Machine learning model with physical constraints for diffuse optical tomography

Abstract

A machine learning model with physical constraints (ML-PC) is introduced to perform diffuse optical tomography (DOT) reconstruction. DOT reconstruction is an ill-posed and under-determined problem, and its quality suffers by model mismatches, complex boundary conditions, tissue-probe contact, noise etc. Here, for the first time, we combine ultrasound-guided DOT with ML to facilitate DOT reconstruction. Our method has two key components: (i) a neural network based on auto-encoder is adopted for DOT reconstruction, and (ii) physical constraints are implemented to achieve accurate reconstruction. Both qualitative and quantitative results demonstrate that the accuracy of the proposed method surpasses that of existing models. In a phantom study, compared with the Born conjugate gradient descent (Born-CGD) reconstruction method, the ML-PC method decreases the mean percentage error of the reconstructed maximum absorption coefficient from 16.41% to 13.4% for high contrast phantoms and from 23.42% to 9.06% for low contrast phantoms, with improved depth distribution of the target absorption maps. In a clinical study, better contrast was obtained between malignant and benign breast lesions, with the ratio of the medians of the maximum absorption coefficient improved from 1.63 to 2.22.

Fig. 1.

Illustration of DOT breast imaging.

Fig. 2.

Cross-section of the FEM simulation geometry.

Fig. 3.

Ultrasound-guided DOT probe with 9 source fibers and 14 light guides.

Fig. 4.

Training process of ML-PC model using simulation and part of phantom data. A and B illustrate the training process of forward ML-PC model and inverse ML-PC model, respectively.

Fig. 5.

Validation process of ML-PC model.

Fig. 6.

Non-homogeneous phantoms. Left (phantom #1) phantom with a high contrast half ball on top; Right (phantom #2) phantom with a low contrast half ball on top.

Fig. 7.

Reconstruction results of phantom #1. Left: ML method without physical constraints; Middle: Born-CGD method; Right: ML-PC. Each figure consists of 7 slices, from the surface to a 3.5 cm depth, with 0.5 cm spacing. Each slice is 9 cm by 9 cm in the x and y dimensions.

Fig. 8.

Reconstruction results of phantom #2. Left: ML method without physical constraints; Middle: Born-CGD method; Right: ML-PC.

Fig. 9.

A, Born-CGD method reconstructed contrast for each layer; B, ML-PC method reconstructed contrast for each layer.

Fig. 10.

Reconstructed maximum ${\mu }_a$ values from the Born-CGD and ML-PC methods for high contrast (0.23 cm⁻¹) and low contrast phantoms (0.11 cm⁻¹).

Fig. 11.

Examples from patient studies. A and D are co-registered ultrasound images. B and E are reconstruction results using the Born-CGD method. C and F are reconstruction results using the ML-PC method. In the top row, A, B, and C are images from a 53-year-old women with a high grade invasive ductal carcinoma. Based on co-registered ultrasound, the center of the mass is located at 1.2 cm depth. In the bottom row, D, E, and F are images from a 55-year-old woman with a benign fibroadenoma. The center of the mass is located at 0.9 cm depth.

Fig. 12.

Clinically reconstructed maximum μ_a values from the Born-CGD and ML-PC methods for malignant (M) and benign (B) cases.

Fig. 13.

A, Contrasts of three reconstructed layers for five malignant cases using the Born-CGD and ML-PC methods; B, contrasts of three reconstructed layers for five benign cases using Born-CGD and ML-PC.