ABSTRACT
A finite element (FE) model is employed to investigate the dynamic response of soft tissues under external excitations, particularly corresponding to the case of harmonic motion imaging. A solid 3D mixed 'u-p' element S8P0 is implemented to capture the near-incompressibility inherent in soft tissues. Two important aspects in structural modelling of these tissues are studied; these are the influence of viscous damping on the dynamic response and, following FE-modelling, a developed state-space formulation that valuates the efficiency of several order reduction methods. It is illustrated that the order of the mathematical model can be significantly reduced, while preserving the accuracy of the observed system dynamics. Thus, the reduced-order state-space representation of soft tissues for general dynamic analysis significantly reduces the computational cost and provides a unitary framework for the 'forward' simulation and 'inverse' estimation of soft tissues. Moreover, the results suggest that damping in soft-tissue is significant, effectively cancelling the contribution of all but the first few vibration modes.
Subject(s)
Connective Tissue/physiology , Finite Element Analysis , Models, Biological , Biomechanical Phenomena , Biomedical Engineering , Elasticity , Humans , Motion , ViscosityABSTRACT
A finite element model was built to simulate the dynamic behavior of soft tissues subjected to sinusoidal excitation during harmonic motion imaging. In this study, soft tissues and tissue-like phantoms were modeled as isotropic, viscoelastic, and nearly incompressible media. A 3D incompressible mixed u-p element of eight nodes, S1P0, was developed to accurately calculate the stiffness matrix for soft tissues. The finite element equations of motion were solved using the Newmark method. The Voigt description for tissue viscosity was applied to estimate the relative viscous coefficient from the phase shift between the response and excitation in a harmonic case. After validating our model via ANSYS simulation and experiments, a MATLAB finite element program was then employed to explore the effect of excitation location, viscosity, and multiple frequencies on the dynamic displacement at the frequency of interest.
Subject(s)
Connective Tissue/diagnostic imaging , Connective Tissue/physiology , Elasticity Imaging Techniques/methods , Image Interpretation, Computer-Assisted/methods , Models, Biological , Movement/physiology , Physical Stimulation/methods , Animals , Computer Simulation , Elastic Modulus , Finite Element Analysis , Humans , ViscosityABSTRACT
Numerous experimental and computational methods have been developed to estimate tissue elasticity. The existing testing techniques are generally classified into in vitro, invasive in vivo and non-invasive in vivo. For each experimental method, a computational scheme is accordingly proposed to calculate mechanical properties of soft biological tissues. Harmonic motion imaging (HMI) is a new technique that performs radio frequency (RF) signal tracking to estimate the localized oscillatory motion resulting from a radiation force produced by focused ultrasound. A mechanical model and computational scheme based on the superposition principle are developed in this paper to estimate the Young's modulus of a tissue mimicking phantom and bovine liver in vitro tissue from the harmonic displacement measured by HMI. The simulation results are verified by two groups of measurement data, and good agreement is shown in each comparison. Furthermore, an inverse function is observed to correlate the elastic modulus of uniform phantoms with amplitude of displacement measured in HMI. The computational scheme is also implemented to estimate 3D elastic modulus of bovine liver in vitro.
