BOUNDARY-CONDITIONS FOR THE DIFFUSION EQUATION IN RADIATIVE-TRANSFER
BOUNDARY-CONDITIONS FOR THE DIFFUSION EQUATION IN RADIATIVE-TRANSFER
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DOI：
10.1364/josaa.11.002727
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发表时间：
1994-10-01
影响因子：
1.9
通讯作者：
TROMBERG, BJ
中科院分区：
文献类型：
--
作者：
HASKELL, RC;SVAASAND, LO;TROMBERG, BJ
利用镜像法，我们研究了半无限混浊介质表面的三种边界条件。我们发现，部分电流和外推边界条件的图像电荷配置具有相同的偶极子和四极矩，并且扩散方程的两个相应的解决方案近似相等。在频域光子迁移（FDPM）数据的扩散理论的应用中，这两种方法产生的散射和吸收系数的值是等于在3%以内。此外，这两个边界条件可以结合起来，以产生一个非常简单，准确，计算速度快的方法，从FDPM数据中提取的光学参数的值。FDPM数据在组织体模的表面和内部深处获取，并且两种几何形状之间的数据差异是惊人的。如果在不考虑边界的情况下分析表面数据，则推导出的光学系数值的误差为50%或更多。正如预期的那样，当铝箔被放置在组织体模的表面上时，相位和调制数据更接近于无限介质几何形状的结果。原则上，提高组织表面的反射率可以消除边界的影响。然而，我们发现相位和调制数据对80- 100%范围内的反射率高度敏感，并且需要98%的最小值来可靠地模拟无限介质几何形状。我们的结论是光学厚组织的非侵入性测量需要严格的组织边界的治疗，我们建议一个统一的部分电流外推边界的方法。
Using the method of images, we examine the three boundary conditions commonly applied to the surface of a semi-infinite turbid medium. We find that the image-charge configurations of the partial-current and extrapolated-boundary conditions have the same dipole and quadrupole moments and that the two corresponding solutions to the diffusion equation are approximately equal. In the application of diffusion theory to frequency-domain photon-migration (FDPM) data, these two approaches yield values for the scattering and absorption coefficients that are equal to within 3%. Moreover, the two boundary conditions can be combined to yield a remarkably simple, accurate, and computationally fast method for extracting values for optical parameters from FDPM data. FDPM data were taken both at the surface and deep inside tissue phantoms, and the difference in data between the two geometries is striking. If one analyzes the surface data without accounting for the boundary, values deduced for the optical coefficients are in error by 50% or more. As expected, when aluminum foil was placed on the surface of a tissue phantom, phase and modulation data were closer to the results for an infinite-medium geometry. Raising the reflectivity of a tissue surface can, in principle, eliminate the effect of the boundary. However, we find that phase and modulation data are highly sensitive to the reflectivity in the range of 80-100%, and a minimum value of 98% is needed to mimic an infinite-medium geometry reliably. We conclude that noninvasive measurements of optically thick tissue require a rigorous treatment of the tissue boundary, and we suggest a unified partial-current-extrapolated boundary approach.