Accurate measurements of longitudinal relaxation time (

*T*_{1}) are essential to many quantitative MRI techniques and clinical applications. Traditional inversion recovery (IR)

*T*_{1} mapping methods often result in prohibitively long acquisitions due to a long repetition time (

*TR*) (

1). The Look-Locker method (

2) may be used to accelerate the IR experiment by frequent sampling of the entire recovery curve. This two-dimensional (2D) approach can be modified to allow multi-slice volumetric coverage (

3,

4). A three dimensional Look-Locker method (

5) has also been proposed to improve the SNR and slice direction resolution of 2D techniques at the cost of blurring in phase encode directions due to segmented k-space acquisition.

The variable flip angle (VFA) method (

6,

7), also known as driven-equilibrium single-pulse observation of

*T*_{1} (DESPOT1) (

7), uses several short

*TR* spoiled gradient echo (SPGR) acquisitions with varying flip angle (FA) to measure

*T*_{1}. It has gained significant popularity over the past decades due to its superior time efficiency, allowing rapid and accurate three-dimensional (3D)

*T*_{1} mapping with high resolution and large spatial coverage (

8–

10). While the acceleration of any

*T*_{1} mapping method is possible by the use of fast readout sequences (e.g. echo-planar or spiral) (

11,

12), applications of such techniques are limited to a large extent due to image artifacts inherent to long gradient-echo signal readouts. In contrast, VFA is the only fast

*T*_{1} mapping method to date which affords clinically reasonable scan times and 3D spatial coverage without a multi-echo readout, and therefore provides an optimal solution for high-resolution anatomic applications. In spite of these benefits, the VFA method suffers from a strong dependence on an accurate knowledge of excitation flip angle, which leads to significant errors in the presence of a non-uniform radiofrequency excitation field (

*B*_{1}), slab excitation pulse profiles, or FA miscalibration (

9,

10,

13). This is particularly problematic at high field strengths, where additional wave effects in tissue may cause

*B*_{1} variations up to 30% at 3T and

*in situ* FA calibration and correction is necessary on a per-subject basis (

14).

It is therefore commonly accepted that VFA

*T*_{1} mapping at 3T or higher field strengths needs to be combined with an appropriate

*B*_{1} correction method (

9,

10), and many methods to measure flip angle have been developed and applied to the correction of VFA

*T*_{1} measurements. Similar to IR-based

*T*_{1} mapping techniques, the double angle method (DAM) (

15) uses a 2D multislice acquisition with a long

*TR* to avoid

*T*_{1} weighting of the acquired maps. Scan time can be reduced by minimizing

*T*_{1} dependence with specialized radiofrequency pre-saturation pulses (

16,

17) to achieve a uniform saturation of magnetization over a large area prior to readout. However, the 2D implementation imposes restrictions on the use of DAM as a correction technique for 3D VFA

*T*_{1} measurements due to slice profile effects.

It is important to note that a 3D

*B*_{1} mapping technique with matched geometry is preferable in the context of VFA

*T*_{1} mapping to simplify registration between data volumes. One 3D approach encodes the flip angle in the phase of the MR signal (

18). This reduces the

*T*_{1} dependence due to previous magnetization history and can image over a large dynamic range of FA, but is sensitive to main field inhomogeneity and requires a long

*TR* relative to

*T*_{1} to avoid phase oscillations. Other fast techniques have recently been proposed based on a stimulated-echo echo-planar acquisition (

19) and a modification of DAM using a catalyzed preparative sequence (

20). Methods which use a steady-state gradient echo readout are particularly well suited as these pulse sequences are closely related to the SPGR sequence used in VFA, and can therefore be acquired with the same matrix size and readout scheme, greatly increasing the consistency between the FA and

*T*_{1} mapping steps. Such methods include a multi-point search of the signal null corresponding to the 180° flip angle (

21,

22), a

*B*_{1}-dependant shift in the spin resonance frequency (

23), an inversion-recovery SPGR termed driven equilibrium single pulse observation of

*T*_{1} with high-speed incorporation of RF field inhomogeneities (DESPOT1-HIFI) (

24), and a dual

*TR* SPGR acquisition termed actual flip-angle imaging (AFI) (

25).

The accurate combination of a

*B*_{1} mapping technique with 3D VFA

*T*_{1} mapping requires consideration of additional factors affecting flip angle values, including excitation slab/slice profile and RF pulse properties (

26). Two recently proposed methods, DESPOT1-HIFI (

24) and AFI (

25), measure FA using the exact same excitation pulse envelope and slab geometry as the VFA experiment, allowing measurements with a very similar FA distribution present in both sequences. DESPOT1-HIFI requires an additional

*B*_{1}-insensitive adiabatic inversion preparation, which, with proper tuning of the inversion time to the expected

*T*_{1} range, enables fast and accurate FA mapping. To avoid

*T*_{1} weighting, the AFI method estimates FA maps using the ratio of two signals from two different

*TRs* (

*TR*_{AFI1,2}) using a linearized form of the signal equation (see next section) which holds under a main assumption that

The calculated flip angle map can then be applied as a pre-calibration step to a traditional VFA

*T*_{1} measurement. AFI is well suited for the correction of VFA measurements because of the identical readout scheme to the SPGR pulse sequence, the use of an identical RF excitation pulse, and lack of a need for additional magnetization preparation with specialized RF pulses (

20,

23,

24).

In spite of the many benefits of AFI, recent studies have shown that large spoiler gradients are required for effective suppression (spoiling) of transverse magnetization and thus accurate FA measurements (

27). Such large gradients require a considerable increase in the

*TR* compared to a standard short

*TR* SPGR sequence, and therefore an overall increase in scan time. While proper spoiling is essential for accurate FA quantification, increasing the

*TR* of the AFI sequence may lead to a violation of the main assumption (

Eq. [1]) (

25), posing another significant problem with the accuracy and overall efficiency of the technique. Similarly, strong spoiler gradients are also necessary in VFA SPGR measurements for accurate

*T*_{1} mapping, especially at larger flip angles (

27,

28). This further increases the overall time of the technique.

An independent mechanism for violation of the AFI assumption (

Eq. [1]) is

*T*_{1} shortening due to contrast agents, which may render post-contrast FA measurements highly inaccurate. Post-contrast

*T*_{1} measurements should therefore be corrected with a pre-contrast

*B*_{1} map. However this is not feasible in some applications, such as manganese-enhanced MRI of axon pathways, which requires injection of a contrast agent approximately 24 hours before the scan (

29). A wide range of applications would greatly benefit from a rapid and accurate method to measure

*T*_{1} and FA in the presence of

*T*_{1} shortening contrast agents (

30,

31).

AFI and VFA are highly complementary methods; AFI suffers inaccuracies due to an assumption about

*T*_{1}, while VFA suffers inaccuracies due to an assumption about FA. In this paper, we propose an efficient method to tackle the quantification of

*T*_{1} and

*B*_{1} in the problematic AFI regime (

*TR*_{AFI1,2} ≈

*T*_{1}) arising from a long AFI

*TR* due to spoiling requirements and/or short

*T*_{1} times. In our method, Variable flip angle – Actual Flip angle Imaging (VAFI),

*T*_{1} and

*B*_{1} are mapped simultaneously using an optimized combination of AFI and VFA SPGR acquisitions. By exploiting the close relationship of the SPGR and AFI signal equations, we demonstrate that the

*TR*_{AFI1,2} <<

*T*_{1} assumption is not necessary when

*T*_{1} and

*B*_{1} are mapped simultaneously, resulting in a high flip angle mapping accuracy over a broad range of

*T*_{1} (

32), an improvement in the precision of

*T*_{1} and

*B*_{1} measurements, and increased time efficiency of such measurements. We also show that VAFI reduces the spoiling requirements of the SPGR portion of the method, allowing a shorter

*TR* and overall decrease in acquisition time.