A gradient-based optical-flow cardiac motion estimation method for cine and tagged MR images
Introduction
Assessment of cardiac function is of a primary importance for care of patients with heart disease. In addition to global parameters, such as ejection fraction, regional quantification of motion is helpful to locally characterize the myocardium in ischemic heart diseases. Cardiac magnetic resonance imaging (MRI), in particular cine-MRI (C-MRI), is an advantageous imaging modality to assess cardiac function. Tagged-MRI (T-MRI) is considered as the reference for regional cardiac motion quantification (Wang and Amini, 2012), although not used in clinical practice.
Numerous approaches have been proposed for either C-MRI and T-MRI sequences processing (Miao, Wang, Pan, Butler, Moran, Liao, 2016, Dosenbach, Koller, Earl, Miranda-Dominguez, Klein, Van, Snyder, Nagel, Nigg, Nguyen, Wesevich, Greene, Fair, 2017, Küstner, Schwartz, Martirosian, Gatidis, Seith, Gilliam, Blu, Fayad, Visvikis, Schick, Yang, Schmidt, Schwenzer, 2017, Parages, Denney, Gupta, Lloyd, DellItalia, Brankov, 2017, Tolouee, Alirezaie, Babyn, 2018). The harmonic phase image method was introduced by Osman and Prince in early 2000 and became the standard method for T-MRI analysis (Osman et al., 1999). Since then, improvements to the original method have been proposed, e.g., the local sine wave modeling method (SinMod) (Arts et al., 2010), the monogenic-signal-based methods (Alessandrini, Basarab, Liebgott, Bernard, 2013, Gao, Liu, Wang, Liu, Croisille, Delachartre, Clarysse, 2016) and the analytic signal phase-based method (Wang et al., 2015). The optical flow-based principle has been adapted to T-MRI processing to account for intensity variations (Prince and McVeigh, 1992), or within 3D multi-resolution (Xu et al., 2010) approaches. Because of the lack of structural information, quantification of the motion in C-MRI requires complementary constraints, e.g., physical constraints such as incompressibility (Bistoquet et al., 2007), geometrical/intensity constraints that can be integrated into an attribute vector to control registration in image sequences (Delhay, Clarysse, Magnin, 2007, Sundar, Litt, Shen, 2009). There is clear interest for motion estimation methods from T-MRI and C-MRI: T-MRI is the gold standard for motion quantification and C-MRI is acquired routinely in the clinic. Indeed, motion estimation is usually independently addressed relative to a specific MR acquisition: cine, tagged, phase contrast, displacement encoding with stimulated echoes (DENSE), or strain encoding (SENC) (Wang and Amini, 2012).
Moreover, gradient-based motion estimation plays an important role in registration algorithms, which have been considered independently for T-MRI or C-MRI sequence motion estimation (Keller and Averbuch, 2004). Hence, gradient-based optical flow strategy could be a possible framework for developing a C-MRI and T-MRI sequence compatible motion estimation method. The gradient constancy assumption has been proposed to handle image illumination changes as a complement to the traditional brightness constancy assumption (Brox, Bruhn, Papenberg, Weickert, 2004, Zimmer, Bruhn, Weickert, 2011). A very large scale integration (VLSI) architecture of the multi-channel gradient model (McGM) proposed by Johnston et al. has also been implemented (Botella et al., 2012). Boonsieng et al. adopted the orientation of the gradient instead of gradient intensity for a robust optical flow estimation, within a method called the gradient orientation-based gradient method (GOGM) (Boonsieng et al., 2014). Revaud et al. also introduced the gradient-constancy assumption in a variational energy minimization function for optical flow estimation integrating descriptor matching (Revaud et al., 2015). In Bristow and Lucey (2016), Bristow and Lucey discussed the gradient-based method by regression for image alignment, illustrating that image alignment can be used as an optical flow estimation method.
In this paper, we propose a method that can equally process both C-MRI and T-MRI sequences. Firstly, a geometrical intensity distribution model is defined by local mean intensity and gradient. Then, invariance of the local model parameters on both intensity and gradient features is imposed through a system of four optical flow equations. An overall cost function is defined based on the invariance equations, the minimization of which results in the optimized displacement between two consecutive images. The proposed method is evaluated on both simulated and clinical, C-MRI and T-MRI sequences. A method is proposed to create a T-MRI sequence from a simulated C-MRI sequence, animated by the same motion. The motion estimation results obtained with the proposed method outperform those of other state-of-the-art methods with the simulated data. Furthermore, the proposed method is applied to the clinical data from a healthy volunteer and an acute myocardial infarction patient for myocardial deformation analysis. In this preliminary experiments, the proposed method’s performance compares favorably to state-of-the-art methods for both C-MRI and T-MRI sequences.
The paper is organized as follows. In Section 2, the proposed method based on optical flow equations is detailed. In Section 3, the synthetic method for T-MRI sequences is introduced. The detailed implementation is described in Section 4 and the results obtained on synthetic and clinical data are given and discussed.
Section snippets
Motion estimation method
The proposed method estimates the motion field between two successive images. It is based on the traditional brightness constancy combined with a local shape constraint. A random walk optimization is adopted to estimate the optimal displacement field. The accumulated motion field over the temporal image sequence is calculated as well for motion analysis and strains computation.
Synthetic C-MRI and T-MRI sequences
Motion estimation accuracy with the proposed approach is quantitatively evaluated from the simulation of both 2D short axis C-MRI and T-MRI sequences. A C-MRI (Fig. 3(a)) is progressively deformed according to a combination of contraction-dilation and rotation motion components that realistically mimic the changes in the left ventricle myocardium within a short axis slice during the cardiac cycle (Clarysse et al., 2011). T-MRI sequences are built from C-MRI sequences. They therefore contain the
Results and discussion
The performance of the proposed method was evaluated on synthetic and clinical as well as C-MRI and T-MRI sequences. Moreover, the proposed method was compared to a selection of state-of-the-art motion algorithms.
Conclusion
We proposed a new myocardial motion estimation method that can be applied to both 2D C-MRI and T-MRI sequences. It is based on the joint respect of local intensity distribution and intensity invariance during motion. The problem is formulated as an energy minimization where the local shape is approximated by four directional gradients. Minimization is achieved through a random walk scheme. The evaluation was first conducted on realistic simulated 2D short-axis C-MRI and T-MRI sequences for
Conflict of interest
We wish to confirm that there are no known conflicts of interest associated with this publication and there has been no significant financial support for this work that could have influenced its outcome.
Acknowledgments
This study was conducted within the framework of the LABEX PRIMES (ANR-11-LABX-0063) and LABEX CELYA (ANR-10-LABX-0060) projects of the University of Lyon, within the “Investissements d’Avenir” (ANR-11-IDEX-0007) program operated by the French National Research Agency (ANR).
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