In this paper, ultrasound measurements of 1:1 scale three-dimensional (3D) printed trabecular bone phantoms are reported. The micro-structure of a trabecular horse bone sample was obtained via synchrotron x-ray microtomography, converted to a 3D binary data set, and successfully 3D-printed at scale 1:1. Ultrasound through-transmission experiments were also performed through a highly anisotropic version of this structure, obtained by elongating the digitized structure prior to 3D printing. As in real anisotropic trabecular bone, both the fast and slow waves were observed. This illustrates the potential of stereolithography and the relevance of such bone phantoms for the study of ultrasound propagation in bone.

Quantitative Ultrasound (QUS) could be a powerful tool for the diagnosis of osteoporosis.1 Various QUS methods have been established and the parameters they measure (mostly related to ultrasound velocity or attenuation) are correlated to bone status. However, some aspects of the propagation of ultrasound through trabecular bone remains poorly understood from a theoretical point of view, such as the possible occurrence of two compressional waves (the so-called fast and slow waves), when ultrasound propagates along the main direction of anisotropy.2,3 Progress toward a better understanding of the fundamental aspects of ultrasound propagation in cancellous bone requires working with reproducible samples with control over the micro-architecture and the mechanical properties. These conditions are hardly met with real bone samples because of the inherent heterogeneity and variability between biological samples. In addition, the development of biomedical devices requires well-calibrated samples (commonly referred to as phantoms) that mimic the relevant properties of tissue. Several approaches have been investigated to design phantoms of trabecular bone, including biphasic materials made of resin and gelatine,4 arrangements of nylon wires,5–7 and a commercial urethane-based homogeneous material (model 063, CIRS, Inc., Norfolk, VA). Although these phantoms reproduce some of the features (velocity, attenuation) observed in real bone, none of them capture the structural complexity of real trabecular bone, due to a distribution of trabecular orientations, separation, and thicknesses. This is, however, precisely what is believed to be responsible for the peculiar characteristics of ultrasound propagation in bone. Indeed, trabecular bone is a complex, porous, and heterogeneous structure, which exhibits a structural anisotropy due to a preferential orientation of the trabeculae. Changes in bone micro-architecture are associated with pathologies such as osteoporosis.

To manufacture trabecular bone phantoms, the idea of using stereolithography has been introduced as early as 1996.8,9 Stereolithography is a three-dimensional (3D) printing technology used to produce 3D objects based on a layer by layer fabrication of structures defined by a numerical data set. In their pioneer paper,10 Langton et al. were limited to printing a 3D bone-like structure obtained from extruding a single two-dimensional (2D) slice of trabecular structure digitized from a photograph. The limitation came in part from computational memory issues, as was discussed in Sisias et al.,10 and also from the limited resolution (around 300 μm) that required pre-processing of the initial structure to a significantly modified structure with constant trabecular thickness. More recent works reported 3D printing of trabecular bone structure based on a 3D data set obtained from x ray computerized microtomography (μ-CT), but to our knowledge, none of them could manufacture 1:1 replicas of trabecular structures.11,12

As a consequence, there are currently no ultrasonic phantoms that mimic in a realistic fashion the structure of trabecular bone. In particular, the occurrence of two compressional waves has not been observed in bone-mimicking material. There is, however, a need to design realistic phantoms with controllable trabecular separation, thickness, and connectivity, for a better understanding of the physical mechanisms involved in the two-wave propagation. Such phantoms would also allow to test the algorithms developed to analyze and separate the two waves for characterization purposes. For instance, Wear has developed algorithms based on curve fitting and the modified least squares Prony's method to assess the velocities and attenuations of the fast and slow waves separately13 and Miller and his group have developed techniques based on the Bayesian probability theory.14 In order to test their algorithms, Wear15 had to artificially mix two waves resulting from through-propagation experiments through low density polyethylene (fast) and Zerdine® (slow) blocks.

The objective of this study is to demonstrate the feasibility of using stereolithography to replicate trabecular structures with fine control over the micro-architecture. We make use of a modified commercially available 3D printer to print a 1:1 replica of a trabecular bone sample. We illustrate the possibility of manipulating 3D data sets prior to printing in order to produce bone-like samples with modified properties such as an enhanced structural anisotropy or exhibiting fast and slow ultrasonic waves, as was reported in real bone samples.

The sample of trabecular bone used in this study was taken from a horse femoral epiphysis. The structure of the sample was obtained by propagation phase contrast synchrotron microtomography (PPC-SR-μ-CT). The horse bone specimen was scanned at the ID19 beamline of the European Synchrotron Radiation Facility (ESRF, Grenoble, France) using a filtered-pink beam with a total integrated energy of 110 keV. We performed PPC-SR-μ-CT with a sample-detector distance of 14 m, acquiring 1200 radiographs of 0.15 s each, over 360°. Radiographs were recorded with a 1× optic setup and a FReLoN 2K camera (ESRF, Grenoble, France), resulting in images with an isotropic pixel size of 12.64 μm. For the tomographic reconstruction, we used the modified version of the Paganin algorithm16 from the software PyHST2.17 This allowed an accurate discretization of the cancellous bone structure and of individual trabeculae. The volume of the measured sample was 34 × 11 × 18 mm3. The numerical structure was binarized to keep only the bone structure while removing contribution from interstitial space filled with air or marrow. The binarized 3D data set was converted into a STL file (standard format for stereolithography).

The 3D printer used for this work is the DigitalWax 028 J Plus, commercialized by DWS Systems (Italy).18 A photo-reactive resin is solidified point by point by a focused laser beam, and the desired 3D structure is built up layer by layer. The lateral resolution is determined by the width of the laser spot (25 μm). The vertical resolution is mechanically defined and set to 50 μm. The printing process lasted 1.75 h. It was performed according to exposure parameters provided by material manufacturer. In particular, the laser speed was set to 1500 mm/s. Pure isopropanol was sprayed on the printed structure for 5 min. This cleaning step, which must be nondestructive, is critical when printing such a complex and porous structure; indeed the liquid resin remaining in the pores must be removed to provide a reliable replica of the original porous sample. Finally, the sample was placed for 30 min in an ultraviolet oven to harden its structure.

The surfaces of both the original sample and the 3D printed phantom show visually similar trabecular structures, as can be seen in Fig. 1. The surfaces were evaluated using a profilometer (Keyence VHX 700), used in 2D mode. The difference between the two surface profiles was estimated smaller than 15%. Both samples were weighed, and based on the mass densities of DL-260 and bulk equine bone,20 their respective solid fractions were found to be 29.4 ± 0.4% and 31.4 ± 1%. In order to optimize the mechanical properties of the fabricated phantoms, the material properties (mass density, compressional and shear speed of sound) of the bulk materials used for printing were tested. Various materials were available for use with the printer, but from a mechanical standpoint few were comparable to bone. To evaluate their properties, ultrasound transmission experiments were achieved through 3D printed homogeneous blocks of 20 × 25 × 30 mm3. Time-of-flight measurements were carried out at 1 MHz, with pairs of identical longitudinal and transverse ultrasonic transducers. The material that was finally chosen will be referred to as DL-260. Table 1 reports its properties, compared to those of bone.

Fig. 1.

(Color online) Comparison between the real horse bone (left) and the printed one (right).

Fig. 1.

(Color online) Comparison between the real horse bone (left) and the printed one (right).

Close modal
Table 1.

Density ρ, longitudinal (cL), and transverse (cT) speeds of sound (values from Ref. 20).

Materialρ (g cm−3)cL (mm μs−1)cT (mm μs−1)
DL-260 1.338 ± 0.004 2.49 ± 0.05 1.21 ± 0.02 
Bulk bone 2.05 1.8 
Materialρ (g cm−3)cL (mm μs−1)cT (mm μs−1)
DL-260 1.338 ± 0.004 2.49 ± 0.05 1.21 ± 0.02 
Bulk bone 2.05 1.8 

A significant difference, of about 30%, could be observed between the mechanical properties of bone reported in the literature20 and those of DL-260. The aim in this study was not to reproduce a sample with the exact ultrasonic properties of bone; the focus was rather on the qualitative aspects of ultrasound propagation in the 3D printed phantoms. With that in mind, the goal of this preliminary study was first, to demonstrate to the possibility of using 3D printing to obtain a 1:1 scale reproduction describing the microstructure of a sample of cancellous bone, and second, to alter it in order to observe two wave-propagation in the 3D printed samples.

Ultrasound measurements were performed in the real bone sample and its replica, using the same experimental setup. Two 1 MHz circular transducers [Panametrics-NDT Olympus V303-SU, 0.5 in. (127 mm) diameter] were immersed in water, 80 mm apart. The sample was equidistantly positioned between the two transducers. The transmitter was connected to a function generator (Tektronix AFG 3101). The transmitted signal was a one-cycle sine wave at 1 MHz. The received signals were amplified and digitized using an oscilloscope (Tektronix TDS 3054B) connected to a computer.

The transmitted waveforms through the real and 3D printed samples are plotted in Fig. 2. The bone sample shows a unique arrival, at a velocity close to that of ultrasound in water. Interestingly, the 3D-printed sample exhibits what could be a fast wave, followed by a slow wave whose amplitude and travel time match those of the actual bone sample. Here, the main difference between the two samples is the lower bulk velocities (both longitudinal and shear) of the 3D-printed, whose acoustic impedance is roughly twice smaller. Therefore, the comparison between the transmitted waveforms seems to indicate that the slow wave properties are mostly dominated by the micro-architecture and the surrounding fluid, whereas the fast wave is more strongly influenced by the mechanical properties of the solid skeleton.

Fig. 2.

(Color online) Transmitted signals resulting from the propagation of a 1 MHz pulse in water, through the bone sample and its 3D-printed replica along the thickest dimension (38 mm). Each signal is normalized by its maximum.

Fig. 2.

(Color online) Transmitted signals resulting from the propagation of a 1 MHz pulse in water, through the bone sample and its 3D-printed replica along the thickest dimension (38 mm). Each signal is normalized by its maximum.

Close modal

Although the original bone samples and its 3D printed version were visually very similar, their response to the propagation of ultrasound pulses were different. Indeed, the 3D printed sample likely exhibits two longitudinal waves, and the real bone sample does not. This could be attributed to a difference in the material properties of the solid phase that differ by 30%. It could also be attributed to an imperfect reproduction of the microstructure due to the resolution of the 3D printing system or to flaws in the cleaning process, leading to a slightly higher connectivity of the solid phase in the 3D printed sample. Previous results have shown that the fast wave propagates preferentially in the solid phase and that its occurrence can be influenced by the connectivity of the structure.19,23 At this stage, we have taken advantage of the numerical flexibility of the CT scans and modified the structure before printing another phantom: a subvolume of the numerical structure was extracted and stretched four-fold along one dimension. We therefore created a new structure with both an enhanced structural anisotropy and a larger thickness along the stretched dimension. Both these features increase the likelihood of observing two distinct longitudinal waves.

A picture of the new printed structure is shown in Fig. 3; its actual dimensions are 38.0 × 33.3 × 13.9 mm3. The same ultrasonic transmission experiment was performed in two directions: along (horizontal arrow) and across (vertical arrow) the direction of elongation. The corresponding transmitted signals are shown in Fig. 3.

Fig. 3.

(Color online) Printed elongated structure (left) and transmitted signals resulting from the propagation of a 1 MHz pulse along (middle) and across (right) the direction of anisotropy.

Fig. 3.

(Color online) Printed elongated structure (left) and transmitted signals resulting from the propagation of a 1 MHz pulse along (middle) and across (right) the direction of anisotropy.

Close modal

Two distinct arrivals were well resolved in time when ultrasonic waves were propagating along the direction of anisotropy. This is in agreement with observations in real cancellous bone in vivo.2,3 From the group delay of each arrival, we infer the group speeds 1.82 and 1.5 mm/μs for the fast and slow wave, respectively. The central frequencies of the fast and slow waves are estimated around 0.4 and 0.85 MHz, respectively.

For a propagation across the direction of anisotropy, it could be hypothesized that the apparent single wave might result from two overlapping fast and slow waves; the first arrival seems to have a lower frequency content (around 0.42 MHz) than the latter one (around 0.95 MHz), similar to that of the fast wave when two waves are clearly distinguished. The phenomenon resulting from the overlap of the fast and slow waves has been studied in real bone samples21 and algorithms have been developed13,14,22 to separate and analyze the two waves. 3D printed phantoms of the trabecular micro-structure such as the ones presented here could be useful in particular to test these algorithms on controlled structures.

As was recently shown by our group,19,23 artificial numerical samples may be generated with controlled statistical properties (such as porosity, anisotropy, etc.), to bring further insight on the propagation of ultrasound in bone-like complex structures.

We have found in particular that only one wave propagates perpendicularly to the direction of anisotropy. This result was reinforced by the quantitative matching of both the velocity and attenuation of ultrasonic waves in bone-like anisotropic structures, to a multiple scattering theory intrinsically predicting only one wave.23 

This seems to be in contradiction with experimental results presented here, where two waves always seem to be observed in the phantom, although they cannot be separated in the case of a propagation across the direction of anisotropy. It might be due to the fact that the numerical samples presented in Refs. 19 and 23 were designed to be transversely isotropic (orthotropic).

In the case of the present paper, stretching the structure has created a clear direction of anisotropy, but probably not strong enough to make the medium transversely isotropic.

More generally it questions the limit of considering cancellous bone as transversely isotropic, a common assumption for trabecular bone.1 

We have shown here that 3D printing is now a sufficiently mature technique to print 1:1 scale phantoms of cancellous bone with an accurate micro-architecture. Moreover, by modifying the 3D data set prior to printing, we were able to stretch the structure to print a sample with an enhanced anisotropy. We have observed, for the first time in a synthetic bone-like structure, the propagation of the fast and slow longitudinal waves. This opens up the possibilities of manufacturing a large range of realistic bone-like structures. 3D printing could be a great asset for the future manufacturing of controlled phantoms of cancellous bone that could help to understand and model the propagation of ultrasound through trabecular bone, as well as the development of devices for the diagnosis of osteoporosis. At the moment, only the trabecular microstructural properties have been replicated accurately, and the mechanical properties of the phantoms fabricated in this study are still different from those of real bone. Future works must focus on the development of a more realistic material, with mechanical properties closer to those of bone. This will be a necessary evolution toward quantitative phantoms.

F.M. is the recipient of a doctoral grant from the AXA Research Fund. P.J. benefited from a Marie Skłodowska-Curie individual fellowship, referenced 629277-FP7-PEOPLE-2013-IEF. This work was also supported by LABEX WIFI (Laboratory of Excellence ANR-10-LABX-24) within the French Program “Investments for the Future” under reference ANR-10-IDEX-0001-02 PSL*. The synchrotron microtomography experiments were performed on the ID19 beamline at the ESRF, Grenoble, France, proposal MD727. We thank Paul Tafforeau, Nicolas Pollet, and Anthony Herrel for their help during the experiment at ESRF.

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