An Improved Tissue-Fraction MRF (TF-MRF) with Additional Fraction Regularization
Xiaozhi Cao1, Congyu Liao1, Zhixing Wang1, Huihui Ye1, Ying Chen1, Hongjian He1, Song Chen1, Hui Liu2, and Jianhui Zhong1

1Center for Brain Imaging Science and Technology, Department of Biomedical Engineering, Zhejiang University, Hangzhou,Zhejiang, China, People's Republic of, 2MR Collaboration NE Asia, Siemens Healthcare, Shanghai, China, People's Republic of

### Synopsis

MR fingerprinting has been used for estimating the intra-voxel tissue component fractions by resolving the equation Svoxel=Dw. In this study, potential fractions of interested components are used for building dictionary instead of T1 and T2, changing the solution of Svoxel =Dw into an optimization problem with regularization terms. The results demonstrate that the proposed method could provide more robust quantification of tissue composition and estimation of partial volume effects.

### Purpose

MR fingerprinting has been used for estimating the intra-voxel tissue component fractions 1, 2. The previous method 2 could lead to over-fitting error, which hinders reliable mapping of tissue fractions. In this work, we propose to use template matching with a dictionary whose entry is dependent on composition fraction, in solving the MRF signal equation.

### Methods

The previous method resolves the MRF signal equation Svoxel=Dw by pseudo-inverse, namely (DHD)-1DHSvoxel=w, where Svoxel is the measured signal evolution, D is pre-calculated signal evolution of interested components and w is the group of component fractions. However, the results often exhibit abnormal fraction values (i.e. negative or above 1), so normalization after fractions obtained are needed, leading to over-fitting error. Besides, no consensus solution for the necessary normalization is reached yet in the field. One approach often used is to take the absolute value of results and then normalize them to summation of 1 2.

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=[w1,w2,…wM], where M is the number of potential fractions groups wi,), to build the dictionary. By using template matching between each column vector of DW and Svoxel, the component fraction is obtained from the best matched one. The solution of Svoxel=Dw actually is therefore turned into an optimization problem:

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

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

where w is the column vector of fractions with N the interested components. Svoxel is 1 vector with L the number of time points for MRF acquisition and w is a 1 vector. The matrix size is L×N for D and N×M for W.

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.

### Results

Figure 1 shows the fractions of interested component (30% PVP solution) with different concentration from 0% to 30%. Results using proposed method are closer to the theoretical values and have a smaller RMSE, demonstrating better precision for estimating components. The results from in-vivo experiment, as shown in Figure 2, exhibit that the proposed method performs better, especially in separating the white matter from gray matter (red arrow). Furthermore, when short WM components was introduced (Figure 3), the performance of previous method deteriorated for all components estimating. The proposed method could distinguish white matters of long T1/T2 from short T1/T2 and did not influence the estimation of CSF and grey matters.

### Discussion and Conclusion

With the regularization introduced to the calculation of component fractions, the results are more precise and robust since the irrational over-fitting error is alleviated. Therefore, the proposed method could provide more robust quantification of tissue composition and estimation of partial volume effects. It also provides a potential for refined classification of tissue by introducing more relevant components.

### Acknowledgements

No acknowledgement found.

### References

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.

### Figures

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)
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