An Improved Tissue-Fraction MRF (TF-MRF) with Additional Fraction Regularization

Xiaozhi Cao^{1}, Congyu Liao^{1}, Zhixing Wang^{1}, Huihui Ye^{1}, Ying Chen^{1}, Hongjian He^{1}, Song Chen^{1}, Hui Liu^{2}, and Jianhui Zhong^{1}

The previous method
resolves the MRF signal equation **S*** _{voxel}*=

In this study, instead
of the dictionary based on T1 or T2 for MRF, potential fractions of interested
components were used. Only the signal evolutions of interested components, **D**, was pre-calculated by extended phase
graph algorithm ^{3}, and then multiplied by **W** (**W**=[**w**_{1},**w**_{2},…**w**_{M}],
where *M* is the number of potential
fractions groups **w**_{i},), to build the
dictionary. By using template matching between each column vector of **DW **and **S**_{voxel}, the
component fraction is obtained from the best matched one. The solution of **S*** _{voxel}*=

$$ \hat{\bf{w}}=argmin\parallel \bf {S}_{\it {voxel}}-\bf{Dw}\parallel^{2}$$

$$s.t.{\sum_{{\it{n}=1}}^{{\it{N}}}{\bf{w}}({\it{n}})=1, {\bf{w}}({\it{n}})\in1}.$$

where
**w** is the column vector of fractions
with *N* the interested components. **S*** _{voxel}* is

To demonstrate the effectiveness
of the proposed method, two types of MRF measurements were performed on a
Siemens 3T Prisma scanner based on an inversion-prepared FISP MRF sequence ^{4}
with TR
varying from 10 to 12ms, flip angle varying from 5 to 80 degrees. The total scanning
time was about 10s.
A Polyvinylpyrrolidone
(PVP) phantom with concentration of, 5%, 10%, 15%, 20%, 30%, and pure water was
made in separate compartment respectively. Since PVP solution has a good linear
relationship between T1, T2 and its concentration especially when the concentration
is smaller than 30% ^{5, 6}, the signal of dilute PVP solution could be
regarded as a mixture of water and thick PVP solution. In the dictionary, the
interested components were water (T1/T2=3200/3000ms) and 30% PVP solution (T1/T2=1100/800ms).
Therefore, the theoretical fraction values of PVP solution with concentration
from 5% to 20% should be regarded as the linear combination of water and 30%
PVP solution.
The in-vivo experiment was performed using
the same imaging parameters. The interested tissue components included CSF
(T1/T2=4000/1500ms), gray matter (T1/T2=1300/120ms) and white matter (T1/T2=800/80ms).
To test whether the methods can separate white matters with long T1/T2 (800/80ms,
WM II) from that with comparatively short T1/T2 (660/70ms, WM II), these plus
CSF and GM were introduced to form a 4-components tissue fractional mapping.

1. Ma D et al. Nature 495:187-92;2013.

2. Deshmane A et al. Proc ISMRM 22 (2014), p. 94.

3. Weigel M, JMRI 2015;41:266-295.

4. Jiang Y. et al, MRM 2014, DOI: 10.1002/mrm.25559.

5. Liao C et al. Proc ISMRM 23 (2015), p. 1696.

6. Pierpaoli C et al. Proc ISMRM 17 (2009), p. 1414.

Fig 1

(a) RMSE of proposed method (blue) and the pseudo-inverse method (green) under different concentration of PVP solution. (b) Fractions of interested component (30 % PVP solution) in different situation, namely different PVP concentration. (c) Fractional mappings of 30% PVP solution from proposed method (middle) and previous method (bottom) with their difference maps (right column, scaled by a factor of 5) compared with theoretical values (top).

Fig 2

The tissue fractions of CSF, gray matter and white matter(from left to right respectively) from proposed method (top) and previous method (bottom).

Fig 3

The tissue fractions of CSF, GM, WM I (with T1/T2=800/80) and WM II (with T1/T2=660/70), from left to right respectively.

Proc. Intl. Soc. Mag. Reson. Med. 24 (2016)

4223