Synopsis

Due to its low costs, high inertness and applicability at thermal polarization, fluorinated gases are promising tracers for imaging lung ventilation using fluorine magnetic resonance imaging. In this work, the joint reconstruction of proton density and ¹⁹F ventilation images in the human lung is shown. To exploit the structural similarity of both imaging modalities, a regularized reconstruction is used, minimizing the parallel level sets. Quantitative analysis of the reconstruction performance could be achieved by retrospective undersampling of data collected during a 2.5-minute breath hold. Furthermore, computation of VDP maps has been analyzed using joint reconstruction in three COPD patients.

Background

Method

In this study, one healthy volunteer and three COPD patients were examined on a 1.5 T scanner (MAGNETOM Avanto, Siemens Healthcare, Erlangen, Germany). Each participant inhaled a mixture of 79% fluorinated gas (C₃F₈) and 21% oxygen. Within one inspiratory breath hold, ¹⁹F pulmonary gas MRI and ¹H low-resolution (LR) morphologic imaging were performed using a transmit and receive coil dedicated to the ¹⁹F frequency. For the ¹⁹F image, a prototype 3D gradient echo sequence with golden-angle stack-of-stars k-space encoding was utilized, while ¹H images were obtained using cartesian 3D gradient echo imaging. Short scan time and the usage of the ¹⁹F coil for ¹H imaging led to low SNR in the ¹H image. Thus, high-resolution (HR) ¹H imaging was performed in a separate breath hold with a coil dedicated for the ¹H frequency. Imaging parameters can be found in table 1. The HR ¹H images were registered to the LR ¹H images using ANTS².

To improve the image quality of ¹⁹F MRI, the structural similarity between ¹H and ¹⁹F imaging was exploited in the reconstruction. Parallel level sets (PLS) $$\textrm{PLS}(u,v) = \int_{\Omega} d_{\varphi, \psi}\left(\nabla u, \nabla v\right)$$ were used as a measure for parallelism of the gradients of ¹⁹F and ¹H images $$$u$$$ and $$$v$$$ in the image domain $$$\Omega$$$ using the distance measure¹: $$ d_{\varphi, \psi}(x,y) = \varphi\left(\psi \left( |x| |y| \right) - \psi \left( | \langle x, y \rangle |\right) \right)$$ In the case of quadratic parallel level sets used in this work, the arbitrary functions $$$\varphi$$$ and $$$\psi$$$ are defined by $$$\varphi(x) = \sqrt{1+x}$$$ and $$$\psi(x) = x^2$$$.³

Firstly, ¹⁹F images were computed using a generalized parallel imaging and compressed sensing (PICS) reconstruction from the BART toolbox, regularized by the total variation (TV) in two spatial dimensions⁴. Then, the joint reconstruction using PLS as penalty term was applied to these images and the HR ¹H images using a quasi-Newton method¹.

To examine the performance of the joint reconstruction, an additional ¹⁹F data set of 104 radial spokes and 20 averages was acquired using the radial stack-of-stars sequence in a single breath hold of approximately 2.5 minutes in an endurance athlete. The discrepancy between images of retrospectively undersampled data, computed with joint reconstruction and fully sampled data, computed with PICS reconstruction, was measured using the root mean square error (RMSE).

To verify the reconstruction performance in three COPD patients, volume defect percentage (VDP) maps were computed from ¹⁹F ventilation images using Otsu’s method⁵. Maps of retrospectively undersampled data, computed with joint reconstruction and fully sampled data, computed with PICS reconstruction, were compared. The accordance of the maps was measured using the Sørensen-Dice coefficient⁶.

Results

For the 2.5-minute breath hold, reconstructions using the full data, only the first 12 seconds (32 spokes, 6 NEX) and only the first 3 seconds (12 spokes, 4 NEX) are shown in figure 1. The dependence of the RMSE on the number of spokes and averages when using joint reconstruction is shown in figure 2. Using 12 spokes and 4 NEX, corresponding to an acquisition time of 3 seconds, leads to an acceptable image quality.

For the three COPD patients, the dependence of the Sørensen-Dice coefficient on the number of spokes and averages of the joint reconstruction is shown in figure 3. Data containing 8 spokes and 4 NEX, corresponding to an acquisition time of 2 seconds, provide Sørensen-Dice coefficients between 0.81 and 0.83. As an example, the good agreement of ventilation images and VDP maps using PICS reconstruction and joint reconstruction is shown in figure 4.

Discussion and Conclusion

Acknowledgements

References

1. Ehrhardt MJ, Thielemans K, Pizarro L, et al. Joint reconstruction of PET-MRI by exploiting structural similarity. Inverse Probl. 2015;31(1).

2. Avants BB, Tustison N, Song G. Advanced normalization tools (ANTS). Insight j 2. 2009:1-35.

3. Ehrhardt MJ, Arridge SR. Vector-valued image processing by parallel level sets. IEEE Trans Image Process. 2014;23(1):9-18.

4. Uecker M, Ong F, Tamir JI, et al. Berkeley advanced reconstruction toolbox. Proc Intl Soc Mag Reson Med. 2015;23:2486.

5. Otsu N. A threshold selection method from gray-level histograms. IEEE Trans Syst Man Cybern. 1979;9(1):62-66.

6. Sørensen T. A method of establishing groups of equal amplitude in plant sociology based on similarity of species and its application to analyses of the vegetation on Danish commons. Biol Skr. 1948;5:1-34.