Evaluation of structural anisotropy in a porous titanium medium mimicking trabecular bone structure using mode-converted ultrasonic scattering

Abstract

The mode-converted (Longitudinal to Transverse, L-T) ultrasonic scattering method was utilized to characterize the structural anisotropy of a phantom mimicking the structural properties of trabecular bone. The sample was fabricated using metal additive manufacturing from high resolution Computed Tomography (CT) images of a sample of trabecular horse bone with strong anisotropy. Two focused transducers were used to perform the L-T ultrasonic measurements. A normal incidence transducer was used to transmit longitudinal ultrasonic waves into the sample, while the scattered transverse signals were received by an oblique incidence transducer. At multiple locations on the sample, four L-T measurements were performed by collecting ultrasonic scattering from four directions. The amplitude of the root mean square (RMS) of the collected ultrasonic scattering signals was calculated for each L-T measurement. The ratios of RMS amplitudes for L-T measurements in different directions was calculated to characterize the anisotropy of sample. The results show that the amplitude of L-T converted scattering is highly dependent on the direction of microstructural anisotropy. A strong anisotropy of the microstructure was observed, which coincides with simulation results previously published on the same structure, as well as with the anisotropy estimated from the CT images. These results suggest the potential of mode-converted ultrasonic scattering methods to assess the anisotropy of materials with porous, complex structures, including trabecular bone.

I. Introduction

Trabecular bone has been evaluated by various quantitative ultrasound methods (QUS) by measuring the speed of sound, the frequency-dependent attenuation (BUA) [1]-[3], and parameters related to the fast and slow longitudinal waves propagating in trabecular bone [4], [5] based on a model developed by Biot [6]. These methods provide measurements related to bone stiffness, porosity, and density [7]-[10]. However, other parameters such as trabecular microarchitecture highly influence bone mechanical properties [8], [9]. These parameters include trabecular thickness, trabecular separation, connectivity and Mean Intercept Length (related to anisotropy).

In general, two structures with same densities and different microarchitectures can have very different mechanical competences. This is also true of bone, where BMD is related to the apparent density or porosity and independent of the microstructure. It is accepted that biomechanical stiffness and strength are affected by bone microstructural changes [11]. The focus has therefore shifted and osteoporosis is now characterized a loss of bone mass and an architectural deterioration of bone tissue, including changes in anisotropy [12]-[15]. A study showed that individuals who suffered hip fracture presented a higher anisotropy in trabecular bone than unfractured individuals after controlling for bone volume [16]. The ultrasonic characterization of anisotropy of a porous structure is the focus of this paper.

Conventional ultrasonic backscatter methods use one single transducer to transmit and receive ultrasonic waves. The backscattered signal is sensitive to the microstructure of the trabeculae. Thus it should be feasible to extract microstructural information on trabecular bone from backscattered signals. Wear and Chaffai et al. have proposed models for the frequency-dependent attenuation and ultrasonic backscatter in trabecular bone [17,18]. Hoffmeister et al. [19,20] and Liu et al. [21] characterized the microstructural anisotropy of bovine cancellous bone from ultrasonic backscatter measured in different directions. Wear et al. [22] showed that regression models combining the BUA, ultrasound velocity, and backscatter coefficient slightly improved the prediction of microstructural parameters. Chaffai et al. [23] showed significant correlations between the ultrasound backscatter coefficient and parameters of the microstructure (r=0.79, p<10⁻⁴, between the backscatter coefficient and trabecular separation). More specifically, multiple groups have studied the influence of anisotropy on ultrasound propagation. Gluer et al showed correlations between anisotropy on one hand, and attenuation and sound velocity on the other hand [24]. Nicholson et al found that correlations between ultrasound parameters and bone density were strongly dependent upon the direction of propagation [25]. Hans et al showed that the speed of sound was dependent upon the direction of propagation [26]. In addition, Wear has used ultrasonic backscatter and shown that it can be related to structural anisotropy [27]. Haïat et al. [28] performed the numerical study to investigate the influence of porosity and structural anisotropy on the properties of the fast and slow waves observed in ultrasound propagation in trabecular bone. Njeh et al. [29] reviewed the propagation of quantitative ultrasound in trabecular bone influenced by structural parameters and density of trabecular bone. Both BUA and speed of sound (SOS) showed significant anisotropy which mirrored mechanical anisotropy in three orthogonal directions in a cube of cancellous bone. Hosokawa and Otani [30] experimentally examined the propagation of both fast and slow waves in bovine cancellous bone in relation to the structural anisotropy. Mizuno et al. [31] investigated the effects of structural anisotropy of cancellous bone on speed of ultrasonic fast waves. Both the ultrasonic and CT results showed that the fast wave speed was significantly dependent on the structural anisotropy, especially on the trabecular orientation and length. Horse bone is particularly interesting because it presents an anisotropy higher than that of human bone. Fujita et al. [32] performed an experimental study on the propagation of the ultrasonic wave in cancellous horse bone and observed the waveform change which was related to the anisotropy. In a numerical study, Du et al. [33] simulated ultrasound diffusion in anisotropic trabecular bone structures obtained from high resolution Computed Tomography (CT) to characterize the anisotropy of trabecular bone.

These ultrasonic measurements were performed either in the pulse-echo configuration or in through transmission, and were collecting the longitudinal-to-longitudinal (L-L) signals. The diffuse scattering field consists in both the L-L signals and the mode-converted, Longitudinal-to-Transverse (L-T), signals. A number of studies suggest that L-T conversion plays a significant role in ultrasound propagation in trabecular bone. Wear et al. [34] have identified and separated three different sources of attenuation in trabecular bone-mimicking phantoms, and demonstrated the contribution of L-T conversion to broadband ultrasound attenuation. Studies by Bossy et al. [35,36] also show the occurrence of L-T scattering, and suggest that L-T scattering dominates L-L scattering at 1 MHz.

Hu et al. [37] developed a time-dependent mode-converted L-T ultrasonic scattering method in a pitch-catch configuration to characterize the grain size in a polycrystalline medium from transverse scattering. Arguelles et al. [38] implemented the L-T ultrasonic scattering method to measure grain elongation in a rolled 7475-T7351 aluminum sample. Recently, Du et al. [39] performed L-T ultrasonic measurements on a railroad wheel sample and characterized the microstructural anisotropy by comparing L-T ultrasonic scattering measured in two perpendicular directions.

There have been few attempts at developing phantoms of trabecular bone, mainly due to the complexity of the task. Langton and Aygün have used stereolithographic methods to fabricate bone replicas [40,41]. We propose here to take advantage of the flexibility of metal additive manufacturing methods, that allow to print arbitrary structures with a very high resolution, in order to showcase the potential of these technique to fabricate bone mimicking phantoms in the future.

With these fabricated samples, we propose to use the mode- converted L-T ultrasonic scattering method to characterize the anisotropy of a trabecular structure 3D printed in titanium. Two focused transducers with a center frequency 5 MHz were deployed. The source (S) was a normal incidence transducer emitting longitudinal waves into the sample. The scattered transverse signals were received by an oblique incidence transducer (R). Four L-T ultrasonic measurements were performed by rotating the source-receiver couple. The root mean squared (RMS) of the received signals was calculated to evaluate the amount of L-T converted scattering for each direction. Ratios of RMS amplitudes were calculated to characterize the anisotropy of sample. We show that the anisotropy calculated by the mode-converted method in different regions of the sample follows the same trend as the true anisotropy estimated from the CT images.

II. MATERIALS AND METHODS

A. 3D-PRINTED SAMPLE

A sample of trabecular horse bone from the femoral epiphysis (18.5 mm *11.2 mm * 3.7 mm) was imaged using propagation phase contrast synchrotron microtomography. The specimen was purchased from a butcher’s shop and the age and gender of the animal were not known. The horse bone specimen was scanned at the ID19 beamline of the European Synchrotron Radiation Facility (Grenoble, France) according to a method described in Meziere et al. [42] with a pixel size of 12.64 μm. The images were reconstructed using algorithms described by Langer et al. [43] and Mirone et al. [44] to keep only the trabecular bone structure. Figure 1a shows a binarized representation of one CT slice of trabecular horse bone sample. The black indicates the background, filled with marrow in bone, while the white indicates the trabecular hone structure.

Fig. 1.

(a) A binarized representation of one CT slice of trabecular horse bone sample. (b) Picture of the surface of the structure 3D printed in Titanium (75 × 45 × 15 mm) using additive manufacturing methods.

Then, the phantom was printed at a scale 4:1 using the following process. The Materialise Mimics software (Materialise, Leuven, Belgium) was used to isolate and reconstruct the three-dimensional geometry of each specimen by thresholding the images below 286 Hounsfield units. These geometries were then exported in standard tessellated format (.stl) with a deviation tolerance of 25μm and exported to an Arcam build assembler software (Arcam, Mölndal, Sweden). The software sliced the 3D STL into two dimensional, 50 μm-thick cross sections that drove the machine control system. An Arcam model A2 Electron Beam Melting System (EBM) was used to fabricate the samples for these experiments. The samples were fabricated from Ti6Al4V ELI gas atomized powder (Arcam) using a DigitalWax printer (DWS Systems, Italy) with a specified size distribution from 45μm-106μm (10^th–90^th volumetric percentiles). Prior to processing the chemical makeup of the powder was measured and confirmed as being within specification (per ASTM F3001–14) using inductively coupled plasma analysis (ICP), Hydrogen and Oxygen content were measured with inert gas fusion (ASTM E1019). The details of the EBM operation and process parameters have been described in detail elsewhere and for this study all processing parameters used are commercially available from Arcam for Ti6Al4V (Arcam Build Control Software V3.2, SP2) [45,46]. However, in brief the EBM process took place under relatively low vacuum conditions. The vacuum chamber maintained an internal pressure of 2 × 10⁻³ mbar, maintained by a controlled vacuum system that introduced small quantities of helium into the chamber. A layer of Ti6Al4V powder was deposited by spreading across a preheated (760°C) build region. Each layer was divided into several separate processing steps which were assigned by the user. The first step was preheating which utilized a defocused electron beam at relatively high current and speed to simulate a near planar heat input and to lightly sinter the powder together. This mechanical bond facilitated the next step, melting. Melting is divided into two sub-steps, contours and hatching. The contours step uses a relatively low current and speed to trace the outline of each layer using a proprietary control step called “multi-beam”. This utilizes the high scan rate capabilities of an e-beam (~180m/s) to jump between multiple locations on the contour approximating multiple beams which are able to simultaneously maintain multiple melt pools (~60). The second component of the melt step is the “hatch”. Here, the beam current and speed were increased and the beam was rostered to melt the area between the contours. It is important to note that the parameters in each step were not held constant throughout the fabrication of a part, but instead varied based on the output of an internal, and proprietary, thermal model designed to maintain a constant surface temperature and a constant melt pool size. A post heating step, similar to the preheating may be utilized to balance the heat equation to satisfy this control. Upon layer completion the build platform was lowered by 50 μm and the process was repeated. The hatch direction was rotated 90° every layer, and the spacing between the hatch lines was offset by 0.05mm each layer. After build completion the build chamber was flooded with helium to accelerate cooling (still below atmospheric pressure). The samples were allowed to cool to room temperature (27°C), as indicated by the thermocouple, before removal from the machine. Upon removal, the samples were encased in lightly sintered titanium powder which was removed using the Arcam Powder Recovery System which resembles an abrasive blasting process, but utilizes the Ti6Al4V powder as a media. The ultrasound properties of melted Titanium powder are similar to those of bulk Titanium (longitudinal wave speed of sound 6100 m/s, shear wave speed of sound 4600 m/s, density 4500 kg/m³). The sample is shown on Figure 1b.

B. MODE-CONVERTED ULTRASONIC SCATTERING

Figure. 2 shows the schematic of a side view of the mode-converted (L-T) configuration. Two identical focused transducers were used (V327 9.53 mm diameter; 2.0 inch focal length in water; central frequency 5 MHz, Olympus NDT, Newton, MA). The normal incidence transducer (S) was used as a source to transmit longitudinal 5 MHz Gaussian pulse waves. The scattered transverse signals converted back to longitudinal waves at the top surface of the sample and were received by the oblique incidence transducer (R). The two transducers were focused at the same location to maximize the amount of scattered energy received. The quantities zf_a and z_α (α = S, R) represent the water and material travel paths for the transmitting and receiving transducers, respectively. Θ is the angle between the normal incidence longitudinal wave unit vector ${\widehat{p}}_0$ and the scattered shear wave unit vector ${\widehat{s}}_0$. This angle was chosen to be 24 degrees, ie greater than the second critical angle (which was 18.8 degrees according to Snell’s law, for Titanium and water). This ensures that converted shear waves will be predominantly collected by the receiver. The unit vector ${\widehat{s}}_{\perp }$ indicates the polarization direction of the scattered shear wave. θ_i and θ_r denote the incident and refraction angles for the receiver, respectively.

Fig. 2.

Side view of the mode-converted ultrasonic scattering setup. To keep the figure easy to read, the longitudinal wave scattering is not illustrated, only the converted shear wave scattering is pictured, although both shear and longitudinal waves propagate in the sample.

The L-T scattering experiments were performed on the 3D-printed structure as shown in Figure 2. Ultrasonic longitudinal pulses, generated by a MicroPulse generator (Peak NDT, Derby UK), were transmitted from the source transducer (S) into the sample. The L-T scattered waves were received by the receiver (R). The focal depth was set at 9.0 mm into the sample. The angle between the two transducers, controlled by a 3D-printed transducer holder, was set to 24 degrees to maximize the collection of L-T scattered energy, as described in [37]. As shown in [37–39], maintaining such an angle between the transmitter and the receiver allows to dominantly collect L-T converted signals. The surface of the sample was scanned with a 5-axis scanning system (Utex Scientific, Ontario), with a step size of 1.0 mm. A 70dB gain was used. To probe the structural anisotropy in the sample, the scattered transverse signals were collected for four directions of the transmitter-receiver axis (Figure 3). First the mode-converted ultrasonic scattering measurement was conducted to collect the scattering in the x axis direction. This measurement was marked as L-T₁ (ψ = 0°) as shown in Figure 3 (a). Then the receiver was rotated counterclockwise 45, 90 and 135 degrees (ψ = 45°, 90°, 135°) around the normal incidence transducer. These three L-T measurements were denoted as L-T₂, L-T₃ and L-T₄ as shown in Figure 3. To evaluate the scattering amplitude, the root mean square (RMS) of the scattered signals collected from multiple transducer positions over a given area was calculated as follows

$$RMS(t)=\sqrt{\frac{1}{M}\sum _{j=1}^M{V}_j^2(t)}.$$ (1)

where V_j (t) denotes the measured scattering voltage at time t for the transducer position j. M represents the number of the transducer positions. To improve the accuracy of determining RMS amplitudes, three time gates of respectively 24.7 μs to 26.3 μs, 25 μs to 26 μs, and 24.8 μs to 26.8 μs around the focal depth were used to fit each RMS curve. The location of the focal spot was estimated to be the time at the maximum value of the fitted RMS curve. Then the ratios of RMS amplitudes for the L-T₁, L-T₂ and L-T₄ measurements to that obtained with the L-T₃ measurement were calculated to characterize the anisotropy of the sample. The average ratio over three time gates and the standard deviation were calculated for each section.

Fig. 3.

(a) The experimental setup for the mode-converted ultrasonic scattering measurement (ψ = 0°), (b) schematics of L-T ultrasonic measurements in four directions

C. MEASURING ANISOTROPY FROM CT IMAGES

The BoneJ freeware (www.bonej.org) was used to measure the Degree of Anisotropy (DA) from the CT-Scan images used to print the sample. The freeware uses the mean intercept length (MIL) algorithm to determine anisotropy. Originating from a random point within the sample, vectors of the same length are drawn through the sample. Whenever a vector hits a boundary between a trabecula and marrow, an intercept is counted for that vector. The mean intercept length is calculated for each vector as the vector length divided by the number of boundary hits, creating a cloud of points. An ellipsoid is then fitted to cloud and a material anisotropy tensor and subsequent eigenvalues are constructed. These eigenvalues correspond to the lengths of the ellipsoid’s axes (as the reciprocal of the semiaxis squared) and eigenvectors associate with the orientation of the axes. DA goes from 0 (isotropic) to 1 (anisotropic). New random points are chosen and sampled by the same vectors. DA is counted until either the coefficient of variation of DA falls below a threshold or the minimum number of sampling points is reached [47,48]. The DA was calculated independently for each section of the sample. The BV/TV of the sample was also calculated using BoneJ and was found to be 18 %.

III. RESULTS

The top image of Figure 4 shows the maximum of the L-T scattering amplitude (the C-scan) for the L-T₁ ultrasonic measurement, obtained by setting a 1.0 us-width time gate from 25 μs to 26 μs as shown at the bottom image of Figure 4. This window was chosen because it covers the focal zone. The bottom image of Figure 4 shows a representative A-scan measured in the sample at the location marked by the solid black line. The saturated signals observed at around 21 μs and 39 μs are reflections from the top and back surfaces, respectively. Between them is the ultrasonic scattering from the structure. To eliminate the scattered signals interfering with the sample’s edges, only the scan area outlined with black boxes shown in Figure 4 was chosen to calculate the RMS of each L-T measurement. The total scan area (for all five boxes) contains about 1000 transducer positions.

Fig. 4.

C-scan image for the mode-converted ultrasonic scattering measurement L-T₁ and a representative A-scan signal. The levels of gray indicates the percentage value of the scattering amplitude (with respect to the reflection on the front surface)as shown in the y-axis of the A-scan signal.

Figure 5 shows four RMS plots as a function of travel time measured for transmitter-receiver axis along four directions. The solid black, dotted, dashed and dot-dashed lines represent the L-T₁, L-T₂, L-T₃ and L-T₄ measurements, respectively. It can be seen that the ultrasonic scattering is strongly dependent on the orientation of the receiver. The RMS of ultrasonic scattering measured in the x axis direction (L-T₁) is highest while the RMS of ultrasonic scattering collected in the y-axis direction (L-T₃) is lowest. The peaks of the RMS plots appear around 25.8 μs, which corresponds to the focal depth in the sample.

Fig. 5.

The RMS curves of ultrasonic scattering measured in four different directions. The solid, dotted, dashed and dot-dashed lines denote the L-T₁, L-T₂, L-T₃ and L-T4 measurement, respectively.

To measure the variations of structural anisotropy along the x axis, the total scan area outlined with black lines in the C-scan image in Figure 4 was divided into five sections. Each section contains about 200 transducers positions, ie 200 scattered signals. The RMS was calculated for each section. Then the RMS amplitude was determined with a Gaussian curve fit. The the ratios of RMS amplitudes, averaged over the three time gates, for the L-T₁, L-T₂ and L-T₄ measurements to that obtained with the L-T₃ measurement (which has the smallest scattering amplitude as shown in Figure 5), were calculated to characterize the anisotropy of the sample. The average ratio over three time gates and the standard deviation were calculated for each section.

Figure 6 shows the average ratios of RMS amplitudes along the x axis. The error bar indicates the standard deviation of ratios obtained with different time gates. The solid line denotes the ratio of RMS amplitudes of L-T₃ to L-T₁. It can be seen that this ratio consistently decreases from section 1 (S₁) to section 5 (S₅) with the value from around 0.67 to around 0.60 along the x axis, indicating an increase of anisotropy along the x axis. The dashed line indicates the ratio of RMS amplitudes for the L-T₃ measurement to that extracted from the L-T2 measurement. The ratio remains constant for regions 1 and 2, then increases from regions 3 to 5. The dash-dotted line represents the ratio of the L-T₃ measurement to the L-T₄ measurement. It can be seen that it decreases slowly from section 1 (S₁) to section 3 (S₃) with the value from 0.87 to 0.74, then the ratio remains nearly consistent at section 4 (S₄) and section 5 (S₅) along the axis with a ratio of roughly 0.75. Figure 7 depicts the Degree of Anisotropy (DA) as measured by the BoneJ freeware from the CT scans images, for the 5 sections shown in figure 5. It can be seen that the DA steadily increases from section 1 to section 5, following the behavior observed for the ratio of L-T₃ to L-T₁ RMS.

Fig. 6.

The ratio of RMS amplitudes along the x axis. The error bar denotes the standard deviation. S_i (i=1~5) indicates the sections shown in the top image of Figure 4.

Fig. 7.

DA versus the ratio of RMS amplitudes (L-T₃/L-T₁)

IV. DISCUSSION

The mode-converted scattering technique allowed to measure a parameter related to the structural anisotropy of a porous medium, consisting of a block of a 3D-printed trabecular structure. In this study, we show that the ratio of mode-converted scattering when the transducers axis is in the x direction (L-T₃), to mode converted scattering when the transducers axis is in the y direction (L-T₁) steadily decreases along the sample (from section 1 to section 5). This indicates that the anisotropy of the structure also increases from section 1 to section 5. These results are consistent with image processing results measuring the degree of anisotropy from the CT scans (Fig. 7). They are also consistent with results previously obtained in a finite difference simulation study, described in [33], where the anisotropy of the same structure was measured using the anisotropy of the Diffusion Constant.

Hu et al. [37] had previously demonstrated that the mode-converted ultrasonic scattering measured in multiple directions are the same in a steel sample with isotropic microstructure. Based on finite difference simulation study of ultrasonic scattering on solid ellipsoidal scatters, it was previously found that ultrasonic scattering is highly dependent on the incident angle with respect to the geometry of scatters [49]. The scattering along the long axis of an ellipsoidal scatterer is much smaller than the scattering measured along the short axis. This suggests that the variation of ultrasonic scattering measured in different directions implies the microstructural anisotropy in the sample.

The critical angle for the receiver was chosen similar to that of [37]. At 5 MHz, we expect the wavelengths in the solid struts to be around 1.2 mm and in water to be around 0.3 mm. These values are of the order of the struts characteristic length. Therefore, the velocity that should be taken into account in the estimation of the critical angle should be the local velocity in the solid, which is similar to the velocity of the solid scatterers in the study by Hu at al. Therefore, the same critical angle was chosen.

There are some limitations to this study. The first set of limitations is related to the printing of the trabecular bone structure. The printed sample had to be scaled 4:1. This is not due to the resolution of the printer, which is high enough to print most trabecular struts, but to the additive manufacturing process. It turned out to be difficult to remove unmelted Titanium powder from the smaller pores, leading to a slightly higher density of the printed sample at a 1:1 scale. This led us to print the sample at a 4:1 scale. Even at a 4:1 scale, the fully enclosed regions of porosity derived from the equine trabecular bone scans rendered complete powder removal impossible However, preliminary tests indicated that high attenuation in the signal associated with the powder cake in these regions could be modeled as empty space. Furthermore, while Ti6Al4V components typically exhibit bulk material properties that are comparable to traditional manufacturing processes, several key differences apply. Internal porosity can result from lack of layer fusion or keyhole type vaporization, or from argon gas present in the powder, as a result of the atomization process, that subsequently become trapped in the rapidly solidifying melt pool. This rapid solidification results in a melt/solidification front that gives rise to epitaxial grain growth the columnar structure with a strong texture component dependent upon build direction [50–53]. Differences in cooling rate can also be associated with microstructural and property variation that result from differences in part geometry orientation and location within the build volume [54–58].

The second set of limitations is related to the implementation of the L-T mode-converted method. First, the four L-T measurements were conducted by rotating the oblique incidence receiver around the normal incidence transducer to receive the mode-converted scattering in four different directions. This resulted in comparing ratios obtained from slightly different regions. Second, since the effective speed of sound couldn’t be measured in the complex microstructure, the actual focal depth could only be approximately evaluated. The chosen time gate around 25 us ~26 us which was used to extract the scattering amplitudes was based on the location of the RMS peaks as shown in Figure 5. To calculate a RMS of ultrasonic scattering, an area has to be scanned to collect measurements from different locations, which results in a lower spatial resolution of the method. Due to the distance between the source and the receiver as well as the dimensions of transducers, the smallest size of the sample has to be greater than 10 mm to ensure eliminating the edge effects.

Finally, the sample used in this paper was fabricated with titanium powder using an additive manufacturing method, from CT images of a horse bone sample. The intrinsic mechanical properties of Titanium are not the same as those of bone (melted titanium has the same modulus and density as bulk Ti64). The speed of sound in Titanium is greater than the speed of sound in bone. The wavelength will therefore be greater as well. However, because the sample was printed at a 4:1 scale, the ratio between the wavelength and trabeculae should actually be smaller in the printed sample than it would be in trabecular bone, at the same frequency. In addition, although shear wave attenuation was not a concern in the present study, in the Titanium printed sample (Fig. 4), it could be a limitation of this technique for application in real trabecular bone. Shear wave attenuation in bone trabeculae was estimated to be high (2 Np/mm at 1 MHz, [59]). Similarly, shear wave attenuation in bone marrow could be an obstacle to the application of this technique in real trabecular bone. The objective of this study was not to reproduce the exact mechanical properties of human bone, but to mimic an anisotropic bone microstructure in order that to investigate the potential of the L-T conversion method for the assessment of trabecular anisotropy, as well as to demonstrate the feasibility of printing such a complex bone resembling medium mimicking the architecture of trabecular bone. The results presented here are a proof of concept showing that the proposed technique could potentially be used for the assessment of anisotropy. However, the applicability of the LT conversion method for the assessment of anisotropy in trabecular bone remains to be determined. The frequency that would be effectively used in bone remains to be determined, and could be adjusted. In fact, multiple frequencies could be used in the future to investigate the frequency dependence of L-T scattering as a function of anisotropy. We therefore put forward that the difference in wavelength to trabeculae ratio is not the major limitation of this study. On this subject, a more serious limitation of our study could be the fact that the impedance difference between titanium and water is larger than between bone and marrow, which could impact scattering L-T conversion. To address this, future work will include measurements on a sample of trabecular bone. The present approach is likely to provide a nondestructive evaluation method to characterize the anisotropy of materials with porous structures in general, and potentially trabecular bone in particular.

In the context of potential clinical applications in-vivo, the presence of cortical bone and soft tissue layers between the transducer and trabecular bone would have to be taken into account. Although LT conversion will likely occur at the interface between soft tissue and cortical bone, we don’t expect the LT scattering to be significant in the thin layer of cortical bone. However, this will need to be explored in future studies.

V. CONCLUSION

Ultrasonic L-T measurements were performed using two focused transducers to characterize the microstructural anisotropy of a trabecular structure 3D printed using additive metal manufacturing. The measurements consisted in collecting L-T converted ultrasonic scattering in four directions in the sample. The RMS of ultrasonic scattering was calculated over the scan area for each L-T measurement and a Gaussian function was fitted to the RMS in the focal region to determine the amplitudes. The ratios of RMS amplitudes for L-T measurements in different directions were calculated to characterize the anisotropy of sample. The results show that mode-converted ultrasonic scattering is strongly dependent on the direction of microstructural anisotropy. This is validated by independent measurements of the degree of structural anisotropy using image processing techniques. This is also consistent with previous results obtained in a simulation study on the same structure and presented in [39]. These results suggest the potential of the mode-converted ultrasonic scattering method for assessing the anisotropy of materials with porous, complex microstructures, including trabecular bone. However, the feasibility of this technique in trabecular bone remains to be demonstrated, as shear attenuation could affect LT scattering. Future studies will include the measurement of L-T scattering in real trabecular bone, as well as the investigation of anisotropy in three orthogonal planes rather than one.

Biography

HUALONG DU received the B.S. and M.S. degree in Mechanical engineering from University of Electronic Science and Technology of China, in 2006 and 2009, respectively, and the Ph.D. degree in Mechanical Engineering and Applied Mechanics from University of Nebraska-Lincoln, NE, USA in 2013. He served as an ultrasonic nondestructive consultant at Applied Research Associates, Inc. from May. 2014 to Oct. 2014. He worked as a postdoctoral researcher with the Department of Mechanical and Aerospace engineering, North Carolina State University from Dec. 2014 to Oct. 2015 and served as a research engineer with the Phased Array Company from Nov. 2015 to Mar. 2016. He has been working as a staff scientist at Applied Research Associates, Inc. since Apr. 2016. His research interests include ultrasonic scattering, material characterization, nondestructive evaluation.

OMID YOUSEFIAN Omid Yousefian received the B.S. degree in mechanical engineering from Isfahan University of Technology, Isfahan, Iran, in 2013 and the M.S. degree in mechanical engineering from University of South Carolina, Columbia, SC, USA in 2015. He is currently pursuing the Ph.D. degree in mechanical engineering at NC State University, Raleigh, NC, USA.Since 2016, he is a Research Assistant in Ultrasound Material Characterization Lab, at Mechanical and Aerospace Department of NCSU. His research interest includes the cortical 3one characterization using quantitative ultrasound.

Dr. TIMOTHY J. HORN is a Research Assistant Professor in the Fitts Department of Industrial and Systems Engineering at NCSU. He is also the Director of Research for the Center for Additive Manufacturing and Logistics. CAMAL is one of the leading international centers for metal and alloy additive manufacturing (AM) and under Dr. Horn has developed new AM systems and applications pertaining to powder-bed fusion processes. Dr. Horn holds a Ph.D. in Industrial Engineering, his research has focused on developing new alloys and parameters for AM technologies, process monitoring and in-situ control. He is recognized as a leading expert in designing operating parameters, machines and materials for powder-bed electron beam and laser melting AM processes. Dr. Horn’s research focuses on developing new metal materials for additive manufacturing technologies; leveraging the unique structure-property relationships feasible with this new manufacturing approach, he has led multiple new material development efforts on behalf of a number of consortia, companies and government agencies. He has overseen the development of process parameters for the additive manufacturing of a variety of materials and alloy systems including, but not limited to: Titanium Alloys, Aluminum Alloys, OFHC Cu, GrCOP-84, Titanium Aluminide, Nickel Superalloys, RRR Niobium and Niobium alloys, several novel bulk metallic glasses (Fe and Zr based), and rare earth magnetic materials such as FeNdB

Dr. MARIE MULLER received her BS in Physics from the Pierre et Marie Curie University in Paris, France in 2002, and her Ph.D in Physical Acoustics from the Paris Diderot University in Paris, France in 2006. After a postdoctorate at the Erasmus Medical Center in Rotterdam, the Netherlands, she returned to Paris, as an Assistant Professor with the Institut Langevin. In 2014, she moved to North Carolina and joined the Mechanical and Aerospace Engineering department at NCSU. She is also an associate Faculty with the Joint Department of Biomedical Engineering at UNC and NCSU. Dr. Muller’s research focuses on ultrasound propagation in highly complex media such as bone, vessel networks or the lung. She leverages the complexity of propagation in such media to extract micro-architectural properties using ultrasound.