Theoretical and numerical modeling of ultrasonic wave propagation in 3D-printed matrix-inclusion composites
Résumé
3D printing technology, capable of manufacturing complex shapes, has recently been introduced to the surgical field to create anatomical twins and design simulators for physicians’ advanced training and operative planning. By training specific surgical operations on anatomic twins that mimic target patient-specific organs, surgeons go through the same experience as in the actual operation, improve their ability and reduce the risk of error and failure. Operations, such as minimally invasive catheter-based endovascular procedures, are guided by ultrasonography. Thus, the 3D-printed anatomical twin should not only mimic the desired mechanical properties of the target organ but also provide similar echography images compared to the real organ. To achieve this goal, composite synthetic tissues are printed by multi-jet technology, which allows the control of the distribution of the materials on a micrometric scale. Thus, by locally controlling the microstructure of printed composites, their acoustic characteristics are expected to be tuned appropriately.
However, the interaction between ultrasonic waves and printed microstructures is complex, and the correlation between them and their ultrasonic signature is not yet well understood. This work proposes to theoretically and numerically model this interaction to improve the echogenicity of printed matrix/inclusions type composites. For the theoretical study, an analytical method of self-consistent homogenization is considered[1]. For the numerical simulation, a well-established space discontinuous Galerkin finite element method is employed, as it is capable of taking into account exactly the printed microstructure[2]. Numerical modeling has the advantage of being able to go beyond the simplifying assumptions of theoretical models and simulate real printed microstructures. A parametric study is presented on microstructural parameters such as material properties, size, shape, or volume fraction of inclusion. The theoretical/numerical comparison of the phase velocity and the attenuation coefficient is carried out on custom-made composite samples. Furthermore, their B-mode image is obtained using an image reconstruction algorithm. Influential microstructural parameters for the phase velocity, the attenuation coefficient, and the B-mode image are identified. Finally, real printed microstructures are simulated and investigated.
References
[1] F. Sabina, J. Willis, A simple self-consistent analysis of wave propagation in particulate composites,
Wave Motion 10(2) (1988) 127–142.
[2] B. Tie, A.-S. Mouronval, Systematic development of upwind numerical fluxes for the space discontinuous
Galerkin method applied to elastic wave propagation in anisotropic and heterogeneous media with physical
interfaces, Comput. Meth. Appl. Mech. Eng. 372 (2020)