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Microdamage evaluation in human trabecular bone based on nonlinear ultrasound vibro-modulation (NUVM)
ARTICLE IN PRESS Journal of Biomechanics 42 (2009) 581–586
Contents lists available at ScienceDirect
Journal of Biomechanics journal homepage: www.elsevier.com/locate/jbiomech www.JBiomech.com
Microdamage evaluation in human trabecular bone based on nonlinear ultrasound vibro-modulation (NUVM) K. Zacharias a, E. Balabanidou b, I. Hatzokos b, I.T. Rekanos a, A. Trochidis a, a b
Physics Division, School of Engineering, Aristotle University of Thessaloniki, Thessaloniki 54124, Greece First Orthopaedics Department, School of Medicine, Aristotle University of Thessaloniki, Thessaloniki 54124, Greece
a r t i c l e in fo
abstract
Article history: Accepted 17 December 2008
The primary aim of this work is to investigate the potential of nonlinear ultrasound for microdamage detection in human bone. Microdamage evaluation in human bone is of great importance, because it is considered a significant parameter for characterizing fracture risk. Experiments employing nonlinear acoustic vibro-modulation were carried out in human femoral trabecular specimens removed during surgery. A frequency mixing (inter-modulation) was observed between an ultrasound wave, propagating in the bone, and a low-frequency vibration applied directly to the bone specimens. The appearance of side frequencies, which are related to the vibrational excitation, around the fundamental ultrasound frequency manifests the modulation nonlinear phenomenon. Instead of inducing microdamage by mechanical fatigue loading, specimens with different degree of osteoporosis were used. The experiments demonstrated that osteoporotic bone exhibits stronger nonlinearity compared to healthy bone presenting significant increase of the modulation amplitude with increasing degree of osteoporosis. The obtained results indicate that, in contrast to conventional hysteretic nonlinearity, dissipative acoustic nonlinearity can be of significance in the generation of nonlinear modulation effects. In the proposed technique the size and the shape of samples are not crucial compared to nonlinear resonant ultrasound spectroscopy (NRUS). Furthermore, the method is sensitive to the presence of microdamage, non-invasive, easy to implement and most important, it can be proved valuable tool for in vivo bone damage characterization. & 2009 Elsevier Ltd. All rights reserved.
Keywords: Trabecular bone Bone damage assessment Nonlinear ultrasound vibro-modulation Nonlinear acoustic dissipation
1. Introduction The standard technique for evaluating bone strength is based on dual energy X-ray absorptiometry (DEXA) through the measurement of bone mineral density (BMD). However, measuring BMD alone does not provide prediction for bone strength because a skeleton at risk of fracture cannot be simply determined by the amount of existing bone. Several other properties, characterized in general by the term bone quality, are involved in bone fragility. Bone quality incorporates micro-architecture, tissue material properties, chemical composition of bone matrix and the presence of microdamage (Bouxsein, 2003). Microdamage in bone accumulated by repetitive loading and its effect on bone fragility has received considerable attention in recent years. It appears as micro-fracture of whole trabeculae and micro-cracks within trabeculae. Micro-fracture occurs less frequently than micro-cracking and is considered to be the final result of microdamage (Wang and Niebur, 2006; Turner, 2002).
Corresponding author. Tel.: +30 2310 995927; fax: +30 2310995928.
E-mail address: [email protected] (A. Trochidis). 0021-9290/$ - see front matter & 2009 Elsevier Ltd. All rights reserved. doi:10.1016/j.jbiomech.2008.12.018
Several studies have revealed strong correlation between crack density and mechanical properties, especially toughness (Zioupos, 2001; Burr, 2003). The precise role, however, of microdamage in bone fracture is yet unclear and has to be defined. Therefore, noninvasive techniques to assess bone microdamage quantitatively are important. They could provide insight into the role of microdamage to bone quality. Assessment of microdamage can mainly be made by histological techniques. However, histological estimation of microdamage requires excision biopsy, which is invasive and, therefore, exacerbates fracture risk. Micro-computerized tomography (Parkesh et al., 2006) and positron emission tomography (Li et al., 2005) seem to be new promising noninvasive techniques but are not yet available in everyday clinical practice. Nonlinear acoustic methods applied earlier in material testing proved to have potential in detection of micro-cracks (Korotkov and Sutin, 1994; van den Abeele et al., 2001). The interaction of ultrasound waves with microdamage results in nonlinear wave propagation, which can be evidenced by appropriate signal processing. In that vein, Muller et al. (2006) used nonlinear resonant ultrasound spectroscopy (NRUS) to detect damage in cortical bone. Their results showed that nonlinear ultrasound can be used to assess progressively induced damage.
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Cleveland et al. (2006) carried out simulations for detecting nonlinear properties in both cancellous and cortical bone by employing the Khokhlov–Zabolotskaya–Kuznetsov equation to model bone. They concluded that nonlinear modulation signals might be detectable in cancellous bone but not in cortical bone due to strong attenuation. In a recent publication, Muller et al. (2008) applied NRUS to estimate the nonlinear hysteretic parameter a of bone by measuring the shift of the resonance frequency of bone samples. In their experiments, it was demonstrated that the nonlinear parameter increases with increasing damage induced to bone samples with mechanical cyclic loading and can be used as an indicator of accumulated damage. In vivo studies regarding the measurement of acoustic nonlinearity in the heel bone have been reported (Hoff et al., 2003; Engan et al., 2006). Also, in vivo measurement of acoustic nonlinearity in calcaneus trabecular bone has been based on time-of-flight modulation measurements (Renaud et al., 2008). In this paper, a new method for microdamage detection in human bone is presented. The method is based on the intermodulation between a high-frequency (HF) ultrasound wave and a low-frequency (LF) vibration. A series of experiments were carried out on human femoral trabecular bone specimens with marrow and soft tissues removed. In our experiments, instead of inducing microdamage by fatigue cycling, specimens with different degree of osteoporosis were used. It is shown that the signal amplitude at side frequencies (frequency components generated by modulation) increases with increasing degree of osteoporosis. Furthermore, during the experiments, downward shift, Df0, of resonance frequencies, f0, and decrease of the corresponding quality factor (the ratio of the resonance frequency to the half-power bandwidth), Q, of the tested samples were observed. Thus, the response amplitude at the side frequencies, as well as, the resonance frequency shift and the quality factor reduction can be considered as quantitative parameters characterizing the microdamage present in bone specimens. The proposed method is non-invasive, easy to implement and feasible for in vivo applications.
2. Nonlinear vibro-modulation method Structures with inhomogeneities or defects exhibit strong nonlinear vibrational and acoustical effects. In particular, strong nonlinear effects have been observed in structures with microcracks. These effects include the generation of higher harmonics and the inter-modulation between a high-frequency acoustic wave and a low-frequency vibration (Ostrovsky and Johnson, 2001). These effects provide a basis for developing different techniques for nondestructive testing. The vibro-modulation method is based on the fact that a highfrequency ultrasound wave propagating in a structure is modulated by a low-frequency vibration. The excitation frequencies of the ultrasound and the vibration are fH and fL, respectively, whereas their amplitudes are AH and AL, respectively. The modulation is generated by the nonlinear propagation of waves in the bone and appears in the response spectrum in the form of side frequencies around fH. The amplitude of the low-frequency vibration, AL, must be high enough to activate the inherent nonlinearity of the damage. Furthermore, during the experiments, the maximum amplitude of the stain induced in the bone is approximately 105, hence, it is not considered harmful for bone. The high-frequency wave, which is transmitted through the sample, interacts with the source of nonlinearity, is received and processed. The resulting spectrum contains both the carrier frequency of the ultrasound as well as the frequency components fH7nfL (n is integer number). Modulation effects have been
observed in several applications. Ekimov et al. (1999) employed modulation of high-frequency torsional waves by low-frequency vibration for crack detection in a rod. Zaitsev et al. (2006) presented applications of nonlinear modulation for crack detection in structures and discussed possible sources of nonlinearity in damaged structures. Donskoy and Sutin (1998) used nonlinear ultrasound modulation to investigate the existence of crack, delamination or poor quality bonding. A review of the nonlinear acoustic vibro-modulation techniques is presented in a very recent publication (Zagrai et al., 2008). Despite various practical applications of nonlinear modulation the origin of the nonlinear effects observed seems not to be understood clearly enough. Very similar nonlinear effects may be caused by quite different nonlinear physical mechanisms. Insight into the actual underlying modulation mechanisms is necessary for optimization of practical implementation of the nonlinear effects to quantify damage. When setting up practical diagnostics, one should realize that, even though the nonlinear effects are increased due to the influence of microdamage, the amplitude of the frequency components generated due to the nonlinearity are usually small compared to the excitation amplitude. Therefore, care must be taken to avoid masking of the nonlinear effects related to the propagation mechanisms by the nonlinearities induced by the operation of electric circuits and actuators. Furthermore, one has to consider for investigation the nonlinear effect that is most sensitive with respect to the nonlinear mechanism that is responsible for its generation. Unlike the methods based on higher harmonics measurements, the techniques that employ modulation effects are relatively insensitive to nonlinearities generated by the electric circuits. From that point of view, the nonlinear vibro-modulation technique has a significant advantage.
3. Experimental results For the experiments, samples of human femoral trabecular bone were used. Bone cubes were extracted from fresh femur heads removed during surgery. In particular, cube samples centered at the middle of the femoral head were cut using a diamond circular saw. Heating and consequent damage was avoided by employing low cutting speed and constant irrigation. Information about the study and the related experiments were given to each patient prior to surgery and a written consent statement was obtained. Before using the samples, marrow and soft tissues were removed after appropriate treatment. For defatting, the bone samples were immersed in a dichloromethanol solution for three days and consequently were cleaned using air jet. The experimental set up is shown in Fig. 1. In particular, the bone samples were mounted on a vibrator to provide the LF vibrations. Two ultrasound transducers were used to transmit and receive the HF ultrasonic waves. First, the bone samples were glued on a circular steel plate of diameter 20 mm. The back plate had screw on its bottom so that it could be firmly attached directly on the transducer providing the HF ultrasonic wave. The diameter of the transducer was the same with that of the back plate, i.e. 20 mm. The HF transducer was screwed on the moving part of the vibrator that provided the LF vibration. Thus, half of the face of the cubic bone sample was in contact with both HF and LF source. Hence, the excitation could be considered uniform rather than local. Both the LF and HF excitations were sinusoidal continuous signals. A miniature transducer was glued on the top of the bone sample to monitor the response to the combined HF and LF excitation. The generation and amplification of the LF vibrations and the HF ultrasonic wave were controlled by two independent circuits to avoid mixing of the signals within the
ARTICLE IN PRESS K. Zacharias et al. / Journal of Biomechanics 42 (2009) 581–586
583
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Bone sample Vibrator
Ultrasonic transmitter
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Fig. 1. Experimental set up.
electric circuits. The measured response was transferred to an acquisition system for further analysis.
Fig. 2. Spectrum of the received signal around fH ¼ 49 kHz for a healthy bone, where the amplitude and the frequency of the vibration signal are AL ¼ 300 mVpp and fL ¼ 270 Hz, respectively.
0
3.1. Frequency components generated by modulation
Relative Amplitude [dB]
-10
First, the response of the ‘‘healthy’’ bone sample was studied under simultaneous excitation of both HF and LF waves. The sample was a cube with size approximately 30 30 30 mm3. The voltage excitation of the vibrator was AL ¼ 300 mV peak to peak and its frequency was fL ¼ 270 Hz, while the magnitude of the vibrational velocity was approximately 104 m/s. The voltage driving the ultrasonic transmitter, AH, was set 40 dB below AL, operating at fH ¼ 49 kHz. The corresponding amplitude AH is kept constant in all experiments that follow. The spectrum of the received ultrasonic signal in the vicinity of fH is shown in Fig. 2. It is clear that the healthy bone exhibits nonlinear behaviour and several side frequencies are present in the response spectrum, generated by vibro-modulation. Actually, the amplitudes of the frequency components at fHfL, fH+fL, fH2fL, and fH+2fL, are approximately 50, 58, 55, and 53 dB, below the amplitude of the ultrasound at fH, respectively, while the noise level was 75 dB. Thus, it is verified that healthy bone itself is a nonlinear material because of its heterogeneous mesoscopic structure. It should be mentioned that the differences of the amplitudes between the frequency components fHfL and fH+fL as well as between fH2fL and fH+2fL, are reasonable. These differences appear due to the generation of standing waves, which result in different amplitudes for different frequencies, at the measurement position. Actually, the asymmetry in the side lobe amplitudes depends on the wave phase velocity and the relation between the different wavelengths and the size of the bone sample. Next, samples with high degree of osteoporosis were examined. A typical result of the spectrum around fH ¼ 49 kHz for a cubic (40 40 40 mm3) osteoporotic bone sample under similar excitation conditions is presented in Fig. 3. It can be seen that osteoporotic bone exhibits stronger nonlinearity, which is attributed to microdamage. The amplitudes at the side frequencies increase substantially. In particular, the amplitudes of the frequency components at fHfL, fH+fL, fH2fL, and fH+2fL, are approximately 31, 32, 45, and 46 dB, below the amplitude of the ultrasound at fH, respectively. This is consistent with the hypothesis that microdamage accumulates easier in humans with low bone density.
-20 -30 -40 -50 -60 -70 -80 47.5
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49.0 49.5 Frequency [kHz]
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Fig. 3. Spectrum of the received signal around fH ¼ 49 kHz for an osteoporotic bone, where the amplitude and the frequency of the vibration signal are AL ¼ 300 mVpp and fL ¼ 270 Hz, respectively.
In the experiments, the effect of the vibration frequency, fL, on the amplitude level of the side frequency components was investigated. Similar results were obtained for different values of fL, in the range from 80 Hz to 1 kHz. Hence, it appears that the modulating vibration frequency is not a crucial parameter and can be chosen rather arbitrarily. Next, the effect of the vibration amplitude AL on the amplitude level of the side frequency components was systematically investigated, keeping AH constant (as mentioned above). For AL ¼ 100 and 200 mVpp, the spectrums around fH ¼ 49 kHz for the osteoporotic bone sample are shown in Figs. 4 and 5, respectively. For AL ¼ 300 mVpp the corresponding spectrum has already been presented in Fig. 3. It can be seen that the amplitudes at side frequencies increase with increasing amplitude of the vibration signal. This is clearly depicted in Fig. 6, where the relative amplitude in dB of the frequency component at fHfL vs. the vibration amplitude AL, is illustrated.
ARTICLE IN PRESS K. Zacharias et al. / Journal of Biomechanics 42 (2009) 581–586
0
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Relative Amplitude [dB]
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100 48.0
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Fig. 4. Spectrum of the received signal around fH ¼ 49 kHz for an osteoporotic bone, where the amplitude and the frequency of the vibration signal are AL ¼ 100 mVpp and fL ¼ 270 Hz, respectively.
150 200 250 Vibration Amplitude [mVpp]
300
Fig. 6. Relative amplitude in dB of the frequency component at fHfL (with respect to the amplitude at fH) vs. the vibration amplitude AL, for an osteoporotic bone.
0 -1 0
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AL = 0mVpp AL = 150mVpp AL = 300mVpp
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48.5
49.5 49.0 Frequency [kHz]
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Fig. 5. Spectrum of the received signal around fH ¼ 49 kHz for an osteoporotic bone, where the amplitude and the frequency of the vibration signal are AL ¼ 200 mVpp and fL ¼ 270 Hz, respectively.
3.2. Resonance frequency shift and quality factor During the experiments, it was observed that the level of the received ultrasound decreased with increasing damage. In particular, when changing from the healthy to the osteoporotic sample the level of the received ultrasound at the frequency fH slightly decreased (approximately 1 dB). This is attributed to increased losses compared to healthy bone even though the excitation conditions were the same in all cases. This effect was further investigated by measuring the quality factor at resonances for both healthy and osteoporotic bones, using the experimental setup described above. In particular, the amplitude of the vibration AL was kept constant and the resonance curve of the sample was obtained by slowly changing the ultrasound frequency fH around a resonance frequency f0 of the sample. For the measurements, wide-band transducers were used.
Fig. 7. Resonance curves of healthy bone derived for different vibration amplitudes.
For the case of healthy bone, the measured resonance curves for different amplitudes of the vibration (AL ¼ 0, 150, and 300 mVpp) are shown in Fig. 7. It can be seen that for the healthy bone, the resonance frequency shift due to variations of the vibration amplitude is negligible, while the quality factor, Q, remains almost constant. The measured resonance spectrum of the system is complex. Therefore, the system was first investigated to determine the resonances related to the sample rather than to the back plate. For that purpose, instead of bone samples, glass rods were initially used where both the dimensions and the sound velocity can be accurately determined. It was demonstrated that the system behaves like having rigid-free boundary conditions. For the healthy bone case (Fig. 7), the particular resonance frequency at approximately 64 kHz was chosen based on two facts. First, it is indeed a resonance frequency because a peak at the spectrum appears as well as it fulfils the rigid-free boundary condition when compared to adjacent resonance frequencies. Second, we observed that no significant interference with adjacent resonance was present. It should also be mentioned that the characteristic of the transducer in the range from 62 to 67 kHz has a gain lower than 2 dB compared to its flat response.
ARTICLE IN PRESS K. Zacharias et al. / Journal of Biomechanics 42 (2009) 581–586
Moreover, the measurements are comparative considering different amplitudes of vibration, hence, the relative change of Q are not significantly affected by the gain of the transducer. The same measurements were carried out for the case of osteoporotic bone. In this case, the resonance present at approximately 44.5 kHz was investigated. As shown in Fig. 8, downward shift of the resonance frequency and reduction of the quality factor occurs by increasing the vibration amplitude. For the cases of a healthy and an osteoporotic bone, the relative change of the quality factor and the resonance frequency shift with increasing vibration amplitude are further presented, in Figs. 9 and 10, respectively.
0 -1 Relative Amplitude [dB]
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AL = 0mVpp
-8
AL = 150mVpp
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4. Discussion
45.5
46.0
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Fig. 8. Resonance curves of osteoporotic bone derived for different vibration amplitudes.
ΔQ [%]
6 5 4 3 2 1 0 -1 -2 -3 -4 -5 -6 -7 -8 -9 -10 -11 -12
Healthy Osteoporotic 0
50
100 150 200 Vibration Amplitude [mVpp]
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300
Fig. 9. Relative change of the quality factor, Q, vs. vibration amplitude, AL, for the cases of a healthy and an osteoporotic bone.
0 -100
Δf0 [Hz]
-200 -300 -400 Healthy Osteoporotic
-500 -600 0
50
585
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Fig. 10. Resonance frequency shift, Df0, vs. vibration amplitude, AL, for the cases of a healthy and an osteoporotic bone.
The nonlinear effects observed during our experiments in human bone samples include nonlinear modulation of HF acoustic waves by LF vibrations, downward shift of the resonance frequencies and decrease of the Q factor of the samples with increasing LF modulating vibration amplitude. The treatment of the bone samples, the experimental arrangement and the measuring procedure were identical for both healthy and osteoporotic samples. The signal-to-noise ratio of the measuring system was 75 dB allowing reliable measurement of the nonlinearity. The main result of the present work is that osteoporotic bone exhibits higher nonlinearity compared to healthy bone. Depending on the amplitude of the LF vibration the measured difference of the nonlinearity, indicated by the level of the inter-modulation frequency components can reach 20 dB. In the absence of LF vibration, hysteretic nonlinearity can explain both the shift of the resonance frequencies and the decrease of Q factor when the excitation amplitude increases. It is well known that acoustic nonlinearity is observed even when only the HF excitation is present. This fact is the base of the NRUS method. Similar experiments were carried out in human bone specimens using only one excitation frequency and the nonlinear hysteretic parameter was estimated using measured resonance frequency shifts (Muller et al., 2008). However, in our experiments, an HF ultrasound wave is used to investigate the nonlinear properties of bone samples under the simultaneous action of an LF vibration. We focus on the effect of the LF vibration keeping the HF unchanged in an effort to highlight the presence of non-classical nonlinearity. The observed decrease of the Q factor for the HF wave depends on the amplitude of the LF vibration. The additional losses, which result in further reduction of Q, could be attributed to viscous-like linear losses. The strong LF vibration alters the magnitude of the thermoelastic losses of the HF leading to decreased Q factor. Thus, in addition to hysteretic nonlinearity, bone specimens seem to exhibit dissipative acoustic nonlinearity. Similar dissipation mechanisms have been observed and described for anomalously strong dissipation in microinhomogeneous rock and sandstone samples (Nazarov et al., 2002). The discrimination, however, of the origins of the observed acoustic nonlinearity is not easy, in the light of these preliminary results (Zaitsev et al., 2005). The observed nonlinear behaviour of bone needs further detailed investigation, which will be the subject of a future publication.
5. Conclusions In this work, the potential of nonlinear ultrasound to detect osteoporosis in human trabecular bone was investigated. The proposed method is based on the nonlinear modulation of a
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high-frequency ultrasound wave by low-frequency vibration. In a series of experiments on human femoral bone samples, it was demonstrated that the amplitude of the nonlinear modulation increases with increasing degree of osteoporosis. Our preliminary results demonstrate that osteoporotic bone exhibits enhanced nonlinear behaviour compared to healthy bone and support existing indications that microdamage accumulates easier in cases of low bone density. To explain the observed experimental results further investigation is required concerning the dissipation mechanisms involved. It seems that, in contrast to conventionally considered hysteretic nonlinearity, nonlinear dissipation may also play a significant role for the observed nonlinear effects. The insight into the underlying physical mechanisms for the modulation effects is necessary for quantitative damage characterization. The proposed modulation method is non-invasive, easy to implement and it could be considered as an alternative approach to nonlinear resonant ultrasound spectroscopy for in vivo applications. Further work for the development of in vivo bone fragility assessment is already under way.
Conflict of interest statement We confirm that there are no conflicts of interest associated with this publication and there has been no financial support for this work that could have influenced its outcome. References Bouxsein, M.L., 2003. Bone quality: where do we go from here? Osteoporosis International 14, S118–S127. Burr, D., 2003. Microdamage and bone strength. Osteoporosis International 14, S67–S72. Cleveland, R.O., Johnson, P.A., Muller, M., Talmant, M., Padilla, F., Laugier, P., 2006. Modelling nonlinear ultrasound propagation in bone. In: Proceedings of the 17th International Symposium on Nonlinear Acoustics including the International Sonic Boom Forum. AIP Conference Proceedings. Donskoy, D.M., Sutin, A.M., 1998. Vibro-acoustic modulation nondestructive evaluation technique. Journal of Material Systems and Structures 9, 765–771.
Ekimov, A.E., Didenkulov, I.N., Kazakov, V.V., 1999. Modulation of torsional waves in a rod with a crack. Journal of the Acoustical Society of America 106, 1289–1292. Engan, H.E., Ingebrigtsen, K.A., Oygarden, K.G., Hagen, E.K., Hoff, L., 2006. Nonlinear ultrasound detection of osteoporosis. In: Proceedings of the 2006 IEEE Ultrasonics Symposium, pp. 2096–2099. Hoff, L., Oygarden, K.G., Hagen, E.K., Falch, J.A., 2003. Diagnosis of osteoporosis using nonlinear ultrasound. In: Proceedings of the 2003 IEEE Ultrasonics Symposium, pp. 1010–1013. Korotkov, A.S., Sutin, A.M., 1994. Modulation of ultrasound by vibrations in metal constructions with cracks. Acoustics Letters 18, 59–62. Li, J., Miller, M.A., Hutchins, G.D., Burr, D.B., 2005. Imaging bone microdamage in vivo with positron emission tomography. Bone 37, 819–824. Muller, M., Tencate, J.A., Darling, T.W., Sutin, A., Guyer, R.A., Talmant, M., Laugier, P., Johnson, P.A., 2006. Bone microdamage assessment using nonlinear resonant ultrasound spectroscopy (NRUS): a feasibility study. Ultrasonics 44, e245–e249. Muller, M., Mitton, D., Talmant, M., Johnson, P., Laugier, P., 2008. Nonlinear ultrasound can detect accumulated damage in human bone. Journal of Biomechanics 41, 1062–1068. Nazarov, V.E., Radostin, A.V., Soustova, I.A., 2002. Effect of an intense sound wave on the acoustic properties of a sandstone bar resonator. Experiment: Acoustical Physics 48, 76–80. Ostrovsky, L., Johnson, P., 2001. Dynamic nonlinear elasticity in geomaterials. Rivista del Nuovo Cimento 24, 1–46. Parkesh, R., Lee, T.C., Gunnlaugsson, T., Gowin, W., 2006. Microdamage in bone: surface analysis radiological detection. Journal of Biomechanics 39, 1552–1556. Renaud, G., Calle´, S., Remenieras, J.-P., Defontaine, M., 2008. Exploration of trabecular bone nonlinear elasticity using time-of-flight modulation. IEEE Transactions on Ultrasonics, Ferroelectrics, and Frequency Control 55, 1497–1507. Turner, C.H., 2002. Biomechanics of bone: determinants of bone skeletal fragility and bone quality. Osteoporosis International 13, 97–104. van den Abeele, K.E.-A., Sutin, A., Carmeliet, J., Johnson, P.A., 2001. Micro-damage diagnostics using nonlinear elastic wave spectroscopy (NEWS). NDT & E International 34, 239–248. Wang, X., Niebur, G.L., 2006. Microdamage propagation in trabecular bone due to change in loading mode. Journal of Biomechanics 39, 781–790. Zagrai, A., Donskoy, D., Chudnovsky, A., Golovin, E., 2008. Micro-and macroscale damage detection using the nonlinear acoustic vibro-modulation technique. Research in Nondestructive Evaluation 19, 104–128. Zaitsev, V.Y., Gusev, V.E., Zaytsev, Y.V., 2005. Mutually induced variations in dissipation and elasticity for oscillations in hysteretic materials: non-simplex interaction regimes. Ultrasonics 43, 699–709. Zaitsev, V., Nazarov, N., Gusev, V., Castagnede, B., 2006. Novel nonlinearmodulation technique for crack detection. NDT & E International 39, 184–189. Zioupos, P., 2001. Accumulation of in-vivo fatigue microdamage and its relation to biomechanical properties in ageing cortical bone. Journal of Microscopy 201, 270–278.
Contents lists available at ScienceDirect
Journal of Biomechanics journal homepage: www.elsevier.com/locate/jbiomech www.JBiomech.com
Microdamage evaluation in human trabecular bone based on nonlinear ultrasound vibro-modulation (NUVM) K. Zacharias a, E. Balabanidou b, I. Hatzokos b, I.T. Rekanos a, A. Trochidis a, a b
Physics Division, School of Engineering, Aristotle University of Thessaloniki, Thessaloniki 54124, Greece First Orthopaedics Department, School of Medicine, Aristotle University of Thessaloniki, Thessaloniki 54124, Greece
a r t i c l e in fo
abstract
Article history: Accepted 17 December 2008
The primary aim of this work is to investigate the potential of nonlinear ultrasound for microdamage detection in human bone. Microdamage evaluation in human bone is of great importance, because it is considered a significant parameter for characterizing fracture risk. Experiments employing nonlinear acoustic vibro-modulation were carried out in human femoral trabecular specimens removed during surgery. A frequency mixing (inter-modulation) was observed between an ultrasound wave, propagating in the bone, and a low-frequency vibration applied directly to the bone specimens. The appearance of side frequencies, which are related to the vibrational excitation, around the fundamental ultrasound frequency manifests the modulation nonlinear phenomenon. Instead of inducing microdamage by mechanical fatigue loading, specimens with different degree of osteoporosis were used. The experiments demonstrated that osteoporotic bone exhibits stronger nonlinearity compared to healthy bone presenting significant increase of the modulation amplitude with increasing degree of osteoporosis. The obtained results indicate that, in contrast to conventional hysteretic nonlinearity, dissipative acoustic nonlinearity can be of significance in the generation of nonlinear modulation effects. In the proposed technique the size and the shape of samples are not crucial compared to nonlinear resonant ultrasound spectroscopy (NRUS). Furthermore, the method is sensitive to the presence of microdamage, non-invasive, easy to implement and most important, it can be proved valuable tool for in vivo bone damage characterization. & 2009 Elsevier Ltd. All rights reserved.
Keywords: Trabecular bone Bone damage assessment Nonlinear ultrasound vibro-modulation Nonlinear acoustic dissipation
1. Introduction The standard technique for evaluating bone strength is based on dual energy X-ray absorptiometry (DEXA) through the measurement of bone mineral density (BMD). However, measuring BMD alone does not provide prediction for bone strength because a skeleton at risk of fracture cannot be simply determined by the amount of existing bone. Several other properties, characterized in general by the term bone quality, are involved in bone fragility. Bone quality incorporates micro-architecture, tissue material properties, chemical composition of bone matrix and the presence of microdamage (Bouxsein, 2003). Microdamage in bone accumulated by repetitive loading and its effect on bone fragility has received considerable attention in recent years. It appears as micro-fracture of whole trabeculae and micro-cracks within trabeculae. Micro-fracture occurs less frequently than micro-cracking and is considered to be the final result of microdamage (Wang and Niebur, 2006; Turner, 2002).
Corresponding author. Tel.: +30 2310 995927; fax: +30 2310995928.
E-mail address: [email protected] (A. Trochidis). 0021-9290/$ - see front matter & 2009 Elsevier Ltd. All rights reserved. doi:10.1016/j.jbiomech.2008.12.018
Several studies have revealed strong correlation between crack density and mechanical properties, especially toughness (Zioupos, 2001; Burr, 2003). The precise role, however, of microdamage in bone fracture is yet unclear and has to be defined. Therefore, noninvasive techniques to assess bone microdamage quantitatively are important. They could provide insight into the role of microdamage to bone quality. Assessment of microdamage can mainly be made by histological techniques. However, histological estimation of microdamage requires excision biopsy, which is invasive and, therefore, exacerbates fracture risk. Micro-computerized tomography (Parkesh et al., 2006) and positron emission tomography (Li et al., 2005) seem to be new promising noninvasive techniques but are not yet available in everyday clinical practice. Nonlinear acoustic methods applied earlier in material testing proved to have potential in detection of micro-cracks (Korotkov and Sutin, 1994; van den Abeele et al., 2001). The interaction of ultrasound waves with microdamage results in nonlinear wave propagation, which can be evidenced by appropriate signal processing. In that vein, Muller et al. (2006) used nonlinear resonant ultrasound spectroscopy (NRUS) to detect damage in cortical bone. Their results showed that nonlinear ultrasound can be used to assess progressively induced damage.
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K. Zacharias et al. / Journal of Biomechanics 42 (2009) 581–586
Cleveland et al. (2006) carried out simulations for detecting nonlinear properties in both cancellous and cortical bone by employing the Khokhlov–Zabolotskaya–Kuznetsov equation to model bone. They concluded that nonlinear modulation signals might be detectable in cancellous bone but not in cortical bone due to strong attenuation. In a recent publication, Muller et al. (2008) applied NRUS to estimate the nonlinear hysteretic parameter a of bone by measuring the shift of the resonance frequency of bone samples. In their experiments, it was demonstrated that the nonlinear parameter increases with increasing damage induced to bone samples with mechanical cyclic loading and can be used as an indicator of accumulated damage. In vivo studies regarding the measurement of acoustic nonlinearity in the heel bone have been reported (Hoff et al., 2003; Engan et al., 2006). Also, in vivo measurement of acoustic nonlinearity in calcaneus trabecular bone has been based on time-of-flight modulation measurements (Renaud et al., 2008). In this paper, a new method for microdamage detection in human bone is presented. The method is based on the intermodulation between a high-frequency (HF) ultrasound wave and a low-frequency (LF) vibration. A series of experiments were carried out on human femoral trabecular bone specimens with marrow and soft tissues removed. In our experiments, instead of inducing microdamage by fatigue cycling, specimens with different degree of osteoporosis were used. It is shown that the signal amplitude at side frequencies (frequency components generated by modulation) increases with increasing degree of osteoporosis. Furthermore, during the experiments, downward shift, Df0, of resonance frequencies, f0, and decrease of the corresponding quality factor (the ratio of the resonance frequency to the half-power bandwidth), Q, of the tested samples were observed. Thus, the response amplitude at the side frequencies, as well as, the resonance frequency shift and the quality factor reduction can be considered as quantitative parameters characterizing the microdamage present in bone specimens. The proposed method is non-invasive, easy to implement and feasible for in vivo applications.
2. Nonlinear vibro-modulation method Structures with inhomogeneities or defects exhibit strong nonlinear vibrational and acoustical effects. In particular, strong nonlinear effects have been observed in structures with microcracks. These effects include the generation of higher harmonics and the inter-modulation between a high-frequency acoustic wave and a low-frequency vibration (Ostrovsky and Johnson, 2001). These effects provide a basis for developing different techniques for nondestructive testing. The vibro-modulation method is based on the fact that a highfrequency ultrasound wave propagating in a structure is modulated by a low-frequency vibration. The excitation frequencies of the ultrasound and the vibration are fH and fL, respectively, whereas their amplitudes are AH and AL, respectively. The modulation is generated by the nonlinear propagation of waves in the bone and appears in the response spectrum in the form of side frequencies around fH. The amplitude of the low-frequency vibration, AL, must be high enough to activate the inherent nonlinearity of the damage. Furthermore, during the experiments, the maximum amplitude of the stain induced in the bone is approximately 105, hence, it is not considered harmful for bone. The high-frequency wave, which is transmitted through the sample, interacts with the source of nonlinearity, is received and processed. The resulting spectrum contains both the carrier frequency of the ultrasound as well as the frequency components fH7nfL (n is integer number). Modulation effects have been
observed in several applications. Ekimov et al. (1999) employed modulation of high-frequency torsional waves by low-frequency vibration for crack detection in a rod. Zaitsev et al. (2006) presented applications of nonlinear modulation for crack detection in structures and discussed possible sources of nonlinearity in damaged structures. Donskoy and Sutin (1998) used nonlinear ultrasound modulation to investigate the existence of crack, delamination or poor quality bonding. A review of the nonlinear acoustic vibro-modulation techniques is presented in a very recent publication (Zagrai et al., 2008). Despite various practical applications of nonlinear modulation the origin of the nonlinear effects observed seems not to be understood clearly enough. Very similar nonlinear effects may be caused by quite different nonlinear physical mechanisms. Insight into the actual underlying modulation mechanisms is necessary for optimization of practical implementation of the nonlinear effects to quantify damage. When setting up practical diagnostics, one should realize that, even though the nonlinear effects are increased due to the influence of microdamage, the amplitude of the frequency components generated due to the nonlinearity are usually small compared to the excitation amplitude. Therefore, care must be taken to avoid masking of the nonlinear effects related to the propagation mechanisms by the nonlinearities induced by the operation of electric circuits and actuators. Furthermore, one has to consider for investigation the nonlinear effect that is most sensitive with respect to the nonlinear mechanism that is responsible for its generation. Unlike the methods based on higher harmonics measurements, the techniques that employ modulation effects are relatively insensitive to nonlinearities generated by the electric circuits. From that point of view, the nonlinear vibro-modulation technique has a significant advantage.
3. Experimental results For the experiments, samples of human femoral trabecular bone were used. Bone cubes were extracted from fresh femur heads removed during surgery. In particular, cube samples centered at the middle of the femoral head were cut using a diamond circular saw. Heating and consequent damage was avoided by employing low cutting speed and constant irrigation. Information about the study and the related experiments were given to each patient prior to surgery and a written consent statement was obtained. Before using the samples, marrow and soft tissues were removed after appropriate treatment. For defatting, the bone samples were immersed in a dichloromethanol solution for three days and consequently were cleaned using air jet. The experimental set up is shown in Fig. 1. In particular, the bone samples were mounted on a vibrator to provide the LF vibrations. Two ultrasound transducers were used to transmit and receive the HF ultrasonic waves. First, the bone samples were glued on a circular steel plate of diameter 20 mm. The back plate had screw on its bottom so that it could be firmly attached directly on the transducer providing the HF ultrasonic wave. The diameter of the transducer was the same with that of the back plate, i.e. 20 mm. The HF transducer was screwed on the moving part of the vibrator that provided the LF vibration. Thus, half of the face of the cubic bone sample was in contact with both HF and LF source. Hence, the excitation could be considered uniform rather than local. Both the LF and HF excitations were sinusoidal continuous signals. A miniature transducer was glued on the top of the bone sample to monitor the response to the combined HF and LF excitation. The generation and amplification of the LF vibrations and the HF ultrasonic wave were controlled by two independent circuits to avoid mixing of the signals within the
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Fig. 1. Experimental set up.
electric circuits. The measured response was transferred to an acquisition system for further analysis.
Fig. 2. Spectrum of the received signal around fH ¼ 49 kHz for a healthy bone, where the amplitude and the frequency of the vibration signal are AL ¼ 300 mVpp and fL ¼ 270 Hz, respectively.
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First, the response of the ‘‘healthy’’ bone sample was studied under simultaneous excitation of both HF and LF waves. The sample was a cube with size approximately 30 30 30 mm3. The voltage excitation of the vibrator was AL ¼ 300 mV peak to peak and its frequency was fL ¼ 270 Hz, while the magnitude of the vibrational velocity was approximately 104 m/s. The voltage driving the ultrasonic transmitter, AH, was set 40 dB below AL, operating at fH ¼ 49 kHz. The corresponding amplitude AH is kept constant in all experiments that follow. The spectrum of the received ultrasonic signal in the vicinity of fH is shown in Fig. 2. It is clear that the healthy bone exhibits nonlinear behaviour and several side frequencies are present in the response spectrum, generated by vibro-modulation. Actually, the amplitudes of the frequency components at fHfL, fH+fL, fH2fL, and fH+2fL, are approximately 50, 58, 55, and 53 dB, below the amplitude of the ultrasound at fH, respectively, while the noise level was 75 dB. Thus, it is verified that healthy bone itself is a nonlinear material because of its heterogeneous mesoscopic structure. It should be mentioned that the differences of the amplitudes between the frequency components fHfL and fH+fL as well as between fH2fL and fH+2fL, are reasonable. These differences appear due to the generation of standing waves, which result in different amplitudes for different frequencies, at the measurement position. Actually, the asymmetry in the side lobe amplitudes depends on the wave phase velocity and the relation between the different wavelengths and the size of the bone sample. Next, samples with high degree of osteoporosis were examined. A typical result of the spectrum around fH ¼ 49 kHz for a cubic (40 40 40 mm3) osteoporotic bone sample under similar excitation conditions is presented in Fig. 3. It can be seen that osteoporotic bone exhibits stronger nonlinearity, which is attributed to microdamage. The amplitudes at the side frequencies increase substantially. In particular, the amplitudes of the frequency components at fHfL, fH+fL, fH2fL, and fH+2fL, are approximately 31, 32, 45, and 46 dB, below the amplitude of the ultrasound at fH, respectively. This is consistent with the hypothesis that microdamage accumulates easier in humans with low bone density.
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Fig. 3. Spectrum of the received signal around fH ¼ 49 kHz for an osteoporotic bone, where the amplitude and the frequency of the vibration signal are AL ¼ 300 mVpp and fL ¼ 270 Hz, respectively.
In the experiments, the effect of the vibration frequency, fL, on the amplitude level of the side frequency components was investigated. Similar results were obtained for different values of fL, in the range from 80 Hz to 1 kHz. Hence, it appears that the modulating vibration frequency is not a crucial parameter and can be chosen rather arbitrarily. Next, the effect of the vibration amplitude AL on the amplitude level of the side frequency components was systematically investigated, keeping AH constant (as mentioned above). For AL ¼ 100 and 200 mVpp, the spectrums around fH ¼ 49 kHz for the osteoporotic bone sample are shown in Figs. 4 and 5, respectively. For AL ¼ 300 mVpp the corresponding spectrum has already been presented in Fig. 3. It can be seen that the amplitudes at side frequencies increase with increasing amplitude of the vibration signal. This is clearly depicted in Fig. 6, where the relative amplitude in dB of the frequency component at fHfL vs. the vibration amplitude AL, is illustrated.
ARTICLE IN PRESS K. Zacharias et al. / Journal of Biomechanics 42 (2009) 581–586
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Fig. 4. Spectrum of the received signal around fH ¼ 49 kHz for an osteoporotic bone, where the amplitude and the frequency of the vibration signal are AL ¼ 100 mVpp and fL ¼ 270 Hz, respectively.
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Fig. 6. Relative amplitude in dB of the frequency component at fHfL (with respect to the amplitude at fH) vs. the vibration amplitude AL, for an osteoporotic bone.
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Fig. 5. Spectrum of the received signal around fH ¼ 49 kHz for an osteoporotic bone, where the amplitude and the frequency of the vibration signal are AL ¼ 200 mVpp and fL ¼ 270 Hz, respectively.
3.2. Resonance frequency shift and quality factor During the experiments, it was observed that the level of the received ultrasound decreased with increasing damage. In particular, when changing from the healthy to the osteoporotic sample the level of the received ultrasound at the frequency fH slightly decreased (approximately 1 dB). This is attributed to increased losses compared to healthy bone even though the excitation conditions were the same in all cases. This effect was further investigated by measuring the quality factor at resonances for both healthy and osteoporotic bones, using the experimental setup described above. In particular, the amplitude of the vibration AL was kept constant and the resonance curve of the sample was obtained by slowly changing the ultrasound frequency fH around a resonance frequency f0 of the sample. For the measurements, wide-band transducers were used.
Fig. 7. Resonance curves of healthy bone derived for different vibration amplitudes.
For the case of healthy bone, the measured resonance curves for different amplitudes of the vibration (AL ¼ 0, 150, and 300 mVpp) are shown in Fig. 7. It can be seen that for the healthy bone, the resonance frequency shift due to variations of the vibration amplitude is negligible, while the quality factor, Q, remains almost constant. The measured resonance spectrum of the system is complex. Therefore, the system was first investigated to determine the resonances related to the sample rather than to the back plate. For that purpose, instead of bone samples, glass rods were initially used where both the dimensions and the sound velocity can be accurately determined. It was demonstrated that the system behaves like having rigid-free boundary conditions. For the healthy bone case (Fig. 7), the particular resonance frequency at approximately 64 kHz was chosen based on two facts. First, it is indeed a resonance frequency because a peak at the spectrum appears as well as it fulfils the rigid-free boundary condition when compared to adjacent resonance frequencies. Second, we observed that no significant interference with adjacent resonance was present. It should also be mentioned that the characteristic of the transducer in the range from 62 to 67 kHz has a gain lower than 2 dB compared to its flat response.
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Moreover, the measurements are comparative considering different amplitudes of vibration, hence, the relative change of Q are not significantly affected by the gain of the transducer. The same measurements were carried out for the case of osteoporotic bone. In this case, the resonance present at approximately 44.5 kHz was investigated. As shown in Fig. 8, downward shift of the resonance frequency and reduction of the quality factor occurs by increasing the vibration amplitude. For the cases of a healthy and an osteoporotic bone, the relative change of the quality factor and the resonance frequency shift with increasing vibration amplitude are further presented, in Figs. 9 and 10, respectively.
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Fig. 8. Resonance curves of osteoporotic bone derived for different vibration amplitudes.
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Fig. 10. Resonance frequency shift, Df0, vs. vibration amplitude, AL, for the cases of a healthy and an osteoporotic bone.
The nonlinear effects observed during our experiments in human bone samples include nonlinear modulation of HF acoustic waves by LF vibrations, downward shift of the resonance frequencies and decrease of the Q factor of the samples with increasing LF modulating vibration amplitude. The treatment of the bone samples, the experimental arrangement and the measuring procedure were identical for both healthy and osteoporotic samples. The signal-to-noise ratio of the measuring system was 75 dB allowing reliable measurement of the nonlinearity. The main result of the present work is that osteoporotic bone exhibits higher nonlinearity compared to healthy bone. Depending on the amplitude of the LF vibration the measured difference of the nonlinearity, indicated by the level of the inter-modulation frequency components can reach 20 dB. In the absence of LF vibration, hysteretic nonlinearity can explain both the shift of the resonance frequencies and the decrease of Q factor when the excitation amplitude increases. It is well known that acoustic nonlinearity is observed even when only the HF excitation is present. This fact is the base of the NRUS method. Similar experiments were carried out in human bone specimens using only one excitation frequency and the nonlinear hysteretic parameter was estimated using measured resonance frequency shifts (Muller et al., 2008). However, in our experiments, an HF ultrasound wave is used to investigate the nonlinear properties of bone samples under the simultaneous action of an LF vibration. We focus on the effect of the LF vibration keeping the HF unchanged in an effort to highlight the presence of non-classical nonlinearity. The observed decrease of the Q factor for the HF wave depends on the amplitude of the LF vibration. The additional losses, which result in further reduction of Q, could be attributed to viscous-like linear losses. The strong LF vibration alters the magnitude of the thermoelastic losses of the HF leading to decreased Q factor. Thus, in addition to hysteretic nonlinearity, bone specimens seem to exhibit dissipative acoustic nonlinearity. Similar dissipation mechanisms have been observed and described for anomalously strong dissipation in microinhomogeneous rock and sandstone samples (Nazarov et al., 2002). The discrimination, however, of the origins of the observed acoustic nonlinearity is not easy, in the light of these preliminary results (Zaitsev et al., 2005). The observed nonlinear behaviour of bone needs further detailed investigation, which will be the subject of a future publication.
5. Conclusions In this work, the potential of nonlinear ultrasound to detect osteoporosis in human trabecular bone was investigated. The proposed method is based on the nonlinear modulation of a
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high-frequency ultrasound wave by low-frequency vibration. In a series of experiments on human femoral bone samples, it was demonstrated that the amplitude of the nonlinear modulation increases with increasing degree of osteoporosis. Our preliminary results demonstrate that osteoporotic bone exhibits enhanced nonlinear behaviour compared to healthy bone and support existing indications that microdamage accumulates easier in cases of low bone density. To explain the observed experimental results further investigation is required concerning the dissipation mechanisms involved. It seems that, in contrast to conventionally considered hysteretic nonlinearity, nonlinear dissipation may also play a significant role for the observed nonlinear effects. The insight into the underlying physical mechanisms for the modulation effects is necessary for quantitative damage characterization. The proposed modulation method is non-invasive, easy to implement and it could be considered as an alternative approach to nonlinear resonant ultrasound spectroscopy for in vivo applications. Further work for the development of in vivo bone fragility assessment is already under way.
Conflict of interest statement We confirm that there are no conflicts of interest associated with this publication and there has been no financial support for this work that could have influenced its outcome. References Bouxsein, M.L., 2003. Bone quality: where do we go from here? Osteoporosis International 14, S118–S127. Burr, D., 2003. Microdamage and bone strength. Osteoporosis International 14, S67–S72. Cleveland, R.O., Johnson, P.A., Muller, M., Talmant, M., Padilla, F., Laugier, P., 2006. Modelling nonlinear ultrasound propagation in bone. In: Proceedings of the 17th International Symposium on Nonlinear Acoustics including the International Sonic Boom Forum. AIP Conference Proceedings. Donskoy, D.M., Sutin, A.M., 1998. Vibro-acoustic modulation nondestructive evaluation technique. Journal of Material Systems and Structures 9, 765–771.
Ekimov, A.E., Didenkulov, I.N., Kazakov, V.V., 1999. Modulation of torsional waves in a rod with a crack. Journal of the Acoustical Society of America 106, 1289–1292. Engan, H.E., Ingebrigtsen, K.A., Oygarden, K.G., Hagen, E.K., Hoff, L., 2006. Nonlinear ultrasound detection of osteoporosis. In: Proceedings of the 2006 IEEE Ultrasonics Symposium, pp. 2096–2099. Hoff, L., Oygarden, K.G., Hagen, E.K., Falch, J.A., 2003. Diagnosis of osteoporosis using nonlinear ultrasound. In: Proceedings of the 2003 IEEE Ultrasonics Symposium, pp. 1010–1013. Korotkov, A.S., Sutin, A.M., 1994. Modulation of ultrasound by vibrations in metal constructions with cracks. Acoustics Letters 18, 59–62. Li, J., Miller, M.A., Hutchins, G.D., Burr, D.B., 2005. Imaging bone microdamage in vivo with positron emission tomography. Bone 37, 819–824. Muller, M., Tencate, J.A., Darling, T.W., Sutin, A., Guyer, R.A., Talmant, M., Laugier, P., Johnson, P.A., 2006. Bone microdamage assessment using nonlinear resonant ultrasound spectroscopy (NRUS): a feasibility study. Ultrasonics 44, e245–e249. Muller, M., Mitton, D., Talmant, M., Johnson, P., Laugier, P., 2008. Nonlinear ultrasound can detect accumulated damage in human bone. Journal of Biomechanics 41, 1062–1068. Nazarov, V.E., Radostin, A.V., Soustova, I.A., 2002. Effect of an intense sound wave on the acoustic properties of a sandstone bar resonator. Experiment: Acoustical Physics 48, 76–80. Ostrovsky, L., Johnson, P., 2001. Dynamic nonlinear elasticity in geomaterials. Rivista del Nuovo Cimento 24, 1–46. Parkesh, R., Lee, T.C., Gunnlaugsson, T., Gowin, W., 2006. Microdamage in bone: surface analysis radiological detection. Journal of Biomechanics 39, 1552–1556. Renaud, G., Calle´, S., Remenieras, J.-P., Defontaine, M., 2008. Exploration of trabecular bone nonlinear elasticity using time-of-flight modulation. IEEE Transactions on Ultrasonics, Ferroelectrics, and Frequency Control 55, 1497–1507. Turner, C.H., 2002. Biomechanics of bone: determinants of bone skeletal fragility and bone quality. Osteoporosis International 13, 97–104. van den Abeele, K.E.-A., Sutin, A., Carmeliet, J., Johnson, P.A., 2001. Micro-damage diagnostics using nonlinear elastic wave spectroscopy (NEWS). NDT & E International 34, 239–248. Wang, X., Niebur, G.L., 2006. Microdamage propagation in trabecular bone due to change in loading mode. Journal of Biomechanics 39, 781–790. Zagrai, A., Donskoy, D., Chudnovsky, A., Golovin, E., 2008. Micro-and macroscale damage detection using the nonlinear acoustic vibro-modulation technique. Research in Nondestructive Evaluation 19, 104–128. Zaitsev, V.Y., Gusev, V.E., Zaytsev, Y.V., 2005. Mutually induced variations in dissipation and elasticity for oscillations in hysteretic materials: non-simplex interaction regimes. Ultrasonics 43, 699–709. Zaitsev, V., Nazarov, N., Gusev, V., Castagnede, B., 2006. Novel nonlinearmodulation technique for crack detection. NDT & E International 39, 184–189. Zioupos, P., 2001. Accumulation of in-vivo fatigue microdamage and its relation to biomechanical properties in ageing cortical bone. Journal of Microscopy 201, 270–278.