CEA, LETI, MINATEC, 17 rue des Martyrs, F-38054 Grenoble, France.
Phys Med Biol. 2009 Dec 7;54(23):7089-105. doi: 10.1088/0031-9155/54/23/004. Epub 2009 Nov 11.
The problem of fluorescence diffuse optical tomography consists in localizing fluorescent markers from near-infrared light measurements. Among the different available acquisition modalities, the time-resolved modality is expected to provide measurements of richer information content. To extract this information, the moments of the time-resolved measurements are often considered. In this paper, a theoretical analysis of the moments of the forward problem in fluorescence diffuse optical tomography is proposed for the infinite medium geometry. The moments are expressed as a function of the source, detector and markers positions as well as the optical properties of the medium and markers. Here, for the first time, an analytical expression holding for any moments order is mathematically derived. In addition, analytical expressions of the mean, variance and covariance of the moments in the presence of noise are given. These expressions are used to demonstrate the increasing sensitivity of moments to noise. Finally, the newly derived expressions are illustrated by means of sensitivity maps. The physical interpretation of the analytical formulae in conjunction with their map representations could provide new insights into the analysis of the information content provided by moments.
荧光漫射光学层析成像问题在于从近红外光测量中定位荧光标记物。在不同的可用采集方式中，时间分辨方式有望提供更丰富的信息量的测量。为了提取这些信息，通常会考虑时间分辨测量的矩。本文针对无限介质几何形状，提出了荧光漫射光学层析成像正问题的矩的理论分析。矩表示为源、探测器和标记物位置以及介质和标记物的光学特性的函数。在此，首次从数学上推导出适用于任何矩阶的解析表达式。此外，还给出了存在噪声时矩的均值、方差和协方差的解析表达式。这些表达式用于演示矩对噪声的敏感性增加。最后，通过灵敏度图来说明新推导出的表达式。结合其图谱表示的解析公式的物理解释可以为矩提供的信息量的分析提供新的见解。
