Anatomical image-guided fluorescence molecular tomography reconstruction using kernel method

Abstract

Fluorescence molecular tomography (FMT) is an important in vivo imaging modality to visualize physiological and pathological processes in small animals. However, FMT reconstruction is ill-posed and ill-conditioned due to strong optical scattering in deep tissues, which results in poor spatial resolution. It is well known that FMT image quality can be improved substantially by applying the structural guidance in the FMT reconstruction. An approach to introducing anatomical information into the FMT reconstruction is presented using the kernel method. In contrast to conventional methods that incorporate anatomical information with a Laplacian-type regularization matrix, the proposed method introduces the anatomical guidance into the projection model of FMT. The primary advantage of the proposed method is that it does not require segmentation of targets in the anatomical images. Numerical simulations and phantom experiments have been performed to demonstrate the proposed approach’s feasibility. Numerical simulation results indicate that the proposed kernel method can separate two FMT targets with an edge-to-edge distance of 1 mm and is robust to false-positive guidance and inhomogeneity in the anatomical image. For the phantom experiments with two FMT targets, the kernel method has reconstructed both targets successfully, which further validates the proposed kernel method.

Fig. 1

Numerical simulation phantom geometry of (a) the cylindrical phantom with target locations at T1 ($-1.7$ and 5.56) and T2 (1.7 and 5.56) and (b) the elliptic cylindrical phantom with target locations at T1 ($-1.2$ and $-5.0$) and T2 (1.2 and $-5.0$).

Fig. 2

The geometry of the phantom experiment with target locations at T1 (1.72 and 4.71) and T2 (5.01 and 1.87).

Fig. 3

For the numerical simulation of two targets: (a) the ground-truth images, (b) simulated anatomical guidance images, and (c) the reconstructed FMT images with the soft prior method. The interval between slices along $z$-axis is 5.33 mm.

Fig. 4

Reconstruction FMT images for the cylindrical phantom simulation of two targets by the kernel method with different nearest neighbor $k$ as indicated by each row and different voxel numbers indicated by each column. The interval between slices along $z$-axis is 5.33 mm.

Fig. 5

For the simulation of elliptic cylindrical phantom with two FMT targets, (a) the ground-truth images, (b) simulated CT images, and (c) the reconstructed FMT images with the soft prior method. The interval between slices along $z$-axis is 4.54 mm.

Fig. 6

Reconstructed FMT images for the elliptic cylindrical phantom simulation of two targets by the kernel method with different nearest neighbor $k$ as indicated by each row and different voxel numbers indicated by each column. The interval between slices along $z$-axis is 4.54 mm.

Fig. 7

For the numerical simulation with false larger target size, (a) the ground-truth images, (b) simulated CT images with the false enlarged target, (c) the reconstructed FMT images with the soft prior method, and (d) the reconstructed FMT images by the kernel method with the nearest neighbor of $k=256$ and the voxel number of $3\times 3\times 3$. The interval between slices along $z$-axis is 4.54 mm.

Fig. 8

Numerical simulation with the rat brain MRI images: (a) MRI images, (b) the reconstructed FMT images with the soft prior method, and (c) the reconstructed FMT images with the kernel method with $k=256$ and the voxel number of $3\times 3\times 3$. The interval between slices along $z$-axis is 2.45 mm.

Fig. 9

(a) Original CT images. The reconstructed FMT images (b) without priors, (c) with the soft prior method and the homogenous background, (d) with the kernel method using original CT images as guidance with $k=64$ and the voxel number of $5\times 5\times 5$. The interval between slices along $z$-axis is 5.33 mm.

Fig. 10

(a) CT images with artificial features. (b) Reconstructed FMT images with the soft prior method and the inhomogenous background in the CT images. (c) Reconstructed FMT images with the kernel method using the CT images with artificial features as the guidance with $k=256$ and the voxel number of $3\times 3\times 3$. The interval between slices along $z$-axis is 5.33 mm.