2-D Ultrasonic Imaging with Circular Array Data Youli Quan Stanford University Lianjie Huang Los Alamos National Laboratory February, 2007

1 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

2 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.

3 Ultrasonic Wave Simulation for a Ring Array Simulate ultrasonic wave propagation through numerical breast phantoms.

4 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.

5 Simulated Ring-Array Data

6 Data Analysis and Travel-Time Picking

7 Cross-Correlation Picking and First-Break Picking

8 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.

9 Reconstruction of a Circular Object

10 Reconstruction of a Square Object

11 Reconstruction of Small Circular Object

12 Reconstruction of an Off-Center Object

13 Reconstruction of a Numerical Phantom

14 Reconstruction of a Numerical Phantom

15 Reconstruction of a Numerical Phantom

16 Reconstruction of a Numerical Phantom

17 Lab Data: First-break Picks

18 Lab Data: Sound-speed Reconstruction

19 Reconstruction of a Numerical Phantom

20 Patient Data: Sound-speed Reconstruction

21 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.

22 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

23 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.