2-D Ultrasonic Imaging with Circular Array Data

Youli Quan

Stanford University

Lianjie Huang

Los Alamos National Laboratory

February, 2007

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Objectives

• Study of sound-speed reconstruction capability

of an efficient time-of-flight tomography method

using synthetic data

• Lab data sound-speed reconstruction

• Reflectivity reconstruction using synthetic data

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Circular Array

• Many research groups have developed circular transducer arrays for acoustic imaging:

Schreiman, Gisvold, Greenleaf & Bahn (1984)Waag & Fedewa (2006)Duric, Littrup, Poulo, Babkin, … (2007)

• Full apertures to improve image resolution.

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Ultrasonic Wave Simulation for a Ring Array

• Simulate ultrasonic wave propagation through numerical breast phantoms.

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Ultrasonic Wave Simulation for a Ring Array

• Use finite-difference time-domain acoustic-wave equation in heterogeneous media.

• Source central frequency: 0.5 MHz

• Grid size of the numerical phantom: 0.1 mm

• 2D grid: 2051 x 2051

• Time signal length: 150 s

• Ring diameter: 20 cm

• Take 1 hour to generate 256 common-channel data on a 128-CPU computer cluster.

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Simulated Ring-Array Data

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Tim

e (m

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Direct Wave

Reflected Wave

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Data Analysis and Travel-Time Picking

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Cross-Correlation Picking and First-Break Picking

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dT

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mic

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CorrelationFirst beak

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Tomographic Reconstruction of Sound-Speed

• Obtain L by tracing bent-rays using a finite-difference scheme to solve the eikonal equation.

• Solve the system using an algorithm for sparse linear equations and sparse least squares.

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LC

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TC

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SLT

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Reconstruction of a Circular Object

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Reconstruction of a Square Object

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Reconstruction of Small Circular Object

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Reconstruction of an Off-Center Object

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Reconstruction of a Numerical Phantom

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Reconstruction of a Numerical Phantom

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Reconstruction of a Numerical Phantom

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Reconstruction of a Numerical Phantom

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Lab Data: First-break Picks

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Lab Data: Sound-speed Reconstruction

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Reconstruction of a Numerical Phantom

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Patient Data: Sound-speed Reconstruction

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Computational Time

Using 1 mm grid spacing, the Tomographic

reconstructions with 10 iterations take less than two

minutes of CPU times on a Dell xeon 3.0GHz

desktop PC.

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Conclusions

• The ring transducer array provides an ideal aperture for sound-speed transmission tomography.

• TOF transmission tomography can accurately reconstruct the sound speed for an object > 5

• For objects < 2 , the reconstruction may indicate the existence of the object, but does not recover the absolute value of the sound speed.

• Reflectivity reconstruction has higher resolution than the sound-speed reconstruction

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Acknowledgements

• Work was supported by U.S. DOE Laboratory-Directed Research and Development program.

• Data were generated using the computer clusters at Stanford Center for Computational Earth and Environmental Science (CEES).

• Numerical breast phantoms were derived from phantom and in-vivo breast data provided by Karmanos Cancer Institute through Neb Duric.