Manufacturing and Characterization of Hybrid Bulk Voxelated Biomaterials Printed by Digital Anatomy 3D Printing

The advent of 3D digital printers has led to the evolution of realistic anatomical organ shaped structures that are being currently used as experimental models for rehearsing and preparing complex surgical procedures by clinicians. However, the actual material properties are still far from being ideal, which necessitates the need to develop new materials and processing techniques for the next generation of 3D printers optimized for clinical applications. Recently, the voxelated soft matter technique has been introduced to provide a much broader range of materials and a profile much more like the actual organ that can be designed and fabricated voxel by voxel with high precision. For the practical applications of 3D voxelated materials, it is crucial to develop the novel high precision material manufacturing and characterization technique to control the mechanical properties that can be difficult using the conventional methods due to the complexity and the size of the combination of materials. Here we propose the non-destructive ultrasound effective density and bulk modulus imaging to evaluate 3D voxelated materials printed by J750 Digital Anatomy 3D Printer of Stratasys. Our method provides the design map of voxelated materials and substantially broadens the applications of 3D digital printing in the clinical research area.


EBME Theory 1
In fluid medium, the velocity is the potential field as ⃗ = ∇ described. When the fluid is homogeneous, the potential is the factor of standard wave equation, + ∇ = 0, with sound velocity . The oscillation of the pressure wave can also represent by the potential as = − , where is the density of fluid medium. Since the operation of effective dynamic density and bulk modulus elastography (EBME) using the short pulse envelope instead of continuous wave, the reflection of the pulse is different from the CW such as a sine wave.
A short pulse ( ) is emitted by a transducer from a flat object, where T is the time factor. The entire package of energy separates into two parts. The first part is the reflected echo from the closer boundary of the sample named as ( ). The second one is transmitted into the target object. The temporal width of the original pulse ( ) has to be short enough comparing with the target sample thickness. Due to this condition, the first boundary maintains stable when the roundtrip pulse arrives there. In another words, the duration of the pulse is needed to be long enough to eliminate the frequency dependent dispersion on the acoustic impedance values of ambient fluid and the target sample . The linear relation in amplitude and length between the input and output pulses on the targe sample can be represented by single frequency component planar waves with angular frequency and its wave vector as = / and = / stated.
The dependence between the source pulse , the first echo , and the transmitted energy is occurred at the interface between the ambient fluid and a sample, where the acoustic pressure and velocity of the wave are linear and continuous as + = and + = . In the potential form of wave equation, then the source and two separated pulses are written as

Numerical Simulation
For a better view of the EBME measurement, we perform two numerical simulation which provides the propagation of pulse interacting with sample being tested (see Figure S1). In the first simulation, we place a bone-like material with higher physical property comparing with ambient water. A transducer is located at the top of the DI water tank. The target sample is placed at the middle region of the water tank. In Figure  S1 (A), we collect two reflected envelopes and from the front and back surface of the sample due to clear impedance mismatch between the ambient water and the target sample.
In the insets, the simulated sound pressure field is plotted in the entire study area at three time points. From left to right, the first inset shows a pulse is excited from the transducer. The second inset shows the pulse travels at the back boundary of the scanned sample. On the upper side of this inset, a reflected pulse is on the way approaching back to the transducer which is the first echo occurred from the front interface between ambient water and sample. In the third inset, along the continuous moving of the time, the main pulse travels to a lower position which completely passes the sample, and another reflection moving backward to the transducer occurs from the back boundary of the sample.
In Figure S1 (B), the simulation is duplicated bistatic setup calibration for obtaining the value of transducer emits source pulse amplitude . In the insets, the numerical experimental setup does not involve sample. The pulse envelope transmits through low attenuation and non-dispersion DI water ambient arriving at another receiver transducer. From the blue line in (A) and red line in (B), the relative amplitude relation between the , and can be comparing and visualized. The typical values of , and are selected from the absolute maximum values of each pulses. For the source pulse in (B), value can be obtained based on the amplitude of the second positive peak. In (A), the and are able to be found from the second positive peak of the first echo and the second negative peak on the second echo.