3-D Wave-Equation-Based Finite-Frequency Tomography for Ultrasound Computed Tomography

Martiartu, Naiara Korta; Boehm, Christian; Fichtner, Andreas

doi:10.1109/tuffc.2020.2972327

Cited by 30 publications

(25 citation statements)

References 59 publications

(80 reference statements)

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“…2. The figure shows that ϕ is not constrained by the forward problem in (6). Hence, we require additional types of observations.…”

Section: B Non-uniquenessmentioning

confidence: 99%

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Toward speed-of-sound anisotropy quantification in muscle with pulse-echo ultrasound

Martiartu¹,

Simutė²,

Frauenfelder³

et al. 2022

Preprint

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<p> The velocity of ultrasound longitudinal waves (speed of sound) is emerging as a valuable biomarker for a wide range of diseases, including musculoskeletal disorders. Muscles are fiber-rich tissues that exhibit anisotropic behavior, meaning that velocities vary with the wave-propagation direction. Quantifying anisotropy is therefore essential to improve velocity estimates while providing a new metric that relates to both muscle composition and architecture. This work presents a method to estimate longitudinal-wave anisotropy in transversely isotropic tissues. We assume elliptical anisotropy and consider an experimental setup that includes a flat reflector located in front of the linear probe. Moreover, we consider transducers operating multistatically. This setup allows us to measure first-arrival reflection traveltimes. Unknown muscle parameters are the orientation angle of the anisotropy symmetry axis and the velocities along and across this axis. We derive analytical expressions for the relationship between traveltimes and anisotropy parameters, accounting for reflector inclinations. To analyze the structure of this nonlinear forward problem, we formulate the inversion statistically using the Bayesian framework. Solutions are probability density functions useful for quantifying uncertainties in parameter estimates. Using numerical examples, we demonstrate that all parameters can be well constrained when traveltimes from different reflector inclinations are combined. Results from a wide range of acquisition and medium properties show that uncertainties in velocity estimates are substantially lower than expected velocity differences in muscle. Thus, our formulation could provide accurate muscle anisotropy estimates in future clinical applications.</p> p { margin-bottom: 0.25cm; line-height: 115%; background: transparent }

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“…2. The figure shows that ϕ is not constrained by the forward problem in (6). Hence, we require additional types of observations.…”

Section: B Non-uniquenessmentioning

confidence: 99%

“…We use an ultrasound probe of 4 cm length with 128 transducer elements from which one acts as a source, and all are in receiving mode. Our artificial observations of traveltimes are numerically computed from (6). Fig.…”

Section: A Unconstrained Problemmentioning

confidence: 99%

Toward speed-of-sound anisotropy quantification in muscle with pulse-echo ultrasound

Martiartu¹,

Simutė²,

Frauenfelder³

et al. 2022

Preprint

View full text Add to dashboard Cite

show abstract

“…ρ(r) = ρ 0 . Within this assumption the vectorial problem reduces to a scalar problem and the cost function Err (1) for CSI that needs to be minimized reduces to, 21…”

Section: Single-parameter Inversionmentioning

confidence: 99%

“…Ultrasound is widely used as a medical imaging modality due to its features such as being non-invasive and safe. To retrieve quantitative information about the tissues in the image, ultrasound tomography [1][2][3] in combination with full-wave inversion [4][5][6][7] is frequently used. Up to date, these methods are successfully applied in cases where the object is surrounded by transducers.…”

Section: Introductionmentioning

confidence: 99%

Multi-parameter inversion with the aid of particle velocity field reconstruction

Taskin

Dongen

2020

The Journal of the Acoustical Society of America

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Multi-parameter inversion for medical ultrasound leads to an improved tissue classification. In general, simultaneous reconstruction of volume density of mass and compressibility would require knowledge of the particle velocity field alongside with the pressure field. However, in practice the particle velocity field is not measured.Here, we propose a method for multi-parameter inversion where the particle velocity field is reconstructed from the measured pressure field. To this end, the measured pressure field is described using outward propagating Hankel functions. For a synthetic setup, it is shown that the reconstructed particle velocity field matches the forward modelled particle velocity field. Next, the reconstructed particle velocity field is used together with the synthetically measured pressure field to reconstruct density and compressibility profiles with the aid of contrast source inversion (CSI).Finally, comparing the reconstructed speed of sound profiles obtained via singleparameter versus multi-parameter inversion shows that multi-parameter outperforms single-parameter inversion with respect to accuracy and stability.

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“…However, because rays inherently assume a high-frequency approximation, diffraction and scattering effects are still neglected [15]. An approach was recently published that applies to weak heterogeneities and broadens the concept of a ray to a sensitivity kernel that includes these phenomena to some extent [45].…”

Section: Introductionmentioning

confidence: 99%

Refraction-corrected ray-based inversion for three-dimensional ultrasound tomography of the breast

2020

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Ultrasound Tomography has seen a revival of interest in the past decade, especially for breast imaging, due to improvements in both ultrasound and computing hardware. In particular, three-dimensional ultrasound tomography, a fully tomographic method in which the medium to be imaged is surrounded by ultrasound transducers, has become feasible. This has led to renewed attention on ultrasound tomography image reconstruction algorithms. In this paper, a comprehensive derivation and study of a robust framework for large-scale bent-ray ultrasound tomography in 3D for a hemispherical detector array is presented. Two ray-tracing approaches are derived and compared. More significantly, the problem of linking the rays between emitters and receivers, which is challenging in 3D due to the high number of degrees of freedom for the trajectory of rays, is analysed both as a minimisation and as a root-finding problem. The ray-linking problem is parameterised for a convex detection surface and two robust, accurate, and efficient derivative-free ray-linking algorithms are formulated and demonstrated and compared with a Jacobian-based benchmark approach. To stabilise these methods, novel adaptive-smoothing approaches are proposed that control the conditioning of the update matrices to ensure accurate linking. The nonlinear UST problem of estimating the sound speed was recast as a series of linearised subproblems, each solved using the above algorithms and within a steepest descent scheme. The whole imaging algorithm was demonstrated to be robust and accurate on realistic data simulated using a full-wave acoustic model and an anatomical breast phantom, and incorporating the errors due to time-of-flight picking that would be present with measured data. This method can used to provide a low-artefact, quantitatively accurate, 3D sound speed maps. In addition to being useful in their own right, such 3D sound speed maps can be used to initialise full-wave inversion methods, or as an input to photoacoustic tomography reconstructions.

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3-D Wave-Equation-Based Finite-Frequency Tomography for Ultrasound Computed Tomography

Cited by 30 publications

References 59 publications

Toward speed-of-sound anisotropy quantification in muscle with pulse-echo ultrasound

Toward speed-of-sound anisotropy quantification in muscle with pulse-echo ultrasound

Multi-parameter inversion with the aid of particle velocity field reconstruction

Refraction-corrected ray-based inversion for three-dimensional ultrasound tomography of the breast

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