多散射介质中光子密度波扩散方程的二阶求解

对于生物医学光子学领域中的新技术-扩散光子密度波技术进行了理论上的研究与扩展,给出了长为a,宽为b,高为无限大的矩形边界条件下光子密度波扩散方程的二阶微扰解析解.由于实际测到的物理量多为光通量,演算出了与入射面相对应面处的光子通量和介质中的吸收系数改变量之间的关系.并利用人体前臂肌肉组织的典型光学参数,给出了二阶微扰解的模拟计算结果,并与一阶微扰计算结果进行了比较.结果表明,二阶微扰解比原有的一阶微扰解在计算精度上有一定的提高,尤其是在异常体附近精度更是有较大的提高.所得二阶结果不仅为利用扩散方程进行生物组织成像问题提供了更加精确的理论基础,而且对于图像质量尤其是分辨异物的能力的提高具有促进作用.

Second-order solution of diffusion equation in multiple-scattering media with photon density wave

The diffusion equation in multiple-scattering media with photon density wave is a hotspot in the field of biomedical photonics. Considered the cubic boundary conditions, a second-order analytical solution of diffusion equation of photon density wave is presented. The relationship between the absorption coefficient and the flux is derived, for the flux can be easily obtained in practical experiments. Using this relationship and the optical properties of typical forearm tissue, the second-order simulation results are given. Compared with the results of first-order solution, second-order one is more accurate and the precision is greatly improved. This method proposed is applicable in the biomedical imaging of multiple-scattering media, and has many advantages in the imaging quality and spatial resolution.