Zaid Bin Mahbub^{1}, Mohammad Golbabaae^{2}, Arnold Julian Vinoj Benjamin^{1,2}, Mike Davies^{2}, and Ian Marshall^{1}

Previous MR fingerprinting studies have used smooth variations in TR and flip angles. In this study we introduce a piecewise constant flip angle train into a standard gradient echo multi shot EPI sequence. The resulting T1, T2 and proton density maps were obtained from a phantom and healthy volunteers using only 3 distinct flip angle values (obtained by optimization over 8 different flip angles) and using iterative reconstruction. The method generates steady states covering full k-space, producing alias-free maps.

All experiments were
conducted on a 1.5T
HDT GE Signa MRI scanner using an 8-channel head coil. GRE EPI with a multi-shot
readout sequence was modified to acquire each individual shot at a specific FA.
Data were acquired
from two healthy volunteers and a phantom with multiple tubes. The scanning parameters
were: axial orientation,
128×128 matrix, FOV 256 mm, slice thickness 4 mm, 16-shots, BW 125 kHz, TR/TE
= 33/12ms and 96 repetitions(NEX). The signal behaviour was modelled
using the extended phase graph (EPG) formalism^{7}. Each of the FAs was maintained for 12 repetitions to make it PC.
Previously
FA optimization using a spoiled gradient echo sequence has been performed for
T1 estimation^{6}
alone. In this work, similar to that of Cohen^{8}, we optimize the FAs to minimize the mutual
coherence between the atoms of the EPG dictionary:$$$\alpha^\star=\begin{array}{c}argmin\\ \alpha\end{array}\begin{array}{c}max\\ i\neq j\end{array}W_{i,j}\mid\langle D(T^{i},\alpha), D(T^{j},\alpha)\rangle\mid$$$ where $$$D(T^{i},\alpha)$$$ denotes the
normalized dictionary atom corresponding to the parameter $$$T^{i}=\left\{T_1^i,T_2^i \right\}$$$ and
the set of FAs $$$\alpha$$$. Since PC FAs cover
the full k-space and hence incur no aliasing, the correlation between atoms
directly measures the parameter sensitivity: a smaller
mutual coherence implies better separation between the EPG responses of
different parameters and thus, brings more sensitivity. Since we only consider
steady state responses, an additional advantage of PC FAs is that the mutual
coherence measure decouples across the FAs making FA optimization easier. In our current experiment
we set $$$W_{i,j}=1$$$, and optimized over 8 PC FAs, each limited to 0-35^{0}. The optimal FAs were [4^{0},4^{0},4^{0},4^{0},4^{0},4^{0},20^{0},35^{0}] resulting in only 3 distinct values, similar to Lewis^{6}. Here the repetition of the angle 4^{0} can be explained as boosting
the discriminative power of the smallest FA where low signal levels are
observed.

Based on observation (Figure 1b),
the first 4 repetitions for each FA excitation were considered as the transient
state and hence discarded and the remaining sequential shots were used
as steady state to create the corresponding maps. A Dictionary was created
based on the EPG model of the sequence for a wide range of $$$ T1 = 60:3:8000ms$$$ and $$$T2 = 30:0.5:2000ms$$$. The parametric maps were created by the BLIP^{4} algorithm, matching to the
dictionary.

Conventional T1 images were acquired using SE and FSE IR and T2 images were acquired using GRE for volunteers and phantom respectively.

Figure 1a: T1, T2 and
PD maps of the volunteers and phantom generated using GRE multi shot EPI
sequence with 3 values of optimized FAs.

Figure 1b: 1b: Comparison of
model and data from phantom background at all repetitions (NEX), for
calculations of parametric maps only steady states are considered.

Figure 2: Comparison
of T1 and T2 measurements from the phantom using the MRF EPI and standard
sequences, a line of identity used for visualization.