Mahesh Bharath Keerthivasan^{1}, Manojkumar Saranathan^{2}, Ali Bilgin^{1,2}, Diego R Martin^{2}, and Maria Altbach^{2}

T2 mapping is a parametric imaging approach that provides quantification of T2-weighted images for a more accurate diagnosis of pathology. 2D multi-slice T2 estimation techniques cannot be used for thin slice isotropic imaging. To overcome this limitation, we present a T2 mapping technique using a 3D radial FSE pulse sequence with a variable flip angle scheme for optimal T2-weighting and T2 mapping within SAR constraints. Data is acquired in a stack-of-stars radial trajectory and T2 maps are reconstructed using model based iterative algorithms. The method is demonstrated in phantoms and in vivo brain and musculoskeletal imaging.

A 3D Cartesian FSE pulse sequence was
modified to support a stack-of-stars trajectory where each kz plane
contains radial views corresponding to multiple TE points (Fig.1). A varFA design
based on a 3 flip angle parameter approach^{4} was implemented. The
refocusing flip angles were optimized to maximize the area under the T2 decay
curve (for improved overall SNR) and minimize SAR. Figure 2 shows (a) the flip
angle scheme and (b) effect of the flip angle modulation on the signal
intensity compared to a constant flip angle scheme.

To achieve fast imaging, data for each TE point
is highly under-sampled (3 views/TE per kz plane). Thus, 3D TE
images are reconstructed using sparsity-based iterative reconstruction
algorithms. Previously our group had proposed^{1} a principal component (PC) based
T2 mapping technique with indirect echo compensation for 2D radial FSE data
based on the slice-resolved extended phase graph model. For 3D
T2 mapping, the reconstruction problem is written as:

$$argmin_{I_0,T2,T1,B1} \sum_{j=1}^{ETL}||FT_j\{C_j(I_0,T2,T1,B1,TR,\alpha_0,\ldots,\alpha_j)\} - K_j||_2^2$$

where $$$FT_j$$$ is the Fourier operator, $$$K_j$$$ is the undersampled k-space data at the jth TE, $$$C_j$$$ is the EPG signal model as a function of I0, T2, T1, B1, TR and the flip angles of the excitation and refocusing RF pulses. The signal model is linearized using a PC basis generated from a set of training curves. The linearized problem is expressed as:

$$argmin_{M}\sum_{l=1}^{coils}\sum_{j=1}^{L}||FT_j\{S_lMP_j^T\} - K_{l,j}||_2^2 + \lambda ||\psi M||_1$$

where $$$P$$$ is a matrix of the
first principal
components, $$$M$$$ is a matrix
corresponding to the PC coefficients, $$$S_l$$$ are the complex coil
sensitivities. The penalty term exploits the spatial compressibility of the PC
coefficient maps using a sparsity transform $$$\psi$$$. The images at $$$TE_j$$$ are obtained using the $$$L$$$ PC coefficients as $$$MP_j^T$$$ , where $$$P_j$$$ is the jth row of the matrix $$$P$$$. T2 maps are estimated by using a pattern recognition
technique^{3} using pre-computed dictionaries based on the EPG
model.

1. Huang C., Bilgin A., Barr T., Altbach M, T2 relaxometry with indirect echo compensation from highly undersampled data, Magnetic Resonance in Medicine, 70(4) 2013

2. Altbach M., Bilgin A., Li Z., Clarkson E., Trouard T., Gmitro A., Processing of radial fast spin-echo data for obtaining T2 estimates from a single k-space data set, Magnetic Resonance in Medicine, 54 2005

3. Keerthivasan MB, Bilgin A, Martin DR, Altbach MI. Isotropic T2 mapping using a 3D radial FSE (or TSE) pulse sequence. In Proceedings of ISMRM, Vol. 23, Toronto, Ontario, Canada, 2015. p. 323

4. Busse RF, Brau ACS, Vu A, Michelich CR, Bayram E, Kijowski R, Reeder SB, Rowley HA. Effects of refocusing flip angle modulation and view ordering in 3D fast spin echo. Magn Reson Med 2008;60: 640–649

5. Huang C., Altbach M, Fakhri G., Pattern recognition for rapid T2 mapping with stimulated echo compensation, Magnetic Resonance Imaging, 32, 2014

Fig 1: Diagram of the 3D radial FSE pulse sequence.

Fig 2: (a) The flip angle modulation scheme and (b) its effect on the signal
evolution compared to a train of constant refocusing flip angles (130 deg) for an echo train length of 64.
Note that the total area under the T2 decay curve is increased compared to the
constant FA case.

Fig 3: Comparison of mean T2 values estimated
from 3D Radial FSE and the SE reference.

Fig 4: Sagittal,
axial and coronal sections of the knee obtained from
the 3D Radial FSE sequence
for a normal volunteer along with the T2 map of a sagittal slice. Data was acquired at 0.7x0.7x1.0 mm resolution in a 7.5 minute scan.

Fig 5: Reformatted cross
sections of the brain and the T2 map for a sagittal slice
reconstructed from data acquired at 1.1 mm isotropic resolution in a 7.8 minute scan.