Osama M. Mukdadi

Three-dimensional modeling and finite element analysis in treatment planning for orthodontic tooth movement

INTRODUCTION The objective of this study was to demonstrate the potential of 3-dimensional modeling and finite element analysis as clinical tools in treatment planning for orthodontic tooth movement. High stresses in bone and miniscrew implants under load can cause fractures and trauma for orthodontic patients, and treatments are typically planned by using clinical experience or simple 2-dimensional radiographs. METHODS Anatomically accurate 3-dimensional models reconstructed from cone-beam computed tomography scans were used to simulate the retraction of a single-rooted mandibular canine with a miniscrew placed as skeletal anchorage. Detailed stress distributions in the implant and peri-implant bone were found, in addition to the effect of the orthodontic bracket hook length and the angulation of retraction force on stress response in the periodontal ligament (PDL). RESULTS The numeric results showed that the equivalent von Mises stress on the miniscrew under a 200-cN tangential load reached 42 MPa at the first thread recession, whereas von Mises stress in the peri-implant bone only reached 11 MPa below the neck. High tightening loads of 200 N·mm of torsion and 460 cN of axial compression resulted in much greater bone and implant von Mises stresses than tangential loading, exceeding the yield strengths of the titanium alloy and the cortical bone. Increasing the hook length on the orthodontic bracket effectively reduced the canine PDL stress from 80 kPa with no hook to 22 kPa with a hook 7 mm long. Angulating the force apically downward from 0° to 30° had a less significant effect on the PDL stress profile and initial canine deflection. The results suggest that stresses on miniscrew implants under load are sensitive to changes in diameter. Overtightening a miniscrew after placement might be a more likely cause of fracture failure and bone trauma than application of tangential orthodontic force. The reduction of stress along the PDL as a result of increasing the bracket hook length might account for steadier tooth translation by force application closer to the center of resistance of a single-rooted canine. The relatively minor effect of force angulation on the PDL response suggests that the vertical placement of miniscrews in keratinized or nonkeratinized tissue might not significantly affect orthodontic tooth movement. CONCLUSIONS This model can be adapted as a patient-specific clinical orthodontic tool for planning movement of 1 tooth or several teeth.

Elastic guided waves in a layered plate with rectangular cross section

Guided waves in a layered elastic plate of rectangular cross section (finite width and thickness) has been studied in this paper. A semianalytical finite element method in which the deformation of the cross section is modeled by two-dimensional finite elements and analytical representation of propagating waves along the length of the plate has been used. The method is applicable to arbitrary number of layers and general anisotropic material properties of each layer, and is similar to the stiffness method used earlier to study guided waves in a laminated composite plate of infinite width. Numerical results showing the effect of varying the width of the plate on the dispersion of guided waves are presented and are compared with those for an infinite plate. In addition, effect of thin anisotropic coating or interface layers on the guided waves is investigated.

Transient ultrasonic guided waves in layered plates with rectangular cross section

Transient ultrasonic guided waves in anisotropic layered plates with finite and infinite width are presented in this article. A semianalytical finite-element method is adopted to study the guided waves in both infinite- and finite-width elastic plates. Three-noded beam elements in the thickness direction are used in infinite plate model, whereas the cross section of the finite-width plate is represented by nine-noded quadrilateral elements. Propagation in the axial direction is modeled by analytical wave functions. Elastodynamic Green’s functions are derived using modal summation in the frequency–wave number and time–space domains. Results for dispersion and transient analysis of guided waves in infinite nickel plates are presented and compared with those of finite-width plates. Group velocities are calculated and wave arrival times are computed for different plate cross sections. Numerical results show a significant influence of the plate aspect ratio on the dispersion and transient wave response. The co...

Nonlinear characterization of breast cancer using multi-compression 3D ultrasound elastography in vivo

The main objective of this article is to introduce a new nonlinear elastography based classification method for human breast masses. Multi-compression elastography imaging is elucidated in this study to differentiate malignant from benign lesions, based on their nonlinear mechanical behavior under compression. Three classification parameters were used and compared in this work: a new nonlinear parameter based on a power-law behavior of the strain difference between breast masses and healthy tissues, mass-soft tissue strain ratio and the mass relative volume between B-mode and elastography imaging. Using 3D elastography, these parameters were tested in vivo. A pilot study on 10 patients was performed, and results were compared with biopsy diagnosis as a gold standard. Initial elastography results showed a good agreement with biopsy outcomes. The new estimated nonlinear parameter had an average value of 0.163±0.063 and 1.642±0.261 for benign and malignant masses, respectively. Strain ratio values for the benign and malignant masses had an average value of 2.135±0.707 and 4.21±2.108, respectively. Relative mass volume was 0.848±0.237 and 2.18±0.522 for benign and malignant masses. In addition to the traditional normal axial strain, new strain types were used for elastography and constructed in 3D, including the first principal, maximum shear and Von Mises strains. The new strains provided an enhanced distinction of the stiff lesion from the soft tissue. In summary, the proposed elastographic techniques can be used as a noninvasive quantitative characterization tool for breast cancer, with the capability of visualizing and separating the masses in a three dimensional space. This may reduce the number of unnecessary painful breast biopsies.

Theoretical predictions of harmonic generation from submicron ultrasound contrast agents for nonlinear biomedical ultrasound imaging

Submicron ultrasound contrast agents have aroused attention for their significant promise in ultrasonic contrast/molecular imaging, targeted therapy and echo particle imaging velocimetry. However, nonlinear acoustic properties of submicron encapsulated gas bubbles for ultrasonic applications are still not clearly understood. In this paper, nonlinear acoustic emission characteristics from submicron bubbles were examined using a numerical study. The modified RP equation incorporating viscosity, acoustic radiation, thermal effects and encapsulated shell was used to study single bubble dynamics. Further, a size integration method, shown previously to be useful in prediction of backscatter spectra from groups of bubbles, was applied to analyse response from a bubble population. We show that bubbles with radii (200-500 nm) produce significant subharmonic and ultraharmonic components of the backscatter spectrum, while smaller bubbles (<200 nm) provide substantial second harmonic components. Additionally, nanoscale bubbles (<100 nm) produce very low backscatter amplitudes and thus may not be useful with the use of current ultrasound technology. Analysing optimal ultrasound driving pressures and bubbles size ranges for maximal subharmonic and ultraharmonic signals showed that sub and ultraharmonic mode nonlinear imaging methods may be potentially competitive for larger size bubbles (>200 nm) in providing proper contrast-to-tissue signal ratios.

Laser-Generated Thermoelastic Waves in an Anisotropic Infinite Plate: FEM Analysis

ABSTRACT In recent years, the study of thermoelastic waves generated by focused laser beams has been undertaken by several researchers because the technique provides a means for noncontact generation of ultrasonic waves. Laser-generated ultrasonic waves have diverse applications ranging from material characterization to nondestructive testing of defects. Transient ultrasonic guided waves generated in an anisotropic infinite plate by a pulsed laser beam are investigated in this study. A semi-analytical finite element method (SAFEM) is adopted for this purpose. In this method, the plate is divided into parallel layers through its thickness and the displacement and temperature in each layer are approximated by quadratic polynomials in the thickness direction (z). They are assumed to be continuous functions of time and in-plane cartesian coordinates (x, y). Transient response is calculated using Fourier transformations in time and space variables (x, y). The analysis technique is applicable to a generally anisotropic plate. Results for dispersion of guided waves and transient displacement in infinite silicon nitride (Si3N4) plates are presented. Numerical results show that for the assumed form of heat deposition by the laser mainly the lowest Lamb modes, namely, the lowest symmetric (S 0) and antisymmetric (A 0) modes, are excited. They also show that the transient response is dominated by the antisymmetric mode A 0, which shows characteristic dispersion. This study provides a quantitative model for laser-generated thermoelastic waves in an anisotropic plate and can be used for nondestructive evaluation.

Elastic guided wave propagation in a periodic array of multi-layered piezoelectric plates with finite cross-sections

In this study, we present a model study of guided wave dispersion and resonance behavior of an array of piezoelectric plates with arbitrary cross-sections. The objective of this work is to analyze the influence of the geometry of an element of a 1D-array ultrasound transducer on generating multi-resonance frequency so as to increase the frequency bandwidth of the transducers. A semi-analytical finite-element (SAFE) method is used to model guided wave propagation in multi-layered 1D-array ultrasound transducers. Each element of the array is composed of LiNbO3 piezoelectric material with rectangular or subdiced cross-section. Four-node bilinear finite-elements have been used to discretize the cross-section of the transducer. Dispersion curves showing the dependence of phase and group velocities on the frequency, and mode shapes of propagating modes were obtained for different geometry consurations. A parametric analysis was carried out to determine the effect of the aspect ratio, subdicing, inversion layer and matching layers on the vibrational behavior of 1D-array ultrasound transducers. It was found that the geometry with subdiced cross-section causes more vibration modes compared with the rectangular section. Modal analysis showed that the additional modes correspond to lateral modes of the piezoelectric subdiced section. In addition, some modes have strong normal displacements, which may influence the bandwidth and the pressure field in front of the transducer. In addition, the dispersion curves reveal strong coupling between waveguide modes due to the anisotropy of the piezoelectric crystal. The effect of the matching layers was to cluster extensional and flexural modes within a certain frequency range. Finally, inversion layer is found to have a minor effect on the dispersion curves. This analysis may provide a means to analyze and understand the dynamic response of 1D-array ultrasound transducers.

Acoustic-phonon dispersion in nanowires

We study phonon dispersion in layered prismatic nanowires that can have an arbitrary cross-sectional geometry. We calculate phonon dispersion using a hybrid analytical/numerical approach that models propagation along the wire analytically, but deformation in the plane of the cross section using the finite element method. In our results we consider only two layers, but the calculational approach is applicable to multiple layers.

Off-axis propagation of ultrasonic guided waves in thin orthotropic layers: theoretical analysis and dynamic holographic imaging measurement

The elastic properties of many materials in sheet or plate form can be approximated with orthotropic symmetry. In many sheet material manufacturing industries (e.g., the paper industry), manufacturers desire knowledge of certain anisotropic elastic properties in the sheet for handling and quality issues. Ultrasonic wave propagation in plate materials forms a method to determine the anisotropic elastic properties in a nondestructive manner. This work explores exact and approximate analysis methods of ultrasonic guided wave propagation in thin layers, explicitly dealing with orthotropic symmetry and propagation off-axis with respect to the manufacturing direction. Recent advances in full-field ultrasonic imaging methods, based on dynamic holography, allow simultaneous measurement of the plate wave motion in all planar directions within a single image. Results from this laser ultrasonic imaging approach are presented that record the lowest anti-symmetric (flexural) mode wavefront in a single image without scanning. Specific numerical predictions for flexural wave propagation in two distinctly different types of paper are presented and compared with direct imaging measurements. Very good agreement is obtained for the lowest anti-symmetric plate mode using paper properties independently determined by a third party. Complete determination of the elastic modulus tensor for orthotropic layers requires measurement of other modes in addition to the lowest anti-symmetric. Theoretical predictions are presented for other guided wave modes [extensional (S), flexural (A), and shear-horizontal (SH)] in orthotropic plates with emphasis on propagation in all planar directions. It is shown that there are significant changes in the dispersion characterization of these modes at certain frequencies (including off-axis mode coupling) that can be exploited to measure additional in-plane elastic moduli of thin layers. At present, the sensitivity of the imaging measurement approach limits experimental investigation to relatively large amplitudes easily produced by flexural wave motion (>0.1 nm). Extension of the measurement range and application to other plate wave modes are in progress and shall be reported in future work.

In vivo vascular wall tissue characterization using a strain tensor measuring (STM) technique for flow-mediated vasodilation analyses

Endothelial dysfunction is considered to be a key factor in the development of atherosclerosis, and the measurement of flow-mediated vasodilation (FMD) in brachial and other conduit arteries has become a common method to assess the status of endothelial function in vivo. Based on the direct relationship between the FMD response and local shear stress on the conduit brachial artery endothelium, we hypothesize that measuring relevant changes in the brachial wall strain tensor would provide a non-invasive tool for assessing vascular mechanics during post-occlusion reactive hyperemia. Direct measurement of the wall strain tensor due to FMD has not yet been reported in the literature. In this work, a noninvasive direct ultrasound-based strain tensor measuring (STM) technique is presented to assess changes in the mechanical parameters of the vascular wall during post-occlusion reactive hyperemia and/or FMD, including local velocities and displacements, diameter change, local strain tensor and strain rates. The STM technique utilizes sequences of B-mode ultrasound images as its input with no extra hardware requirement, and its algorithm starts with segmenting a region of interest within the artery and providing the acquisition parameters. Then a block matching technique based on speckle tracking is employed to measure the frame-to-frame local velocities. Displacements, diameter change, local strain tensor and strain rates are then calculated by integrating or differentiating velocity components. The accuracy of the STM algorithm was assessed in vitro using phantom studies, where an average error of 7% was reported using different displacement ranging from 100 microm to 1000 microm. Furthermore, in vivo studies using human subjects were performed to test the STM algorithm during pre- and post-occlusion. Good correlations (|r| >0.5, P < 0.05) were found between the post-occlusion responses of diameter change and local wall strains. Results indicate the validity and versatility of the STM algorithm and describe how parameters other than the diameter change are sensitive to reactive hyperemia following occlusion. This work suggests that parameters such as local strains and strain rates within the arterial wall are promising metrics for the assessment of endothelial function, which can then be used for accurate assessment of atherosclerosis. In summary, this study describes a simple and computationally efficient algorithm that can be integrated with ultrasound machines for vascular research. Moreover, it suggests that monitoring the local strain and strain rates of the brachial artery wall can replace or augment the measurement of arterial diameter in FMD studies.