Drake A. Guenther

Optimal apodization design for medical ultrasound using constrained least squares part I: theory

Aperture weighting functions are critical design parameters in the development of ultrasound systems because beam characteristics affect the contrast and point resolution of the final output image. In previous work by our group, we developed a metric that quantifies a broadband imaging systems contrast resolution performance. We now use this metric to formulate a novel general ultrasound beamformer design method. In our algorithm, we use constrained least squares (CLS) techniques and a linear algebra formulation to describe the system point spread function (PSF) as a function of the aperture weightings. In one approach, we minimize the energy of the PSF outside a certain boundary and impose a linear constraint on the aperture weights. In a second approach, we minimize the energy of the PSF outside a certain boundary while imposing a quadratic constraint on the energy of the PSF inside the boundary. We present detailed analysis for an arbitrary ultrasound imaging system and discuss several possible applications of the CLS techniques, such as designing aperture weightings to maximize contrast resolution and improve the system depth of field

Optimal apodization design for medical ultrasound using constrained least squares part II simulation results

For Part I see ibid., vol. 54, p. 332-342 (2007). In the first part of this work, we introduced a novel general ultrasound apodization design method using constrained least squares (CLS). The technique allows for the design of system spatial impulse responses with narrow mainlobes and low sidelobes. In the linear constrained least squares (LCLS) formulation, the energy of the point spread function (PSF) outside a certain mainlobe boundary was minimized while maintaining a peak gain at the focus. In the quadratic constrained least squares (QCLS) formulation, the energy of the PSF outside a certain boundary was minimized, and the energy of the PSF inside the boundary was held constant. In this paper, we present simulation results that demonstrate the application of the CLS methods to obtain optimal system responses. We investigate the stability of the CLS apodization design methods with respect to errors in the assumed wave propagation speed. We also present simulation results that implement the CLS design techniques to improve cystic resolution. According to novel performance metrics, our apodization profiles improve cystic resolution by 3 dB to 10 dB over conventional apodizations such as the Hat, Hamming, and Nuttall windows. We also show results using the CLS techniques to improve conventional depth of field (DOF)

A spline-based approach for computing spatial impulse responses

Computer simulations are an essential tool for the design of phased-array ultrasonic imaging systems. FIELD II, which determines the two-way temporal response of a transducer at a point in space, is the current de facto standard for ultrasound simulation tools. However, the need often arises to obtain two-way spatial responses at a single point in time, a set of dimensions for which FIELD II is not well optimized. This paper describes an analytical approach for computing the two-way, far-field, spatial impulse response from rectangular transducer elements under arbitrary excitation. The described approach determines the response as the sum of polynomial functions, making computational implementation quite straightforward. The proposed algorithm, named DELFI, was implemented as a C routine under Matlab and results were compared to those obtained under similar conditions from the well-established FIELD II program. Under the specific conditions tested here, the proposed algorithm was approximately 142 times faster than FIELD II for computing spatial sensitivity functions with similar amounts of error. For temporal sensitivity functions with similar amounts of error, the proposed algorithm was about 1.7 times slower than FIELD II using rectangular elements and 19.2 times faster than FIELD II using triangular elements. DELFI is shown to be an attractive complement to FIELD II, especially when spatial responses are needed at a specific point in time

Robust finite impulse response beamforming applied to medical ultrasound

We previously described a beamformer architecture that replaces the single apodization weights on each receive channel with channel-unique finite impulse response (FIR) filters. The filter weights are designed to optimize the contrast resolution performance of the imaging system. Although the FIR beamformer offers significant gains in contrast resolution, the beamformer suffers from low sensitivity, and its performance rapidly degrades in the presence of noise. In this paper, a new method is presented to improve the robustness of the FIR beamformer to electronic noise as well as variation or uncertainty in the array response. A method is also described that controls the sidelobe levels of the FIR beamformers spatial response by applying an arbitrary weighting function in the filter design algorithm. The robust FIR beamformer is analyzed using a generalized cystic resolution metric that quantifies a beamformers clinical imaging performance as a function of cyst size and channel input SNR. Fundamental performance limits are compared between 2 robust FIR beamformers the dynamic focus FIR (DF-FIR) beamformer and the group focus FIR (GF-FIR) beamformer-the conventional delay-and-sum (DAS) beamformer, and the spatial-matched filter (SMF) beamformer. Results from this study show that the new DF- and GF-FIR beamformers are more robust to electronic noise compared with the optimal contrast resolution FIR beamformer. Furthermore, the added robustness comes with only a slight loss in cystic resolution. Results from the generalized cystic resolution metric show that a 9-tap robust FIR beamformer outperforms the SMF and DAS beamformer until receive channel input SNR drops below -5 dB, whereas the 9-tap optimal contrast resolution beamformers performance deteriorates around 50 dB SNR. The effects of moderate phase aberrations, characterized by an a priori root-mean-square strength of 28 ns and an a priori full-width at half-maximum correlation length of 3.6 mm, are investigated on the robust FIR beamformers. Full sets of robust FIR beamformer filter weights are constructed using an in silico model scanner and the L14-5/38 mm probe. Using the derived weights, a series of simulated point target and anechoic cyst B-mode images are generated to investigate further the potential increases in contrast resolution when using the robust FIR beamformers. Under the investigated conditions, the 7-tap optimal contrast resolution beamformer and the 7-tap robust beamformer with added SNR constraint increase lesion detectability by 247 and 137% compared with the conventional DAS beamformer, respectively. Finally, experimental phantom and in vivo images are produced using this novel receive architecture. The simulated and experimental images clearly show a reduction in clutter and an increase in contrast resolution compared with the conventionally beamformed images. This novel receive beamformer can be applied to any conventional ultrasound system where the system response is reasonably well characterized.

Generalized cystic resolution: a metric for assessing the fundamental limits on beamformer performance

Existing methods for characterizing the imaging performance of ultrasound systems do not clearly quantify the impact of contrast, spatial resolution, and signal-to-noise ratio (SNR). Although the beamplot, contrast resolution metrics, SNR measurements, ideal observer methods, and contrast-detail analysis provide useful information, it remains difficult to discern how changes in system parameters affect these metrics and clinical imaging performance. In this paper, we present a rigorous methodology for characterizing the pulse-echo imaging performance of arbitrary ultrasound systems. Our metric incorporates the 4-D spatio-temporal system response, which is defined as a function of the individual beamformer channel weights. The metric also incorporates the individual beamformer channel electronic SNR. Whereas earlier performance measures dealt solely with contrast resolution or echo signal-to-noise ratio, our metric combines them so that tradeoffs between these parameters are easily distinguishable. The new metric quantifies an arbitrary systems contrast resolution and SNR performance as a function of cyst size, beamformer channel weights, and beamformer channel SNR. We present a theoretical derivation of the unified performance metric and provide simulation and experimental results highlighting the metrics utility. We compare the fundamental performance limits of 2 beamforming strategies: the dynamic focus finite impulse response (FIR) filter beamformer and the spatial matched filter (SMF) beamformer to the performance of the conventional delay-and-sum (DAS) beamformer. Results from this study show that the SMF beamformer and the FIR beamformer offer significant gains in beamformer SNR and contrast resolution compared with the DAS beamformer, respectively. The metric clearly distinguishes the performance of the SMF beamformer, which enhances system sensitivity, from the FIR beamformer, which optimizes system contrast resolution. Finally, the metric provides one quantitative goal for optimizing a broadband beamformers contrast resolution performance.

P1A-6 A Novel Spline-Based Algorithm for Multidimensional Displacement and Strain Estimation

In medical ultrasound, motion estimation is used to align images in extended field of view applications, estimate blood or tissue motion, and estimate radiation force or mechanically induced displacements for elasticity imaging. In all of these applications the sampled nature of real-world images makes precise estimation of sub-sample displacements computationally costly at best, and impossible at worst. In this paper we describe a novel MUlti-dimensional Spline-based motion Estimator (MUSE). We performed simulations and experiments to assess the intrinsic bias and standard deviation of this algorithm for speckle kernels 4 samples wide and 16 samples deep. In 1000 noise-free simulations we found that MUSE exhibits maximum bias errors of 0.002 and 0.0003 samples (0.040 mum and 0.045 mum) in range and azimuth respectively. The maximum simulated standard deviation of estimates in both dimensions was comparable at 0.0026 samples (0.05 mum in range and 0.78 mum in azimuth). 25,600 motion estimates were also performed using experimental data acquired using an Ultrasonix Sonix RP imaging system with a L14-5/38 linear array transducer operated at 6.6 MHz. With this experimental data we found that bias errors were apparently significantly smaller than geometric errors induced by machining of the transducer mount. These simulated and experimental results significantly outperform other published algorithms. Straightforward extension to include companding and shear estimation make this algorithm particularly attractive for tissue elasticity imaging applications

A method for accurate in silico modeling of ultrasound transducer arrays.

This paper presents a new approach to improve the in silico modeling of ultrasound transducer arrays. While current simulation tools accurately predict the theoretical element spatio-temporal pressure response, transducers do not always behave as theorized. In practice, using the probes physical dimensions and published specifications in silico, often results in unsatisfactory agreement between simulation and experiment. We describe a general optimization procedure used to maximize the correlation between the observed and simulated spatio-temporal response of a pulsed single element in a commercial ultrasound probe. A linear systems approach is employed to model element angular sensitivity, lens effects, and diffraction phenomena. A numerical deconvolution method is described to characterize the intrinsic electro-mechanical impulse response of the element. Once the response of the element and optimal element characteristics are known, prediction of the pressure response for arbitrary apertures and excitation signals is performed through direct convolution using available tools. We achieve a correlation of 0.846 between the experimental emitted waveform and simulated waveform when using the probes physical specifications in silico. A far superior correlation of 0.988 is achieved when using the optimized in silico model. Electronic noise appears to be the main effect preventing the realization of higher correlation coefficients. More accurate in silico modeling will improve the evaluation and design of ultrasound transducers as well as aid in the development of sophisticated beamforming strategies.

Receive channel FIR filters for enhanced contrast in medical ultrasound

Aperture weighting functions are critical design parameters in the development of ultrasound systems because beam characteristics determine the contrast and point resolution of the final image. In previous work by our group, we developed a general apodization design method that optimizes a broadband imaging systems contrast resolution performance [1, 2]. In that algorithm we used constrained least squares (CLS) techniques and a linear algebra formulation of the system point spread function (PSF) as a function of the scalar aperture weights. In this work we replace the receive aperture weights with individual channel finite impulse response (FIR) filters to produce PSFs with narrower mainlobe widths and lower sidelobe levels compared to PSFs produced with conventional apodization functions. Our approach minimizes the energy of the PSF outside a defined boundary while imposing a quadratic constraint on the energy of the PSF inside the boundary. We present simulation results showing that FIR filters of modest tap lengths (3-7) can yield marked improvement in image contrast and point resolution. Specifically we show results that 7-tap FIR filters can reduce sidelobe and grating lobe energy by 30dB and improve cystic contrast [3] by as much as 20dB compared to conventional apodization profiles. We also show experimental results where multi-tap FIR filters decrease sidelobe energy in the resulting 2D PSF and maintain a narrow mainlobe. Our algorithm has the potential to significantly improve ultrasound beamforming in any application where the system response is well characterized. Furthermore, this algorithm can be used to increase contrast and resolution in novel receive only beamforming systems [4, 5].

Synthetic aperture angular scatter imaging: system refinement

Angular scatter imaging has been proposed as a new source of image contrast in medical ultrasound and as a parameter for tissue characterization. We describe a new method that combines the translating apertures algorithm (TAA) with synthetic aperture methods to coherently obtain angular scatter information with high resolution in both space and scattering angle. This method, which we term synthetic aperture angular scatter (SAAS) imaging effectively applies the TAA to single array elements and then focuses the data synthetically to form high resolution images at precisely defined scattering angles. In this paper, we present experimental results implementing SAAS to form angular scatter images of a 5-wire depth of field phantom, a tissue mimicking 3-wire phantom, and in vivo human thyroid. We discuss the degree of uniformity necessary in element response for successful SAAS imaging. These experiments show new image information previously unavailable in conventional B-mode images and suggest that angular scatter imaging may have applications in the breast, thyroid, and peripheral vasculature.

Ultrasonic synthetic aperture angular scatter imaging

Conventional coherent imaging systems map the energy which is reflected directly back towards the transducer. While extremely useful, these systems fail to utilize information in the energy field which has been scattered at other angles. Angular scatter imaging attempts to form images from the scattered energy field at angles other than the 180/spl deg/ backscattered path. We propose a synthetic aperture based imaging scheme for acquiring angular scatter data in medical ultrasound. We describe this technique in k-space and provide an intuitive explanation of the imaging systems behavior. This method, which we term Synthetic Aperture Angular Scatter (SAAS) imaging effectively uses single element geometries to acquire data at a range of scattering angles. In this paper, we present experimental results implementing SAAS on a GE Logiq 700MR system. We applied the SAAS method to form angular scatter images of a 5-wire depth of field (DOF) phantom and a tissue mimicking 3-wire phantom (steel, nylon and cotton). We present results from this data and discuss the degree of uniformity necessary in element response for successful SAAS imaging. Results from these experiments show new image information previously unavailable in conventional B-mode images and suggest that angular scatter imaging may have applications in the breast, thyroid and peripheral vasculature.