DSpace at VNU: Excitation of ultrasonic Lamb waves using a phased array system with two array probes: Phantom and in vitro bone studies

ULTRAS 4652 No of Pages 7, Model 5G 29 August 2013 Ultrasonics xxx (2013) xxx–xxx Contents lists available at ScienceDirect Ultrasonics journal homepage: www.elsevier.com/locate/ultras Excitation of ultrasonic Lamb waves using a phased array system with two array probes: Phantom and in vitro bone studies Q1 a 10 Department of Radiology and Diagnostic Imaging, University of Alberta, Edmonton, Alberta T6G 2B7, Canada Department of Biomedical Engineering, Ho Chi Minh City University of Technology, Ho Chi Minh City, Viet Nam c Department of Surgery, University of Alberta, Edmonton, Alberta T6G 2B7, Canada b 11 12 a r t i c l e 4 15 16 17 18 19 20 21 22 23 Kim-Cuong T Nguyen a,b, Lawrence H Le a,⇑, Tho N.H.T Tran a, Edmond H.M Lou c i n f o Article history: Available online xxxx Q3 Keywords: Ultrasound Phased array Beam steering Osteoporosis Cortical bone a b s t r a c t Long bones are good waveguides to support the propagation of ultrasonic guided waves The low-order guided waves have been consistently observed in quantitative ultrasound bone studies Selective excitation of these low-order guided modes requires oblique incidence of the ultrasound beam using a transducer-wedge system It is generally assumed that an angle of incidence, hi, generates a specific phase velocity of interest, co, via Snell’s law, hi = sinÀ1(vw/co) where vw is the velocity of the coupling medium In this study, we investigated the excitation of guided waves within a 6.3-mm thick brass plate and a 6.5-mm thick bovine bone plate using an ultrasound phased array system with two 0.75-mm-pitch array probes Arranging five elements as a group, the first group of a 16-element probe was used as a transmitter and a 64-element probe was a receiver array The beam was steered for six angles (0°, 20°, 30°, 40°, 50°, and 60°) with a 1.6 MHz source signal An adjoint Radon transform algorithm mapped the time-offset matrix into the frequency-phase velocity dispersion panels The imaged Lamb plate modes were identified by the theoretical dispersion curves The results show that the 0° excitation generated many modes with no modal discrimination and the oblique beam excited a spectrum of phase velocities spread asymmetrically about co The width of the excitation region decreased as the steering angle increased, rendering modal selectivity at large angles The phenomena were well predicted by the excitation function of the source influence theory The low-order modes were better imaged at steering angle P30° for both plates The study has also demonstrated the feasibility of using the two-probe phased array system for future in vivo study Ó 2013 Elsevier B.V All rights reserved 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 Introduction Osteoporosis is a systemic skeletal disease characterized by gradual loss of bone density, micro-architectural deterioration of bone tissue, and thinning of the cortex, leading to bone fragility and an enhanced risk of fractures Cortical thickness of long bone measurement has been investigated for the incidence of osteoporosis Loss of cortical bone involves an increase of intracortical porosity due to trabecularization of cortical bone [1,2] and cortical thinning due to the expansion of marrow cavity on the endosteal surface [3] The cortical thicknesses at distal radius and tibia in postmenopausal women with osteopenia were found to be thinner than those of normal women in an in vivo study using highresolution peripheral quantitative computed tomography [4] Recently, a high correlation was demonstrated between proximal humeral cortical bone thickness measured from anteroposterior shoulder radiographs and bone mineral density measured by 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 Q2 ⇑ Corresponding author Tel.: +1 (780)4071153; fax: +1 (780)4077280 E-mail address: lawrence.le@ualberta.ca (L.H Le) Dual-energy X-ray absorptiometry in an in vivo study for osteoporosis diagnosis [5] Ultrasound has been exploited to study long bones using the socalled axial transmission technique, where the transmitter and the receiver are deployed as a pitch–catch configuration with the receiver moving away from the transmitter Since the acoustic impedance (density  velocity) of the cortex is much higher than those of the surrounding soft-tissue materials, the cortex is a strong ultrasound waveguide The propagation of ultrasound is guided by the cortical boundaries and its propagation characteristics depend on the geometry (thickness) and material properties (elasticities and density) of the cortex and the surrounding tissues Ultrasonic guided waves (GWs) propagate within long bone in their natural vibrational modes, known as guided modes at different phase velocities, which depend on frequency The GWs travel longer distance and suffer less energy loss than the bulk waves because the boundaries keep most of the GW energies within the waveguide The application of GWs to study long bones is quite recent but the results so far are quite interesting Nicholson et al found the velocity of the fundamental Lamb mode A0 differed by 15% 0041-624X/$ - see front matter Ó 2013 Elsevier B.V All rights reserved http://dx.doi.org/10.1016/j.ultras.2013.08.004 Q1 Please cite this article in press as: K.-C.T Nguyen et al., Excitation of ultrasonic Lamb waves using a phased array system with two array probes: Phantom and in vitro bone studies, Ultrasonics (2013), http://dx.doi.org/10.1016/j.ultras.2013.08.004 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 ULTRAS 4652 No of Pages 7, Model 5G 29 August 2013 Q1 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130 131 132 133 134 135 136 137 138 139 140 141 142 143 144 145 146 147 148 Kim-Cuong T Nguyen et al / Ultrasonics xxx (2013) xxx–xxx between eight healthy and eight osteoporotic subjects (1615 m/s versus 1300 m/s) [6] The same group studied a population of 106 pubertal girls and also found the velocity of a slow-traveling wave (1500–2300 m/s) consistent with that of the fundamental A0 mode [7] Protopappas et al identified four low-order modes, S0, S1, S2, and A1 in an ex vivo study of an intact sheep tibia [8] Lee et al found a strong correlation between the phase velocities of A0 and S0 modes with cortical thicknesses in bovine tibiae [9] Ta et al found that the L(0, 2) mode was quite sensitive to the thickness change in the cortex [10] Basically in most studies, the first few low-order guided modes have been consistently observed and further studied for their potential to characterize long bones Guided modes are dispersive and might come close together, posing a challenge for their identification The ability to isolate the guided modes of interest is the key for a successful analysis of ultrasound data Post-acquisition signal processing techniques such as singular value decomposition [11], s À p transform [12], group velocity filtering [13], dispersion compensation [14], and the joint approximate diagonalization of eigen-matrices algorithm (JADE) [15] are viable methods to separate wavefields Guided modes can also be selectively excited by using angle beam Preferential modal excitation and selectivity using angle beam is widely used in ultrasonic non-destructive testing and material characterization It is generally assumed that given the compressional wave velocity of the angle wedge and an incident angle, only a phase velocity is generated via Snell’s law However in practice, the ultrasound beam has a finite beam size and does not generate just a single phase velocity for a given wedge angle The element size of the transducer and the incident angle influence the excitation of the GWs within the structure, which is generally known as the source influence [16–18] Instead of being excited with a definitive phase velocity (single excitation), GWs with a spectrum of phase velocities are generated at oblique incidence For normal incidence, the phase velocity spectrum is very broad and dispersive, which implies infinite phase velocities to be excited, thus making mode isolation difficult For a fixed size transducer, increasing the beam angle decreases the width of the phase velocity spectrum, thus generating fewer guided modes The use of angle beam to study long bone is very limited Le et al used a 51° angle beam to study bulk waves at receivers deployed downstream from the point of excitation [19] Ta et al used various angle beams to excite low-order longitudinal modes and was the first to mention briefly the concept of phase velocity spectrum in the bone community without much details [10,20] Although a pair of transducers is still the most common means to acquire bone data, ultrasound array system has been used in axial transmission bone study [21] The array system or multi-transmitter–multi-receiver system has many advantages over single-transmitter–single-receiver system The former has better resolution because of the smaller element footprint, fast acquisition speed, accurate coordination of the receivers, and less motion-related problems In case the system is a phased array (PA) system, beam steering is possible The objective of this work is to investigate the use of a PA system to excite guided waves in brass and bone plates The system has two multi-element array probes with one acting as a transmitter and the other as a receiver The acquired data are processed and transformed to the dispersion maps via an adjoint Radon transform The theoretical dispersion curves based on plate models are used for modal identification We attempt to explain the variation of guided-wave excitation with the incident angle using the source influence theory (SIT) The novelties of our work lie in our employment of two phased array probes and the use of Radon transform to estimate dispersion energy To our knowledge, these have never been done in the bone community While the SIT has been studied for a circular disk transducer, we find it interesting to apply the theory to our data acquired by a PA system Materials and methods 149 2.1 Preparation of samples 150 We performed experiments on a brass plate and a bovine bone plate The brass plate was 6.3 mm thick with a 255 mm  115 mm surface dimension We prepared a bone plate from a fresh bovine tibia The skin and soft tissue were removed Using a table bandsaw, both ends of the tibia were cut and then the diaphysis was cut along the axial direction to make a plate Both surfaces of the plate were sanded and smoothed by a disk sander The resultant bone plate had a relatively flat (190 mm  48 mm) surface area with a thickness of approximately 6.5 mm The top face was polished further to prepare the surface ready for the placement of the probes 151 2.2 Ultrasound phased array system 162 We used an Olympus TomoScan FOCUS LTTM Ultrasound PA system (Olympus NDT Inc., Canada) with two array probes as shown in Fig 1a The system has the following specifications: 0.5–20 MHz bandwidth, 20 kHz pulsing rate, 10-bit A/D converter, and up to 100 MHz sampling frequency Real-time data compression and signal averaging are also available The scanner has a high-speed data acquisition rate of MB/s with maximum GB file size and 8192 data point per A-scan (or time series) The unit is connected to a computer via Ethernet port The Windows XP-based computer was loaded with the TomoviewTM software (Version 2.9 R6) to control the data acquisition process and to modify the parameters of the ultrasound beam such as scanning mode, beam angle, focal position, and active aperture The acquired data can be exported to the computer for further post-acquisition analysis The scanner also supports multi-probe operations such as single-transducer-multi-element probe combination or two multi- 163 Fig The ultrasound phased array system: (a) The TomoScan FOCUS LTTM phased array acquisition system (1), the Windows XP-based computer with the TomoViewTM software to control the acquisition process (2), and the probe unit (b) The housing with the 16-element and 64-element probes The P16 was the transmitter array while the P64 was the receiver array Q1 Please cite this article in press as: K.-C.T Nguyen et al., Excitation of ultrasonic Lamb waves using a phased array system with two array probes: Phantom and in vitro bone studies, Ultrasonics (2013), http://dx.doi.org/10.1016/j.ultras.2013.08.004 152 153 154 155 156 157 158 159 160 161 164 165 166 167 168 169 170 171 172 173 174 175 176 177 178 ULTRAS 4652 No of Pages 7, Model 5G 29 August 2013 Q1 179 180 181 182 183 184 185 186 187 188 189 190 191 192 193 194 195 196 197 198 199 200 201 202 203 204 205 206 207 208 209 210 211 212 213 214 215 216 217 218 219 220 221 222 223 224 225 Kim-Cuong T Nguyen et al / Ultrasonics xxx (2013) xxx–xxx element probes up to 128 elements Beam steering and focusing (transmit focus) at oblique angle can be achieved by electronically delaying the firing of the elements without mechanical movement Receive-focusing is also possible The recorded echoes are stored, delayed, and then summed to produce an ultrasound signal The scanner was previously used to study scoliosis [22] The two array probes used are the 16-element (2.25L16) and 64-element (2.25L64) array probes with a central frequency of 2.25 MHz (Fig 1b) Here we denote them as P16 and P64 respectively The two probes sat tightly within a housing, which was designed and built in-house to ensure the probes were stabilized and the relative distance between them were fixed during data acquisition The active areas of the P16 and the P64 probes are respectively 12 mm  12 mm and 48 mm  12 mm Both have the same pitch of 0.75 mm Pitch is defined as the distance between the centers of two adjacent elements 2.3 Data acquisition The data were acquired using an axial transmission configuration The experiment setup is schematically shown in Fig The setup shows the arrangement of two probes (within housing) on ultrasound coupling media, which were in contact with the underlying plate The plate was a brass plate or a bone plate in our case Two pieces of 5-mm thick ultrasound gel pad, acting as coupling medium, were cut from a commercial ultrasound gel pad (Aquaflex, Parker Laboratories, Inc., USA) with surface areas slightly larger so that the probes rested comfortably on the pads The whole set up was held in place by the 3MTM transpose medical tape The ultrasound gel (Aquasonic 100, Parker Laboratories, Inc., USA) was applied to all contact surfaces to ensure good coupling The experiments were performed at room temperature of 22 °C We chose to use five transducer elements as a group due to the compromise between maximum steering angle and frame size (number of acquired A-scan) The first five elements of P16 probe were used as the transmitter For the receivers, five elements worked as a group and each group was spaced by one pitch (0.75 mm) increment, that is, 1-2-3-4-5, 2-3-4-5-6, etc The offset spanned from 22.75 mm to 67 mm with an aperture of 44.25 mm The scanner had an option to select source pulse of different dominant period, thus controlling the central frequency of the incident pulse We chose a pulse with 1.6 MHz central frequency The calculated near field length L, was around 3.7 mm, as given by L = kA2f/4v [23], where the aspect ratio constant k, which is the ratio between the short and long dimensions of the transmitter, is 0.99; the transmitter aperture, A is 3.75 mm for a five-element source; the frequency, f, is 1.6 MHz; v is 1500 m/s, the sound velocity in the ultrasound gel pad The axial resolution of the beam was 0.24 mm based on one-half of the pulse length There were 60 A-scans and each A-scan was 2500-point long with a sampling interval of 0.02 ls The data filled a 60  2500 timeoffset (t À x) matrix of amplitudes In our experiments, we steered both the transmitter and receiver in sync at six angles: 0° (normal incidence), 20°, 30°, 40°, 50°, and 60° The synchronization at the same inclination enhanced the sensitivity of the receivers to record the guided waves traveling at the phase velocity of interest [24] Depending on the steering angle, the calculated lateral resolution ranged from 0.23 mm to 0.78 mm [25] In this paper, beam was steered at an incident angle and thus we use the terms, steering angle and incident angle, interchangeably 226 2.4 Beam steering 237 When an ultrasound beam incidents on the bone surface at an angle, hi, a guided wave traveling with a phase velocity, co, between the transmitter and receiver and along the bone structure (parallel to the interface within the bone structure) will be generated according to Snell’s law (Fig 2): 238 À1  hi ¼ sin vw  ð1Þ co or 227 228 229 230 231 232 233 234 235 236 239 240 241 242 243 245 246 247 ko ¼ kw sin hi ¼ x sin hi vw ð2Þ where vw is the ultrasonic velocity of the coupling medium, kw = x/vw is the incident wavenumber in the coupling medium, ko = x/co is the horizontal wavenumber of the guided wave in the cortex, and x is the radial frequency Based on Eqs (1) or (2), only phases with a single phase velocity or wavenumber are generated, which corresponds to a horizontal excitation line at co for all frequencies in the f À c panel However, we observed more phase velocities in our experimental data and thus Snell’s law was not adequate to explain the phenomenon Based on the SIT [16,17], there exists an excitation zone where guided waves traveling with phase velocities around co are excited The excited phase velocity spectrum is mainly governed by the size of the transducer element and the incident angle and can be approximated by the excitation function F for a piston-type source of width, A [17],   ro jRðhi Þj Aðk À ko Þ Fðf ; cÞ ¼ sin 2ðk À ko Þ cos hi ð3Þ where k = x/c and ro is the uniform pressure on the source surface The factor jR(hi)j accounts for the change in traction at the interface and more detail about this factor is referred to [16,17] In our work, we assume ro and jR(hi)j take the values of unity and A = 3.75 mm for a five-element source For the six steering angles we considered and using 1.6 MHz as the central frequency of the incident pulse, their excitation spectra are shown in Fig We also follow Ditri and Rose [16] to define a À9 dB phase velocity bandwidth, r9dB, for the source array: r9dB cỵ co Dco ÞÀ9dB ¼ o ¼ co co cÀ o Fig A cross-section of the experiment setup The housing hosted two ultrasound probes in place: a 16-element (P16) probe as the transmitter and a 64-element probe as the receiver The probes rested on the ultrasound gel pads, which acted as coupling media The pads then overlaid the plate Only one group (five elements) in P16 was used as source generator and 60 groups in P64 as receivers The receivers were steered at the same inclination as the transmitting beam to enhance the receiving sensitivities to propagating guided waves with phase velocity, co related to the inclination, hi by Snell’s law, sin hi = vw/co where vw is the velocity of the coupling medium 4ị cỵ o 249 250 251 252 253 254 255 256 257 258 259 260 261 262 263 264 265 267 268 269 270 271 272 273 274 275 276 277 279 where and are the phase velocities smaller and larger than co respectively when jFj drops by À9 dB of the maximum 280 2.5 Adjoint radon transform 282 Following [12], we consider a series of ultrasonic time signals d(t, xn) acquired at different offsets, x0, x1, , xNÀ1 where t denotes time and the x-axis is not necessarily evenly sampled We write the time signals as a superposition of Radon signals, m(s, p): 283 Q1 Please cite this article in press as: K.-C.T Nguyen et al., Excitation of ultrasonic Lamb waves using a phased array system with two array probes: Phantom and in vitro bone studies, Ultrasonics (2013), http://dx.doi.org/10.1016/j.ultras.2013.08.004 281 284 285 286 ULTRAS 4652 No of Pages 7, Model 5G 29 August 2013 Q1 Q5 Fig The normalized excitation spectra for six different steering angles The velocity value shown above each figure is the phase velocity determined by Snell’s law (Eq (1) ỵ in the text) The phase velocity determined by Snell’s law is denoted by co; The phase velocities, cÀ o and c o , are defined at the values of jFj equal to À9 dB of the maximum; The À cÀ p1 and c p2 refer to the phase velocities (