# Double-Angle Method for B1+ Mapping

### Description

For in vivo MRI at high field (*>=3* 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

1 | ```
doubleAngleMethod(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). |

### 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: *I1* with
prescribed tip *alpha1* and *I2* with prescribed tip
*alpha2 = 2*alpha1*. All other signal-affecting
sequence parameters are kept constant. For each voxel, the ratio of
magnitude images satisfies

where *r* represents spatial position and *alpha1(r)*
and *alpha2(r)* are tip angles that vary with the spatially
varying B1+ field. If the effects of *T1* and *T2*
relaxation can be neglected, then the actual tip angles as a function of
spatial position satisfy

A long repetition time (*TR <= 5*T1*) is typically used
with the double-angle methods so that there is no *T1* dependence
in either *I1* or *I2* (i.e.,
*f1(T1,TR) = f2(T1,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 *alpha2* excitation was used for
the preceding acquisition (i.e.,
*f1(T1,TR) = f2(T1,TR) != 1.0*).

### 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.

### Author(s)

Brandon Whitcher bwhitcher@gmail.com

### 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.