The solution of the forward problem in fluorescence molecular imaging strongly influences the successful convergence of the fluorophore reconstruction. The most common approach to meeting this problem has been to apply the diffusion approximation. However, this model is a first-order angular approximation of the radiative transfer equation, and thus is subject to some well-known limitations. This manuscript proposes a methodology that confronts these limitations by applying the radiative transfer equation in spatial regions in which the diffusion approximation gives decreased accuracy. The explicit integro differential equations that formulate this model were solved by applying the Galerkin finite element approximation. The required spatial discretization of the investigated domain was implemented through the Delaunay triangulation, while the azimuthal discretization scheme was used for the angular space. This model has been evaluated on two simulation geometries and the results were compared with results from an independent Monte Carlo method and the radiative transfer equation by calculating the absolute values of the relative errors between these models. The results show that the proposed forward solver can approximate the radiative transfer equation and the Monte Carlo method with better than 95% accuracy, while the accuracy of the diffusion approximation is approximately 10% lower.

译文

:荧光分子成像中前向问题的解决方案强烈影响荧光团重建的成功收敛。解决此问题的最常用方法是应用扩散近似。但是,该模型是辐射传递方程的一阶角近似,因此受到一些众所周知的限制。该手稿提出了一种通过在空间区域应用辐射传递方程来解决这些局限性的方法,其中扩散近似会降低精度。通过应用Galerkin有限元逼近法解决了表达该模型的显式积分微分方程。通过Delaunay三角剖分实现了所研究域的所需空间离散化,而方位角离散化方案则用于角空间。该模型已在两种模拟几何条件下进行了评估,并将结果与​​独立蒙特卡罗方法和辐射传递方程的结果进行了比较,方法是计算这些模型之间的相对误差的绝对值。结果表明,所提出的前向求解器可以近似于95%的精度近似辐射传递方程和蒙特卡罗方法,而扩散近似的精度则低约10%。

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