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Bone micro-damage assessment using non-linear resonant ultrasound spectroscopy (NRUS) techniques: A feasibility study
Ultrasonics 44 (2006) e245–e249 www.elsevier.com/locate/ultras
Bone micro-damage assessment using non-linear resonant ultrasound spectroscopy (NRUS) techniques: A feasibility study M. Muller a
a,*
, J.A. Tencate b, T.W. Darling b, A. Sutin c, R.A. Guyer d, M. Talmant a, P. Laugier a, P.A. Johnson b
Laboratoire d’Imagerie Parame´trique, CNRS, Universite´ Paris VI, 15 rue de l’e´cole de me´decine, 75006, Paris, France b University of California, Los Alamos National Laboratory, Los Alamos, NM, USA c Stevens Institute of Technology, Hoboken, NJ, USA d Department of Physics, University of Massachussets, Amherst, MA, USA Available online 30 June 2006
Abstract Non-linear resonant ultrasound spectroscopy (NRUS) is a technique exploiting the significant non-linear behavior of damaged materials, related to the presence of damage. This study shows for the first time the feasibility of this technique for damage assessment in bone. Two samples of bovine cortical bone were subjected to a progressive damage experiment. Damage accumulation was progressively induced in the samples by mechanical testing. For independent assessment of damage, X-ray CT imaging was performed at each damage step, but only helped in the detection of the prominent cracks. Synchrotron micro-CT imaging and histology using epifluorescence microscopy were performed in one of the two samples at the last damage step and allowed detection of micro-cracks for this step. As the quantity of damage accumulation increased, NRUS revealed a corresponding increase in the non-linear response. The measured change in non-linear response is much more sensitive than the change in elastic modulus. The results suggest that NRUS could be a potential tool for micro-damage assessment in bone. Further work has to be carried out for a better understanding of the physical nature of damaged bone, and for the ultimate goal of in vivo implementation of the technique where bone access will be a challenging problem. 2006 Elsevier B.V. All rights reserved. Keywords: Bone; Micro-damage; Non-linear resonant ultrasound spectroscopy; Non-destructive evaluation
1. Introduction The diagnosis of bone fragility is currently obtained through the measurement of bone mineral density (BMD) using X-ray densitometric techniques. However, other structural or material bone characteristics such as bone micro-architecture and bone micro-damage have been recognized as independent predictors of bone strength. Several studies have revealed a strong correlation between microdamage and bone fragility [1]. In vivo micro-damage assessment could therefore provide important information regarding skeletal status and fracture risk. However,
*
Corresponding author. Fax: +33 146 335 673. E-mail address: [email protected] (M. Muller).
0041-624X/$ - see front matter 2006 Elsevier B.V. All rights reserved. doi:10.1016/j.ultras.2006.06.043
in vivo micro-damage has remained relatively poorly documented due to the lack of non-invasive techniques for its in vivo assessment. In non-healthy or aged bone, micro-damage accumulates as micro-cracks (with a typical dimension in a range of 5–400 lm). As fatigue damage accumulates in bone, the stress–strain curve exhibits a more and more pronounced bend and an increased hysteresis [2]. In materials in general, micro-cracks are responsible for an enhanced non-linear response, acting as an ensemble of soft inclusions in a rigid matrix and thus giving to the material characteristic non-linear mesoscopic elastic properties [3]. Non-linear resonant ultrasound spectroscopy (NRUS) is a non-linear acoustic technique exploiting these characteristic properties, that has proved to be valuable for damage detection of materials, because of its high sensitivity [4].
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M. Muller et al. / Ultrasonics 44 (2006) e245–e249
The objective of this study was to explore for the first time the potential of NRUS to assess progressively induced bone damage. 2. Non-linear non-classical behavior of damaged bone When materials are subjected to strains above roughly 106, it is currently thought that macro and micro-cracks, as soft mesoscopic structural features in a rigid matrix, are responsible for a characteristic non-linear response related to the presence of strain memory and hysteresis in the stress–strain relation. A phenomenological model [5] has been developed to describe this specific response. In this formalism, the elastic modulus of the material is written as follows K ¼ K 0 ½1 þ be þ de2 a½e; e_
ð1Þ
where K0 is the linear modulus, e the strain and a the hysteretic non-linear parameter depending on the strain derivative due to the hysteresis. The non-linear parameters b and d describe the classical non-linear terms due to standard anharmonicity. The hysteretic non-linear parameter in the model, a, dominates the non-linear behavior at large drive strains. One of the manifestations of this specific behavior is a downward shift of the resonance frequency as the excitation level increases. This phenomenon can be understood as a softening of the material when the excitation level increases, that becomes more pronounced with accumulated damage. It can be shown that the frequency shift Df is directly proportional to a and to the average strain applied to the material over a cycle ( Eq. (2)). Therefore, the parameter a correlates directly to accumulated damage. Df f f0 ¼ aDe f0 f0
ð2Þ
where f is the resonance frequency and f0 is the resonance frequency at the lowest, linear drive level. Using Eq. (2), we can extract a from the frequency shift as a function of strain, as the sample is progressively damaged and becomes more elastically non-linear. 3. Experimental procedure The study was carried out on two bovine femur specimens with marrow and soft tissue removed. The samples were kept hydrated during the whole experiment. The two samples (termed B1 and B2) were progressively damaged in 11 steps (termed steps 0–10, step 0 corresponding to the intact sample) by compressional fatigue cycling in an INSTRON press (INSTRON 5569). At each damage step, NRUS experiments were performed on the samples: each sample was probed using a step-sweep in frequency around one of its eigenmodes and the process was repeated at gradually increasing drive levels. An analytical simulation based on a unidimensional propagation model helped in the selection of an eigenmode
of the bone sample which would be well separated from adjacent modes in order to avoid peak contamination which could impair the measurement of the resonance frequency. Particle velocities related to the radial displacement close to the top of the bone sample were measured using a laser vibrometer (Polytec OFV 3001). For an independent assessment of damage, three-dimensional X-ray computed tomography (CT) was performed on the whole samples at damage steps 0, 1, 2, 3, 4, 5, 6, 7, 9 and 11 (Hytec Inc, Los Alamos, NM, USA). The pixel size of the CT images was 127 lm. The common length of bone microcracks is in a range of 5–500 lm so this resolution only allowed the detection of the larger cracks. Nonetheless, imaging the samples at each step allowed us to control that we were actually inducing macro-damage in the samples. The CT images at different steps were registered using a maximization of the mutual information criterion. Macrodamage accumulation between two damage steps was then detected using mathematical morphology operators. In order to detect micro-damage, micro-CT imaging using Synchrotron radiation (SR-lCT) with a voxel size of 5.3 lm was performed (ESRF, Grenoble, France) on sample B1 at the last damage step. Ten small samples (10 mm · 5 mm · 5 mm) were cut from specimen B1. Micro-cracks were detected by studying the volumetric porosity. Four criterions were used to discriminate microcracks from regular cortical porosity. To be considered as a micro-crack, an object had: (i) to have an irregular structure, (ii) to show an orientation different from the general orientation of the pores, (iii) to have no strong connectivity to the pores network and (iv) to be completely included in the observed volume, in order to make sure that the studied object is not part of a pore. Before the cut, sample B1 had been stained with xylenol orange, a fluorescent chelating agent, capable of selectively labeling bone micro-damage by binding calcium. Microscope observation of xylenol orange fluorescence on the external surfaces of the small samples allowed a histological assessment of micro-damage [6]. 4. Results Fig. 1 shows resonance curves for increasing excitation levels, obtained by measuring the radial velocity close to the top of sample B1 for damage steps #0 and #9, and corresponding damage assessment from CT images. Fig. 1b illustrates the damage accumulated between damage steps #0 and #1 (obtained using mathematical morphology). Fig. 1d illustrates the damage accumulated between damage steps #0 and #7. The pixel size on Fig. 1b and d was 127 lm. These figures show that macro-damage has accumulated in the sample during the experiment but don’t allow micro-damage assessment. The resonant peak shift was more significant in the progressively damaged states (Fig. 1c) than in the undamaged sample (Fig. 1a). The non-linear parameter a was extracted at each damage step according to Eq. (2).
M. Muller et al. / Ultrasonics 44 (2006) e245–e249
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Fig. 3b shows the porosity of the same volume. It is a negative image, obtained from the Synchrotron micro-CT images, in which the observable structures represent pores and cracks. A large crack (300 lm length, 20 lm width) shows through on the upper surface of Fig. 3a (solid line arrow). The extension of this crack through the whole volume can be observed on Fig. 3b (in black), across the pores network. Two other structures look like cracks on Fig. 3a (dashed line arrows) but the 3D porosity image of Fig. 3b demonstrates that they belong to the porous network. In the volume represented in Fig. 3c, the top surface corresponds to an external surface of a small sample. A microscope observation of a region of the same surface is shown on Fig. 3d. The four criterions cited above helped in discriminating three micro-cracks (about 60 lm length, 8 lm width) on Fig. 3b. The one marked with an arrow is very close to the surface and therefore can be observed under epifluorescence microscopy. Fig. 3d shows this micro-crack stained with xylenol orange. The dimensions measured on Fig. 3d (60 lm length, 6 lm width) are comparable to those of the micro-crack observed on the porosity image of Fig. 3c. Fig. 1. Left: example of resonance curves, obtained around the 42 kHz eigenmode of the system for damage steps 0 (top) and 9 (bottom). Right: accumulated damage obtained by mathematical morphology between steps 0 and 1 (top), and 0 and 7 (bottom).
14
Normalized velocity, sample B1 12
Normalized velocity, sample B2
10
Normalized α, sample B1
8
Normalized α, sample B2
6 4 2 0 0
2
4
6
8
10
12
#step Fig. 2. Normalized non-linear parameter a (B1: squares, B2: stars) and normalized velocity (B1: triangles, B2: crosses) as a function of damage step in the two samples.
Fig. 2 shows the behavior of the speed of sound in the sample (derived from the linear resonance frequency f0 at each step) and the non-linear parameter a as a function of damage step for the two samples. As damage accumulates, the speed of sound remains almost constant while a dramatically increases with accumulated damage. The difference between linear and non-linear measurements is remarkable. On Fig. 3 are shown the results from the Synchrotron micro-CT and histological studies. Fig. 3a represents 3D reconstructions of a 500 lm · 1 mm · 500 lm volume.
5. Discussion Fig. 1 shows a resonance frequency shift in both the ‘‘intact’’ and damaged samples. This suggests that even intact bone exhibits a non-linear behavior. This may be due to the fact that healthy bone contains continually-healing micro-cracks. Moreover, intact bone by itself could be classified as a non-linear mesoscopic elastic material, because of its heterogeneous mesoscopic structure. However, an increase of the frequency shift as macro-damage accumulates in the samples is observable. The a parameter (related to the frequency shift) measured in this study increases as micro-damage accumulates, and might prove useful for the quantification of damage. The behavior of a and the speed of sound (SOS) as a function of damage is illustrated in Fig. 2. Clearly, the non-linear parameter a measured by NRUS is much more sensitive to damage than the speed of sound, related to the Young’s modulus of the material, which slightly decreases during the entire progressive damage experiment. The parameter a begins to increase at the first damage step, even though macro-damage is not discernable on the Xray CT images above noise level (Fig. 2b). Indeed, the dark structures observed in Fig. 1b are hardly above the noise level (noise due to image acquisition, reconstruction, registration and processing for damage detection). Micro-cracks lengths in bone are in a range of 5 lm to 400 lm so the resolution of the CT images (the pixel size is 127 lm) doesn’t allow a quantification of micro-damage. Nonetheless, imaging the samples at each step allowed us to control that we were progressively inducing macro-damage in the samples. Indeed, the structures shown in Fig. 1d are well above the noise level and actually reveal the presence of accumulated macro-damage.
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Fig. 3. (a) 3D volume rendering obtained with Synchrotron micro-CT imaging. (b, c): negative images showing the 3D reconstructed porosity network in two different regions of sample B1. A large crack is visible on (b). Three micro-cracks are visible on (c), (d): a micro-crack labelled by xylenol orange observed under epifluorescence microscopy.
Micro-damage can be detected in bone by higher resolution imaging techniques such as Synchrotron micro-CT imaging or histology. But both of them are destructive techniques. Therefore, they could only be performed for the last damage step of the progressive damage experiment, and didn’t allow the progressive evaluation of damage. Moreover, the high resolution provided by both techniques (5.3 lm for Synchrotron micro-CT and 0.2 lm for histology using epifluorescence microscopy) require long data acquisition times and large data management capacities. Therefore, these methods only allow the characterization of small parts of a sample tested by NRUS. On one hand, X-ray CT allowed the assessment of progressively induced macro-damage. On the other hand, Synchrotron micro-CT imaging and histology allowed the assessment of micro-damage for the last damage step. A quantitative evaluation of progressively induced micro-damage would have been useful here to determine a semi-quantitative relation between the measured non-linear parameter a and micro-damage, in order to validate the NRUS method for bone micro-damage evaluation. Another limitation of this study is certainly the small number of data points. In any case, the trend is clearly demonstrated in this work: there is a strong relation between bone microdamage and the non-linear hysteretic parameter a.
age experiment conducted on two samples of bovine bone, in which the NRUS technique provided the means to characterize damage via the non-linear hysteretic parameter a. The increasing amount of damage mechanically induced in the sample lead to an increased shift in the resonance frequency with wave amplitude, indicating a progressively more non-linear behavior of the sample as damage accumulates. In order to validate the use of NRUS to assess bone damage, three imaging modalities were employed. X-ray CT was performed at each step but only helped in the detection of macro-damage. Synchrotron micro-CT and histology allowed the quantification of micro-damage but could only be performed at the last damage step. All techniques showed that micro and macro-damage were actually induced in the samples. The non-linear parameter a has clearly proved to correlate to accumulated microdamage but no quantitative correlation could be determined because no quantitative evaluation of progressively accumulated damage could be achieved. This will be done in further work, using a larger number of samples and data points. Further work will also have to be carried on for the in vivo application of the technique to see if it may be viable as a diagnostic tool for skeletal status assessment. Acknowledgements
6. Conclusions The main purpose of this preliminary study was to demonstrate for the first time the ability of non-linear resonant ultrasound spectroscopy (NRUS) techniques to detect damage in bone. This has been done in a progressive dam-
This work was supported by Institutional Support (LDRD) and by the Institute of Geophysics and Planetary Physics at Los Alamos, and the Centre National pour la Recherche Scientifique (CNRS, France). The authors would like to acknowledge Hytec Incorporated (www.hyte-
M. Muller et al. / Ultrasonics 44 (2006) e245–e249
cinc.com) for the X-ray CT imaging facility, Joanna Hoszowska and the ESRF beamline 05 staff for the Synchrotron Radiation Facility, Philippe Zysset and Franc¸oise Peyrin for helpful discussions and comments, Mathieu Santin for the X-ray CT image processing and Emmanuel Bossy for his large contribution to the Synchrotron micro-CT results. References [1] P. Zioupos, Accumulation of in vivo fatigue microdamage and its relation to biomechanical properties in ageing human cortical bone, J. Microsc. 201 (2001) 270–278.
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[2] D.R. Carter et al., Fatigue behavior of adult cortical bone: the influence of mean strain and strain range, Acta Orthop. Scand. 52 (1981) 481–490. [3] Ostrovsky, Johnson, Dynamic nonlinear elasticity in geomaterials, La Rivista del Nuovo Cimento della` Socita` Italiana de Fisica 24 (2001). [4] K.V.D. Abeele et al., Nonlinear elastic wave spectroscopy (NEWS) techniques to discern material damage, Part II: Single-mode nonlinear resonance acoustic spectroscopy, Res. Non-Destruct. Eval. 12 (2000) 31–42. [5] R.A. Guyer, K.R. McCall, Hysteresis, discrete memory, and nonlinear wave propagation in rock: a new paradigm, Phys. Rev. Lett. 74 (1995) 3491–3494. [6] T.C. Lee et al., Detecting microdamage in bone, J. Anat. 203 (2003) 161–172.
Bone micro-damage assessment using non-linear resonant ultrasound spectroscopy (NRUS) techniques: A feasibility study M. Muller a
a,*
, J.A. Tencate b, T.W. Darling b, A. Sutin c, R.A. Guyer d, M. Talmant a, P. Laugier a, P.A. Johnson b
Laboratoire d’Imagerie Parame´trique, CNRS, Universite´ Paris VI, 15 rue de l’e´cole de me´decine, 75006, Paris, France b University of California, Los Alamos National Laboratory, Los Alamos, NM, USA c Stevens Institute of Technology, Hoboken, NJ, USA d Department of Physics, University of Massachussets, Amherst, MA, USA Available online 30 June 2006
Abstract Non-linear resonant ultrasound spectroscopy (NRUS) is a technique exploiting the significant non-linear behavior of damaged materials, related to the presence of damage. This study shows for the first time the feasibility of this technique for damage assessment in bone. Two samples of bovine cortical bone were subjected to a progressive damage experiment. Damage accumulation was progressively induced in the samples by mechanical testing. For independent assessment of damage, X-ray CT imaging was performed at each damage step, but only helped in the detection of the prominent cracks. Synchrotron micro-CT imaging and histology using epifluorescence microscopy were performed in one of the two samples at the last damage step and allowed detection of micro-cracks for this step. As the quantity of damage accumulation increased, NRUS revealed a corresponding increase in the non-linear response. The measured change in non-linear response is much more sensitive than the change in elastic modulus. The results suggest that NRUS could be a potential tool for micro-damage assessment in bone. Further work has to be carried out for a better understanding of the physical nature of damaged bone, and for the ultimate goal of in vivo implementation of the technique where bone access will be a challenging problem. 2006 Elsevier B.V. All rights reserved. Keywords: Bone; Micro-damage; Non-linear resonant ultrasound spectroscopy; Non-destructive evaluation
1. Introduction The diagnosis of bone fragility is currently obtained through the measurement of bone mineral density (BMD) using X-ray densitometric techniques. However, other structural or material bone characteristics such as bone micro-architecture and bone micro-damage have been recognized as independent predictors of bone strength. Several studies have revealed a strong correlation between microdamage and bone fragility [1]. In vivo micro-damage assessment could therefore provide important information regarding skeletal status and fracture risk. However,
*
Corresponding author. Fax: +33 146 335 673. E-mail address: [email protected] (M. Muller).
0041-624X/$ - see front matter 2006 Elsevier B.V. All rights reserved. doi:10.1016/j.ultras.2006.06.043
in vivo micro-damage has remained relatively poorly documented due to the lack of non-invasive techniques for its in vivo assessment. In non-healthy or aged bone, micro-damage accumulates as micro-cracks (with a typical dimension in a range of 5–400 lm). As fatigue damage accumulates in bone, the stress–strain curve exhibits a more and more pronounced bend and an increased hysteresis [2]. In materials in general, micro-cracks are responsible for an enhanced non-linear response, acting as an ensemble of soft inclusions in a rigid matrix and thus giving to the material characteristic non-linear mesoscopic elastic properties [3]. Non-linear resonant ultrasound spectroscopy (NRUS) is a non-linear acoustic technique exploiting these characteristic properties, that has proved to be valuable for damage detection of materials, because of its high sensitivity [4].
e246
M. Muller et al. / Ultrasonics 44 (2006) e245–e249
The objective of this study was to explore for the first time the potential of NRUS to assess progressively induced bone damage. 2. Non-linear non-classical behavior of damaged bone When materials are subjected to strains above roughly 106, it is currently thought that macro and micro-cracks, as soft mesoscopic structural features in a rigid matrix, are responsible for a characteristic non-linear response related to the presence of strain memory and hysteresis in the stress–strain relation. A phenomenological model [5] has been developed to describe this specific response. In this formalism, the elastic modulus of the material is written as follows K ¼ K 0 ½1 þ be þ de2 a½e; e_
ð1Þ
where K0 is the linear modulus, e the strain and a the hysteretic non-linear parameter depending on the strain derivative due to the hysteresis. The non-linear parameters b and d describe the classical non-linear terms due to standard anharmonicity. The hysteretic non-linear parameter in the model, a, dominates the non-linear behavior at large drive strains. One of the manifestations of this specific behavior is a downward shift of the resonance frequency as the excitation level increases. This phenomenon can be understood as a softening of the material when the excitation level increases, that becomes more pronounced with accumulated damage. It can be shown that the frequency shift Df is directly proportional to a and to the average strain applied to the material over a cycle ( Eq. (2)). Therefore, the parameter a correlates directly to accumulated damage. Df f f0 ¼ aDe f0 f0
ð2Þ
where f is the resonance frequency and f0 is the resonance frequency at the lowest, linear drive level. Using Eq. (2), we can extract a from the frequency shift as a function of strain, as the sample is progressively damaged and becomes more elastically non-linear. 3. Experimental procedure The study was carried out on two bovine femur specimens with marrow and soft tissue removed. The samples were kept hydrated during the whole experiment. The two samples (termed B1 and B2) were progressively damaged in 11 steps (termed steps 0–10, step 0 corresponding to the intact sample) by compressional fatigue cycling in an INSTRON press (INSTRON 5569). At each damage step, NRUS experiments were performed on the samples: each sample was probed using a step-sweep in frequency around one of its eigenmodes and the process was repeated at gradually increasing drive levels. An analytical simulation based on a unidimensional propagation model helped in the selection of an eigenmode
of the bone sample which would be well separated from adjacent modes in order to avoid peak contamination which could impair the measurement of the resonance frequency. Particle velocities related to the radial displacement close to the top of the bone sample were measured using a laser vibrometer (Polytec OFV 3001). For an independent assessment of damage, three-dimensional X-ray computed tomography (CT) was performed on the whole samples at damage steps 0, 1, 2, 3, 4, 5, 6, 7, 9 and 11 (Hytec Inc, Los Alamos, NM, USA). The pixel size of the CT images was 127 lm. The common length of bone microcracks is in a range of 5–500 lm so this resolution only allowed the detection of the larger cracks. Nonetheless, imaging the samples at each step allowed us to control that we were actually inducing macro-damage in the samples. The CT images at different steps were registered using a maximization of the mutual information criterion. Macrodamage accumulation between two damage steps was then detected using mathematical morphology operators. In order to detect micro-damage, micro-CT imaging using Synchrotron radiation (SR-lCT) with a voxel size of 5.3 lm was performed (ESRF, Grenoble, France) on sample B1 at the last damage step. Ten small samples (10 mm · 5 mm · 5 mm) were cut from specimen B1. Micro-cracks were detected by studying the volumetric porosity. Four criterions were used to discriminate microcracks from regular cortical porosity. To be considered as a micro-crack, an object had: (i) to have an irregular structure, (ii) to show an orientation different from the general orientation of the pores, (iii) to have no strong connectivity to the pores network and (iv) to be completely included in the observed volume, in order to make sure that the studied object is not part of a pore. Before the cut, sample B1 had been stained with xylenol orange, a fluorescent chelating agent, capable of selectively labeling bone micro-damage by binding calcium. Microscope observation of xylenol orange fluorescence on the external surfaces of the small samples allowed a histological assessment of micro-damage [6]. 4. Results Fig. 1 shows resonance curves for increasing excitation levels, obtained by measuring the radial velocity close to the top of sample B1 for damage steps #0 and #9, and corresponding damage assessment from CT images. Fig. 1b illustrates the damage accumulated between damage steps #0 and #1 (obtained using mathematical morphology). Fig. 1d illustrates the damage accumulated between damage steps #0 and #7. The pixel size on Fig. 1b and d was 127 lm. These figures show that macro-damage has accumulated in the sample during the experiment but don’t allow micro-damage assessment. The resonant peak shift was more significant in the progressively damaged states (Fig. 1c) than in the undamaged sample (Fig. 1a). The non-linear parameter a was extracted at each damage step according to Eq. (2).
M. Muller et al. / Ultrasonics 44 (2006) e245–e249
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Fig. 3b shows the porosity of the same volume. It is a negative image, obtained from the Synchrotron micro-CT images, in which the observable structures represent pores and cracks. A large crack (300 lm length, 20 lm width) shows through on the upper surface of Fig. 3a (solid line arrow). The extension of this crack through the whole volume can be observed on Fig. 3b (in black), across the pores network. Two other structures look like cracks on Fig. 3a (dashed line arrows) but the 3D porosity image of Fig. 3b demonstrates that they belong to the porous network. In the volume represented in Fig. 3c, the top surface corresponds to an external surface of a small sample. A microscope observation of a region of the same surface is shown on Fig. 3d. The four criterions cited above helped in discriminating three micro-cracks (about 60 lm length, 8 lm width) on Fig. 3b. The one marked with an arrow is very close to the surface and therefore can be observed under epifluorescence microscopy. Fig. 3d shows this micro-crack stained with xylenol orange. The dimensions measured on Fig. 3d (60 lm length, 6 lm width) are comparable to those of the micro-crack observed on the porosity image of Fig. 3c. Fig. 1. Left: example of resonance curves, obtained around the 42 kHz eigenmode of the system for damage steps 0 (top) and 9 (bottom). Right: accumulated damage obtained by mathematical morphology between steps 0 and 1 (top), and 0 and 7 (bottom).
14
Normalized velocity, sample B1 12
Normalized velocity, sample B2
10
Normalized α, sample B1
8
Normalized α, sample B2
6 4 2 0 0
2
4
6
8
10
12
#step Fig. 2. Normalized non-linear parameter a (B1: squares, B2: stars) and normalized velocity (B1: triangles, B2: crosses) as a function of damage step in the two samples.
Fig. 2 shows the behavior of the speed of sound in the sample (derived from the linear resonance frequency f0 at each step) and the non-linear parameter a as a function of damage step for the two samples. As damage accumulates, the speed of sound remains almost constant while a dramatically increases with accumulated damage. The difference between linear and non-linear measurements is remarkable. On Fig. 3 are shown the results from the Synchrotron micro-CT and histological studies. Fig. 3a represents 3D reconstructions of a 500 lm · 1 mm · 500 lm volume.
5. Discussion Fig. 1 shows a resonance frequency shift in both the ‘‘intact’’ and damaged samples. This suggests that even intact bone exhibits a non-linear behavior. This may be due to the fact that healthy bone contains continually-healing micro-cracks. Moreover, intact bone by itself could be classified as a non-linear mesoscopic elastic material, because of its heterogeneous mesoscopic structure. However, an increase of the frequency shift as macro-damage accumulates in the samples is observable. The a parameter (related to the frequency shift) measured in this study increases as micro-damage accumulates, and might prove useful for the quantification of damage. The behavior of a and the speed of sound (SOS) as a function of damage is illustrated in Fig. 2. Clearly, the non-linear parameter a measured by NRUS is much more sensitive to damage than the speed of sound, related to the Young’s modulus of the material, which slightly decreases during the entire progressive damage experiment. The parameter a begins to increase at the first damage step, even though macro-damage is not discernable on the Xray CT images above noise level (Fig. 2b). Indeed, the dark structures observed in Fig. 1b are hardly above the noise level (noise due to image acquisition, reconstruction, registration and processing for damage detection). Micro-cracks lengths in bone are in a range of 5 lm to 400 lm so the resolution of the CT images (the pixel size is 127 lm) doesn’t allow a quantification of micro-damage. Nonetheless, imaging the samples at each step allowed us to control that we were progressively inducing macro-damage in the samples. Indeed, the structures shown in Fig. 1d are well above the noise level and actually reveal the presence of accumulated macro-damage.
e248
M. Muller et al. / Ultrasonics 44 (2006) e245–e249
Fig. 3. (a) 3D volume rendering obtained with Synchrotron micro-CT imaging. (b, c): negative images showing the 3D reconstructed porosity network in two different regions of sample B1. A large crack is visible on (b). Three micro-cracks are visible on (c), (d): a micro-crack labelled by xylenol orange observed under epifluorescence microscopy.
Micro-damage can be detected in bone by higher resolution imaging techniques such as Synchrotron micro-CT imaging or histology. But both of them are destructive techniques. Therefore, they could only be performed for the last damage step of the progressive damage experiment, and didn’t allow the progressive evaluation of damage. Moreover, the high resolution provided by both techniques (5.3 lm for Synchrotron micro-CT and 0.2 lm for histology using epifluorescence microscopy) require long data acquisition times and large data management capacities. Therefore, these methods only allow the characterization of small parts of a sample tested by NRUS. On one hand, X-ray CT allowed the assessment of progressively induced macro-damage. On the other hand, Synchrotron micro-CT imaging and histology allowed the assessment of micro-damage for the last damage step. A quantitative evaluation of progressively induced micro-damage would have been useful here to determine a semi-quantitative relation between the measured non-linear parameter a and micro-damage, in order to validate the NRUS method for bone micro-damage evaluation. Another limitation of this study is certainly the small number of data points. In any case, the trend is clearly demonstrated in this work: there is a strong relation between bone microdamage and the non-linear hysteretic parameter a.
age experiment conducted on two samples of bovine bone, in which the NRUS technique provided the means to characterize damage via the non-linear hysteretic parameter a. The increasing amount of damage mechanically induced in the sample lead to an increased shift in the resonance frequency with wave amplitude, indicating a progressively more non-linear behavior of the sample as damage accumulates. In order to validate the use of NRUS to assess bone damage, three imaging modalities were employed. X-ray CT was performed at each step but only helped in the detection of macro-damage. Synchrotron micro-CT and histology allowed the quantification of micro-damage but could only be performed at the last damage step. All techniques showed that micro and macro-damage were actually induced in the samples. The non-linear parameter a has clearly proved to correlate to accumulated microdamage but no quantitative correlation could be determined because no quantitative evaluation of progressively accumulated damage could be achieved. This will be done in further work, using a larger number of samples and data points. Further work will also have to be carried on for the in vivo application of the technique to see if it may be viable as a diagnostic tool for skeletal status assessment. Acknowledgements
6. Conclusions The main purpose of this preliminary study was to demonstrate for the first time the ability of non-linear resonant ultrasound spectroscopy (NRUS) techniques to detect damage in bone. This has been done in a progressive dam-
This work was supported by Institutional Support (LDRD) and by the Institute of Geophysics and Planetary Physics at Los Alamos, and the Centre National pour la Recherche Scientifique (CNRS, France). The authors would like to acknowledge Hytec Incorporated (www.hyte-
M. Muller et al. / Ultrasonics 44 (2006) e245–e249
cinc.com) for the X-ray CT imaging facility, Joanna Hoszowska and the ESRF beamline 05 staff for the Synchrotron Radiation Facility, Philippe Zysset and Franc¸oise Peyrin for helpful discussions and comments, Mathieu Santin for the X-ray CT image processing and Emmanuel Bossy for his large contribution to the Synchrotron micro-CT results. References [1] P. Zioupos, Accumulation of in vivo fatigue microdamage and its relation to biomechanical properties in ageing human cortical bone, J. Microsc. 201 (2001) 270–278.
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