Numerical Investigation of Echogenicity for 3D-Printed Tissue-Mimicking Material Toward the Development of Synthetic Organs' Digital Twins

This thesis explores the use of tissue-mimicking 3D-printed materials to create anatomical phantom twins. These twins are intended to provide sophisticated training stations for medical practitioners to rehearse patient-specific interventions. The main target of this study is a 3D-printed synthetic material that mimics cardiac tissue to provide ultrasound images similar to those of real biological tissue. However, the current ultrasound images of the 3D printed material do not match those of biological tissue. To overcome this problem, a polymer-based composite material with a matrix inclusion microstructure is being developed to replicate the acoustic properties of real tissue. The microstructure of 3D printed materials plays a critical role in their response to ultrasound due to the ultrasound-microstructure interaction over the involved wavelengths. However, the relationship between the 3D-printed microstructure and the ultrasonic response of the synthetic tissue is not fully understood. This thesis aims to step toward establishing this correlation using numerical simulations and experimental observations. For this, advanced numerical techniques are required to overcome the standard tools' limitations to accurately simulate wave propagation in heterogeneous microstructures with characteristic lengths of the same order of magnitude as the propagated wavelengths.The discontinuous Galerkin (dG) finite element method is chosen to perform the numerical simulation of ultrasound propagation in matrix-inclusion composites due to its low numerical dispersion and the possibility of using the solver on supercomputers with massively parallel solvers. A unified mathematical framework of the acoustic and elastic wave propagation is presented, and upwind numerical fluxes for acoustic-acoustic, elastic-elastic, and acoustic-elastic interfaces are developed by solving the Riemann problem. The coupled acoustic-elastic dG solver based on these numerical fluxes is implemented and then validated by comparison with the analytical solution of an acoustic domain containing a circular elastic inclusion.Using the developed dG solver, a finite element-based approach is introduced to study the scattering behavior of the microstructure and estimate the phase velocity and scattering-induced attenuation coefficient. This numerical approach is validated by comparing it to the analytical solution obtained from Willis' self-consistent homogenization framework. The elastic properties of the effective medium can be analytically obtained, as well as the phase velocity and attenuation coefficient. The validated numerical approach is subsequently used to estimate the phase velocity and attenuation coefficient for 3D-printed synthetic tissue, considering different microstructure characteristics.A simplified numerical model of the ultrasound transducer is also proposed and developed to simulate wave propagation in the microstructure of 3D-printed materials for B-mode ultrasound image reconstruction. An image reconstruction algorithm is used, and the echogenicity of synthetic tissues with different microstructural characteristics is quantitatively compared. The actual shape of 3D printed inclusions is also observed experimentally and incorporated into the numerical simulation.