磁共振扩散张量成像扩散椭球面积的简化计算方法

The Concise Algorithm for Computing the Surface Area of Diffusion Ellipsoids in Magnetic Resonance Diffusion Tensor Imaging

目的:提出一种可以精确计算磁共振扩散张量成像扩散椭球表面积的方法。方法:根据理想扩散椭球是旋转椭球及扩散张量矩阵均正定,可将三轴椭球校正为旋转椭球,进而由A.M.Legendre公式推出计算扩散椭球表面积的简化公式。分别利用A.M.Legendre、Knud Thomsen及本文提出的方法计算四种扩散椭球的表面积以评价本文方法的可行性。结果:对于旋转椭球,本文所提方法的计算结果与A.M.Legendre方法的结果一致。结论:本文所提方法计算量较小,可以精确地计算扩散椭球表面积。

Objective:To propose a concise algorithm that can precisely calculate the surface area of diffusion ellipsoids in magnetic resonance diffusion tensor imaging.Methods:Due to the ideal diffusion ellipsoid was a rotational ellipsoid and diffusion tensor matrix was a positive-definite matrix,the triaxial ellipsoids were modified to rational ellipsoids,so a concise algorithm may be derived from A.M.Legendre formula.A.M.Legendre,Knud Thomsen and our method was used to calculate four kinds of ellipsoidal surface a...