Report on the Study of Fluorescence Molecular Tomography for Morphological Reconstruction of Glioma Based on Group Sparsity Priors

1. Academic Background and Research Motivation

Fluorescence Molecular Tomography (FMT) is an important tool in life sciences that allows non-invasive real-time three-dimensional (3D) visualization of fluorescence source locations. Due to its high sensitivity and low costs, FMT is widely utilized in tumor research. However, the reconstruction process in FMT is complex and challenging. Although FMT reconstruction methods have rapidly advanced in recent years, morphological reconstruction remains a difficult problem. Therefore, this study aims to achieve FMT morphological reconstruction performance in glioma research.

2. Paper Source and Author Information

This paper was published in the IEEE Transactions on Biomedical Engineering, Volume 67, Issue 5, May 2020, titled “Fluorescence Molecular Tomography Based on Group Sparsity Priori for Morphological Reconstruction of Glioma.” The authors of the paper include Shixin Jiang, Jie Liu, Yu An, Yuan Gao, Hui Meng, Kun Wang, and Jie Tian. The research was supported by the National Key Research and Development Program of China, the National Natural Science Foundation of China, and the Beijing Natural Science Foundation.

3. Detailed Research Process

a) Research Process

1. Photon Propagation Model

The study first describes the propagation characteristics of photons in the near-infrared spectrum within biological tissues. Steady-state FMT uses the Diffusion Equation (DE) to describe photon propagation in highly scattering media. This includes photon transmission during excitation and emission stages and the significant variations on the surface of the imaging object.

\begin{cases}
-\nabla [d_x (r) \nabla \phi_x (r)] + \mu_{ax} (r) \phi_x (r) = \theta \delta (r - r_l) (r \in \omega) \\
-\nabla [d_m (r) \nabla \phi_m (r)] + \mu_{am} (r) \phi_m (r) = \phi_x (r) \eta \mu_{af} (r) (r \in \omega)
\end{cases}

The study simplified the diffusion equation using the finite element method. To accurately describe photon transmission at the boundaries, Robin boundary conditions were applied.

2. FMT Problem Reconstruction

FMT has the characteristics of an ill-posed problem. To obtain satisfactory reconstruction results, regularization constraints were adopted. The study first introduced the traditional Tikhonov regularization method (with L2 norm constraints) and then introduced the more commonly used sparse reconstruction method (with L1 norm constraints).

\min_x e(x) = \frac{1}{2} \|Ax - \phi\|_2^2 + \lambda \|x\|_1

To improve the issue where traditional methods ignore fluorescence source morphology information, a reconstruction method based on group sparsity priors was proposed. The group sparsity method utilizes the sparsity and group structure characteristics of the fluorescence source. The model adopted the Fused Lasso Method (FLM).

\min_x e(x) = \frac{1}{2} \|Ax - \phi\|_2^2 + \gamma (x)

Where γ(x) = λ1 Σ |xi| + λ2 Σ |xi - xi-1| is the fused lasso penalty term.

b) Detailed Experimental Results

Numerical Simulation Experiment

The study used a numerical mouse model to simulate glioma. To simplify the dataset, it focused on the mouse head, mainly including muscle, skull, and brain sections, with a 2 mm high and 2 mm diameter cylindrical fluorescence source set in the brain. For numerical experiments, the model was meshed using Amira 5.4 software, and the optical parameters are shown in the table.

The experimental results showed that the reconstruction region of NFLM was closer to the real region, while the IS-L1 method failed to reconstruct the fluorescence region due to its sparsity. The reconstruction results of Tikhonov-based methods tended to be overly smooth at the source boundary. Compared with FLM, NFLM showed better morphological reconstruction performance, validating the effectiveness of NFLM.

In Vivo Experiment

An in vivo glioma model was established in Balb/c nude mice. Fluorescence data were collected using continuous-wave laser combined with specific band filters and an ultrasensitive CCD camera. The experiment analyzed the in vivo experiment results through three steps: data acquisition, data processing, and data reconstruction.

The results showed that NFLM performed the best in morphology and localization in three mice. When compared with MRI images, higher Dice values and smaller Position Error (PE) values were obtained, proving the significant advantages of NFLM in FMT reconstruction.

4. Research Conclusions, Value, and Highlights

1. Research Conclusion

The NFLM method based on group sparsity priors can effectively maintain the morphological information of fluorescence sources, significantly improving the accuracy and spatial resolution of FMT reconstruction. The research results confirmed the feasibility and potential of group sparsity-based methods in FMT reconstruction.

2. Research Value

This study demonstrated the great application potential of morphology reconstruction based on group sparsity in tumor research, particularly in glioma research. The NFLM method has significant advantages in solving the reconstruction accuracy problem of deep tumors.

3. Research Highlights

The study is the first to propose using group sparsity priors to reconstruct the morphology of gliomas, adopting the improved FLM method. By normalizing the columns of the system matrix, it enhanced the compensation effect of mail intensities. Compared with traditional Tikhonov and L1 regularization methods, the NFLM method demonstrated significant advantages in reconstruction accuracy and morphology preservation.

The fluorescence molecular tomography method based on group sparsity priors has notable advantages and application prospects in tumor research, playing an important role in future clinical and small animal research.