FAMUS II: A Fast and Mechanistic Ultrasound Simulator Using an Impulse Response Approach.

Real-time simulation of ultrasound images is increasingly important for providing a means of presenting a wide variety of clinical images for the training of ultrasound specialists and technologists. In order to realistically represent the visual effects caused by changes to the transducer position or its focal properties, very rapid transducer field response calculations are needed, typically on the order of a fraction of a second. Currently available methods are severely limited in this regard. Based on the impulse response, a point source/receiver method for accurately calculating the fields produced by ultrasound transducer arrays is proposed and illustrated with realistic B-mode and Doppler spectral display simulations. The results of this method (FAMUS II), which accounts for the attenuation frequency dependence of the propagating medium, are compared with those obtained with Field II both in terms of quality and computational speed. From a clinical simulation perspective, the qualitative differences are small. Because the method is inherently parallelizable, significant gains in computational speed can be achieved. For example, in B-mode imaging using an eight-core CPU, FAMUS II is shown to be more than two orders of magnitude faster than that achieved by Field II. As a result, we believe that this new method represents a significant step toward achieving real-time performance.

A perfectly matched layer formulation for modeling transient wave propagation in an unbounded fluid-solid medium.

Wave propagation in an infinite medium can be numerically simulated by surrounding a finite region by a perfectly matched layer (PML). When the medium is heterogeneous consisting of both solids and liquids, careful consideration is needed in specifying the properties of the PML especially because parts of it lie at the solid-fluid interface. While such a situation could arise in many important fields including marine seismology, where water is in contact with earth, and in biomedical ultrasound, where soft tissue is in contact with bone, no PML formulation exists to appropriately model such coupled problems. Here, a second-order time-domain PML formulation for fluid-solid heterogeneous media in two dimensions that satisfies the interface coupling boundary condition throughout the computational domain is presented. Numerical results are given to establish the applicability and accuracy of such a PML formulation in discrete settings without causing stability issues, spurious reflections, or any other problems. In particular, the effectiveness of the PML in absorbing all kinds of bulk waves, as well as surface and evanescent waves, is studied.

Accelerated Compressed Sensing Based CT Image Reconstruction.

In X-ray computed tomography (CT) an important objective is to reduce the radiation dose without significantly degrading the image quality. Compressed sensing (CS) enables the radiation dose to be reduced by producing diagnostic images from a limited number of projections. However, conventional CS-based algorithms are computationally intensive and time-consuming. We propose a new algorithm that accelerates the CS-based reconstruction by using a fast pseudopolar Fourier based Radon transform and rebinning the diverging fan beams to parallel beams. The reconstruction process is analyzed using a maximum-a-posterior approach, which is transformed into a weighted CS problem. The weights involved in the proposed model are calculated based on the statistical characteristics of the reconstruction process, which is formulated in terms of the measurement noise and rebinning interpolation error. Therefore, the proposed method not only accelerates the reconstruction, but also removes the rebinning and interpolation errors. Simulation results are shown for phantoms and a patient. For example, a 512 × 512 Shepp-Logan phantom when reconstructed from 128 rebinned projections using a conventional CS method had 10% error, whereas with the proposed method the reconstruction error was less than 1%. Moreover, computation times of less than 30 sec were obtained using a standard desktop computer without numerical optimization.

Adaptively Tuned Iterative Low Dose CT Image Denoising.

Improving image quality is a critical objective in low dose computed tomography (CT) imaging and is the primary focus of CT image denoising. State-of-the-art CT denoising algorithms are mainly based on iterative minimization of an objective function, in which the performance is controlled by regularization parameters. To achieve the best results, these should be chosen carefully. However, the parameter selection is typically performed in an ad hoc manner, which can cause the algorithms to converge slowly or become trapped in a local minimum. To overcome these issues a noise confidence region evaluation (NCRE) method is used, which evaluates the denoising residuals iteratively and compares their statistics with those produced by additive noise. It then updates the parameters at the end of each iteration to achieve a better match to the noise statistics. By combining NCRE with the fundamentals of block matching and 3D filtering (BM3D) approach, a new iterative CT image denoising method is proposed. It is shown that this new denoising method improves the BM3D performance in terms of both the mean square error and a structural similarity index. Moreover, simulations and patient results show that this method preserves the clinically important details of low dose CT images together with a substantial noise reduction.

On estimating the directionality distribution in pedicle trabecular bone from micro-CT images.

Our interest in the trabecular alignment within bone stems from the need to better understand the manner in which it can affect ultrasound propagation, particularly in pedicles. Within long bones it is well established that trabecular structures are aligned in an organized manner associated with the direction of load distribution; however, for smaller bones there are limited alignment studies. To investigate the directionality distribution in a quantitative manner we used a micro-CT to obtain three-dimensional (3D) structural data and developed analytical methods based on the special properties of Gabor filters. Implementation of these techniques has been developed and tested on a variety of simulated images as well as on 3D structures whose geometry is well-defined. To test the use of this technique we compared the results obtained on vertebral body trabecular bone with visual directionality and previous measurements by others. The method has been applied to six human pedicle samples in two orthogonal planes with results that provide reasonable proof-of-principle evidence that the method is well suited for estimating the directionality distribution within pedicle bones.

Optimal image reconstruction for detection and characterization of small pulmonary nodules during low-dose CT.

OBJECTIVES: To optimize the slice thickness/overlap parameters for image reconstruction and to study the effect of iterative reconstruction (IR) on detectability and characterization of small non-calcified pulmonary nodules during low-dose thoracic CT. MATERIALS AND METHODS: Data was obtained from computer simulations, phantom, and patient CTs. Simulations and phantom CTs were performed with 9 nodules (5, 8, and 10 mm with 100, -630, and -800 HU). Patient data were based on 11 ground glass opacities (GGO) and 9 solid nodules. For each analysis the nodules were reconstructed with filtered back projection and IR algorithms using 10 different combinations of slice thickness/overlap (0.5-5 mm). The attenuation (CT#) and the contrast to noise ratio (CNR) were measured. Spearman's coefficient was used to correlate the error in CT# measurements and slice thickness. Paired Student's t test was used to measure the significance of the errors. RESULTS: CNR measurements: CNR increases with increasing slice thickness/overlap for large nodules and peaks at 4.0/2.0 mm for smaller ones. Use of IR increases the CNR of GGOs by 60 %. CT# measurements: Increasing slice thickness/overlap above 3.0/1.5 mm results in decreased CT# measurement accuracy. CONCLUSION: Optimal detection of small pulmonary nodules requires slice thickness/overlap of 4.0/2.0 mm. Slice thickness/overlap of 2.0/2.0 mm is required for optimal nodule characterization. IR improves conspicuity of small ground glass nodules through a significant increase in nodule CNR. KEY POINTS: • Slice thickness/overlap affects the accuracy of pulmonary nodule detection and characterization. • Slice thickness ≥3 mm increases the risk of misclassifying small nodules. • Optimal nodule detection during low-dose CT requires 4.0/2.0-mm reconstructions. • Optimal nodule characterization during low-dose CT requires 2.0/2.0-mm reconstructions. • Iterative reconstruction improves the CNR of ground glass nodules by 60 %.

Guided pedicle screw insertion: techniques and training.

BACKGROUND CONTEXT: In spinal fusion surgery, the accuracy with which screws are inserted in the pedicle has a direct effect on the surgical outcome. Accurate placement generally involves considerable judgmental skills that have been developed through a lengthy training process. Because the impact of misaligning one or more pedicle screws can directly affect patient safety, a number of navigational and trajectory verification approaches have been described and evaluated in the literature to provide some degree of guidance to the surgeon. PURPOSE: To provide a concise review to justify the need and explore the current state of developing navigational or trajectory verification techniques for ensuring proper pedicle screw insertion along with simulation methods for better educating the surgical trainees. STUDY DESIGN: Recent literature review. METHODS: To justify the need to develop new methods for optimizing pedicle screw paths, we first reviewed some of the recent publications relating to the statistical outcomes for different types of navigation along with the conventional freehand (unassisted) screw insertion. Second, because of the importance of providing improved training in the skill of accurate screw insertion, the training aspects of relevant techniques are considered. The third part is devoted to the description of specific navigational assist methods or trajectory verification techniques and these include computer-assisted navigation, three-dimensional simulations, and also electric impedance and optical and ultrasonic image-guided methods. CONCLUSIONS: This article presents an overview of the need and the current status of the guidance methods available for improving the surgical outcomes in spinal fusion procedures. It also describes educational aids that have the potential for reducing the training process.

Non-local total variation based low-dose Computed Tomography denoising.

Radiation dose of X-ray Computed Tomography (CT) imaging has raised a worldwide health concern. Therefore, low-dose CT imaging has been of a huge interest in the last decade. However, lowering the radiation dose degrades the image quality by increasing the noise level, which may reduce the diagnostic performance of the images. As a result, image denoising is one of the fundamental tasks in low-dose CT imaging. One of the state of art denoising methods, which has been successfully used in this area, is Total Variation (TV) denoising. Nevertheless, if the parameters of the TV denoising are not optimally adjusted or the algorithm is not stopped in an appropriate point, some of the small structures will be removed by this method. Here, we provide a solution to this problem by proposing a modified nonlocal TV method, called probabilistic NLTV (PNLTV). Denoising performance of PNLTV is improved by using better weights and an appropriate stopping criterion based on statistics of image wavelet coefficients. Non-locality allows the algorithm to preserve the image texture, which combined with the proposed stopping criterion enables PNLTV to keep fine details unchanged.

Fast and mechanistic ultrasound simulation using a point source/receiver approach.

Ultrasound simulators relying on impulse response methods are faithful to the mechanisms of image formation from the underlying radio-frequency signals, but as a result tend to be relatively slow. At the other extreme are fast techniques, often motivated by the development of teaching and training simulators, which approximate the image formation processes rather than rigorously modeling the underlying physics. Previously, we have shown that transmit field distributions from linear phased-array transducers can be modeled accurately and efficiently using arrays of point sources. This approach is now extended to point sources/receivers, which allows for simulation of the transmit/receive fields, and thus the physical processes underlying ultrasound image formation. Field distributions and fast-time signals are shown to compare favorably to those obtained using the impulse response method. Doppler spectrogram and B-mode images derived from these signals also show excellent agreement with the results obtained using the impulse response method, but with a computational savings of nearly two orders of magnitude. Because of the inherent simplicity of our Fast and Mechanistic Ultrasound Simulation (FAMUS) approach, CPU parallelization was readily achieved, and further orders of magnitude speed improvements, and thus real-time performance, can be anticipated via extension to modern graphics processing units.

Estimating the local viscoelastic properties from dispersive shear waves using time-frequency ridge analysis.

Modulated low-frequency shear waves can be non-invasively generated locally within a medium, by the oscillatory acoustic radiation force resulting from the interference of two focused quasi-CW ultrasound beams of slightly different frequencies. The propagation of such shear waves within a viscoelastic medium is known to be affected by the dispersive effects of viscosity. Specifically, a low-frequency (LF) spectral component was shown to arise with increased viscosities and higher modulation frequencies and appear as a 'slow' wave at the end of the shear waveform. In this paper, the shear dispersion characteristics are studied based on the Pseudo-Wigner-Ville distribution (PWVD) in the time-frequency domain. The ridges of the PWVD are then extracted and used to calculate the frequency-dependent shear speed, by identifying the LF dispersive component both in time and frequency. Using numerical simulations, it is shown that this way of estimating the shear dispersion is more efficient and robust than the conventional phase-delay Fourier method. Thus, more accurate estimates of the local shear modulus and viscosity of the propagating medium could be achieved. The effects of noise on the proposed method are also discussed.

Target detection in diagnostic ultrasound: Evaluation of a method based on the CLEAN algorithm.

A technique is proposed for the detection of abnormalities (targets) in ultrasound images using little or no a priori information and requiring little operator intervention. The scheme is a combination of the CLEAN algorithm, originally proposed for radio astronomy, and constant false alarm rate (CFAR) processing, as developed for use in radar systems. The CLEAN algorithm identifies areas in the ultrasound image that stand out above a threshold in relation to the background; CFAR techniques allow for an adaptive, semi-automated, selection of the threshold. Neither appears to have been previously used for target detection in ultrasound images and never together in any context. As a first step towards assessing the potential of this method we used a widely used method of simulating B-mode images (Field II). We assumed the use of a 256 element linear array operating at 3.0MHz into a water-like medium containing a density of point scatterers sufficient to simulate a background of fully developed speckle. Spherical targets with diameters ranging from 0.25 to 6.0mm and contrasts ranging from 0 to 12dB relative to the background were used as test objects. Using a contrast-detail analysis, the probability of detection curves indicate these targets can be consistently detected within a speckle background. Our results indicate that the method has considerable promise for the semi-automated detection of abnormalities with diameters greater than a few millimeters, depending on the contrast.

An accurate analysis of the radiation characteristics of a plane piston transducer with phase apodization for focusing.

A plane piston transducer can be focused by a continuous variation of the excitation signal phase (or time delay) over the transducer surface. Prior analyses of this scheme used the Fresnel approximation, thereby limiting the validity. Using the angular spectrum method, an accurate radiation model of such a transducer has been developed that includes amplitude and phase apodization. The derivation includes the effects of diffraction and evanescent waves without using the Fresnel approximation. Moreover, this model develops insights into radiated field characteristics, including: (a) the spatial frequency bandwidth is constant over axial depth, suggesting that spatial resolution can be improved away from the focus; (b) the phase of the angular spectrum determines the spatial resolution for a given transducer configuration-a constant phase is optimal on any observation plane; (c) focusing can significantly increase the spatial frequency bandwidth; (d) the velocity potential on a plane parallel to the transducer is the Hankel convolution of the transducer surface velocity with the Green's function; and (e) evanescent waves decay both with increasing spatial frequency and axial depth. The analytical model and associated insights enhance understanding of the radiated field characteristics, which can be of value in the development of signal processing techniques for image enhancement.

Slow and fast ultrasonic wave detection improvement in human trabecular bones using Golay code modulation.

The identification of fast and slow waves propagating through trabecular bone is a challenging task due to temporal wave overlap combined with the high attenuation of the fast wave in the presence of noise. However, it can provide valuable information about bone integrity and become a means for monitoring osteoporosis. The objective of this work is to apply different coded excitation methods for this purpose. The results for single-sine cycle pulse, Golay code, and chirp excitations are compared. It is shown that Golay code is superior to the other techniques due to its signal enhancement while exhibiting excellent resolution without the ambiguity of sidelobes.

Focused, phased-array plane piston and spherically-shaped concave piston transducers: comparison for the same aperture and focal point.

It has sometimes been assumed that the phased-array plane piston transducer and the spherically-shaped concave piston transducer are equivalent structures when both have the same aperture and focal point. This assumption has not been previously examined, nor has an expression for the on-axis impulse response of the focused, phased-array plane piston transducer been derived. It is shown in this paper how such an expression can be obtained. Comparisons of the impulse response for both structures show similarities, as well as some differences that could be significant as the observation point approaches the focal point. Comparisons are also performed for wide-band pulses close to the focus as well as for sinusoidal excitation. A physical explanation for the cause of the impulse response discrepancy is shown to be due to the nature of the piston focusing delay and its effect on the Rayleigh integral.

On ultrasound imaging for guided screw insertion in spinal fusion surgery.

Spinal fusion surgery generally involves the insertion of screws in the pedicle, a three-dimensional (3-D) process that requires great skill if serious consequences are to be avoided. This article describes an image guidance technique based on generating B­mode images from within a small bore hole in the pedicle's trabecular bone. The purpose is to determine the viability and safety of the hole placement for subsequent insertion of the screw. Toward this end, this article endeavours to understand the factors that govern B-mode image quality. Specifically, the results of numerical simulations on the effects of transducer frequency and bone volume on image quality are presented along with demonstrations of B-mode image formation obtained in vitro on human pedicles using a 3.2 MHz probe. The results of the numerical simulations suggest that high frequency and high bone volume generally reduce the image quality. The in vitro experiments showed that the trabecular and cortical bone can be detected in the B-mode images.

Mapping the local shear modulus and viscosity using a transient finite-amplitude modulated radiation force.

Localized narrowband low-frequency shear waves can be non-invasively generated within tissue, by a modulated finite-amplitude radiation force, resulting from the interference of two focused quasi-CW ultrasound beams of slightly different frequencies. Assuming a Voigt viscoelastic model, this paper describes the use of a finite-element-method model, to simulate two-dimensional shear-wave propagation in viscoelastic media, containing circular inclusions (lesions). Using this model, an inverse approach is used to extract maps of the local shear modulus and viscosity. The performance is evaluated based on three metrics: the lesion contrast, the contrast-transfer-efficiency (CTE), and the contrast-to-noise ratio (CNR). Modified definitions of these metrics are proposed and used in order to account for the time-varying nature of the shear waves and the inverse reconstruction algorithm. In the absence of any noise, it is shown that accurate reconstruction can be achieved not only with the fundamental, but also with the higher harmonics, as well as, with a low-frequency component that occurs for high viscosity and high modulation frequencies. For low-viscosity conditions, the lesion contrast, CTE, and CNR are shown to exhibit very good performance not only for the fundamental, but also, for the higher harmonics. In the case of increased viscosities and modulation frequencies, the generated low-frequency component is shown to provide superior contrast performance even when compared to that of the fundamental. The effects of noise on the reconstruction quality are examined. Depending on the lesion and background properties, it is shown that noise can seriously degrade reconstruction from the higher harmonics.

On the synthesis of sample volumes for real-time spectral Doppler ultrasound simulation.

A variety of methods for simulating the ultrasound field produced by transducers are currently used in ultrasound imaging system design. However, simulations can be time-consuming, making them difficult to apply in real-time environments when the observation field changes rapidly with time. This is particularly true for interactive real-time Doppler and B-mode ultrasound simulators designed for use as training tools. In this paper, it is demonstrated that the use of a distribution of monopole sources can be used to simulate the field from a phased linear array and the accuracy should be sufficient for simulating pulsed spectral Doppler. Very good agreement can be achieved in comparison with that obtained by a more exact method and, because of the simplicity of the calculations, real-time simulations of flow in the arterial system becomes possible. Specifically, quantitative measurements were made and compared against an analytic solution for the case of a piston transducer and against Field II for the phased array. The root-mean-square error shows that it is possible to achieve 10% or less error for the latter case. For comparable conditions, the computational speed for the transmit field of phased array using the Field II method as compared with the monopole approach was found to be at least an order of magnitude faster. It is pointed out that the simplicity of the monopole approach provides the opportunity for a further order of magnitude gain. Our findings can have direct application on the simulation of spectral Doppler and other ultrasound techniques for the purpose of teaching and training.

Propagation of shear waves generated by a modulated finite amplitude radiation force in a viscoelastic medium.

An effective way to generate localized narrowband low-frequency shear waves within tissue noninvasively, is by the modulated radiation force, resulting from the interference of two confocal quasi-CW ultrasound beams of slightly different frequencies. By using approximate viscoelastic Green's functions, investigations of the properties of the propagated shear-field component at the fundamental modulation frequency were previously reported by our group. However, high-amplitude source excitations may be needed to increase the signal-to-noise-ratio for shear-wave detection in tissue. This paper reports a study of the generation and propagation of dynamic radiation force components at harmonics of the modulation frequency for conditions that generally correspond to diagnostic safety standards. We describe the propagation characteristics of the resulting harmonic shear waves and discuss how they depend on the parameters of nonlinearity, focusing gain, and absorption. For conditions of high viscosity (believed to be characteristic of soft tissue) and higher modulation frequencies, the approximate shear wave Green's function is inappropriate. A more exact viscoelastic Green's function is derived in k-space, and using this, it is shown that the lowpass and dispersive effects, associated with a Voigt model of tissue, are more accurately represented. Finally, it is shown how the viscoelastic properties of the propagating medium can be estimated, based on several spectral components of the shearwave spectrum.

Development of a method for ultrasound-guided placement of pedicle screws.

Abstract-Many forms of spinal fusion involve the placement of long screws through the pedicles into the vertebral body. During the procedure, there is substantial risk of damage to vital neural and vascular structures due to the limited visibility of anatomic landmarks and high anatomic variability. As an alternative to current guidance systems, we have investigated the feasibility of performing ultrasound imaging through cancellous bone for the purpose of pedicle screw guidance. Quantitative ultrasonic characterization and A-mode imaging of seven defatted vertebral cancellous bone specimens was performed along the craniocaudal axis in water with unfocused, 1-MHz and 3.5- MHz broadband transducers. The center frequency attenuation increased considerably from 10.5 +/- 4.6 dB/cm at 1 MHz to 24.1 +/- 7.2 dB/cm at 3.5 MHz, while the speed of sound exhibited moderate positive dispersion, increasing from 1489 +/- 4.7 m/s at 1 MHz to 1494 +/- 4.2 m/s at 3.5 MHz. Despite the high attenuation and large specimen thickness (1.0-1.9 cm), A-mode imaging through cancellous bone to detect an aluminum reflector was possible in 83.2% and 70.1% of the cases at 1 MHz and 3.5 MHz, respectively. Specimen boundaries were identifiable with clinically sufficient average accuracy of 1.1 mm and 0.9 mm in the 1 MHz and 3.5 MHz A-mode images, respectively.

Single-ensemble-based eigen-processing methods for color flow imaging--Part I. The Hankel-SVD filter.

Because of their adaptability to the slow-time signal contents, eigen-based filters have shown potential in improving the flow detection performance of color flow images. This paper proposes a new eigen-based filter called the Hankel-SVD filter that is intended to process each slowtime ensemble individually. The new filter is derived using the notion of principal Hankel component analysis, and it achieves clutter suppression by retaining only the principal components whose order is greater than the clutter eigen-space dimension estimated from a frequency based analysis algorithm. To assess its efficacy, the Hankel-SVD filter was first applied to synthetic slow-time data (ensemble size: 10) simulated from two different sets of flow parameters that model: 1) arterial imaging (blood velocity: 0 to 38.5 cm/s, tissue motion: up to 2 mm/s, transmit frequency: 5 MHz, pulse repetition period: 0.4 ms) and 2) deep vessel imaging (blood velocity: 0 to 19.2 cm/s, tissue motion: up to 2 cm/s, transmit frequency: 2 MHz, pulse repetition period: 2.0 ms). In the simulation analysis, the post-filter clutter-to- blood signal ratio (CBR) was computed as a function of blood velocity. Results show that for the same effective stopband size (50 Hz), the Hankel-SVD filter has a narrower transition region in the post-filter CBR curve than that of another type of adaptive filter called the clutter-downmixing filter. The practical efficacy of the proposed filter was tested by application to in vivo color flow data obtained from the human carotid arteries (transmit frequency: 4 MHz, pulse repetition period: 0.333 ms, ensemble size: 10). The resulting power images show that the Hankel-SVD filter can better distinguish between blood and moving-tissue regions (about 9 dB separation in power) than the clutter-downmixing filter and a fixed-rank multi ensemble-based eigen-filter (which showed a 2 to 3 dB separation).