Adaptive hp finite element method for fluorescence molecular tomography with simplified spherical harmonics approximation

Hongbo Guo,Jingxing Cheng,Yuqing Hou,Xin Pu,Xiaowei He,Jingjing Yu

doi:10.1142/s1793545813500570

Abstract

Recently, the simplified spherical harmonics equations (SPN) model has attracted much attention in modeling the light propagation in small tissue geometries at visible and near-infrared wavelengths. In this paper, we report an efficient numerical method for fluorescence molecular tomography (FMT) that combines the advantage of SPN model and adaptive hp finite element method (hp-FEM). For purposes of comparison, hp-FEM and h-FEM are, respectively applied to the reconstruction process with diffusion approximation and SPN model. Simulation experiments on a 3D digital mouse atlas and physical experiments on a phantom are designed to evaluate the reconstruction methods in terms of the location and the reconstructed fluorescent yield. The experimental results demonstrate that hp-FEM with SPN model, yield more accurate results than h-FEM with diffusion approximation model does. The phantom experiments show the potential and feasibility of the proposed approach in FMT applications.

Highlights

As an increasingly important tool for in vivo preclinical research, °uorescence molecular tomography (FMT) aims at the quantitative reconstruction of the 3D spatial distribution of a photon source inside an animal volume from the photon density detected on the surface of the animal
Hp-FEM and h-FEM are respectively applied in the reconstruction process with di®usion approximation (DA) model and spherical harmonics equations (SPN) model
The results show that: (1) Generally, two forward models combined with two FEMs can estimate the position of °uorescence sources; (2) The proposed method, hp-FEM with SPN model, yield more accurate results than h-FEM with DA model does

Summary

Introduction

As an increasingly important tool for in vivo preclinical research, °uorescence molecular tomography (FMT) aims at the quantitative reconstruction of the 3D spatial distribution of a photon source inside an animal volume from the photon density detected on the surface of the animal. In this imaging modality, the photon source is typically a °uorescent probe tagging the molecule of interest.[1,2] An external excitation light source is needed to. By reconstructing the targeted °uorescent probes with an inverse method one can achieve 3D imaging of molecular processes noninvasively.[3,4]

Methods

Results

Conclusion