doubleAngleMethod.RdFor in vivo MRI at high field (\(\geq3\) T) it is essential to consider the homogeneity of the active B1 field (B1+). The B1+ field is the transverse, circularly polarized component of B1 that is rotating in the same sense as the magnetization. When exciting or manipulating large collections of spins, nonuniformity in B1+ results in nonuniform treatment of spins. This leads to spatially varying image signal and image contrast and to difficulty in image interpretation and image-based quantification.
doubleAngleMethod(low, high, low.deg)| low | is the (3D) array of signal intensities at the low flip angle. |
|---|---|
| high | is the (3D) array of signal intensities at the high flip angle (note, 2*low = high). |
| low.deg | is the low flip angle (in degrees). |
An array, the same dimension as the acquired signal intensities, is returned containing the multiplicative factor associated with the low flip angle acquisition. That is, if no B1+ inhomogeneity was present then the array would only contain ones. Numbers other than one indicate the extent of the inhomogeneity as a function of spatial location.
The proposed method uses an adaptation of the double angle method (DAM). Such methods allow calculation of a flip-angle map, which is an indirect measure of the B1+ field. Two images are acquired: \(I_1\) with prescribed tip \(\alpha_1\) and \(I_2\) with prescribed tip \(\alpha_2=2\alpha_1\). All other signal-affecting sequence parameters are kept constant. For each voxel, the ratio of magnitude images satisfies $$\frac{I_2(r)}{I_1(r)}=\frac{\sin\alpha_2(r)f_2(T_1,\mbox{TR})}{\sin\alpha_1(r)f_1(T_1,\mbox{TR})}$$ where \(r\) represents spatial position and \(alpha_1(r)\) and \(\alpha_2(r)\) are tip angles that vary with the spatially varying B1+ field. If the effects of \(T_1\) and \(T_2\) relaxation can be neglected, then the actual tip angles as a function of spatial position satisfy $$\alpha(r)=\mbox{arccos}\left(\left|\frac{I_2(r)}{2I_1(r)}\right|\right)$$ A long repetition time (\(TR\leq{5T_1}\)) is typically used with the double-angle methods so that there is no \(T_1\) dependence in either \(I_1\) or \(I_2\) (i.e., \(f_1(T_1,TR)=f_2(T_1,TR)=1.0\)). Instead, the proposed method includes a magnetization-reset sequence after each data acquisition with the goal of putting the spin population in the same state regardless of whether the or \(\alpha_2\) excitation was used for the preceding acquisition (i.e., \(f_1(T_1,TR)=f_2(T_1,TR)\ne1.0\)).
Cunningham, C.H., Pauly, J.M. and Nayak, K.S. (2006) Saturated Double-Angle Method for Rapid B1+ Mapping, Magnetic Resonance in Medicine, 55, 1326-1333.
Brandon Whitcher bwhitcher@gmail.com