For 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.
Usage
dam(low, high, low.deg)
Arguments
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).
Value
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.
Details
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.,
$f_1(T_1,TR)=f_2(T_1,TR)\ne1.0$).
References
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.