Schematic of the system for breast ultrasound tomography. (a) The patient lies prone with the breast suspended in a water tank. A transducer array begins at the chest wall and gathers sets of data at many slices through the breast. Shown in (b) is a single illumination and the scattered field produced which is measured by the transducer array. We define x′ as a point inside the scatterer.
Flow chart of the stages that make up the original BF/DT algorithm and the additional TFT stage that is included in HARBUT.
3D numerical model of a breast with nonuniform sound speed and density.
Matrices of processed data, plotted for all send-receive pairs. (a) gives the arrival times of the modeled signals relative to the incident signal estimated by a frequency domain deconvolution. (b) presents the amplitude taken at 750 kHz. In both plots, the regions marked 1 correspond to the transmit- receive pairs with a line-of-sight passing through the subcutaneous fat layer and those marked 2 to the transducer pairs that “see through” the volume of the phantom.
(a) The original central slice of the sound speed map as in Fig. 3 with the locations of the transducer array marked. (b) is the TFT sound speed reconstruction. This is used as the background for the corrected beamforming at 750 kHz in (c). The modulus of the complex reconstruction is given. This is then filtered to get the object function perturbation component Oδ given in (d). (e) is the full object function O generated by combining (d) and the background object function Ob calculated from (b). (f) is the hybrid sound speed reconstruction from the object function (e).
Standard DT reconstructions. The size and the contrast of the original phantom (a) are large enough that the standard Born approximation is invalid, causing the reconstruction (b) to have extensive artifacts that obscure the inclusions.
Comparison of the HARBUT reconstruction from 3D data (a) and 2D data (b). The boundaries of the glandular region and the phantom itself in the 3D reconstruction are blurred in comparison to the 2D reconstruction. The random medium which makes up the glandular region is also more homogeneous in the 3D reconstruction. These effects are a result of averaging in the out-of-plane direction.
Normalized point spread function at the center of the array for the system modeled in this paper — 12 mm tall transducers with an array diameter of 120 mm. The PSF is thin—about 1mm (λ/2) wide—within the plane due to the resolution of the Born approximation used in the reconstruction. As shown in (d), taking a threshold at –6 dB relative to the maximum, the PSF extends in the region –4.5 mm < z < 4.5 mm, making its height around 9 mm. This is significantly wider than the in-plane PSF dimensions.
(a) is a schematic 3D diagram of the arrangement of scatterers in the spiral staircase model. (b) gives the 2D reconstruction of data from such a model, simulated with the 3D FDTD method for heights 0–10 mm at 0.5 mm gaps and radii of 15–50 mm at 5 mm gaps. The artifacts surrounding each scatterer are a result of the relatively course FDTD mesh used, rather than the imaging process, and are ignored. The transducers are modeled as the 12 mm tall line sources used in all the simulations in this paper and are at a radius of 60 mm. There is a clear drop in response as the height of the scatterer is increased due to the transducer beam height. Following Fig. 8(d), the 4.5 mm z offset points lie around the –6 dB threshold, indicating this is the boundary of the slice captured by the transducer array.
Image generated by imaging ψδ = ψb in the corresponding background velocity field. This is present in the final image if the subtraction is not performed. The error is within ±1 m/s through the majority of the imaging domain.
The artifacts caused by ignoring density variations in the velocity reconstructions. This image is produced from a new 2D simulation. This simulation uses a constant sound speed field of 1500 m/s and a density field corresponding to the central slice from Fig. 3. The reconstruction, as with the rest of the paper, assumes density to be negligible and reconstructs the resulting field as velocity perturbations.
Amplitude of signal around the array relative to the incident signal at 750 kHz. Averaging has been performed across all illuminations by matching up the measurements in the same positions relative to the source. The average amplitude drop of the signal, caused by passing through the phantom, was taken to be 0.5.
Material properties of the structures in the breast phantom.
Dimensions of the inclusions in the breast phantom. Inclusion numbering is performed clockwise from the top as shown in Fig. 3.
Reconstructed average sound speeds within each inclusion.
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