Evaluation of a pipeline for simulation, reconstruction, and classification in ultrasound-aided diffuse optical tomography of breast tumors

Abstract

Significance: Diffuse optical tomography is an ill-posed problem. Combination with ultrasound can improve the results of diffuse optical tomography applied to the diagnosis of breast cancer and allow for classification of lesions.

Aim: To provide a simulation pipeline for the assessment of reconstruction and classification methods for diffuse optical tomography with concurrent ultrasound information.

Approach: A set of breast digital phantoms with benign and malignant lesions was simulated building on the software VICTRE. Acoustic and optical properties were assigned to the phantoms for the generation of B-mode images and optical data. A reconstruction algorithm based on a two-region nonlinear fitting and incorporating the ultrasound information was tested. Machine learning classification methods were applied to the reconstructed values to discriminate lesions into benign and malignant after reconstruction.

Results: The approach allowed us to generate realistic US and optical data and to test a two-region reconstruction method for a large number of realistic simulations. When information is extracted from ultrasound images, at least 75% of lesions are correctly classified. With ideal two-region separation, the accuracy is higher than 80%.

Conclusions: A pipeline for the generation of realistic ultrasound and diffuse optics data was implemented. Machine learning methods applied to a optical reconstruction with a nonlinear optical model and morphological information permit to discriminate malignant lesions from benign ones.

Keywords: breast cancer; breast digital phantom; diffuse optical tomography; lesion classification; ultrasound.

Fig. 1

Geometry definition. A VICTRE phantom is compressed between two paddles to 45 mm. A cuboid region $\mathrm{\Omega }$ is extracted to serve as functional ground truth in the discussion. A SOLUS-like probe is simulated on the top surface of the considered domain. The plane $y=0$ is set to be the imaging plane of the US transducer.

Fig. 2

Spectra used in simulations for the components generated by VICTRE. Blood vessels and other tissues are presented in different images for visualization purposes due to the scale. (a) Absorption spectra of blood vessels. A smaller saturation has been chosen for veins. (b) Absorption spectra simulated for the other tissues.

Fig. 3

Spectral plot of optical coefficients for breast bulk (blue), benign (green), and malignant (red) inclusions. The effective optical coefficient values for the breast have been obtained by fitting a homogeneous analytical model to the reference optical data obtained by simulating a breast with no inclusion. (a) Absorption spectra of malignant lesions, benign lesions, and healthy breast tissues. (b) Scattering spectra of malignant lesions, benign lesions (excluding cysts), cysts, and healthy breast tissues.

Fig. 4

B-mode image generation: Example 1. (a) Map of ${\bar{v}}_s$ over ${\mathrm{\Omega }|}_{y=0}$. (b) Map of ${\sigma }_{\text{micro}}$ over ${\mathrm{\Omega }|}_{y=0}$. (c) $v_s(\mathbf{r})$ for $\mathbf{r}\in {\mathrm{\Omega }|}_{y=0}$. (d) B-mode image. (e) Segmentation. Blue is the user-defined segmentation, green is the final one. $\mathrm{SDI}=0.80$, $\mathrm{d}A=-0.26$.

Fig. 5

B-mode image generation: Example 2. (a) Map of ${\overline{v}}_s$ over $\mathrm{\Omega }{|}_{y=0}$. (b) Map of ${\sigma }_{\mathrm{micro}}$ over $\mathrm{\Omega }{|}_{y=0}$. (c) $v_s(\mathbf{r})$ for $\mathbf{r}\in \mathrm{\Omega }{|}_{y=0}$. (d) B-mode image. (e) Segmentation. Blue is the user-defined segmentation, green is the final one. $\mathrm{SDI}=0.76$, $\mathrm{d}A=-0.32$.

Fig. 6

Ground truth and final extrapolation for example 1 from Fig. 4 and example 2 from Fig. 5. (a) Example 1: ground truth lesion. (b) Example 1: distance transform extrapolated shape, $\mathrm{SDI}=0.46$, $\mathrm{d}V=-0.68$. (c) Example 2: ground truth lesion. (d) Example 2: distance transform extrapolated shape, $\mathrm{SDI}=0.68$, $\mathrm{d}V=-0.39$.

Fig. 7

Comparison of ground truth optical coefficients and reconstructed ones using the ground truth shape as two-region delimiter. In (a) and (b), a scatter plot of reconstructed inclusions versus ground truth values are shown. Each scatter plot consists of $724\text{\hspace{0.17em}\hspace{0.17em}lesions}\times 8\text{\hspace{0.17em}\hspace{0.17em}wavelengths}$ scatter points. As can be seen, points tend to cluster around the optimal behavior highlighted by the black dashed line. As expected, this behavior is more accentuated for absorption. (a) Scatter plot of ground truth lesion absorption versus reconstructed lesion absorption. (b) Scatter plot of ground truth lesion scattering versus reconstructed lesion scattering. (c) Violin plot of ground truth (dark) and retrieved (light) absorptions by wavelength. Green represents benign lesions and red malignant ones. Blue ticks represent the 5th, 25th, 75th and 95th percentiles of the distribution of the retrieved absorptions. (c) Display of the statistics of the ground truth and retrieved values by wavelength.

Fig. 8

PCA of ground truth and reconstructed values of the inclusion with the three axes representing the first three principal components of the dataset. The separation is neat on the ground truth. A certain degree of separation can also be observed after reconstruction with the ground truth shape defining the two regions. Results are apparently worse when defining the two-region extrapolating a shape from the US B-mode simulations. However, the dataset can have better separability in higher dimensions or applying a nonlinear transformation. (a) PCA of ground truth—log normalization. (b) PCA of nonlinear model fit—log normalization. (c) PCA of nonlinear model fit with US prior—log normalization.