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Chandrasekaran S, Tripathi BB, Espindola D, Pinton GF. Modeling Ultrasound Propagation in the Moving Brain: Applications to Shear Shock Waves and Traumatic Brain Injury. IEEE TRANSACTIONS ON ULTRASONICS, FERROELECTRICS, AND FREQUENCY CONTROL 2021; 68:201-212. [PMID: 32894713 DOI: 10.1109/tuffc.2020.3022567] [Citation(s) in RCA: 5] [Impact Index Per Article: 1.7] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/11/2023]
Abstract
Traumatic brain injury (TBI) studies on the living human brain are experimentally infeasible due to ethical reasons and the elastic properties of the brain degrade rapidly postmortem. We present a simulation approach that models ultrasound propagation in the human brain, while it is moving due to the complex shear shock wave deformation from a traumatic impact. Finite difference simulations can model ultrasound propagation in complex media such as human tissue. Recently, we have shown that the fullwave finite difference approach can also be used to represent displacements that are much smaller than the grid size, such as the motion encountered in shear wave propagation from ultrasound elastography. However, this subresolution displacement model, called impedance flow, was only implemented and validated for acoustical media composed of randomly distributed scatterers. Herein, we propose a generalization of the impedance flow method that describes the continuous subresolution motion of structured acoustical maps, and in particular of acoustical maps of the human brain. It is shown that the average error in simulating subresolution displacements using impedance flow is small when compared to the acoustical wavelength ( λ /1702). The method is then applied to acoustical maps of the human brain with a motion that is imposed by the propagation of a shear shock wave. This motion is determined numerically with a custom piecewise parabolic method that is calibrated to ex vivo observations of shear shocks in the porcine brain. Then the fullwave simulation tool is used to model transmit-receive imaging sequences based on an L7-4 imaging transducer. The simulated radio frequency data are beamformed using a conventional delay-and-sum method and a normalized cross-correlation method designed for shock wave tracking is used to determine the tissue motion. This overall process is an in silico reproduction of the experiments that were previously performed to observe shear shock waves in fresh porcine brain. It is shown that the proposed generalized impedance flow method accurately captures the shear wave motion in terms of the wave profile, shock front characteristics, odd harmonic spectrum generation, and acceleration at the shear shock front. We expect that this approach will lead to improvements in image sequence design that takes into account the aberration and multiple reflections from the brain and in the design of tracking algorithms that can more accurately capture the complex brain motion that occurs during a traumatic impact. These methods of modeling ultrasound propagation in moving media can also be applied to other displacements, such as those generated by shear wave elastography or blood flow.
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Looby K, Herickhoff CD, Sandino C, Zhang T, Vasanawala S, Dahl JJ. Unsupervised clustering method to convert high-resolution magnetic resonance volumes to three-dimensional acoustic models for full-wave ultrasound simulations. J Med Imaging (Bellingham) 2019; 6:037001. [PMID: 31338389 DOI: 10.1117/1.jmi.6.3.037001] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/30/2018] [Accepted: 07/02/2019] [Indexed: 11/14/2022] Open
Abstract
Simulations of acoustic wave propagation, including both the forward and the backward propagations of the wave (also known as full-wave simulations), are increasingly utilized in ultrasound imaging due to their ability to more accurately model important acoustic phenomena. Realistic anatomic models, particularly those of the abdominal wall, are needed to take full advantage of the capabilities of these simulation tools. We describe a method for converting fat-water-separated magnetic resonance imaging (MRI) volumes to anatomical models for ultrasound simulations. These acoustic models are used to map acoustic imaging parameters, such as speed of sound and density, to grid points in an ultrasound simulation. The tissues of these models are segmented from the MRI volumes into five primary classes of tissue in the human abdominal wall (skin, fat, muscle, connective tissue, and nontissue). This segmentation is achieved using an unsupervised machine learning algorithm, fuzzy c-means clustering (FCM), on a multiscale feature representation of the MRI volumes. We describe an automated method for utilizing FCM weights to produce a model that achieves ∼ 90 % agreement with manual segmentation. Two-dimensional (2-D) and three-dimensional (3-D) full-wave nonlinear ultrasound simulations are conducted, demonstrating the utility of realistic 3-D abdominal wall models over previously available 2-D abdominal wall models.
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Affiliation(s)
- Kevin Looby
- Stanford University, Department of Electrical Engineering, Palo Alto, California, United States
| | - Carl D Herickhoff
- Stanford University, Department of Radiology, Palo Alto, California, United States
| | - Christopher Sandino
- Stanford University, Department of Electrical Engineering, Stanford, California, United States
| | - Tao Zhang
- Subtle Medical, Menlo Park, California, United States
| | - Shreyas Vasanawala
- Stanford University, Department of Radiology, Palo Alto, California, United States
| | - Jeremy J Dahl
- Stanford University, Department of Radiology, Palo Alto, California, United States
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Joshi A, Lindsey BD, Dayton PA, Pinton G, Muller M. An iterative fullwave simulation approach to multiple scattering in media with randomly distributed microbubbles. Phys Med Biol 2017; 62:4202-4217. [PMID: 28266925 DOI: 10.1088/1361-6560/aa6523] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/12/2022]
Abstract
Ultrasound contrast agents (UCA), such as microbubbles, enhance the scattering properties of blood, which is otherwise hypoechoic. The multiple scattering interactions of the acoustic field with UCA are poorly understood due to the complexity of the multiple scattering theories and the nonlinear microbubble response. The majority of bubble models describe the behavior of UCA as single, isolated microbubbles suspended in infinite medium. Multiple scattering models such as the independent scattering approximation can approximate phase velocity and attenuation for low scatterer volume fractions. However, all current models and simulation approaches only describe multiple scattering and nonlinear bubble dynamics separately. Here we present an approach that combines two existing models: (1) a full-wave model that describes nonlinear propagation and scattering interactions in a heterogeneous attenuating medium and (2) a Paul-Sarkar model that describes the nonlinear interactions between an acoustic field and microbubbles. These two models were solved numerically and combined with an iterative approach. The convergence of this combined model was explored in silico for 0.5 × 106 microbubbles ml-1, 1% and 2% bubble concentration by volume. The backscattering predicted by our modeling approach was verified experimentally with water tank measurements performed with a 128-element linear array transducer. An excellent agreement in terms of the fundamental and harmonic acoustic fields is shown. Additionally, our model correctly predicts the phase velocity and attenuation measured using through transmission and predicted by the independent scattering approximation.
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Affiliation(s)
- Aditya Joshi
- Department of Mechanical and Aerospace Engineering, NC State University, Raleigh, NC, United States of America
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Pinton GF. Subresolution Displacements in Finite Difference Simulations of Ultrasound Propagation and Imaging. IEEE TRANSACTIONS ON ULTRASONICS, FERROELECTRICS, AND FREQUENCY CONTROL 2017; 64:537-543. [PMID: 27992333 PMCID: PMC5741097 DOI: 10.1109/tuffc.2016.2638801] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/12/2023]
Abstract
Time domain finite difference simulations are used extensively to simulate wave propagation. They approximate the wave field on a discrete domain with a grid spacing that is typically on the order of a tenth of a wavelength. The smallest displacements that can be modeled by this type of simulation are thus limited to discrete values that are integer multiples of the grid spacing. This paper presents a method to represent continuous and subresolution displacements by varying the impedance of individual elements in a multielement scatterer. It is demonstrated that this method removes the limitations imposed by the discrete grid spacing by generating a continuum of displacements as measured by the backscattered signal. The method is first validated on an ideal perfect correlation case with a single scatterer. It is subsequently applied to a more complex case with a field of scatterers that model an acoustic radiation force-induced displacement used in ultrasound elasticity imaging. A custom finite difference simulation tool is used to simulate propagation from ultrasound imaging pulses in the scatterer field. These simulated transmit-receive events are then beamformed into images, which are tracked with a correlation-based algorithm to determine the displacement. A linear predictive model is developed to analytically describe the relationship between element impedance and backscattered phase shift. The error between model and simulation is λ/ 1364 , where λ is the acoustical wavelength. An iterative method is also presented that reduces the simulation error to λ/ 5556 over one iteration. The proposed technique therefore offers a computationally efficient method to model continuous subresolution displacements of a scattering medium in ultrasound imaging. This method has applications that include ultrasound elastography, blood flow, and motion tracking. This method also extends generally to finite difference simulations of wave propagation, such as electromagnetic or seismic waves.
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Londhe ND, Suri JS. Superharmonic Imaging for Medical Ultrasound: a Review. J Med Syst 2016; 40:279. [PMID: 27787782 DOI: 10.1007/s10916-016-0635-x] [Citation(s) in RCA: 10] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/26/2016] [Accepted: 10/12/2016] [Indexed: 01/28/2023]
Abstract
Ultrasound with harmonics has emerged as an exceptional alternative to competitively low resolution fundamental ultrasound imaging. The use of second harmonic is already a trend now but higher harmonics are also being seen as even better option due to its improved resolution. The resolution improved with frequency but achieves penetration of reduced energy. The cumulative addition of higher harmonics during propagation yields higher harmonics giving better resolution with adequate penetration. This paper summarizes the progress of such similar decade old harmonic ultrasound imaging technique i.e., superharmonic imaging (SHI) geared towards medical field. It comprises of harmonics higher than second harmonic preferably up to 5th harmonic. We conclude that SHI can be an advanced ultrasound imaging with comprehensive high resolution and adequate penetration depth on sole and coded modes.
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Affiliation(s)
- Narendra D Londhe
- Department of Electrical Engineering, NIT Raipur, Raipur, Chhattisgarh, India
| | - Jasjit S Suri
- Point-of-Care Devices, Global Biomedical Technologies, Inc., Roseville, CA, USA. .,Monitoring and Diagnostic Division, AtheroPoint™, Roseville, CA, USA.
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Jing Y, Wang T, Clement GT. A k-space method for moderately nonlinear wave propagation. IEEE TRANSACTIONS ON ULTRASONICS, FERROELECTRICS, AND FREQUENCY CONTROL 2012; 59:1664-73. [PMID: 22899114 PMCID: PMC3777432 DOI: 10.1109/tuffc.2012.2372] [Citation(s) in RCA: 13] [Impact Index Per Article: 1.1] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/23/2023]
Abstract
A k-space method for moderately nonlinear wave propagation in absorptive media is presented. The Westervelt equation is first transferred into k-space via Fourier transformation, and is solved by a modified wave-vector time-domain scheme. The present approach is not limited to forward propagation or parabolic approximation. One- and two-dimensional problems are investigated to verify the method by comparing results to analytic solutions and finite-difference time-domain (FDTD) method. It is found that to obtain accurate results in homogeneous media, the grid size can be as little as two points per wavelength, and for a moderately nonlinear problem, the Courant-Friedrichs-Lewy number can be as large as 0.4. Through comparisons with the conventional FDTD method, the k-space method for nonlinear wave propagation is shown here to be computationally more efficient and accurate. The k-space method is then employed to study three-dimensional nonlinear wave propagation through the skull, which shows that a relatively accurate focusing can be achieved in the brain at a high frequency by sending a low frequency from the transducer. Finally, implementations of the k-space method using a single graphics processing unit shows that it required about one-seventh the computation time of a single-core CPU calculation.
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Affiliation(s)
- Yun Jing
- Department of Mechanical and Aerospace Engineering, North Carolina State University, Raleigh, NC, USA.
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Mougenot C, Tillander M, Koskela J, Köhler MO, Moonen C, Ries M. High intensity focused ultrasound with large aperture transducers: A MRI based focal point correction for tissue heterogeneity. Med Phys 2012; 39:1936-45. [DOI: 10.1118/1.3693051] [Citation(s) in RCA: 26] [Impact Index Per Article: 2.2] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/07/2022] Open
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Jing Y, Meral FC, Clement GT. Time-reversal transcranial ultrasound beam focusing using a k-space method. Phys Med Biol 2012; 57:901-17. [PMID: 22290477 PMCID: PMC3366238 DOI: 10.1088/0031-9155/57/4/901] [Citation(s) in RCA: 38] [Impact Index Per Article: 3.2] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/20/2022]
Abstract
This paper proposes the use of a k-space method to obtain the correction for transcranial ultrasound beam focusing. Mirroring past approaches, a synthetic point source at the focal point is numerically excited, and propagated through the skull, using acoustic properties acquired from registered computed tomography of the skull being studied. The received data outside the skull contain the correction information and can be phase conjugated (time reversed) and then physically generated to achieve a tight focusing inside the skull, by assuming quasi-plane transmission where shear waves are not present or their contribution can be neglected. Compared with the conventional finite-difference time-domain method for wave propagation simulation, it will be shown that the k-space method is significantly more accurate even for a relatively coarse spatial resolution, leading to a dramatically reduced computation time. Both numerical simulations and experiments conducted on an ex vivo human skull demonstrate that precise focusing can be realized using the k-space method with a spatial resolution as low as only 2.56 grid points per wavelength, thus allowing treatment planning computation on the order of minutes.
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Affiliation(s)
- Yun Jing
- Department of Mechanical and Aerospace Engineering, North Carolina State University Raleigh, NC 27695, USA.
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Jing Y. On the use of an absorption layer for the angular spectrum approach (L). THE JOURNAL OF THE ACOUSTICAL SOCIETY OF AMERICA 2012; 131:999-1002. [PMID: 22352473 DOI: 10.1121/1.3675967] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/31/2023]
Abstract
Reducing the spatial aliasing error of the angular spectrum method by using an absorption layer is investigated in this paper. The acoustic equation including the absorption layer is presented and is transformed in the spatial frequency domain, where an implicit analytic solution is readily available. Its approximation, which is more suitable for numerical simulation, is derived and is numerically implemented. The comparisons between the present method and available methods demonstrate its validity and advantages.
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Affiliation(s)
- Yun Jing
- Department of Mechanical and Aerospace Engineering, North Carolina State University, Raleigh, North Carolina 27695, USA.
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Pinton GF, Trahey GE, Dahl JJ. Sources of image degradation in fundamental and harmonic ultrasound imaging: a nonlinear, full-wave, simulation study. IEEE TRANSACTIONS ON ULTRASONICS, FERROELECTRICS, AND FREQUENCY CONTROL 2011; 58:1272-83. [PMID: 21693410 PMCID: PMC4443447 DOI: 10.1109/tuffc.2011.1938] [Citation(s) in RCA: 7] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/03/2023]
Abstract
A full-wave equation that describes nonlinear propagation in a heterogeneous attenuating medium is solved numerically with finite differences in the time domain. This numerical method is used to simulate propagation of a diagnostic ultrasound pulse through a measured representation of the human abdomen with heterogeneities in speed of sound, attenuation, density, and nonlinearity. Conventional delay-and-sum beamforming is used to generate point spread functions (PSFs) that display the effects of these heterogeneities. For the particular imaging configuration that is modeled, these PSFs reveal that the primary source of degradation in fundamental imaging is due to reverberation from near-field structures. Compared with fundamental imaging, reverberation clutter in harmonic imaging is 27.1 dB lower. Simulated tissue with uniform velocity but unchanged impedance characteristics indicates that for harmonic imaging, the primary source of degradation is phase aberration.
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Affiliation(s)
- Gianmarco F. Pinton
- Institut Langevin, École Supérieure de Physique et
de Chimie Industrielles de la ville de Paris (ESPCI) ParisTech, Centre
National de la Recherche Scientifique (CNRS), UMR 7587, Paris, France
| | - Gregg E. Trahey
- Duke University, Department of Biomedical Engineering, Durham,
NC
- Duke University Medical Center, Department of Radiology, Durham,
NC
| | - Jeremy J. Dahl
- Duke University, Department of Biomedical Engineering, Durham,
NC
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Pinton GF, Trahey GE, Dahl JJ. Sources of image degradation in fundamental and harmonic ultrasound imaging using nonlinear, full-wave simulations. IEEE TRANSACTIONS ON ULTRASONICS, FERROELECTRICS, AND FREQUENCY CONTROL 2011; 58:754-65. [PMID: 21507753 PMCID: PMC3140000 DOI: 10.1109/tuffc.2011.1868] [Citation(s) in RCA: 32] [Impact Index Per Article: 2.5] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/19/2023]
Abstract
A full-wave equation that describes nonlinear propagation in a heterogeneous attenuating medium is solved numerically with finite differences in the time domain (FDTD). This numerical method is used to simulate propagation of a diagnostic ultrasound pulse through a measured representation of the human abdomen with heterogeneities in speed of sound, attenuation, density, and nonlinearity. Conventional delay-andsum beamforming is used to generate point spread functions (PSF) that display the effects of these heterogeneities. For the particular imaging configuration that is modeled, these PSFs reveal that the primary source of degradation in fundamental imaging is reverberation from near-field structures. Reverberation clutter in the harmonic PSF is 26 dB higher than the fundamental PSF. An artificial medium with uniform velocity but unchanged impedance characteristics indicates that for the fundamental PSF, the primary source of degradation is phase aberration. An ultrasound image is created in silico using the same physical and algorithmic process used in an ultrasound scanner: a series of pulses are transmitted through heterogeneous scattering tissue and the received echoes are used in a delay-and-sum beamforming algorithm to generate images. These beamformed images are compared with images obtained from convolution of the PSF with a scatterer field to demonstrate that a very large portion of the PSF must be used to accurately represent the clutter observed in conventional imaging.
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12
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Haynes M, Moghaddam M. Large-Domain, Low-Contrast Acoustic Inverse Scattering for Ultrasound Breast Imaging. IEEE Trans Biomed Eng 2010; 57. [DOI: 10.1109/tbme.2010.2059023] [Citation(s) in RCA: 27] [Impact Index Per Article: 1.9] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/07/2022]
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Mast TD. Convolutional modeling of diffraction effects in pulse-echo ultrasound imaging. THE JOURNAL OF THE ACOUSTICAL SOCIETY OF AMERICA 2010; 128:EL99-104. [PMID: 20815433 PMCID: PMC2937047 DOI: 10.1121/1.3462233] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/09/2023]
Abstract
A model is presented for pulse-echo imaging of three-dimensional, linear, weakly-scattering continuum media by ultrasound array transducers. The model accounts for the diffracted fields of focused array subapertures in both transmit and receive modes, multiple transmit and receive focal zones, frequency-dependent attenuation, and aberration caused by mismatched medium and beamformer sound speeds. For a given medium reflectivity function, computation of a B-scan requires evaluation of a depth-dependent transmit/receive beam product, followed by two one-dimensional convolutions and a one-dimensional summation. Numerical results obtained using analytic expressions for transmit and receive beams agree favorably with measured B-scan images and speckle statistics.
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Affiliation(s)
- T Douglas Mast
- Department of Biomedical Engineering, University of Cincinnati, Cincinnati, Ohio 45267, USA.
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Salahura G, Tillett JC, Metlay LA, Waag RC. Large-scale propagation of ultrasound in a 3-D breast model based on high-resolution MRI data. IEEE Trans Biomed Eng 2010; 57:1273-84. [PMID: 20172794 DOI: 10.1109/tbme.2009.2040022] [Citation(s) in RCA: 11] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/18/2023]
Abstract
A 40 x 35 x 25-mm(3) specimen of human breast consisting mostly of fat and connective tissue was imaged using a 3-T magnetic resonance scanner. The resolutions in the image plane and in the orthogonal direction were 130 microm and 150 microm, respectively. Initial processing to prepare the data for segmentation consisted of contrast inversion, interpolation, and noise reduction. Noise reduction used a multilevel bidirectional median filter to preserve edges. The volume of data was segmented into regions of fat and connective tissue by using a combination of local and global thresholding. Local thresholding was performed to preserve fine detail, while global thresholding was performed to minimize the interclass variance between voxels classified as background and voxels classified as object. After smoothing the data to avoid aliasing artifacts, the segmented data volume was visualized using isosurfaces. The isosurfaces were enhanced using transparency, lighting, shading, reflectance, and animation. Computations of pulse propagation through the model illustrate its utility for the study of ultrasound aberration. The results show the feasibility of using the described combination of methods to demonstrate tissue morphology in a form that provides insight about the way ultrasound beams are aberrated in three dimensions by tissue.
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Affiliation(s)
- Gheorghe Salahura
- Department of Electrical and Computer Engineering, University of Rochester, Rochester, NY 14627, USA.
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Daoud MI, Lacefield JC. Distributed three-dimensional simulation of B-mode ultrasound imaging using a first-order k-space method. Phys Med Biol 2009; 54:5173-92. [PMID: 19671970 DOI: 10.1088/0031-9155/54/17/007] [Citation(s) in RCA: 10] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/12/2022]
Abstract
Computational modeling is an important tool in ultrasound imaging research, but realistic three-dimensional (3D) simulations can exceed the capabilities of serial computers. This paper uses a 3D simulator based on a k-space method that incorporates relaxation absorption and nonreflecting boundary conditions. The simulator, which runs on computer clusters, computes the propagation of a single wavefront. In this paper, an allocation algorithm is introduced to assign each scan line to a group of nodes and use multiple groups to compute independent lines concurrently. The computational complexity required for realistic simulations is analyzed using example calculations of ultrasonic propagation and attenuation in the 30-50 MHz band. Parallel efficiency for B-mode imaging simulations is evaluated for various numbers of scan lines and cluster nodes. An aperture-projection technique is introduced to simulate imaging with a focused transducer using reduced computation grids. This technique is employed to synthesize B-mode images that show realistic 3D refraction artifacts. Parallel computing using 20 nodes to compute groups of ten scan lines concurrently reduced the execution time for each image to 18.6 h, compared to a serial execution time of 357.5 h. The results demonstrate that fully 3D imaging simulations are practical using contemporary computing technology.
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Affiliation(s)
- Mohammad I Daoud
- Department of Electrical and Computer Engineering, University of Western Ontario, London, Ontario, N6A 5B9, Canada.
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Pinton GF, Dahl J, Rosenzweig S, Trahey GE. A heterogeneous nonlinear attenuating full-wave model of ultrasound. IEEE TRANSACTIONS ON ULTRASONICS, FERROELECTRICS, AND FREQUENCY CONTROL 2009; 56:474-88. [PMID: 19411208 PMCID: PMC4437716 DOI: 10.1109/tuffc.2009.1066] [Citation(s) in RCA: 91] [Impact Index Per Article: 6.1] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/05/2023]
Abstract
A full-wave equation that describes nonlinear propagation in a heterogeneous attenuating medium is solved numerically with finite differences in the time domain (FDTD). Three-dimensional solutions of the equation are verified with water tank measurements of a commercial diagnostic ultrasound transducer and are shown to be in excellent agreement in terms of the fundamental and harmonic acoustic fields and the power spectrum at the focus. The linear and nonlinear components of the algorithm are also verified independently. In the linear nonattenuating regime solutions match results from Field II, a well established software package used in transducer modeling, to within 0.3 dB. Nonlinear plane wave propagation is shown to closely match results from the Galerkin method up to 4 times the fundamental frequency. In addition to thermoviscous attenuation we present a numerical solution of the relaxation attenuation laws that allows modeling of arbitrary frequency dependent attenuation, such as that observed in tissue. A perfectly matched layer (PML) is implemented at the boundaries with a numerical implementation that allows the PML to be used with high-order discretizations. A -78 dB reduction in the reflected amplitude is demonstrated. The numerical algorithm is used to simulate a diagnostic ultrasound pulse propagating through a histologically measured representation of human abdominal wall with spatial variation in the speed of sound, attenuation, nonlinearity, and density. An ultrasound image is created in silico using the same physical and algorithmic process used in an ultrasound scanner: a series of pulses are transmitted through heterogeneous scattering tissue and the received echoes are used in a delay-and-sum beam-forming algorithm to generate a images. The resulting harmonic image exhibits characteristic improvement in lesion boundary definition and contrast when compared with the fundamental image. We demonstrate a mechanism of harmonic image quality improvement by showing that the harmonic point spread function is less sensitive to reverberation clutter.
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Jing Y, Cleveland RO. Modeling the propagation of nonlinear three-dimensional acoustic beams in inhomogeneous media. THE JOURNAL OF THE ACOUSTICAL SOCIETY OF AMERICA 2007; 122:1352. [PMID: 17927398 DOI: 10.1121/1.2767420] [Citation(s) in RCA: 10] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/25/2023]
Abstract
A three-dimensional model of the forward propagation of nonlinear sound beams in inhomogeneous media, a generalized Khokhlov-Zabolotskaya-Kuznetsov equation, is described. The Texas time-domain code (which accounts for paraxial diffraction, nonlinearity, thermoviscous absorption, and absorption and dispersion associated with multiple relaxation processes) was extended to solve for the propagation of nonlinear beams for the case where all medium properties vary in space. The code was validated with measurements of the nonlinear acoustic field generated by a phased array transducer operating at 2.5 MHz in water. A nonuniform layer of gel was employed to create an inhomogeneous medium. There was good agreement between the code and measurements in capturing the shift in the pressure distribution of both the fundamental and second harmonic due to the gel layer. The results indicate that the numerical tool described here is appropriate for propagation of nonlinear sound beams through weakly inhomogeneous media.
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Affiliation(s)
- Yuan Jing
- Department of Aerospace and Mechanical Engineering, Boston University, Boston, Massachusetts 02215, USA
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18
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Al-Bataineh OM, Collins CM, Park EJ, Lee H, Smith NB. MR thermometry characterization of a hyperthermia ultrasound array designed using the k-space computational method. Biomed Eng Online 2006; 5:56. [PMID: 17064421 PMCID: PMC1635715 DOI: 10.1186/1475-925x-5-56] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/13/2005] [Accepted: 10/25/2006] [Indexed: 11/11/2022] Open
Abstract
Background Ultrasound induced hyperthermia is a useful adjuvant to radiation therapy in the treatment of prostate cancer. A uniform thermal dose (43°C for 30 minutes) is required within the targeted cancerous volume for effective therapy. This requires specific ultrasound phased array design and appropriate thermometry method. Inhomogeneous, acoustical, three-dimensional (3D) prostate models and economical computational methods provide necessary tools to predict the appropriate shape of hyperthermia phased arrays for better focusing. This research utilizes the k-space computational method and a 3D human prostate model to design an intracavitary ultrasound probe for hyperthermia treatment of prostate cancer. Evaluation of the probe includes ex vivo and in vivo controlled hyperthermia experiments using the noninvasive magnetic resonance imaging (MRI) thermometry. Methods A 3D acoustical prostate model was created using photographic data from the Visible Human Project®. The k-space computational method was used on this coarse grid and inhomogeneous tissue model to simulate the steady state pressure wavefield of the designed phased array using the linear acoustic wave equation. To ensure the uniformity and spread of the pressure in the length of the array, and the focusing capability in the width of the array, the equally-sized elements of the 4 × 20 elements phased array were 1 × 14 mm. A probe was constructed according to the design in simulation using lead zerconate titanate (PZT-8) ceramic and a Delrin® plastic housing. Noninvasive MRI thermometry and a switching feedback controller were used to accomplish ex vivo and in vivo hyperthermia evaluations of the probe. Results Both exposimetry and k-space simulation results demonstrated acceptable agreement within 9%. With a desired temperature plateau of 43.0°C, ex vivo and in vivo controlled hyperthermia experiments showed that the MRI temperature at the steady state was 42.9 ± 0.38°C and 43.1 ± 0.80°C, respectively, for 20 minutes of heating. Conclusion Unlike conventional computational methods, the k-space method provides a powerful tool to predict pressure wavefield in large scale, 3D, inhomogeneous and coarse grid tissue models. Noninvasive MRI thermometry supports the efficacy of this probe and the feedback controller in an in vivo hyperthermia treatment of canine prostate.
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Affiliation(s)
- Osama M Al-Bataineh
- Department of Bioengineering, The Pennsylvania State University, University Park, PA 16802, USA
| | | | - Eun-Joo Park
- Department of Bioengineering, The Pennsylvania State University, University Park, PA 16802, USA
| | - Hotaik Lee
- Graduate Program in Acoustics, The Pennsylvania State University, University Park, PA 16802, USA
| | - Nadine Barrie Smith
- Graduate Program in Acoustics, The Pennsylvania State University, University Park, PA 16802, USA
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Tabei M, Mast TD, Waag RC. Simulation of ultrasonic focus aberration and correction through human tissue. THE JOURNAL OF THE ACOUSTICAL SOCIETY OF AMERICA 2003; 113:1166-1176. [PMID: 12597210 DOI: 10.1121/1.1531986] [Citation(s) in RCA: 20] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/24/2023]
Abstract
Ultrasonic focusing in two dimensions has been investigated by calculating the propagation of ultrasonic pulses through cross-sectional models of human abdominal wall and breast. Propagation calculations used a full-wave k-space method that accounts for spatial variations in density, sound speed, and frequency-dependent absorption and includes perfectly matched layer absorbing boundary conditions. To obtain a distorted receive wavefront, propagation from a point source through the tissue path was computed. Receive focusing used an angular spectrum method. Transmit focusing was accomplished by propagating a pressure wavefront from a virtual array through the tissue path. As well as uncompensated focusing, focusing that employed time-shift compensation and time-shift compensation after backpropagation was investigated in both transmit and receive and time reversal was investigated for transmit focusing in addition. The results indicate, consistent with measurements, that breast causes greater focus degradation than abdominal wall. The investigated compensation methods corrected the receive focus better than the transmit focus. Time-shift compensation after backpropagation improved the focus from that obtained using time-shift compensation alone but the improvement was less in transmit focusing than in receive focusing. Transmit focusing by time reversal resulted in lower sidelobes but larger mainlobes than the other investigated transmit focus compensation methods.
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Affiliation(s)
- Makoto Tabei
- Department of Electrical and Computer Engineering, University of Rochester, Rochester, New York 14627, USA
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