Effect of the chest wall on breast lesion reconstruction

Abstract

The chest wall underneath the breast tissue affects near-infrared (NIR) diffusive waves measured with reflection geometry. With the assistance of a co-registered ultrasound, the depth and the tilting angle of the chest wall can be determined and are used to model the breast as a two-layer medium. Finite element method (FEM) is suitable for modeling complex boundary conditions and is adapted to model the breast tissue and chest wall. Four parameters of bulk absorption and reduced scattering coefficients of these two layers are estimated and used for imaging reconstruction. Using a two-layer model, we have systematically investigated the effect of the chest wall on breast lesion reconstruction. Results have shown that chest-wall depth, titling angle, and difference between optical properties of two layers of lesion and reference sites affect the lesion reconstruction differently. Our analysis will be valuable and informative to researchers who are using reflectance geometry for breast imaging. The analysis can also provide guidelines for imaging operators to minimize image artifacts and to produce the best reconstruction results.

Figures

Fig. 1

Co-registered ultrasound images of a two-layer phantom with the second layer located at 1.0 cm and 1.4 cm depth (flat interface) (b, top) and −14.7 deg (tilted interface) (d, top). Corresponding light reflectance data (logarithmic scale) versus source–detector distance of the two-layer phantom (bottom). Parts (a) and (c) show simulation results, and (b) and (d) show experimental data. Each figure shows three sets of data obtained from a homogenous medium (black), a two-layer phantom with the second layer located at 1 cm (blue) and 1.4 cm (red) depth, respectively. The slopes of the first order fit to simulated data shown in (c) are −0.94 (homogeneous medium), −1.49 (1.0 cm depth), and −1.21 (1.4 cm depth), respectively. The slopes of experimental data shown in (d) are −0.9 (homogeneous), −1.38 (1.0 cm), and −1.23 (1.4 cm depth), respectively. (Color online only.)

Fig. 2

A B-scan ultrasound image (a) and its corresponding two–layer model (b).

Fig. 3

Effect of second-layer depth mismatch between the reference site and the target site. The second layer at the reference site was located at (a) 1.5 cm, (b) 1.75 cm, (c) 2 cm, (d) 1.4 cm, and (e) 1.3 cm in depth. The second layer of the target site was located at 1.5 cm depth. Background optical properties at both reference and target sites are μa1=0.02, μs1′=7.0, μa2=0.1, and μs2′=7.0cm−1. The top picture of each part shows the position of the second layer and the target, and the bottom pictures [(a-1) and (b) to (e)] show the reconstructed absorption maps using an ROI of eight times the target size, while the bottom picture (a-2) shows the absorption maps reconstructed with an ROI of two times the target size. The color bar is the absorption coefficient in units of cm−1, and color bars in (a-2) was adjusted to 0.2 cm−1 for better visualization of the target. In the absorption map, each slice presents a spatial image of 8 cm×8 cm obtained from 0.4 cm underneath the probe surface to 2.9 cm in depth, with 0.5-cm spacing between slices. The spatial image dimensions for each slice in the absorption map and the spacing between the slices were kept the same as in Fig. 3 in the following figures except in Fig. 14. (Color online only.)

Fig. 4

Percentage of maximum reconstructed absorption coefficient of the target normalized to the no-background mismatch case as a function of the two-layer interface depth at the reference site using both calibrated background and fitted background optical properties (simulation data). The two-layer interface at the target side is located at 1.5 cm from the probe.

Fig. 5

Reconstructed absorption map of a 1-cm-diam spherical target with calibrated optical properties μa=0.07 and μs′=5.5cm−1, located at (x,y,z)=(0,0,0.9 cm). (a) B-scan ultrasound image of a two-layer medium with the target. A plastisol phantom was located at 1.4 cm underneath the probe surface with a zero-degree tilting angle. (b) B-scan ultrasound image of the phantom without the target. (c) Reconstructed target absorption map at 780 nm. (d) B-scan ultrasound image of the two-layer medium with the target [same as (a)]. (e) The two-layer medium with the plastisol phantom located at 2 cm with a zero-degree tilting angle. (f) Reconstructed target absorption map at 780 nm.

Fig. 6

Percentage of the maximum reconstructed μa normalized to the no-background mismatch case as a function of the two-layer interface depth at the reference site (phantom data) using both calibrated background and fitted background optical properties values. The two-layer interface at the target site is located at 1.5 cm depth from the probe.

Fig. 7

Reconstructed absorption maps of a target located at (x,y,z) =(0,0,0.9 cm). The first-and second-layer interfaces of both the target and the reference site were positioned at 1.5 cm depth. The interface at the target site has a zero-degree tilting angle. (a) to (i) sequentially show the absorption maps of the target with a target–reference layer tilting angle mismatch of (a) 0 deg, (b) 10 deg, (c) 5 deg, (d) −10 deg, and (e) −5 deg in the x direction, and of (f) 10 deg, (g) 5 deg, (h) −10 deg, and (i) −5 deg mismatch in the y direction. Optical properties of both the reference and target sites are μa1=0.02, μs1′=7.0, μa2=0.1, and μs2′=7.0cm−1 The top picture of each part shows the position of the second layer and the target, and bottom picture shows the reconstructed absorption map.

Fig. 8

Percentage of maximum reconstructed μa relative to the values obtained with the flat interface (no-background mismatch) as a function of the difference between the tilting angle of the two-layer interface at the target and reference sites.

Fig. 9

Reconstructed absorption map of 1-cm-diam spherical target located at (0, 0, 0.9 cm) with calibrated optical properties μa =0.07 cm−1 and μs′=5.5cm−1. (a) B-scan ultrasound image of a two-layer medium with target. The plastisol phantom was located at 1.4 cm with a zero-degree tilting angle. (b) B-scan ultrasound image of the same phantom without the target. The layer was located at 1.4 cm with −8-deg tilting angle. (c) Reconstructed target absorption map at 780 nm.

Fig. 10

Effect of first-layer μa mismatch between the reference site and the target site on the reconstructed image. First-layer optical properties at the target and reference sites are (a) μa1_tar=0.023, μa1_ref=0.023; (b) μa1_tar=0.04, μa1_ref=0.023; (c) μa1_tar=0.04, μa1_ref=0.04; and (d) μa1_tar =0.023, μa1_ref=0.04. The other background optical properties of both the reference and target sites are μs1′=7.5, μa2=0.08, and μs2′=6.5cm−1. The optical properties of the target are μa=0.23 and μs′=5.45cm−1.

Fig. 11

Percentage of maximum reconstructed μa normalized to the no-background mismatch case using both calibrated and fitted background values. Lower μa1_tar shows the results when μa1_tar=0.023 and μa1_ref=0.04 cm−1, and higher μa1_tar shows the results when μa1_tar=0.04, and μa1_ref=0.023 cm−1. The other optical properties of both the target and reference sites are μs1′=7.5, μa1=0.08, and μs2′=6.5cm−1.

Fig. 12

Effect of the first-layer μs1′ mismatch on the reconstructed absorption map of the target. The first-layer reduced scattering coefficient at the target site is (a) μs1′=5.8cm−1, (b) μs1′=6.5cm−1, (c) μs1′=7cm−1, (d) μs1′=7.3cm−1, (e) μs1′=7.7cm−1, and (f) μs1′=8.15cm−1, respectively. μs1′ at the reference site is 7.0 cm−1. Other optical properties of both the reference and lesion sites are μa1=0.024, μa2=0.08, and μs2′=6.5cm−1.

Fig. 13

Percentage of maximum reconstructed μa normalized to the no-background mismatch case as a function of first-layer reduced scattering coefficient at the target site using both calibrated and fitted background optical properties. The reduced scattering coefficient is 7.0 cm−1 at the reference site.

Fig. 14

Co-registered ultrasound and reconstructed absorption maps of a benign fibroadenoma. (a) B-scan ultrasound image of the lesion site. The chest-wall layer was located at 1.5 cm with 8 deg tilt. (b) B-scan ultrasound of the first reference site and the reconstructed absorption maps at 830 nm. (c) B-scan ultrasound of the tilted reference site and the reconstructed absorption maps at 830 nm. (d) B-scan ultrasound of the third reference site and the reconstructed absorption maps at 830 nm. Each slice presents a spatial image of 8 cm×8 cm obtained from 0.18 cm underneath the probe surface to 2.68 cm in depth, with 0.5-cm spacing between slices.