Cardiac motion estimation by joint alignment of tagged MRI sequences
Graphical abstract
Highlights
► We tackle the recovery of dense myocardial deformations and strains from tagged MRI. ► k-Nearest Neighbors Graphs to assess the joint similarity between frames. ► kNNGs combined information from different cardiac views in an unified metric. ► Significantly higher accuracy compared to standard pairwise alignment was shown. ► Strains in patients with myocardial infarction was studied and evaluated.
Introduction
Tagged Magnetic Resonance Imaging (tMRI) is currently the reference modality for obtaining regional information on myocardial deformation. Since its introduction by Zerhouni et al. (1988) for cardiac function assessment, this technique has rapidly evolved due to advances in image acquisition, image processing, and clinical applications. Fig. 1 shows an example of images of the heart obtained with tMRI. The continuous efforts of researchers to obtain a completely automatic and reliable method for recovering cardiac motion and deformation, have generated interest in this modality. Pai and Axel (2006) have presented a review of technical and clinical advances in this arena.
The estimation of cardiac displacement fields from tMRI sequences can be formulated as an image registration problem (Chandrashekara et al., 2004a, Ledesma-Carbayo et al., 2005, Petitjean et al., 2003, Radeva et al., 1997, Shen et al., 2005), since it requires finding a point correspondence between component frames of the sequence. The application of registration techniques based on information theory (IT) (Chandrashekara et al., 2004a, Petitjean et al., 2003) is an interesting approach to cope with the non linear changes in tag intensity along the cardiac cycle. However, the evolution of transformation models towards the use of 3D + t models (Chandrashekara et al., 2004b, Ledesma-Carbayo et al., 2005) needs the definition of a metric of joint alignment to optimize simultaneously the transformation parameters. This problem can be circumvented by using a linear combination of the pairwise metrics between each phase and the reference (Chandrashekara et al., 2004b, Ledesma-Carbayo et al., 2005), but this approach still measures the image similarity with respect to the first phase and fails to exploit the temporal correlation between phases.
In this paper, we have explored an extension of IT-based registration techniques that finds the optimal transformation parameters of a 3D + t model by maximization of a metric of joint frame alignment. The main challenge in computing such metrics is the estimation of the probability density function (PDF) from a set of samples in a high-dimensional space (in our case, the sequence length). Neemuchwala et al. (2007) have recently presented estimators of α-Mutual Information MIα based on kNNG when high dimensional features are employed, and the use of histograms is not possible due to the curse of dimensionality (Bellman, 2003). Ma et al. (2007) have applied these estimators for computing deformations in a synthetic sequence of tumor images, and introduced joint similarity extensions of MIα. More recently, Leonenko et al. (2008) have presented a class of estimators of Hα based on the kth nearest-neighbor distances computed from a sample of N i.i.d. vectors with distribution f. In this article, we have extended kNNG estimators of Hα to quantify the joint alignment of multiview sequences, and applied it to tMRI sequences to recover cardiac displacement fields. For quantitative evaluation of our method, a comparison was run against the method proposed by Chandrashekara et al. (2004a) for six healthy subjects. Results show a significant decrease in positional error with respect to manually placed landmarks. The estimated strains were compared with those obtained by cine harmonic phase (HARP) magnetic resonance imaging as the ground truth. For assessing consistency with other modalities, we have studied two patients with myocardial infarction and compared the strain maps with the information provided by delayed-enhancement MRI of Gadolinium (deMRI) and cardiac catheterization.
Section snippets
Dataset
The database used for the experiments consisted of six healthy subjects (three females and three males between 24 and 33 years old) and two patients (males, 54 and 70 years old) with transmural infarction of the myocardium. For all subjects, cine MRI (cMRI), tMRI, and deMRI images were acquired in breath-hold by using a General Electric Signa CV/i, 1.5 T scanner (General Electric, Milwaukee, USA). Healthy subjects were also imaged with deMRI to have a proof of their clinical status. The values of
Entropy evolution
As the Hα is minimized during the registration process, the distribution of the pixel stack after registration should be more compact with respect to the original data. To visualize this expected change in distribution, we have performed a reduction of dimensionality by applying a Principal Components Analysis (PCA) (Rao, 2002) and projected in the subspace spanned by the first three principal directions qi=1:3. Fig. 4 shows that the point distribution before registration presents a larger
Discussion
The MSE with respect to manual measurements obtained by JA was shown to be significantly lower than for the PA approach. The p-values obtained from the Mann–Whitney test (Table 1) show significant differences at 5% level between the errors obtained with PA and JA for most of the analyzed time points. The simultaneous parameter optimization guided by a joint metric suggested a uniform error distribution over time, but Fig. 6 shows an increase in the MSE over time. To find an explanation to these
Conclusions
In this paper, we have used JA of tMRI sequences for cardiac motion estimation, motivated by the promising results reported for methods based on information-theoretic metrics, and from a probabilistic point of view in Section 2.3. To cope with the high computational cost of the kNNG estimators of Hα, an analytical expression for metric derivatives was obtained, resulting in a O(N log N) complexity, which reduces drastically the registration time. The strategy to combine different views performed
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