHz for the two samples are 0.35 and 0.26 and these are much less than the corresponding ratios for velocity, which are 0.71 and 0.74. This is a further illustration of the greater influence of bone structure on attenuation than velocity in this frequency range. The intercept of the straight line in Figure 4 gives a velocity of 3476 m s-1 for bone at zero porosity, which compares well with published values z5 for cortical bone. Acknowledgements We would like to thank the staff of the Mechanical and Electronic Workshops, of the Department of Medical Physics for building the apparatus used in this study. We are grateful to Dr C.M. Langton for helpful comments and discussions as well as the loan of the transducers and press.
Effect of bone structure on attenuation and velocity: M.B. Tavakofi and J.A. Evans
On6 of us (MBT) would like to acknowledge the financial support of the Government of Iran for a scholarship during this period.
16
References
18
1 2 3 4
5 6 7
8
9 10 11
12
13
14
15
Rings, B.L. and Melton, L.J. Osteoporosis, Etiology, Diagnosis, and Management Raven Press, New York (1988) Speller, R.D., Royle, G.R. and Horrocks, J.A. Instrumentation and techniques in bone density measurement J Phys E Sci Instrum (1989) 22 202-214 Adler, L. and Cook, K.V. Ultrasonic parameters of freshly frozen dog tibia J Acous Soc Am (1975) 58 1107-1108 Barger, J.E. Attenuation and dispersion of ultrasound in cancellous bone Ultrasonic Tissue Characterisation II, (Ed Linzer, M.) National Bureau of Standards Special Publication 525, US Government Printing Office, Washington, DC (1979) Evans, J.A. and Tavakoli, M.R. Ultrasonic attenuation and velocity in bone Phys Med Biol (1990) 35 1387-1396 Fry, F.J. and Barger, J.E. Acoustical properties of human skull J Acous Soc Am (1978) 63 1576-1590 Lang, S.B. Ultrasonic method for measuring elastic coefficients of bone and results on fresh and dried bovine bone IEEE Trans Biomed Eng (1970) 17 101-105 Langton, C.M., Evans, G.P., Hodgskinson, R. and Rings, C.M. Current research in osteoporosis and bone mineral measurement Bath Conference on Osteoporosis and Bone Mineral Measurement (Ed Ring, E.F.) (1990) Published by the British Institute of Radiology (BIR) Shalanskii, I., Grazdira, I., Kuntsmann, R , Shiruchek, I. and Uger, I. Propagation of ultrasonics in bones Polymer Mech (1976) 12 946-949 Yoon, H.S. and Katz, J . L Ultrasonic wave propagation in human cortical bone II: measurements of elastic properties and microhardness J Biochem (1976) 9 459-464 Yoon, H.S. and Katz, J . L Ultrasonic properties and microtexture of human cortical bone Ultrasonic Tissue Characterisation II, (Ed Linzer, M.) National Bureau of Standards, Special Publication 525, US Government Printing Office, Washington, DC (1979) 189-195 Baran, D.T., Kelly, A.M., Karellas, A., Gionet, M., Price, M., Leahey, D., Stanterman, S., Sherry, B. and Roche, J. Ultrasonic attenuation of the Os calcis in women with osteoporosis and hip fractures Calcif Tissue Int (1988) 43 138-142 Heaney, R.P., Avioli, L.V., Chesoot, C., Lappe, J., Recker, R.R. and Brandenbnrger, G.H. Osteoporotic bone fragility detection by ultrasound transmission velocity J Am Med Assoc (1989) 261 2986-2991 Murray, S.A., Miller, C. and Kants, J. Specificity and sensitivity of ultrasound attenuation in bone Ultrasonic Studies of Bone (Eds Palmer, S.B. and Langton, C.M.) IOP Publishing Ltd, Bristol (1987) 67-73 Rossman, P., Zagzebski, J., Mesina, C., Sorenson, J. and Mazess, R. Comparison of speed of sound and ultrasonic attenuation in the Os calcis to bone density of radius, femur and lumbar spine Clin Phys Physiol Meas (1989) 10 353-360
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19
20 21
22
23 24
25 26 27 28 29 30 31 32 33
Evans,W.D., Crawley, E.O., Compston, J.E., Evans, C. and Owen, G.M. Ultrasonic attenuation and bone mineral density Clin Phys Physiol Meas (1988) 9 163-165 Grinner, D. and Doherty, S.M. In: Osteoporosis and Bone Mineral Measurements (Eds Ring, E.F.T., Evans, W.D. and Dixon, A.S.) Proceedings of an International Conference, Bath 18-19 April, 1988 (1989) 136 Petley, G.W., Haines, T.K., Cooper, C., Langton, C.M. and Cawley, M.I.D. A comparison of single photon absorptiometry and broadband ultrasonic attenuation, past, present and future, in: Ultrasonic Studies of Bone (Eds Palmer, S.B. and Langton, C.M.) IOP Publishing Ltd, Bristol (1987) 15-20 Poll, V., Cooper, C. and Cawley, MI.D. Broadband ultrasonic attenuation in the Os calcis and single photon absorption in the distal forearm: a comparative study Clin Phys Physiol Meas (1986) 7 375-379 Resch, H., Pietsehmann, B., Krexner, E. and Willvonseder, R. Broadband ultrasonic measurement: a new diagnostic method in osteoporosis Am J Roent (1990) 155 825-828 Smith, D.A., Hosie, C.J. and Deacon, A.D. Broadband ultrasonic attenuation of the Os calcis: comparison with CT measurements of bone Ultrasonic Studies of Bone (Eds Palmer, S.B. and Langton, C.M.) IOP Publishing Ltd, Bristol (1987) 21-27 Hosie, C.J., Smith, D.A., Deacon, A.D. and Langton, C.M. Comparison of broadband ultrasonic attenuation of the os-calcis and quantitative computed tomography of the distal radius Clin Phys Physiol Meas (1987) 8 303-308 MeKelvie, M. Ultrasonic propagation in cancellous bone PhD Thesis University of Hull (1988) McCIoskey, E.V., Murray, S.A, Charlesworth, D., Miller, C., Fordham, J., Clifford, K., Atkins, R. and Kanis, J.A. Assessment of broadband ultrasound attenuation of the Os calcis in-vitro Clin Sci (1990) 78 221-227 Mennier, A., Yoon, H.S. and Katz, J . L Ultrasonic characterization of some pathological human femora Ultrasonic Symposium Proceedings IEEE (1982) 713-717 Rich, C., Klinik, E., Smith, R. and Graham, B. Measurement of bone mass from ultrasonic transmission time Proc Soc Exp Bio Med (1966) 123 282-285 Papadakis, E.P., Flower, K.A. and Lynnworth, LC. Ultrasonic attenuation by spectrum analysis of pulses in buffer rods; method and diffraction corrections J Acoust Soc Am ( 1973) 531336-1343 Kaye, G.W.C. and Lahy, T.H. Tables of Physical and Chemical Contents, Longmans, London (1968) Tavakoli, M.B. An investigation of ultrasonic attenuation and velocity in bone PhD Thesis University of Leeds (1991) Harley, R., James, D., Miller, A. and White, J.D Phonons and the elastic moduli of collagen and muscle Nature (1977) 267 285 Lees, S., Cleary, P.F., Heeley, J.D. and Gariepy, El. Distribution of sonic plesio-velocity in a compact bone sample J Acous Soc Am (1979) 66 641-646 Mason, W.P. and McSkimin, H.J. Attenuation and scattering of high frequency sound waves in metals and glasses J Acoust Soc Am (1947) 19 464-473 Robins, P.A., Petley, G., Aindow, J.D. and Bottle, J. Ultrasonic bone assessment: is wavefront abberation the principal limitation of current technology? Paper given at BMUS'91, 23rd Annual Scientific Meeting of the British Medical Ultrasound Society, Bournemouth, Dec 1991 (1991)
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Received 31 July 1991; revised 6 April 1992 The relationship between the structure of bovine cancellous bone, and its ultrasonic propagation parameters is investigated by means of a novel technique involving the application of large static loads, thereby changing the porosity in a controlled manner. The results show that for frequencies in the range 0.4 to 1 MHz, porosity decreases up to 35% are associated with a reduction in attenuation of up to 500%, whereas the velocity increases by roughly 35% for the same changes. The data taken overall suggest that in determining the ultrasonic attenuation coefficient at these frequencies, the amount of material in a given bone section is significantly less important than the distribution of that material.
Keywords: ultrasonic scattering; velocity and attenuation; osteoporosis; bone mineral
Osteoporosis is rapidly becoming a major health problem, particularly for the two major at risk groups, the elderly and post-menopausal women. The disease is identified by a decrease in mass in both cortical and cancellous bone with a more pronounced effect on cancellous bone 1. Currently available non-invasive clinical methods for the detection of osteoporosis include: single photon absorptiometry (SPA) of the cortical bone (usually the forearm), dual photon absorptiometry (DPA) of the spine, and quantitative computed tomography (QCT). All of these methods are associated with ionizing radiation 2. Ultrasonic assessment of bone disease has been introduced more recently. The ultrasonic parameters involved, attenuation and velocity, have been measured in normal and pathological bone, both cortical and cancellous, by a number of workers 3-11. Attempts have been made to relate these properties to bone mineral density (BMD) using DPA 12-15, bone mineral content (BMC) using SPA 14-21 and bone mineral density (BMD) using QCT t6,21-2a. The results obtained have been contradictory and inconsistent. Other workers have attempted to correlate the attenuation or velocity with physical density (PD) 5's'22-24'2~. The acoustic properties of any composite material such as bone depend not only upon the amount of the various constituent materials present, but also on the spatial arrangement of those materials. In bone, the main constituents are hydoxyapatite (HAP), collagen and fat and these three have quite different acoustic properties. It would therefore be predicted that the acoustic 0041-624X/92/060389-07 © 1992 Butterworth-Heinemann Ltd
impedance mismatch found at interfaces involving these constituents would cause significant scattering and hence attenuation. Furthermore, the scattering characteristics are likely to depend upon the local architecture, particularly because the inhomogeneities in question are a small fraction of a wavelength in size. Despite the recognition that the scattering due to structure is an important component of the total ultrasonic attenuation mechanism, the magnitude and nature of this component have not been identified. Theoretical models have also failed so far to elucidate the problem 23. In this study, we have devised a technique to monitor the attenuation and velocity of bone samples during the application of large loads. Under such loads, the trabecular structure begins to fracture giving significant structural change, while at the same time there is a general increase in physical density anda corresponding decrease in porosity. However, the total mass of bone material between the transducers remains constant.
Instrumentation A block diagram of the instrument is shown in Figure 1. The instrument consists of two parts: (a) an electric and electronic system and (b) a sample holder including transducers and press. The electric and electronic system This system consists of a high voltage pulse generator (RPIO0, Vigilant) connected to the transmitting transducer
Ultrasonics 1992 Vol 30 No 6
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Effect of bone structure on attenuation and velocity: M.B. Tavakofi and J.A. Evans
Experimental method
Press
Attenuation
Perspex buffer
IEEE-488
0Peroexbu er° t To synchronous output of pulser 1-Steel cylinder to protect the transducers 2-Aluminium cylinder 3--Backing spring 4--Transmitting transducer 5 - Receiving transducer
-
Press
Ultrasonic waves produced by the transmitting transducer travel along the buffer in contact with the transmitter. In the absence of a sample, the ultrasonic energy is transmitted directly to the buffer in contact with the receiving transducer although some is reflected. When the two buffers are of the same material and provided that no air or foreign bodies are trapped, the reflected signal is negligible. The transmitted signal then travels through the receiving buffer and is detected by the receiving transducer. When a sample is sandwiched between the two buffers, some of the energy is reflected back into the first buffer at the first boundary, thereby attenuating the energy transmitted into the sample. A further reflection takes place at the second boundary and hence there is an additional attenuation of the signal sent into the second buffer. The energy transmitted into the receiving buffer is detected by the receiving transducer, where the electronic signal produced is processed and stored. A correction for
a
Receiver
I
Figure 1 The diagram of the system used for measurement of acoustical properties of bone at different porosities
I
j•A1
I
(f)
Receivingbuffer
and a 100 M Hz sampling rate digital oscilloscope (Philips PM 3350) connected to the receiving transducer. The oscilloscope was also connected to a BBC-computer through an IEEE-488 interface. The synchronous output of the pulser was connected to the trigger input of the oscilloscope. The delay function of the digital oscilloscope was used to bring the desired signal on to the oscilloscope screen, hence removing the necessity for electronic gating. The signal could then be recorded on a floppy disc for later processing.
Sample holder, transducers and press The rest of the system includes the sample holder, transducers and a 40 ton hydraulic press. The diagram of the sample holder is shown in Figure 1. It consists of an aluminium cylinder of diameter 7 cm and two identical perspex buffers which can move inside the cylinder. The thickness of both of the buffers is 2.5 cm and their diameters are 7 cm. Each perspex buffer is in contact on one side with the sample and, on the other side, with the corresponding transducer. The transducers are housed in steel cylinders to protect them when the sample holder is inside the hydraulic press. Alignment of the transducers is achieved by producing a small recess for the steel case on the perspex buffer surfaces facing the transducers. At the rear of each transducer a spring is located to push it against the perspex buffer with constant pressure. Ultrasonic gel is used for coupling. The transducers used were two identical 2.5 cm diameter 0.6 MHz broadband transducers and the hydraulic press (Moores, Birmingham) was capable of applying loads up to 40 000 kg, although it was not used above 20 000 kg in this study.
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Transmitting buffer j~ A0(f)
I
I Transmitter
b
I
Receiver
I
I
I
I
I
I
Transmitter
Figure 2 The diagram shows the ultrasonic propagation in the buffers and sample: (a) with no sample present; (b) with the sample present
Effect of bone structure on attenuation and velocity: M.B. Tavakofi and J.A. Evans the losses due to reflections at the boundaries was performed using the method described below. Further corrections were applied to allow for losses due to diffraction. The whole system was then validated with the use of a standard reference material, polythene. The details of the calculation used are given below. In Figure 2a the signal arriving at the receiver in the absence of a sample can be expressed as:
A l ( f ) = tAo(f)ex p -- (~lbl +
~2b2)
(1)
where Ao(f) and A l ( f ) are the amplitudes of the signal at the surface of the transmitting transducer and at the surface of the receiving transducer respectively when there is no sample between the buffer. ~x and ~2 are the attenuation coefficients of the transmitting and receiving buffers, bl and b2 are the thicknesses of those buffers and t is the amplitude transmission coefficient. When the buffers are identical and the contact between them is good, t h e n b ~ = b 2 = x , 0 q = ~ 2 = % a n d t = l therefore; a 1( f ) = Ao(f)exp( -- 2~pX)
(2)
When the sample is sandwiched between the buffers (Figure 2b) then;
A s ( f ) = Av(f)exp(-0tpx)
(3)
AT(f) = t2A5(f)
(4)
As(f) = A,(f)exp(-cz,d)
(5)
Aa(f) = q A 2 ( f )
(6)
A2(f) = Ao exp(-~XpX)
(7)
where t t and t 2 are the amplitude transmission coefficients at the two boundaries, d is the sample thickness and ~s is the ultrasonic attenuation coefficient in the sample. From the above equations, it can be deduced that: aq(dB c m - 1) =
8.686 I n ( A a ( f ) ~ = 8.686 I n ( A " ( f ) ~ d \T~I(~),/ d \AI(f)] + In(1)
(8)
where A 8( f ) and A 1( f ) are the received signal amplitudes with and without the sample and T is the energy transmission coefficient which could be calculated using the equation;
T-
4Z2Z2 (Zb + Z,) 2
(9)
where Z b = pbcb and Zs = psc~ are the mechanical impedances of buffer and sample, Pb and p~ are the densities and perspex and the sample, and c b and cs are the velocities of ultrasound in Perspex and the sample. The densities were measured using Archimedes' principle as described in the results section, and the velocities in perspex and in the sample were measured directly using a time-of-flight method as detailed below. Thus, by using Equations (8) and (9) one can calculate T a n d cts if the sample thickness d, is known. Alternatively, the total attenuation in the sample can be evaluated as ~sd (dB). The validity of the above method depends upon an appropriate choice of geometry for sample and apparatus. The main constraints are as described below. 1 The buffer and sample thicknesses should be great enough to prevent interference between the reflected
2
and transmitted signals in each case. This is achieved if the pulse duration is short relative to the transit time in question. The Perspex thickness used for the buffer was 2.5 cm and hence the transit time is about 18/~s which is much longer than the pulse duration. The thickness of the bone samples was about 1.6 cm with a corresponding transit time of about 17/~s which was felt to be acceptable. The diameter of the buffer and sample should be large enough to prevent wall effects as a result of diffraction of the ultrasound beam over the frequency range of interest. As the diameter of the transducers was 2.5 cm, the near-field length in the Perspex buffer at 0.4 MHz (the lowest frequency measured in this experiment) is roughly 2.3 cm and the diffraction angle 0 is given by: 0 = sin- 10.61,1. - ~
2o o
(lO)
a
For a sample with 2 cm thickness and a receiving buffer with a 2.5 cm thickness, the diameter of the beam at 6.5 cm is about 6 cm which is still less than the diameter of the buffer and sample in this experiment. A diffraction correction was performed at each frequency using the method of Papadakis zT. This is necessary because the separation of the transducer alters when the sample is introduced between the buffer rods and because the sound velocity differs between the rods and the sample.
Velocity In all cases, the velocity was measured using a time-of-flight method (TOF). The time shift At of the ultrasound pulse with a sample present relative to that without the sample, was measured directly from the oscilloscope screen. The thickness of the sample d was also measured with a micrometer. The velocity e was calculated using the equation e = d/At. For the polyethylene standard, the values obtained for both velocity and attenuation coefficient showed good agreement with those reported in the literature ( Table 1).
Porosity The primary aim of the study was to investigate the relationship between both velocity and attenuation in bone samples and the porosity ~b. This is defined strictly as the volume fraction of the less dense phase, in this case marrow, i.e.
~= Volume occupied by marrow Volume of whole sample If the densities of the sample, mineralized bone fibre and marrow fat are p,, Pm and pf respectively and the corresponding masses in a particular sample are ms, mm Table 1
The results of attenuation and velocity measurements in polyethylene used as the standard material to test the instrument )erformance Attenuation (dB cm -1) Velocity ( m s -1 ) at 0.6 MHz at 1.0MHz Frequency ( M H z ) Measured value Reported value 28
2005 2000
0.6 2.9 -
1.0 4.6 4.75
Ultrasonics 1992 Vol 30 No 6
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Effect of bone structure on attenuation and velocity: M.B. Tavakofi and J.A. Evans and mf, then Volume occupied by marrow fat = sample volume - bone fibre volume i.e. /T/f
-
m s
Pf Ps and then
m m
(11)
length at different pressures using a dial gauge placed between the two sides of the press. The resolution of the dial gauge was 5 #m. The experiment was repeated for both samples. In both cases, the attenuation in the bone decreased dramatically as the pressure increased. The detailed results from one of the samples are shown in Figures 3 and 4 and the
Pm 40
~p : (m_~ mm~(rns~-' Pm/ \Pm,/
:1
minos ms Pm
A F = 0.4 MHz
and if the mass of marrow is small relative to the mass of mineralized bone fibre, then we can say ~b= 1
30
Ps Pv
•
F = 0.6 MHz
o
F = 0.8 MHz
•
BUA
C O_
Sample
preparation
=:
A bovine femur was obtained fresh from a local abattoir. A coring drill of 7 cm inside diameter was used to obtain bone cores from both proximal and distal ends of the bone. The end faces of the cores obtained were made parallel and smooth using a rotary electric saw and a coarse sandpaper. The final cores obtained had thicknesses of 1.8 and 1.2 cm as measured by a micrometer and these were then preserved in phosphate buffer solution for about one month before the start of the experiment. The air bubbles trapped in the samples were removed before the start of the measurement by placing them underwater in a dessicator overnight and vacuum degassing. Measurements
and
results
The sample was placed at room temperature between the two Perspex buffers and the ultrasonic signal received by the receiving transducer, with just enough pressure to obtain good contact, was recorded (ultrasonic gel was used as a coupling material between sample and buffers). To change the porosity and therefore the structural pattern of the bone samples without changing the amount of bony tissue in the ultrasound path, the thickness of the sample was then reduced by increasing the pressure on it. As the bone samples were located in between the two Perspex buffers in the aluminium cylinder, which had the same diameter as the buffers, and the aluminium cylinder itself, the bone tissue could not escape and hence the amount of bone tissue in the ultrasonic path remained constant while the thickness of the sample, and therefore its porosity, decreased. The received ultrasonic signals at different pressures, and therefore different porosities or structural patterns, were recorded and were used in conjunction with the signal received when there was no sample between the two buffers, to calculate the attenuation in the sample. In calculating the attenuation in bone samples, corrections for the two reflections at the Perspex-bone and bone-Perspex boundaries were made as discussed earlier. The densities of the samples at the beginning of the experiment were measured using Archimedes' principle with a submersion technique. The change of density during the experiment as a result of increasing the pressure was measured by noting the change in the sample
392
Ultrasonics 1 9 9 2 Vol 3 0 N o 6
20
2600
2600
2400
2200
I 1.2
I 1.4
I
[ 1.6
,
I 1.8
,
I 2.0
= 2.2
Density (g cm -3 ) Figure 6 Ultrasonic velocity (m s -1 ) in bone under pressure as a function of density (g c m - 3 ) . The sample is the same as in Figure 3. Note the apparent discontinuity at a density of around 1.6 g cm 3
The reproducibility of the measurement was also evaluated for the standard by measuring attenuation and velocity three times after removing the sample from its position and putting it back in position. The standard deviation of the reproducibility obtained for attenuation was 0.3 dB for attenuation values less than 10 dB and 0.5 for higher attenuation values. For velocity the standard deviation was 0.3%.
Discussion and conclusion As mentioned earlier, the method used reduces the thickness of the sample (and hence its porosity) while keeping constant the amount of bony material in the ultrasonic path. Thus, in the absence of scatter, although the attenuation coefficient in dB cm-1 will change as a result of increasing the density, it would be anticipated that the total attenuation in the sample would remain unchanged. This facilitates an investigation of the role of structure in determining the acoustical properties of the bone. As the applied load increases, structural changes occur and hence the porosity of the bone alters. As the porosity q~is reduced, the density of the sample approaches that of pure compact mineralized bone fibre (MBF) and the value of ~b can be calculated from a consideration of the density changes. Bone is taken to be a two-component system comprising MBF and fat with densities Pm and pf respectively. In order to obtain a value for Pro, it is necessary to consider its make-up further. MBF can be considered as consisting of roughly 46% collagen and 46% HAP with the remaining 8% water. Assuming a density of 1430kgcm -3 for collagen 3° and 3170kgcm -3 for HAP 61, then the calculated value of Pm is about 2200 kg cm- 3. The porosity can then be calculated from
394
Ultrasonics 1992 Vol 30 No 6
(11)
•
where Ps is the sample density. In the above calculation the effect of fat on the porosity calculation is neglected, as its density is assumed to be close to 1 g cm-3 and therefore negligible. The results obtained are tabulated in Table 2. From Figure 3 it is clear that the attenuation in the 1.2cm thick sample under normal conditions with a porosity of 41% is about 18 dB at 0.6 MHz. When the porosity is reduced to 5%, the attenuation decreases to less than 5 dB and almost by the same ratio at other frequencies. The ratio of the attenuation at highest porosity (i.e. normal bone) to that at the lowest porosity achieved, is about 4 for this sample at this frequency which means that, in this sample, the attenuation depends mostly on the structure rather than on the component materials. Similar results were obtained from the other sample (1.8 cm thick). Even at the lowest attenuation shown in the graph the porosity is still not zero. Also, since there are at least two constituent materials even at zero porosity, the density and velocity differences between them ensure that there will still be a scattering component. The size of the individual particles of the constituent materials is very small compared with the wavelength used in this experiment and hence, according to the Mason and McSkimin32 theory for polycrystalline systems with grain sizes much smaller than a wavelength, the scattering depends on 2 -4 . Scattering is more important in this experiment as the sample is not only a polycrystalline material but also a multiphase system, and therefore the absorption in bone must be significantly less than the attenuation value at zero porosity. A potential source of error in all measurements of this type on heterogeneous materials is that due to phase cancellation artefacts. It might be argued that the observed reduction in attenuation with decreasing porosity should be attributed in part to the increase in homogeneity of the sample associated with the porosity change. However, recent evidence from Robins et al. 33 suggests that this is not significant in the specific case of ultrasonic bone measurements. The change of velocity as a result of reducing porosity while keeping the amount of material constant, shows much less change than the attenuation, as is shown in Fi#ures 5 and 6 and Table 2. The ratios of the minimum to the maximum of the attenuation obtained at 0.6 MHz for the two samples are 0.35 and 0.26 and these are much less than the corresponding ratios for velocity, which are 0.71 and 0.74. This is a further illustration of the greater influence of bone structure on attenuation than velocity in this frequency range. The intercept of the straight line in Figure 4 gives a velocity of 3476 m s-1 for bone at zero porosity, which compares well with published values z5 for cortical bone. Acknowledgements We would like to thank the staff of the Mechanical and Electronic Workshops, of the Department of Medical Physics for building the apparatus used in this study. We are grateful to Dr C.M. Langton for helpful comments and discussions as well as the loan of the transducers and press.
Effect of bone structure on attenuation and velocity: M.B. Tavakofi and J.A. Evans
On6 of us (MBT) would like to acknowledge the financial support of the Government of Iran for a scholarship during this period.
16
References
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8
9 10 11
12
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