A two-step numerical computation of T2* signal weighting maps in gradient echo magnetic resonance imaging in the presence of an object with varied susceptibility property is presented. In the first step, the magnetic scalar potential is computed for an arbitrary 2D magnetic susceptibility distribution using an algebraic solver. The corresponding magnetic field disturbance is computed from the magnetic scalar potential. In the second step, nonlinear operations are used to compute T2* from the magnetic field disturbance and then to generate a map of T2* signal weighting. The linearity of the first step of the solution process is used to implement a superposition of basis solutions approach that increases computational efficiency. Superposition of basis solutions, computed from a system composed of a single node of differing magnetic susceptibility from the surround, herein referred to as the base system, is found to provide an accurate estimation of the scalar potential for arbitrary susceptibility distributions. Afterwards, nonlinear computation of the T2* signal weighting maps can be performed. The properties of the algebraic magnetic scalar potential solver are discussed in this work. Finally, the linearity of the magnetic scalar potential solver is used to estimate the magnetic susceptibility of various objects from in vitro MR-imaging data acquired at 9.4T.

中文翻译：

---

计算磁场失真和对 T2* 加权 MRI 的影响，并应用于磁化率参数估计

提出了在存在具有不同磁化率特性的物体的情况下梯度回波磁共振成像中 T2* 信号加权图的两步数值计算。在第一步中，使用代数求解器计算任意二维磁化率分布的磁标量势。相应的磁场扰动由磁标量势计算得出。在第二步中，非线性运算用于根据磁场干扰计算 T2*，然后生成 T2* 信号加权图。求解过程的第一步的线性用于实现基础求解方法的叠加，以提高计算效率。基础解的叠加，发现从由来自周围的具有不同磁化率的单个节点组成的系统（这里称为基础系统）计算出的磁化率可提供对任意磁化率分布的标量势的准确估计。之后，可以执行 T2* 信号加权图的非线性计算。在这项工作中讨论了代数磁标量势求解器的特性。最后，利用磁标量势求解器的线性度，从 9.4T 采集的体外 MR 成像数据中估计各种物体的磁化率。可以执行 T2* 信号加权图的非线性计算。在这项工作中讨论了代数磁标量势求解器的特性。最后，利用磁标量势求解器的线性度，从 9.4T 采集的体外 MR 成像数据中估计各种物体的磁化率。可以执行 T2* 信号加权图的非线性计算。在这项工作中讨论了代数磁标量势求解器的特性。最后，利用磁标量势求解器的线性度，从 9.4T 采集的体外 MR 成像数据中估计各种物体的磁化率。