Biomechanical performance of resin composite on dental tissue restoration: A finite element analysis.

This study investigates the biomechanical performance of various dental materials when filled in different cavity designs and their effects on surrounding dental tissues. Finite element models of three infected teeth with different cavity designs, Class I (occlusal), Class II mesial-occlusal (MO), and Class II mesio-occluso-distal (MOD) were constructed. These cavities were filled with amalgam, composites (Young's moduli of 10, 14, 18, 22, and 26 GPa), and glass carbomer cement (GCC). An occlusal load of 600 N was distributed on the top surface of the teeth to carry out simulations. The findings revealed that von Mises stress was higher in GCC material, with cavity Class I (46.01 MPa in the enamel, 23.61 MPa in the dentin), and for cavity Class II MO von Mises stress was 43.64 MPa, 39.18 MPa in enamel and dentin respectively, while in case of cavity Class II MOD von Mises stress was 44.67 MPa in enamel, 27.5 in the dentin. The results showed that higher stresses were generated in the non-restored tooth compared to the restored one, and increasing Young's modulus of restorative composite material decreases stresses in enamel and dentin. The use of composite material showed excellent performance which can be a good viable option for restorative material compared to other restorative materials.

Biomechanical analysis of printable functionally graded material (FGM) dental implants for different bone densities.

The long-term success of a dental implant is related to the material and design of the implant, and bone density. Conventional implants cause stress-shielding due to a mismatch between the implant and bone stiffness. Functionally graded porous materials and designs are a great choice for the design of implants to control the local stiffness at a certain location to meet the biomechanical requirements. The purpose of this study is to analyze five designs of axial and radial functionally graded materials (FGM) implants besides the conventional implant and conical and cylindrical shapes that were simulated with five different bone densities. The results showed that strain in bone increased with a decrease in cancellous bone density. The shape of the implant did not play an important role in strain/stress distribution. Conventional implants showed optimal strain (1000-2240 µÎµ) in low-density (0.7-0.8 g/cm3) bone, however, FGM implants produced optimal strain (990-1280 µÎµ) in the high-density bone (0.9-1 g/cm3) as compared to conventional implants. The proposed designs of FGM implants have the potential to address the complications of conventional implants in high-density bone.

Stress influence on orthodontic system components under simulated treatment loadings.

BACKGROUND AND OBJECTIVE: Mini-implants have been developed and effectively used by clinicians as anchorage for orthodontic tooth movement. The objective of this study was to elucidate the stress response of orthodontic forces on the periodontal system, bone tissues, mini-implant and the bracket-enamel interface. METHODS: Computer tomography images of a commercially available mini-implant, an orthodontic bracket bonded to a central incisor, and jawbone section models were used to reconstruct three dimensional computer models. These models were exported and meshed in an ABAQUSⓇ finite-element package. Material properties, multi-segment interactions, boundary and loading conditions were then applied to each component. Finite-element analyses were conducted to elucidate the effect of orthodontic force on the equivalent von Mises stress response within the simulated orthodontic system. RESULTS: The highest stress values in the orthodontic system were predicted at the mini-implant neck, at the interface of the cortical bone, and gradually decreased in the internal apical direction of the miniscrew. On the alveolar bone, the maximum stress values were located in the alveolar cortical bone near the cervical areas of the mini-implant, which is in line with clinical findings of area where bone loss was found post orthodontic tooth treatment. Another peak of von Mises stress response was found in the enamel bracket junction with a maximum up to 186.05 MPa. To ensure good bonding between the enamel and bracket, it is vital to select carefully the type and amount of bonding materials used in the bracket-enamel interface to assure an appropriate load distribution between the teeth and alveolar bone. The results also revealed the significance of the periodontal ligaments, acting as an intermediate cushion element, in the load transfer mechanism. CONCLUSIONS: This study is sought to identify the stress response in a simulated orthodontic system to minimize the failure rate of mini-implants and bracket loss during orthodontic treatment.

Finite-Element analysis of a lateral femoro-tibial impact on the total knee arthroplasty.

BACKGROUND AND OBJECTIVE: Total knee arthroplasty (TKA) is a routine surgery performed to treat patients with severe knee osteoarthritis. The success of a TKA depends strongly on the initial stability of the prosthetic components and its long-term osseointegration due to the optimal distribution of mechanical stresses in the surrounding bones under the effect of the different biomechanical loads applied to the Femur-TKA-Tibia system. The purpose of this study is to analyze the level and the distribution of the induced stresses in a Femur-TKA-Tibia system subjected to combined triaxial forces, which mimic a femoral mechanical shock. METHODS: In this study, complex TKA system implanted in both femoral and tibial bones has been analyzed numerically with a three-dimensional finite-element method. A virtual model is designed to examine in silico the effect of the combined triaxial forces acting on this prosthesis in femoral region. Anatomical three-dimensional finite-element models of both femoral and tibial bones were constructed to calculate the interfacial stresses around the TKA components. The 3D finite-element processing program ABAQUS was used to perform the analysis. RESULTS: The stresses propagated in the bone regions adjacent to the TKA osseointegrated components, and the decreased in their magnitude to the outer region. These stresses reached the highest level in the cortical bone areas that are right next to the proximal upper attachment portions of the TKA osseointegrated components. The magnitude of the stresses in the tibial component is higher than that in the femoral component. Finally, it is very important to emphasize the role of the polyethylene articulating spacer in the shock absorption of bone support sections. Thus, this component should be preserved mechanically from the impact of high shocks in order to maintain healthy TKA systems. CONCLUSIONS: Optimizing TKA model by controlling the biomechanical stresses distributed within its both components and supporting bones is a valid approach to achieving favorable long-term outcomes. The 3D finite-element analysis provides an effective pre-operative method for planning patient-specific TKA prostheses, and for designing future models that preserves the biomechanical function of the Femur-TKA-Tibia system.

Finite-Element Study of Biomechanical Explanations for Bone Loss around Dental Implants.

Since the advent of osteointegrated implantology and its precepts issued by the Swedish School, assessment of peri-implant bone loss criteria has often been debated by professionals in this field. Long-term success of dental implants is highly reliant on structural and functional osseointegration between implant and surrounding intraoral tissues. In this context, the current study aims to provide biomechanical explanations for causes of bone loss around the dental implant after osseointegration by computational analysis, using a three-dimensional finite-element (FE) method. We design an approximate virtual model that includes the smooth, cylindrical dental implant and alveolar bone. We use SolidWorks software and export to ABAQUS for computational stress analysis at the bone-implant interface. The numerical model is created and loaded with a compressive occlusal force that is applied at the top of the implant platform. We thoroughly investigate the generated FE results and stress responses of the bone-implant system. The developed model is extremely useful for indicating biomechanical phenomena in the bone-implant interface that play a key part in bone loss around the dental implant. In addition, obtained results tend to deliver an improved understanding to designers in the biomedical engineering field and in dentistry.

3-D visualization and non-linear tissue classification of breast tumors using ultrasound elastography in vivo.

The goal of the study described here was to introduce new methods for the classification and visualization of human breast tumors using 3-D ultrasound elastography. A tumor's type, shape and size are key features that can help the physician to decide the sort and extent of necessary treatment. In this work, tumor type, being either benign or malignant, was classified non-invasively for nine volunteer patients. The classification was based on estimating four parameters that reflect the tumor's non-linear biomechanical behavior, under multi-compression levels. Tumor prognosis using non-linear elastography was confirmed with biopsy as a gold standard. Three tissue classification parameters were found to be statistically significant with a p-value < 0.05, whereas the fourth non-linear parameter was highly significant, having a p-value < 0.001. Furthermore, each breast tumor's shape and size were estimated in vivo using 3-D elastography, and were enhanced using interactive segmentation. Segmentation with level sets was used to isolate the stiff tumor from the surrounding soft tissue. Segmentation also provided a reliable means to estimate tumors volumes. Four volumetric strains were investigated: the traditional normal axial strain, the first principal strain, von Mises strain and maximum shear strain. It was noted that these strains can provide varying degrees of boundary enhancement to the stiff tumor in the constructed elastograms. The enhanced boundary improved the performance of the segmentation process. In summary, the proposed methods can be employed as a 3-D non-invasive tool for characterization of breast tumors, and may provide early prognosis with minimal pain, as well as diminish the risk of late-stage breast cancer.

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.

High-resolution vascular tissue characterization in mice using 55MHz ultrasound hybrid imaging.

Ultrasound and Duplex ultrasonography in particular are routinely used to diagnose cardiovascular disease (CVD), which is the leading cause of morbidity and mortality worldwide. However, these techniques may not be able to characterize vascular tissue compositional changes due to CVD. This work describes an ultrasound-based hybrid imaging technique that can be used for vascular tissue characterization and the diagnosis of atherosclerosis. Ultrasound radiofrequency (RF) data were acquired and processed in time, frequency, and wavelet domains to extract six parameters including time integrated backscatter (T(IB)), time variance (T(var)), time entropy (T(E)), frequency integrated backscatter (F(IB)), wavelet root mean square value (W(rms)), and wavelet integrated backscatter (W(IB)). Each parameter was used to reconstruct an image co-registered to morphological B-scan. The combined set of hybrid images were used to characterize vascular tissue in vitro and in vivo using three mouse models including control (C57BL/6), and atherosclerotic apolipoprotein E-knockout (APOE-KO) and APOE/A(1) adenosine receptor double knockout (DKO) mice. The technique was tested using high-frequency ultrasound including single-element (center frequency=55 MHz) and commercial array (center frequency=40 MHz) systems providing superior spatial resolutions of 24 µm and 40 µm, respectively. Atherosclerotic vascular lesions in the APOE-KO mouse exhibited the highest values (contrast) of -10.11±1.92 dB, -12.13±2.13 dB, -7.54±1.45 dB, -5.10±1.06 dB, -5.25±0.94 dB, and -10.23±2.12 dB in T(IB), T(var), T(E), F(IB), W(rms), W(IB) hybrid images (n=10, p<0.05), respectively. Control segments of normal vascular tissue showed the lowest values of -20.20±2.71 dB, -22.54±4.54 dB, -14.94±2.05 dB, -9.64±1.34 dB, -10.20±1.27 dB, and -19.36±3.24 dB in same hybrid images (n=6, p<0.05). Results from both histology and optical images showed good agreement with ultrasound findings within a maximum error of 3.6% in lesion estimation. This study demonstrated the feasibility of a high-resolution hybrid imaging technique to diagnose atherosclerosis and characterize plaque components in mouse. In the future, it can be easily implemented on commercial ultrasound systems and eventually translated into clinics as a screening tool for atherosclerosis and the assessment of vulnerable plaques.

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.

High-resolution 3D ultrasound jawbone surface imaging for diagnosis of periodontal bony defects: an in vitro study.

Although medical specialties have recognized the importance of using ultrasonic imaging, dentistry is only beginning to discover its benefit. This has particularly been important in the field of periodontics which studies infections in the gum and bone tissues that surround the teeth. This study investigates the feasibility of using a custom-designed high-frequency ultrasound imaging system to reconstruct high-resolution (< 50 µm) three-dimensional (3D) surface images of periodontal defects in human jawbone. The system employs single-element focused ultrasound transducers with center frequencies ranging from 30 to 60 MHz. Continuous acquisition using a 1 GHz data acquisition card is synchronized with a high-precision two-dimensional (2D) positioning system of ±1 µm resolution for acquiring accurate measurements of the mandible, in vitro. Signal and image processing algorithms are applied to reconstruct high-resolution ultrasound images and extract the jawbone surface in each frame. Then, all edges are combined and smoothed in order to render a 3D surface image of the jawbone. In vitro experiments were performed to assess the system performance using mandibles with teeth (dentate) or without (nondentate). The system was able to reconstruct 3D images for the mandible's outer surface with superior spatial resolution down to 24 µm, and to perform the whole scanning in < 30 s. Major anatomical landmarks on the images were confirmed with the anatomical structures on the mandibles. All the anatomical landmarks were detected and fully described as 3D images using this novel ultrasound imaging technique, whereas the 2D X-ray radiographic images suffered from poor contrast. These results indicate the great potential of utilizing high-resolution ultrasound as a noninvasive, nonionizing imaging technique for the early diagnosis of the more severe form of periodontal disease.

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.

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.

Noninvasive assessment of human jawbone using ultrasonic guided waves.

The problem of detecting defects in jawbones is an important problem. Existing methods based on Xrays are invasive and constrain the achievable image quality. They also may carry known risks of cancer generation or may be limited in accurate diagnosis scope. This work is motivated by the lack of current imaging modalities to accurately predict the mechanical properties and defects in jawbone. Ultrasonic guided waves are sensitive to changes in microstructural properties and thus have been widely used for noninvasive material characterization. Using these waves may provide means for early diagnosis of marrow ischemic disorders via detecting focal osteoporotic marrow defect, chronic nonsuppurative osteomyelitis, and cavitations in the mandible (jawbone). Guided waves propagating along the mandibles may exhibit dispersion behavior that depends on material properties, geometry, and embedded cavities. In this work, we present the first study in the theoretical and experimental analysis of guided wave propagation in jawbone. Semianalytical, finite-element (SAFE) method is used to analyze dispersion behavior of guided waves propagating in human mandibles. The geometry of the cross section is obtained by segmenting the computed tomography (CT) images of the jawbone. The cross section of the mandible is divided in two regions representing the cortical and trabecular bones. Each region is modeled as a linear Hookean material. The material properties for both regions are adopted from the literature. The experimental setup for the guided waves experiment is described. The results from both numerical analysis and guided waves experiment exhibit variations in the group velocity of the first arrival signal and in the dispersion behavior of healthy and defected mandibles. These results shall provide a means to noninvasively characterize the jawbone and accurately assess the bone mechanical properties. Our study is not aimed at characterizing the bone density in human mandibles. Rather, it is aimed to assess bone mechanical properties and defects that cannot be diagnosed by X-ray or other imaging modalities. This work may pave the way to the development of inexpensive noninvasive devices to detect small defects in human mandibles.

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.

Advantages in using multifrequency excitation of contrast microbubbles for enhancing echo particle image velocimetry techniques: initial numerical studies using rectangular and triangular waves.

Accurate measurement of velocity profiles, multiple velocity vectors and local shear stress in arteries is very important for a variety of cardiovascular diseases. We have recently developed an ultrasound based velocimetry technique, termed echo particle image velocimetry (echo PIV). This method takes advantage of the nonlinear backscatter characteristics of ultrasound contrast microbubbles when exposed to certain ultrasonic forcing conditions. Preliminary in vitro, animal and clinical studies have shown significant promise of this method for measuring multiple velocity components with good temporal (up to 2 ms) and spatial (<1 mm) resolution. However, there is still difficulty in maximizing the nonlinearity of bubble backscatter using conventional Gaussian-pulse excitation techniques because: (1) significant harmonic components may not be produced at modest pressure amplitudes; and (2) the higher incident pressure amplitudes required to induce nonlinear behavior may cause bubble destruction. We present here a potential solution to this problem through the use of multifrequency excitation, where rectangular and triangular pulses with four harmonics are used to drive the bubble. The nonlinear behavior of the microbubble, as well as fragility and backscatter, were studied through numerical modeling via a modified Rayleigh-Plesset equation. Results show that the rectangular wave is effective in improving the visibility of microbubbles, with effective scattering cross-section area significantly higher (up to 35 times) than the widely-used Gaussian waveform. However, velocity and acceleration analysis of the bubble wall shows that the rectangular wave may threaten bubble stability. Due to lower wall velocity and acceleration, the triangular wave should decrease the potential for bubble destruction yet maintain relatively high second harmonic backscatter components. The impact of higher harmonics was studied by examining backscatter differences from incident rectangular and triangular pulses with four and two harmonics. Results indicate that a two-frequency excitation (which may be easier to implement practically) may be sufficient to induce nonlinear behavior of the microbubbles at modest incident pressures. These predictions provide support for the use of multifrequency driving to enhance echo PIV applications.

Numerical modeling of microbubble backscatter to optimize ultrasound particle image velocimetry imaging: initial studies.

We have developed a promising non-invasive ultrasound-based method for performing particle image velocimetry (PIV) in vivo. This method, termed echo PIV, provides multi-component blood velocity data with good ( approximately 2 ms) temporal resolution. The method takes advantage of the non-linear ultrasound backscatter characteristics of small gas-filled microbubbles (ultrasound contrast) that are seeded into the blood stream. In this study, we use a numerical model to explore potential areas to focus future work in echo PIV. Ultrasound backscatter from encapsulated microbubbles was modeled using a modified Rayleigh-Plesset equation (Church model, 1995), taking into account the protein/lipid shell layer as a thick, mass-conserving incompressible fluid surrounded by incompressible blood-like fluid. The equation of motion was solved numerically to characterize the fundamental and second harmonic components of the backscattered pressure. Results show a significant advantage in using the second harmonic component for echo PIV, especially for small bubble sizes less than 3 microm in diameter at 2.2 MHz frequency. The effect of the shell thickness ranging from 10 to 500 nm on the vibration amplitude of the bubble was examined and it is shown that the presence of the shell requires mechanical index (MI) > 0.2 of incident pressure amplitude to improve bubble detectability. Analysis of the effect of pulse length shows a tradeoff between axial resolution (short pulse length) and bubble detectability (longer pulse length) will most likely be required. The effect of varying MI between 0.1 and 0.6 was also studied at a center frequency of 2.2 MHz and the results indicate that the resonance of the second harmonic is maximized for bubbles with diameter of approximately 2.75 microm. Bubble non-linearities at MI > 0.2 induced a resonant frequency shift away from the integer multiple of the incident frequency in the second harmonic backscatter. For a given bubble size, there is a combination of optimal incident frequency and mechanical index range that maximizes the ratio of the second harmonic compared to the fundamental. This resonant frequency decreases with increasing bubble radius. Further, a narrow bandwidth pulse is shown to increase signal strength. Both of these effects may cause conflict with factors governing spatial resolution. Optimization of the incident frequency, microbubble size and mechanical index to enhance bubble detectability will depend on the particular clinical application. These theoretical predictions provide further understanding of the physics behind our echo PIV technique, and should be useful for guiding the design of echo PIV systems.

Ultrasound wave propagation in tissue and scattering from microbubbles for echo particle image velocimetry technique.

Nonlinear wave propagation in tissue can be employed for tissue harmonic imaging, ultrasound surgery, and more effective tissue ablation for high intensity focused ultrasound (HIFU). Wave propagation in soft tissue and scattering from microbubbles (ultrasound contrast agents) are modeled to improve detectability, signal-to-noise ratio, and contrast harmonic imaging used for echo particle image velocimetry (Echo-PIV) technique. The wave motion in nonlinear material (tissue) is studied using KZK-type parabolic evolution equation. This model considers ultrasound beam diffraction, attenuation, and tissue nonlinearity. Time-domain numerical model is based on that originally developed by Lee and Hamilton [J. Acoust. Soc. Am 97:906-917 (1995)] for axi-symmetric acoustic field. The initial acoustic waveform emitted from the transducer is assumed to be a broadband wave modulated by Gaussian envelope. Scattering from microbubbles seeded in the blood stream is characterized. Hence, we compute the pressure field impinges the wall of a coated microbubble; the dynamics of oscillating microbubble can be modeled using Rayleigh-Plesset-type equation. Here, the continuity and the radial-momentum equation of encapsulated microbubbles are used to account for the lipid layer surrounding the microbubble. Numerical results show the effects of tissue and microbubble nonlinearities on the propagating pressure wave field. These nonlinearities have a strong influence on the waveform distortion and harmonic generation of the propagating and scattering waves. Results also show that microbubbles have stronger nonlinearity than tissue, and thus improves S/N ratio. These theoretical predictions of wave phenomena provide further understanding of biomedical imaging technique and provide better system design.

Advantages in using multi-frequency driving ultrasound for optimizing echo particle image velocimetry techniques.

We have recently developed an ultrasound based velocimetry technique, termed echo particle image velocimetry (echo PIV). This method takes advantage of the non-linear backscatter characteristics of ultrasound contrast microbubbles when exposed to certain ultrasonic field. Preliminary in vitro, animal and clinical studies have shown significant promise of this method for measuring multiple velocity components with good temporal and spatial resolution. However, there is still difficulty in maximizing the non-linearity of bubble backscatter using conventional Gaussian-pulse excitation techniques because significant harmonic components may not be produced at modest pressure amplitudes and the higher incident pressure amplitudes required to induce non-linear behavior may cause bubble destruction. We present here a potential solution to this problem through the use of multi-frequency excitation. A rectangular pulse with multiple harmonics is used to drive the bubble. The backscatter process is studied through a modified Rayleigh-Plesset equation. Results show that the rectangular wave is effective in improving the visibility of microbubbles with ultrasound backscattered efficiency significantly higher than the widely used Gaussian waveform. Use of rectangular pulses with 4 and 2 harmonics showed no significant difference in bubble backscatter behavior, indicating that a two-frequency excitation may be sufficient to induce non-linear behavior of the microbubbles practically at modest incident pressures.