k-Wave Toolbox Research Articles

Numerical investigation of the number of excitation elements-dependent acoustic field characteristics of a histotripter

Abstract Histotripsy is an emerging ultrasound technology for disintegrating various soft tissues noninvasively and accureately. However, it is difficult to characterize the acoustic field of a histotripter using the existing measurement methods (i.e., hydrophones) because of the damage potential of bubble cavitation on the sensing element under such high irradiation power. In this work, according to a quantitative relationship between the acoustic pressure and ultrasonic focusing gain G, nonlinearity β, attenuation coefficient α, a numerical reconstruction method is proposed to accurately and reliably estimate the acoustic field of a histotripter. The k-Wave toolbox was used to calculate the acoustic field produced from identical sectors on a common concave surface by gradually increasing the number of excitation elements (i.e., up to 256 that cover the whole surface). The excitation frequency is 0.8 MHz, and the initial pressure at the transducer surface is 0.4 MPa. The focusing gains, peak positive and negative pressure, positive to negative peak acoustic pressure ratio, and harmonic distributions in the focal region under different numbers of excited elements were analysed. It is found that when about a quarter of the transducer surface is excited (64 elements), the nonlinear effect becomes obvious, resulting in significant peak pressures and harmonics. Furthermore, the relationship between the positive and negative pressure peaks (p + and p ¬) and the number of excited elements fits a quadratic curve function quite well (R = 0.999). Altogether, the proposed method can be applied to estimate the acoustic pressure at an extremely high intensity that exceeds the range of current measurement apparatus. Acoustic pressures using a low number of excited elements are measured first and then extrapolated to the full surface coverage using the built-in regression models. In the near future, the field calculation scheme for the therapeutic focused transducers with higher irradiation power and larger dimensions, as well as experimental work, will be done to further validate our model.

Treatment Planning and Aberration Correction Algorithm for HIFU Ablation of Renal Tumors.

High-intensity focused ultrasound (HIFU) applications for thermal or mechanical ablation of renal tumors often encounter challenges due to significant beam aberration and refraction caused by oblique beam incidence, inhomogeneous tissue layers, and presence of gas and bones within the beam. These losses can be significantly mitigated through sonication geometry planning, patient positioning, and aberration correction using multielement phased arrays. Here, a sonication planning algorithm is introduced, which uses the simulations to select the optimal transducer position and evaluate the effect of aberrations and acoustic field quality at the target region after aberration correction. Optimization of transducer positioning is implemented using a graphical user interface (GUI) to visualize a segmented 3-D computed tomography (CT)-based acoustic model of the body and to select sonication geometry through a combination of manual and automated approaches. An HIFU array (1.5 MHz, 256 elements) and three renal cell carcinoma (RCC) cases with different tumor locations and patient body habitus were considered. After array positioning, the correction of aberrations was performed using a combination of backpropagation from the focus with an ordinary least squares (OLS) optimization of phases at the array elements. The forward propagation was simulated using a combination of the Rayleigh integral and k-space pseudospectral method (k-Wave toolbox). After correction, simulated HIFU fields showed tight focusing and up to threefold higher maximum pressure within the target region. The addition of OLS optimization to the aberration correction method yielded up to 30% higher maximum pressure compared to the conventional backpropagation and up to 250% higher maximum pressure compared to the ray-tracing method, particularly in strongly distorted cases.

A static memory method for modelling time-fractional power law absorption

The attenuation of ultrasound propagation through tissue is known to follow a frequency power-law in the time domain. This can be modelled as a loss operator in the equation of state within the Euler equations that takes the form of a fraction time derivative operator. This can be treated through a second order accurate transfer between the fractional time derivative and a fractional Laplacian spacial operator in order to avoid storage of the full time history. This is used for example by the k-Wave toolbox. As an alternate finite history methods have been suggested. Building on recent work, here, we re-write the time fractional derivative as a finite sum using a recursion relation. This allows the time fractional derivative to be directly computed with a static memory requirement. For homogeneous media, the advantage of this over the fractional Laplacian methods may not initially be obvious with a base higher memory requirement and computational cost with only a small increase in accuracy. However, upon introducing a heterogeneous medium with regions of different power law attenuation; the increased computational cost of the time fractional method is contained exclusively within the pre-computation, while the increased cost for the fractional Laplacian is applied to each time step.

K-Wave II: Introduction, progress, and road map

k-Wave is an open-source toolbox for simulating the propagation of acoustic and ultrasound waves in complex and tissue-realistic media that is widely used across academia and industry. In this talk, we present an introduction to k-Wave II. k-Wave-II is a major re-write of the original k-Wave toolbox developed with the following aims: (1) re-engineering the code base to leverage object orientated programming, making it simpler to use for model inversions and coupled physics problems, (2) extending the algorithms to facilitate general boundary conditions on arbitrary surfaces, and to increase performance for narrow-band simulations, (3) improving the development and release process to incorporate good practice and advance long-term sustainability, and (4) improving training, user engagement, and support. We will introduce the new toolbox, discuss current progress, and a provide a road map for future development.

Self-image-guided ultrasonic transceiver design for reliably powering mm-sized implants

This paper presents the design of a self-image-guided ultrasonic (SIG-US) transceiver for reliable wireless power transmission (WPT) to miniaturized biomedical implants. In the receiver (RX) mode, this paper proposes a method for high precision time interval measurement (TIM) between two signals independent of their amplitudes. In the transmitter (TX) mode, a 15 V Class-DE driver by stacking 3.3 V transistors of 180 nm standard CMOS technology is designed to drive a 32-element linear array. The designed TX efficiency is 90.93%. The post-layout and the Matlab k-Wave toolbox simulation results show that the designed system is capable of transmitting power to the implant with less than 0.9% reduction compared to the ideal SIG-US system over the ±45° steering range. Considering the mismatch effect between transistors, the power reduction is less than 2% in the worst case. The RX with a power consumption of 628.83 μW from a nominal supply voltage of 1.8 V, is capable of detecting time delays between two signals over the input range of 1 mV to 10 mV, with high accuracy.

Window size analysis in ultrasonic temperature estimation with timeshifts

In this work, ultrasonic timeshift method for temperature change estimation was investigated for 2D simulated in-silico synthetic ultrasonic signals. Digital phantom tissue was created in MATLAB environment and acoustic simulation was running on k-Wave toolbox for two different temperature conditions. First temperature distribution was assigned to tissue as uniform 37 °C. Second temperature distribution is Gaussian form with peak at tissue center as 45 °C and tails of Gaussian curve is 37 °C. Signal was analyzed with ultrasonic timeshift method for temperature change estimation. This method is based on four steps, calibration with tissue constant, finding timeshift with cross correlation algorithm, find slope of timeshift vector respect to timestep, and multiply tissue constant and slope of local timeshift vector. This multiplication gives temperature change of local point. In this work, window size of smoothing filter of timeshift vector and linear fitting to timeshift—timestep data was analyzed as parametrically with range 3λ to 10λ with a 1λ increment for both windows equally. As a result, window parameters as 5λ to 7λ give best results, maximum absolute error is 0.82 °C, 0.97 °C and 0.92 °C respectively and mean absolute error is ∼0.35 °C. As a verify, different analysis was performed on different temperature distribution with discrete two peak curves.

Simulation study of protoacoustics as a real-time in-line dosimetry tool for FLASH proton therapy.

Applying ultra-high dose rates to radiation therapy, otherwise known as FLASH, has been shown to be just as effective while sparing more normal tissue compared to conventional radiation therapy. However, there is a need for a dosimeter that is able to detect such high instantaneous dose, particularly in vivo. To fulfill this need, protoacoustics is introduced, which is an in vivo range verification method with submillimeter accuracy. The purpose of this work is to demonstrate the feasibility of using protoacoustics as a method of in vivo real-time monitoring during FLASH proton therapy and investigating the resulting protoacoustic signal when dose per pulse and pulsewidth are varied through multiple simulation studies. The dose distribution of a proton pencil beam was calculated through a Monte Carlo toolbox, TOPAS. Next, the k-Wave toolbox in MATLAB was used for performing protoacoustic simulations, where the initial proton dose deposition was inputted to model acoustic propagations, which were also used for reconstructions. Simulations involving the manipulation of the dose per pulse and pulsewidth were performed, and the temporal and spatial resolution for protoacoustic reconstructions were investigated as well. A 3D reconstruction was performed with a multiple beam spot profile to investigate the spatial resolution as well as determine the feasibility of 3D imaging with protoacoustics. Our results showed consistent linearity in the increasing dose-per-pulse, even up to rates considered for FLASH. The simulations and reconstructions were performed for a range of pulsewidths from 0.1 to 10μs. The results show the characteristics of the proton beam after convolving the protoacoustic signal with the varying pulsewidths. 3D reconstruction was successfully performed with each beam being distinguishable using an 8cm×8cm planar array. These simulation results show that measurements using protoacoustics has the potential for in vivo dosimetry in FLASH therapy during patient treatments in real time. Through this simulation study, the use of protoacoustics in FLASH therapy was verified and explored through observations of varying parameters, such as the dose per pulse and pulsewidth. 2D and 3D reconstructions were also completed. This study shows the significance of using protoacoustics and provides necessary information, which can further be explored in clinical settings.

Transcranial Ultrasonic Focusing by a Phased Array Based on Micro-CT Images.

In this paper, we utilize micro-computed tomography (micro-CT) to obtain micro-CT images with a resolution of 60 μm and establish a micro-CT model based on the k-wave toolbox, which can visualize the microstructures in trabecular bone, including pores and bone layers. The transcranial ultrasound phased array focusing field characteristics in the micro-CT model are investigated. The ultrasonic waves are multiply scattered in skull and time delays calculations from the transducer to the focusing point are difficult. For this reason, we adopt the pulse compression method and the linear frequency modulation Barker code to compute the time delay and implement phased array focusing in the micro-CT model. It is shown by the simulation results that ultrasonic loss is mainly caused by scattering from the microstructures of the trabecular bone. The ratio of main and side lobes of the cross-correlation calculation is improved by 5.53 dB using the pulse compression method. The focusing quality and the calculation accuracy of time delay are improved. Meanwhile, the beamwidth at the focal point and the sound pressure amplitude decrease with the increase in the signal frequency. Focusing at different depths indicates that the beamwidth broadens with the increase in the focusing depth, and beam deflection focusing maintains good consistency in the focusing effect at a distance of 9 mm from the focal point. This indicates that the phased-array method has good focusing results and focus tunability in deep cranial brain. In addition, the sound pressure at the focal point can be increased by 8.2% through amplitude regulation, thereby enhancing focusing efficiency. The preliminary experiment verification is conducted with an ex vivo skull. It is shown by the experimental results that the phased array focusing method using pulse compression to calculate the time delay can significantly improve the sound field focusing effect and is a very effective transcranial ultrasound focusing method.

Hermite-scan imaging for differentiating glioblastoma from normal brain: Simulations and ex vivo studies for applications in intra-operative tumor identificationa).

Hermite-scan (H-scan) imaging is a tissue characterization technique based on the analysis of raw ultrasound radio frequency (RF) echoes. It matches the RF echoes to Gaussian-weighted Hermite polynomials of various orders to extract information related to scatterer diameter. It provides a color map of large and small scatterers in the red and blue H-scan image channels, respectively. H-scan has been previously reported for characterizing breast, pancreatic, and thyroid tumors. The present work evaluated H-scan imaging to differentiate glioblastoma tumors from normal brain tissue ex vivo. First, we conducted 2-D numerical simulations using the k-wave toolbox to assess the performance of parameters derived from H-scan images of acoustic scatterers (15-150 μm diameters) and concentrations (0.2%-1% w/v). We found that the parameter intensity-weighted percentage of red (IWPR) was sensitive to changes in scatterer diameters independent of concentration. Next, we assessed the feasibility of using the IWPR parameter for differentiating glioblastoma and normal brain tissues (n = 11 samples per group). The IWPR parameter estimates for normal tissue (44.1% ± 1.4%) were significantly different (p < 0.0001) from those for glioblastoma (36.2% ± 0.65%). These findings advance the development of H-scan imaging for potential use in differentiating glioblastoma tumors from normal brain tissue during resection surgery.

Adhesive Single-Lap Joint Evaluation Using Ultrasound Guided Waves

This work deals with the evaluation of adhesive single-lap joints using ultrasound guided waves; in particular, it is intended to characterize the signal propagation when defects are present in the adhesive joint by simulation and experimental approaches. The propagation of guided waves in the joint is developed from matrix formulations. The behavior of the guided wave modes that exist in the bonded region is characterized. It is found that its amplitudes can be estimated from the properties of the incoming wave that propagates in the non-bonded region. It is verified that the excitation of these modes is related to the degree to which the shapes of both modes match each other. A 3D simulation of two aluminum-bonded plates using 500 kHz ultrasonic transducers in a pitch-and-catch configuration was implemented using the Matlab k-Wave toolbox. Scattering effects, due to some defects located in the bond line of the joints, were simulated. The experimental setup with some artificial defects produced in the aluminum joints was used in order to compare it with the simulation. Qualitative agreement was observed between the two approaches. The observed deviation can be due to the different characteristics of the experimental and simulated defects.

Characterization of the Targeting Accuracy of a Neuronavigation-Guided Transcranial FUS System In Vitro, In Vivo, and In Silico.

Focused ultrasound (FUS)-enabled liquid biopsy (sonobiopsy) is an emerging technique for the noninvasive and spatiotemporally controlled diagnosis of brain cancer by inducing blood-brain barrier (BBB) disruption to release brain tumor-specific biomarkers into the blood circulation. The feasibility, safety, and efficacy of sonobiopsy were demonstrated in both small and large animal models using magnetic resonance-guided FUS devices. However, the high cost and complex operation of magnetic resonance-guided FUS devices limit the future broad application of sonobiopsy in the clinic. In this study, a neuronavigation-guided sonobiopsy device is developed and its targeting accuracy is characterized in vitro, in vivo, and in silico. The sonobiopsy device integrated a commercially available neuronavigation system (BrainSight) with a nimble, lightweight FUS transducer. Its targeting accuracy was characterized in vitro in a water tank using a hydrophone. The performance of the device in BBB disruption was verified in vivo using a pig model, and the targeting accuracy was quantified by measuring the offset between the target and the actual locations of BBB opening. The feasibility of the FUS device in targeting glioblastoma (GBM) tumors was evaluated in silico using numerical simulation by the k-Wave toolbox in glioblastoma patients. It was found that the targeting accuracy of the neuronavigation-guided sonobiopsy device was 1.7 ± 0.8 mm as measured in the water tank. The neuronavigation-guided FUS device successfully induced BBB disruption in pigs with a targeting accuracy of 3.3 ± 1.4 mm. The targeting accuracy of the FUS transducer at the GBM tumor was 5.5 ± 4.9 mm. Age, sex, and incident locations were found to be not correlated with the targeting accuracy in GBM patients. This study demonstrated that the developed neuronavigation-guided FUS device could target the brain with a high spatial targeting accuracy, paving the foundation for its application in the clinic.

Effect of HIFU-Induced Thermal Ablation in Numerical Breast Phantom

Breast cancer is a leading cause of cancer-related deaths in women, and treatment involved invasive surgery such as lumpectomy. In the last decade, a non-invasive, non-contact high-intensity focused ultrasound (HIFU) therapy was developed for treatment with promising results. However, its success rate depends on patient selection, tissue heterogeneities, HIFU operational parameters, and even imaging techniques. In this emerging field, computer simulations can provide us with a much-needed platform to learn, test, and deduce results virtually before conducting experiments. In this study, we used three different classes of anatomically realistic numerical breast phantoms from clinical contrast-enhanced magnetic resonance imaging (MRI) data, including scattered-, heterogeneous-, and extremely dense-type breasts. Upon assigning the appropriate acoustic and optical parameters to the tissues within, we simulated HIFU propagation by using the k-Wave toolbox in MATLAB and compared the changes introduced in the three types of breasts. It was found that scattered-type breast was best-suited for HIFU therapy. Furthermore, we simulated light-beam propagation with the ValoMC toolbox in MATLAB after introducing the lesion to compare the distribution of the initial pressure generated via the photoacoustic effect. This simulation study will be of significant clinical impact, especially in the study and management of HIFU-based treatments, which are individual/tissue-selective in nature.

Numerical simulations for characterization of missing articulatory information in ultrasound imaging of speech

The air–tissue interface at the tongue surface allows submental (below the chin) B-mode ultrasound images to depict the shape of the tongue in real time, useful for measuring and understanding typical and disordered tongue articulation during speech production. However, parts of the tongue are obscured; depending on an individual speaker's anatomy and tongue movement patterns, the anterior tongue tip may be shadowed by the mandible bone and the sublingual airspace. To characterize this missing information about the tongue tip in ultrasound images, midsagittal ultrasound images were numericallysimulated. Three-dimensional anatomic models were constructed using magnetic resonance imaging (MRI) data to map tongue tissue, surrounding air, and an estimated position of the mandible. Pulse-echo ultrasound images were then numerically simulated using the open-source k-Wave toolbox. Acoustic properties of the medium and an imaging array model are identified that allow simulations to replicate features in ultrasound images recorded from the same speakers as the MRI data, while maintaining computational efficiency. The potential to recover missing information on the tongue tip position from reverberation artifacts is assessed.

Quantifying tongue tip visibility in ultrasound images of /r/ tongue shapes using numerical ultrasound simulations

Midsagittal ultrasound images provide important articulatory information about tongue shape by showing much of the tongue surface from the root to the tip. However, portions of the tongue tip are often obscured due to shadowing from the mandible bone and the sublingual airspace. Information about tongue tip position can be important for understanding tongue movement patterns, e.g., classification of a retroflex or bunched shape for the American English rhotic /r/. Here, numerical simulations of acoustic wave propagation in tissue were performed using the open-source k-Wave toolbox to recreate ultrasound images of the tongue for a range of retroflex and bunched tongue shapes segmented from magnetic resonance imaging (MRI). Extent of the tongue tip visibly missing from the simulated ultrasound images is quantified by comparison with the known tongue shape from MRI. The fraction of the tongue surface visible in ultrasound images is compared between tongue shapes that appear retroflex versus bunched in MRI. Implications for ultrasound biofeedback therapy are discussed, including possible ambiguity of retroflex versus bunched classification.

Combined Monte Carlo and k-Wave Simulations for Reconstruction of Blood Oxygen Saturation in Optoacoustics: A Pilot Study

Optoacoustic (OA) imaging of biological tissues is a modern technique allowing for three-dimensional blood oxygen saturation mapping based on OA spectroscopy data. Since biological tissues are optically inhomogeneous and the spatial distribution of optical parameters within a biological tissue is a priori unknown, Monte Carlo simulation technique is traditionally used to estimate the distribution of probing illumination within tissues in quantitative OA reconstruction. Currently, machine learning techniques are actively employed for reconstructing 3D distribution of blood oxygen saturation or estimating optical properties of biological tissues based on training datasets. In this paper, systemic calculations of synthetic OA images of a medium with embedded vessel-like structures were performed to create a training dataset for machine learning employing combined application of the Monte Carlo technique for direct solution of optical problem and difference-space pseudo-spectral approach implemented through k-Wave Toolbox calculations for the acoustical part. The calculations were performed for probing wavelengths of 532 nm, 658 nm and 1064 nm, which are commonly employed in spectral OA imaging. Simulated OA data for different orientation, diameter and embedding depth of blood vessels allows analyzing the effect of these parameters on the formation of OA image and the reconstruction of blood oxygen saturation. The ratio of OA signals corresponding to probing wavelengths of 658 nm and 1064 nm was employed for simple reconstruction of blood oxygen saturation in silico for different vessel geometries with the precision of &lt; 3–15% for the most of blood vessels diameters and embedding depths and the range of blood oxygen saturation values ≥ 0.8. The obtained set of synthetic OA data has high potential as a training set for employment in machine learning techniques aiming at mapping blood oxygenation based on spectral OA data.

Research on the Multi-Element Synthetic Aperture Focusing Technique in Breast Ultrasound Imaging, Based on the Ring Array.

As a widely clinical detection method, ultrasonography (US) has been applied to the diagnosis of breast cancer. In this paper, the multi-element synthetic aperture focusing (M-SAF) is applied to the ring array of breast ultrasonography (US) imaging, which addresses the problem of low imaging quality due to the single active element for each emission and the reception in the synthetic aperture focusing. In order to determine the optimal sub-aperture size, the formula is derived for calculating the internal sound pressure of the ring array with a 200 mm diameter, and the sound pressure distribution is analyzed. The ring array with 1024 elements (1024 ring array) is established in COMSOL Multiphysics 5.6, and the optimal sub-aperture size is 16 elements, according to the sound field beam simulation and the directivity research. Based on the existing experimental conditions, the ring array with 256 elements (256 ring array) is simulated and verified by experiments. The simulation has a spatial resolution evaluation in the k-Wave toolbox, and the experiment uses nylon rope and breast model imaging. The results show that if the sub-aperture size has four elements, the imaging quality is the highest. Specifically, the spatial resolution is the best, and the sound pressure amplitude and signal-to-noise ratio (SNR) are maintained at a high level in the reconstructed image. The optimal sub-aperture theory is verified by the two kinds of ring arrays, which also provide a theoretical basis for the application of the multi-element synthetic aperture focusing technology (M-SAF) in ring arrays.

Computational Simulation of Microflaw Detection in Carbon-Fiber-Reinforced Polymers

The evaluation of microflaws in carbon-fiber-reinforced composite laminate (CFRP) via ultrasound requires the knowledge of some important factors in addition to its structural composition. Since the laminates are heterogeneous, the high-frequency requirements to acquire high-resolution signals have limitations due to the great scattering that prevents good signal-to-noise ratios. Additionally, the ultrasonic probe’s spatial and lateral resolution characteristics are important parameters for determining the detectability level of microflaws. Modelling appears as a good approach to evaluating the abovementioned factors and the probability of detection of defects in the micron range because it makes it possible to reduce the time and cost associated with developments based on experimental tests. Concerning the subject of this work, simulation is the best way to evaluate the detectability level of the proposed defects since experimental samples are not available. In this work, the simulation was implemented using the Matlab k-Wave toolbox. A 2D matrix for mimicking a CFRP was constructed with 1 μm of resolution. Four different defect types in the micron range were created in the matrix. The simulated and experimental results presented good agreement. It was concluded that the highest frequency probe that could be used to detect the simulated defects without ambiguity was 25 MHz.

Effects of Beamforming Techniques on Quality of Ultrasound Computed Tomography Images.

Background: In body tissues, tumors generally have different speeds of sound (SOS) than normal tissues. In this respect, ultrasound computed tomography (UCT) can generate a cross-sectional SOS map as an innovative ultrasound imaging method. This technique can produce images with a resolution of millimeters and a high signal-to-noise ratio. Objective: This study aimed to improve UCT image quality without increasing breast cancer screening and diagnosis time.Material and Methods: In this analytical study, a ring-shaped UCT breast imaging system was simulated using the K-wave toolbox of MATLAB. The system has a 20 cm diameter and 256 ultrasonic piezoelectrics placed in the ring’s circumference. Different beamforming techniques imaged two designed phantoms (i.e., resolution and contrast), and the resolution and contrast to noise ratio (CNR) were calculated.Results: The results of resolution phantom imaging without any beamforming showed that only bars with the value of 0.125 and 0.167 lp/mm were distinguishable, and the 0.1 bars were not recognizable in the imaging. In addition, increasing the number of transmitters led to no noticeable change in resolution for 0.125 and 0.167 lp/mm bars. In all beamforming techniques for imaging the contrast phantom, the CNR parameter up to an object with a diameter of 8 mm increases with increasing diameter without any change.Conclusion: The beamforming technique using three simultaneous transmitters improved the resolution by about 1 mm compared to the normal strategy. In addition to high-contrast images, beamforming with 9 simultaneous transmitters led to a preferable technique.

Fast and efficient PAT image reconstruction algorithms: A comparative performance analysis

Medical imaging technology efficiency is determined by how accurate, rapid, invasive, or non-invasive it is. Photoacoustic tomography (PAT) is a noninvasive emerging technology for medical imaging that is able to produce images with high resolution and high contrast in long penetration depths. In PAT, image reconstruction accuracy relies on the accuracy of the system model. Accurate model-based methods can be made use of for efficiently reconstructing a PAT image from the sensor measurements using a pseudo-spectral method which is suggested to produce exactly the same results as that of the k-Wave toolbox in MATLAB. Compressive sensing has been successfully applied for medical image reconstruction as it allows for sparse sampling and sparse reconstruction. Compressive sensing combined with PAT allows for deep tissue imaging at higher resolution at a much lower computational time. A fast and efficient PAT image reconstruction compressive sensing algorithm is needed to be developed, which can image dense tissues (such as breast tissue) rapidly, for early detection of cancer. In this paper, relaxed- Basis pursuit using alternating direction method of multipliers and split Bregman formulation of the total variation regularized least-squares problem is proposed and is observed to work under practical scenarios with fewer samples and sensors. Moreover, a comparative study for the performance analysis of the different compressive sensing algorithms, both iterative and non-iterative, is carried out for a decreased number of sensors and samples. The proposed split Bregman total variation algorithm is fast and produces a high-resolution sparsity preserving image compared to the state-of-the-art algorithms. Moreover, for a reduced number of samples, the proposed relaxed-Basis Pursuit is desired and performs much better than all the algorithms discussed. Implementing Cholesky factorization to the proposed algorithms further reduces the computation time of the split-Bregman algorithm by 90%. The new methods outperform existing ones in practical circumstances recreating a high-resolution image, even when the number of sensors and samples is reduced.

Femoral neck phantom imaging using time-domain topological energy method.

Ultrasonic bone imaging is a complex task, primarily because of the low energy contained in the signals reflected from the internal bone structures. In this study, the reconstruction of a bone-mimicking phantom echographic image using time-domain topological energy (TDTE) is proposed. A TDTE image results from a combination of forward and adjoint fields. The first is a solution of a numerical model that reproduces the setup of the experimental data acquisition to the best extent possible. The second has similar characteristics, but the source term is the time-reversed residue between the forward field and signals obtained from the experiment. The acquisition-reconstruction system used a linear phased-array transducer with a 5 MHz center frequency to acquire the signals and was coupled with a k-wave toolbox to implement the numerical models and perform the image reconstruction. The results showed good agreement between the geometry of the real phantom and the ultrasonic images. However, thickness evaluation errors were observed, which may be due to incorrect assumptions about the velocity models throughout the medium, a priori assumed to be known. Thus, this method has shown promising results and should be applied to the real femoral neck as a long-term objective.