Baoxiang Shan’s research while affiliated with Rutgers, The State University of New Jersey and other places

An integrated system is built to model and simulate the dynamic response of soft tissues. The mathematical formulation employs finite element and model order reduction approaches to develop a state space model for soft tissues that allows for time-efficient numerical analysis. The stimulus device and signal processing routines are built in Matlab/Simulink and then integrated with the finite element state space model. This integrated system facilitates expeditious numerical evaluation of different soft tissue models subjected to dynamic excitation. It further elucidates the effect of different stimulus sources, as well as relative influences of different sources of uncertainty.

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.

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.

Research on the biomechanical behavior of soft tissues has drawn a lot of recent attention due to its application in tumor pathology, rehabilitation, surgery and biomaterial implants. In this study a finite element (FE) model is applied to represent soft tissues and phantoms with complex geometry and heterogeneous material properties. A solid 3D mixed u-p element S8P0 (8-node for displacement and 1-node for internal pressure) is implemented to capture the near-incompressibility inherent in soft tissues. A dynamic analysis of soft tissues’ response to excitation is explored in which, the second order differential equation representing the soft tissues in FE necessitates a time-consuming numerical solution procedure. Moreover, the second-order representation is complicated in estimating the tissue mechanical properties by inverse procedure. Thus, a state space (SS) model is used to equivalently represent soft tissues by transforming the second-order differential equation into a system of linear first-order differential equations. The linear and time-invariant SS representation of soft tissues for general dynamic analysis can reduce the computational cost and a provide framework for the “forward” simulation and “inverse” identification of soft tissues.

We investigate the problem of a kinking crack at a bimaterial interface when the two surfaces are in contact near the crack tip. Using a potential function and the dislocation technique, we relate, by a singular integral equation, the stress intensity factors (SIF) at the kinking crack tip to the SIF before crack kinking. We use Gauss-Chebyshev integration formulas to solve this integral equation numerically. We evaluate the kinking angles from a bimaterial interface under conditions of contact using the maximum energy release rate criterion and compare these angles with our experiments and those in the literature. The interfacial crack is demonstrated by simulation and experiments to kink into the more compliant material at an angle of about 80°.

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.

Research on the biomechanical behavior of soft tissues has drawn a lot of recent attention due to its application in tissue evaluation, early cancer detection, rehabilitation and surgery. Dynamic analysis of soft tissues not only provides histological, pathological and physiological information of the tissues, but also presents theoretical support for the modern medical imaging modalities (like Acoustic Radiation Force Imaging, Harmonic Motion Imaging, Supersonic Shear Imaging and Shear Wave Elasticity Imaging) based on tissue dynamics. Using our FEMSS (Finite Element Method with a State Space representation) technique, a realistic model of breast soft tissue with hard inclusions is geometrically discretized in ANSYS using finite elements, while a state space representation is adopted to characterize the motions of tissues stimulated by an internal radiation force. Our objective for this paper is to investigate the effects of size, location and mechanical properties of hard inclusions on the tissues’ response, frequency spectrum and forced vibration. The response differentiation between soft tissues with and without hard inclusions may reveal the resolution and delectability of the dynamic measurement and could lead in the development of new, more effective diagnostic techniques. Our simulation results indicate that the existence of hard inclusion(s) can significantly change the dynamic response of the tissue system. Specifically, hard inclusions may shift the spectrum of an elastic tissue system to a range of higher frequency, with larger sized hard inclusions causing bigger shifts. Furthermore, the location effect of hard inclusions is exhibited when a shallow one tends to vibrate with a larger magnitude at lower frequency than a deep hard inclusion. Finally, the tissue viscosity can significantly compress the range of high frequencies in the tissue system spectrum and cause the magnitude decrease of the forced vibration.

To investigate the effect of serrations in an interfacial crack between dissimilar materials, we introduce into the Finite Element (FE) framework a unit cell (UC) at microscale. By assigning material-specific properties to these unit cells, we can model various serration profiles and distributions and calculate their effect on the mixed-mode stress intensity factor (SIF), including its magnitude and phase angle. The simulation demonstrates that serration profoundly changes the local behavior of an interfacial crack. The serrations decrease the SIF in mode I, increase it in mode II, and, when the serration's height-to-width ratio increases, the mode mixity SIF increases as well. We find that sparse serration confines variation in the SIFs to the local peaks and that dense serrations cause widespread undulations in the SIF's magnitude and phase angle.

We have developed a solid mechanics model of nearly incompressible, viscoelastic soft tissue for finite element analysis (FEA) in MATLAB 7.2. Newmark’s method was used to solve the finite element equations of motion for our model. The solution to our dynamic problem was validated with a transient dynamic analysis in ANSYS 10.0. We further demonstrated that our MATLAB FEA qualitatively agrees with those results observed with acoustic radiation force methods on soft tissues and tissue-mimicking materials. We showed that changes in Young’s modulus and the damping coefficient affect the displacement amplitude and phase shift of the response data in the same manner: An increase in Young’s modulus or damping coefficient decreases both the displacement amplitude and response lag. Future work on this project will involve frequency analysis on response data and studying the initial transient region to help uncouple the effects of Young’s modulus and damping coefficient on response characteristics. This will get us one step closer to being able to explicitly determine Young’s modulus and the damping coefficient from the temporal response data of acoustic radiation force methods, which is the ultimate goal of our project.

The complex fracture behavior of a cross-ply composite cantilever beam with artificially embedded delamination is investigated analytically, numerically, and experimentally. The analysis of the cantilever beam is divided into two geometric configurations: the global bending of the undelaminated cantilever and the local buckling of the delaminated part. A finite element model developed in ANSYS is used to concurrently analyze the effects of contact zone and delamination in the aforementioned asymmetrically loaded structure. The obtained experimental data are correlated and compared with the findings of the FEM simulations. All numerical, analytical, and experimental results illustrate that the fracture behavior of the laminate cantilever beam is dominated by mode II, mainly due to the effect of a large contact zone. The latter is determined by geometric and loading parameters. The dominance of mode II over mode I, leads to the initiation and propagation of an interfacial crack rather than an intralayer one. Furthermore, experimental evidence indicates that crack kinking during propagation depends on the architecture of the specimens.