Synopsis

A motion correction technique for 3D dynamic cardiac perfusion MRI using rigid and non-rigid image registrations to improve quantification of cardiac perfusion is presented. This method is unique because it employs a 3D image registration which not only resolves in plane motion but also resolves the out of plane motion for all slices in a 3D volume. This method also ensures smooth registration between all time frames of the data giving a more accurate analysis of the flow values.

Introduction

Dynamic contrast-enhanced magnetic resonance imaging can be useful to quantify myocardial ischemia. However, patient respiratory motion can affect the accuracy of subsequent analyses making the quantification poor. Motion correction techniques are always an extra challenge for dynamic contrast enhanced data since the intensity changes rapidly over time. In case of myocardial perfusion, there is respiratory motion, cardiac motion and the patient can move. All these things combined make the problem difficult to solve.

Most cardiac perfusion sequences acquire multiple 2D slices. Several 3D methods have been published ^6,7 but they have employed breath-holding and no registration in the post-processing steps for quantification. Here, we present a new motion correction technique which uses rigid and nonrigid registration methods for removing motion from 3D time series data. The 3D acquisition has the advantage that out-of-plane motion can be registered (though not out-of-slab motion).

Methods

In our method, the problem of contrast change is dealt by creating model based image volumes.³ Fig 1 shows the general idea of using a model-based method to create individual reference image for each time frame. These model images are reference volumes for the rigid registration which uses a normalized cross correlation metric for finding rigid shifts. Next, we use a non-rigid registration method which is a greedy diffeomorphic algorithm. These “greedy” algorithms iteratively apply gradient updates to a single deformation field, rather than update a full time-dependent flow each iteration. Algorithms in this class include the original diffeomorphic image registration algorithm of Christensen et al. ¹ and the diffeomorphic demon’s algorithm of Vercauteren et al.⁴

In our method,$$$I_{0}$$$ is the 3D image volume taken at time frame T and $$$I_{1}$$$ is the 3D image volume taken at T+1. Also, the deformation field is initially defined as identity and changes as the algorithm progresses with the number of iterations. Fig 2 is a deformed 3D field at time T which is used to interpolate the input image.

This greedy non-rigid image registration technique uses the cost function^1,2 given below

$$E(\phi) = \parallel I_{0}\circ\phi-I_{1}\parallel_{L_{2}}^{2}.$$

where $$$\phi$$$ is the deformation field which changes for every iteration till the cost function converges.

Formally, the greedy algorithm can be interpreted as gradient descent of the manifold of diffeomorphisms:

$$ \frac{\text{d}\phi^{-1}}{\text{d}t} = K\triangledown(I_{0}\circ\phi^{-1})(I_{0}\circ\phi^{-1}-I_{1}).$$

Here $$$K$$$ is a linear differential kernel operator defined as $$$ K = (1-\alpha\triangle)^{-S} $$$, $$$\triangle$$$ is a Laplacian operator and $$$K$$$ in general acts as a low pass filter and suppresses high frequency components in the image matching gradient. For best deformations, S should be 2<S<5.

The algorithm was tested for five 3D datasets. All the acquired MRI dataset have matrix size 144x144x8 and were initially registered rigidly with the model images using a normalized cross correlation metric. Then a greedy diffeomorphic registration is performed with the following parameters α=30, S=2. With 100 iterations for gradient descent, our model takes ~12 minutes to register the entire 3D data +100 time frames in MATLAB 2017a ,The MathWorks, Inc., Natick, Massachusetts, United States.

Results

Discussion

Conclusion

Acknowledgements

References

1. Christensen, G.E., Rabbitt, R.D., Miller, M.I.: Deformable templates using large deformation kinematics. IEEE Transactions on Image Processing 5(10), 1435–1447 (1996).
2. Beg, M., Miller, M., Trouv´e, A., Younes, L.: Computing large deformation metric mappings via geodesic flows of diffeomorphisms. International Journal of Computer Vision 61(2), 139–157 (2005)
3. G. Adluru, E. V. R. DiBella, and M. C. Schabel. Model-based registration for dynamic cardiac perfusion mri. Journal of Magnetic Resonance Imaging, 24(5):1062– 1070, 2006.
4. Vercauteren, T., Pennec, X., Perchant, A., Ayache, N.: Diffeomorphic demons: Efficient non-parametric image registration. NeuroImage 45(1), S61–S72 (2009).
5. D. Likhite, G. Adluru, E. DiBella, "Deformable and rigid model-based image registration for quantitative cardiac perfusion" in Statistical Atlases and Computational Models of the Heart-Imaging and Modelling Challenges, New York, NY, USA:Springer, pp. 41-50, 2015.
6. Wissmann, L., Gotschy, A., Santelli, C. Analysis of spatiotemporal fidelity in quantitative 3D first-pass perfusion cardiovascular magnetic resonance. J Cardiovasc Magn Reson. 2017.
7. Wissmann, L., Niemann, M., Gotschy, A., Manka, R. Quantitative three-dimensional myocardial perfusion cardiovascular magnetic resonance with accurate two-dimensional arterial input function assessment. J Cardiovasc Magn Reson. 2015.