【摘要】 漫射方程是目前光学成像中应用最广泛的光传输模型,通常采用有限元方法进行求解。但是,有限元方法依赖于对整个求解域的网格剖分,而对于类似生物组织的非规则形状求解域的网格剖分是非常困难的,甚至昂贵的商业软件也难以很好地处理。本文将点加权最小二乘无网格法应用于漫射方程的求解。这种方法只需要在求解域内布置一系列规则分布的配点即可进行数值求解,从而可以完全避免有限元方法中困难的剖分工作。此外,这种方法通过最小化控制方程和边界条件在每个配点上产生的残量加权平方和,建立光源功率和光流率密度之间的关系,不需要进行任何数值积分运算,非常适合应用于非规则求解域的求解。基于数字鼠模型的数值仿真实验验证了该方法的准确性和有效性。更多还原

【Abstract】 Diffusion equation is a widely used model for photon transport in biological tissues.Commonly,it can be solved by the finite element method,which depends on the mesh discretization of interesting area.However,this kind of discretization is quite difficult for complex geometries such as biological tissues,even using commercial software.In this paper,a point weighted least-squares(PWLS) meshless method for the photon transport in diffusive biological tissues with complex and irregular geometries is presented.The proposed method does the calculation with some collocation points distributed regularly in the interesting area,so that complicated mesh generation required by finite element method can be avoided.Moreover,our method establishes the relationship between the source distribution and the photon flux density by minimizing the weighted residuals quadratic sum of all collocation points.Thus,it doesn’t need the complicated integration calculation,which provides more convenience for the application in irregular shaped region like biological tissues.Numerical simulations with the phantoms constructed based on mouse tissues demonstrate the accuracy and effectiveness of the proposed method.更多还原