Two-step reconstruction method using global optimization and conjugate gradient for ultrasound-guided diffuse optical tomography

Abstract

Ultrasound-guided diffuse optical tomography (DOT) is a promising method for characterizing malignant and benign lesions in the female breast. We introduce a new two-step algorithm for DOT inversion in which the optical parameters are estimated with the global optimization method, genetic algorithm. The estimation result is applied as an initial guess to the conjugate gradient (CG) optimization method to obtain the absorption and scattering distributions simultaneously. Simulations and phantom experiments have shown that the maximum absorption and reduced scattering coefficients are reconstructed with less than 10% and 25% errors, respectively. This is in contrast with the CG method alone, which generates about 20% error for the absorption coefficient and does not accurately recover the scattering distribution. A new measure of scattering contrast has been introduced to characterize benign and malignant breast lesions. The results of 16 clinical cases reconstructed with the two-step method demonstrates that, on average, the absorption coefficient and scattering contrast of malignant lesions are about 1.8 and 3.32 times higher than the benign cases, respectively.

Figures

Fig. 1

The maximum fitted (a) absorption coefficient; (b) reduced scattering coefficient; and (c) diameter of simulated targets using GA. The targets are located at depths of 0.5 to 2 cm. The dotted line shows the true values.

Fig. 2

An example of the reduction of the mean error, Er, of the population calculated at each generation of GA.

Fig. 3

The maximum reconstructed (a) absorption coefficient and (b) reduced scattering coefficient of 1-, 1.5-, and 2.5-cm diameter simulated targets located at depths of 0.5 to 2 cm. The dotted line shows the true values.

Fig. 4

The maximum reconstructed (a) absorption coefficient and (b) reduced scattering coefficient versus size calculated for simulated targets located at depths of 0.5 to 2 cm. The dotted line shows the true values.

Fig. 5

Maximum reconstructed absorption versus reduced scattering of simulated targets of different sizes located at depths of 0.5 to 2 cm: (a) reconstructed with CG method and (b) with CG after fitting with GA.

Fig. 6

Fitted diameter of phantom targets using GA. The targets are located at depths of 0.5 to 2 cm.

Fig. 7

Maximum reconstructed (a) absorption and (b) reduced scattering of medium (1.5 cm diameter) and big (2.5 cm diameter) phantom targets located at depths of 0.5 to 2 cm.

Fig. 8

A benign lesion obtained from patient #2: (a) ultrasound B-scan, spatial absorption map reconstructed at depths from 0.5 to 3 cm with (b) CG method and (c) after GA fitting; (d) reconstructed scattering distribution after GA fitting.

Fig. 9

A malignant lesion obtained from patient #11: (a) ultrasound B-scan, spatial absorption map reconstructed at depths from 0.5 to 3 cm with (b) CG method and (c) after GA fitting; (d) reconstructed scattering distribution after GA fitting.

Fig. 10

Maximum absorption of nine benign (1 to 9) and seven malignant (10 to 16) cases reconstructed with CG method started from zero initial values compared with the CG after GA fitting.

Fig. 11

Scattering contrast calculated for nine benign (one to nine) and seven malignant (10 to 16) cases.

Fig. 12

(a) Maximum reconstructed absorption and (b) scattering contrast of the nine benign and seven malignant cases.