Tanase Costin, Boada Fernando E
Department of Physics and Astronomy, University of Pittsburgh, 35905 O'Hara Street, Pittsburgh, PA 15213, USA.
J Magn Reson. 2005 Apr;173(2):236-53. doi: 10.1016/j.jmr.2004.12.009.
The dynamics of spin 3/2 systems is analyzed using the density matrix theory of relaxation. By using the superoperator formalism, an algebraic formulation of the density matrix's evolution is obtained, in which the contributions from free relaxation and RF application are easily factored out. As an intermediate step, an exact form for the propagator of the density matrix for a spin 3/2 system, in the presence of static quadrupolar coupling, inhomogeneous static magnetic field, and relaxation is demonstrated. Using this algebraic formulation, exact expressions for the behavior of the density matrix in the classical one-, two-, and three-pulse experiments are derived. These theoretical formulas are then used to illustrate the bias introduced on the measured relaxation parameters by the presence of large spatial variations in the B0 and B1 fields. The theoretical predictions are easily evaluated through simple matrix algebra and the results agree very well with the experimental observations. This approach could prove useful for the characterization of the spatial variations of the signal intensity in multiple quantum-filtered sodium MRI experiments.
利用弛豫密度矩阵理论分析了自旋3/2系统的动力学。通过使用超算符形式，得到了密度矩阵演化的代数表达式，其中自由弛豫和射频应用的贡献很容易分解出来。作为中间步骤，给出了在存在静态四极耦合、非均匀静磁场和弛豫情况下自旋3/2系统密度矩阵传播子的精确形式。利用这种代数表达式，推导了经典单脉冲、双脉冲和三脉冲实验中密度矩阵行为的精确表达式。然后用这些理论公式来说明由于B0和B1场中存在大的空间变化而给测量的弛豫参数带来的偏差。通过简单的矩阵代数很容易对理论预测进行评估，结果与实验观测非常吻合。这种方法对于多量子滤波钠MRI实验中信号强度空间变化的表征可能是有用的。
