Reconstruction of localized fluorescent target from multi-view continuous-wave surface images of small animal with lp sparsity regularization

Abstract

Fluorescence diffuse optical tomography using a multi-view continuous-wave and non-contact measurement system and an algorithm incorporating the lp (0 < p ≤ 1) sparsity regularization reconstructs a localized fluorescent target in a small animal. The measurement system provides a total of 25 fluorescence surface 2D-images of an object, which are acquired by a CCD camera from five different angles of view with excitation from five different angles. Fluorescence surface emissions from five different angles of view are simultaneously imaged on the CCD sensor, thus leading to fast acquisition of the 25 images within three minutes. The distributions of the fluorophore are reconstructed by solving the inverse problem based on the photon diffusion equations. In the reconstruction process incorporating the lp sparsity regularization, the regularization term is reformulated as a differentiable function for gradient-based non-linear optimization. Numerical simulations and phantom experiments show that the use of the lp sparsity regularization improves the localization of the target and quantitativeness of the fluorophore concentration. A mouse experiment demonstrates that a localized fluorescent target in a mouse is successfully reconstructed.

Keywords: (170.3880) Medical and biological imaging; (170.6280) Spectroscopy, fluorescence and luminescence.

Fig. 1

(a) Schematics of the CW measurement system to acquire the surface fluorescence images of the measured object, and the angular positions of (b) excitation and (c) emission light.

Fig. 2

The geometry of a cylindrical object, and true and reconstructed x–y sectional images of the ICG concentration normalized by their maxima for Case (i). True images (first column), reconstructed images using the Tikhonov regularization (second column) and using the l_p sparsity regularization with p = 1 (third column) and p = 0.5 (fourth column) for the depths of the true target being 4 mm (top row), 6 mm (middle row) and 9 mm (bottom row).

Fig. 3

Reconstructed quantities of ICG in the VOI using the Tikhonov regularization (blue dashed line) and the l_p sparsity regularization with p = 1 (green chained line) and p = 0.5 (red solid line) as a function of the depth of the target.

Fig. 4

True and reconstructed x–y sectional images of the ICG concentration normalized by their maxima for Case (ii). True images (first column), reconstructed images using the Tikhonov regularization (second column) and the l_p sparsity regularization with p = 1 (third column) and p = 0.5 (fourth column) for the true quantity of ICG in the targets of 100 pmol (top row), 10 pmol (middle row) and 1 pmol (bottom row).

Fig. 5

Reconstructed quantities of ICG in the VOI using the Tikhonov regularization (blue dashed line) and the l_p sparsity regularization with p = 1 (green chained line) and p = 0.5 (red solid line) as a function of the true fluorophore quantity.

Fig. 6

True and reconstructed x–y sectional images of the normalized ICG concentration for Case (iii). True images (first column), reconstructed images using the Tikhonov regularization (second column) and the l_p sparsity regularization with p = 1 (third column) and p = 0.5 (fourth column) for the true targets of 1 mm³ (top row), 8 mm³ (middle row) and 27 mm³ (bottom row).

Fig. 7

True and reconstructed x–y sectional images of the normalized ICG concentration for Case (iv). True images (first column), reconstructed images using the Tikhonov regularization (second column) and the l_p sparsity regularization with p = 1 (third column) and p = 0.5 (fourth column) for the distances between the targets of 4 mm (top row), 6 mm (middle row) and 8 mm (bottom row).

Fig. 8

The profiles of the reconstructed quantities of ICG along the line connecting the two target centers, Q(x), using the Tikhonov regularization (blue dashed line) and the l_p sparsity regularization with p = 1 (green chained line) and p = 0.5 (red solid line) for Case (iv) when the distance between the two targets is (a) 4mm, (b) 6 mm and (c) 8 mm. The true quantities are 100 pmol for both targets.

Fig. 9

True and reconstructed x–y sectional images of the ICG concentration normalized by the maxima of the reconstructed ICG concentration for Case (v) for Case (v). True images (first column), reconstructed images using the Tikhonov regularization (second column) and the l_p sparsity regularization with p = 1 (third column) and p = 0.5 (fourth column). The two targets are at the fixed positions but with different ICG quantities; 100 pmol and 75 pmol (top row), 100 pmol and 50 pmol (middle row), and 100 pmol and 25 pmol (bottom row).

Fig. 10

Profiles of Q(x) reconstructed using the Tikhonov regularization (blue dashed line) and the l_p sparsity regularization with p = 1 (green chained line) and p = 0.5 (red solid line) for Case (v). The target on the left hand side contain 100 pmol of ICG while the targets on the right hand side contain (a) 75 pmol, (b) 50 pmol and (c) 25 pmol of ICG.

Fig. 11

Fluorescence surface images superimposed on the visible light images of the phantom acquired by Clairvivo OPT with 5 angular positions of the excitation light, Ex 1 to 5 (numbered in Fig. 1(b)), for the targets at the depths of (a) 4 mm, (b) 6 mm and (c) 9 mm. Five views of Emissions 4, 5, 1, 2, and 3 (numbered in Fig. 1(c)) are aligned from left to right in each images. Color bars indicate the photon counts per second.

Fig. 12

True and reconstructed x–y sectional images of the ICG concentration in the phantom experiments for the true targets at the depths of (a) 4 mm (top row), (b) 6 mm (middle row) and (c) 9 mm (bottom row); true images (first column), reconstructed images using the Tikhonov regularization (second column) and the l_p sparsity regularization with p = 1 (third column) and p = 0.5 (fourth column).

Fig. 13

Reconstructed quantities of ICG in the VOI using the Tikhonov regularization (blue dashed line) and the l_p sparsity regularization with p = 1 (green chained line) and p = 0.5 (red solid line) as a function of the target depth of the target in the phantom experiment.

Fig. 14

Fluorescence surface images of the mouse acquired by Clairvivo OPT with 5 angular positions of excitation light, Excitation 1 to 5 (numbered in Fig. 1(b)). Five views of Emission 4, 5, 1, 2, and 3 (numbered in Fig. 1(c)) are aligned from left to right in each image. Color bar indicates the photon counts per second.

Fig. 15

MR images (first column) and reconstructed fluorescence tomographic images using the Tikhonov regularization (second column), and the l_p sparsity regularization with p = 1 (third column) and p = 0.5 (fourth column). The sagittal (top row), coronal (middle row) and axial (bottom row) images are shown. Red circles in the MR images indicate the correct position of the target.

Fig. 16

Reconstructed quantities of ICG, Q(y), (right) along the y-axis indicated in the reconstructed axial MR image (left). The reconstructed values using the Tikhonov regularization (blue dashed line), and the l_p sparsity regularization with p = 1 (green chained line) and p = 0.5 (red solid line) are shown together with the true values (black dotted line).