Myocardium segmentation from DE MRI with guided random walks and sparse shape representation

Abstract

Purpose

For patients with myocardial infarction (MI), delayed enhancement (DE) cardiovascular magnetic resonance imaging (MRI) is a sensitive and well-validated technique for the detection and visualization of MI. The myocardium viability assessment with DE MRI is important in diagnosis and treatment management, where myocardium segmentation is a prerequisite. However, few academic works have focused on automated myocardium segmentation from DE images. In this study, we aim to develop an automatic myocardium segmentation algorithm that targets DE images.

Methods

We propose a segmentation framework based on both prior shape knowledge and image intensity. Instead of the strong request of the pre-segmentation of cine MRI in the same session, we use the sparse representation method to model the myocardium shape. Data from the Cardiac MR Left Ventricle Segmentation Challenge (2009) are used to build the shape template repository. The method of guided random walks is used to integrate the shape model and intensity information. An iterative approach is used to gradually improve the results.

Results

The proposed method was tested on the DE MRI data from 30 MI patients. The proposed method achieved Dice similarity coefficients (DSC) of 74.60 ± 7.79% with 201 shape templates and 73.56 ± 6.32% with 56 shape templates, which were close to the inter-observer difference (73.94 ± 5.12%). To test the generalization of the proposed method to routine clinical images, the DE images of 10 successive new patients were collected, which were unseen during the method development and parameter tuning, and a DSC of 76.02 ± 7.43% was achieved.

Conclusion

The authors propose a novel approach for the segmentation of myocardium from DE MRI by using the sparse representation-based shape model and guided random walks. The sparse representation method effectively models the prior shape with a small number of shape templates, and the proposed method has the potential to achieve clinically relevant results.

Appendices

Appendix A: Some explanation about the derivation of solution equation

The energy function in Eq. (5) can be written as:

$$ \begin{aligned} E\left( \varvec{x} \right) & = \varvec{x}^{T} \varvec{Lx} + \frac{\gamma }{2}\left( {\varvec{x}^{T} \varvec{x} - 2\varvec{x}^{T} \varvec{y}^{\text{shape}} + \varvec{y}^{{{\text{shape}}T}} \varvec{y}^{\text{shape}} } \right) \\ & = \varvec{x}^{T} \left( {\varvec{L} + \frac{\gamma }{2}\varvec{I}} \right)\varvec{x} - \gamma \varvec{x}^{T} \varvec{y}^{\text{shape}} + \frac{\gamma }{2}\varvec{y}^{{{\text{shape}}T}} \varvec{y}^{\text{shape}} , \\ \end{aligned} $$

where $\varvec{x}$ is the vector of the probability of all the voxels; $\varvec{y}^{\text{shape}}$ is the prior shape for all the slices; $\varvec{L}$ is the Laplacian matrix, as defined in Eqs. (6) and (7).

Since $\varvec{L}$ is positive semi-definite and the value of parameter $\gamma$ is positive, the matrix $\left( {\varvec{L} + \frac{\gamma }{2}\varvec{I}} \right)$ is positive definite. So the only critical points of $E\left( \varvec{x} \right)$ will be the minima. Differentiating $E\left( \varvec{x} \right)$ with respect to $\varvec{x}$, and the minimizer of $E\left( \varvec{x} \right)$ is given by the linear equations in Eq. (8). By solving this system of linear equations, the probability map of myocardium can be obtained.

Appendix B: The effects of parameters and the recommended value ranges

There are totally five parameters in the proposed method, as summarized in Table 4. Among these parameters, the threshold $T$, which is used to generate the binary segmentation from probability map, critically affects the results. We have recorded the DSC of myocardium with the threshold $T$ increasing from 0.3 to 0.5, and the results are demonstrated in Fig. 7. The highest average DSC is achieved when the threshold is between 0.4 and 0.42, which contradicts to the convention of setting the threshold at 0.5 for probability binarization. This result is probably due to the elongated shape and relative small area of myocardium, as well as the relative low intensity contrast between myocardium and surrounding tissues. Since there is a neighborhood-related term in the energy function of random walks method, the probabilities of myocardium are easily affected by the pixels of background, including the blood pool encountered by the endocardium and the tissues around the epicardium. Therefore, a threshold below 0.5 is helpful to prevent the myocardium from being “swallowed” by the background. Evaluated with our testing data sets, when the threshold decreases from 0.4, the DSC decreases slowly because of the tendency to wrongly classify the surrounding pixels into myocardium. When the threshold increases to 0.48, in some data sets, the myocardium begins to be incorporated into the background, which results in a low average DSC and high DSC variance. When the method is applied for myocardium segmentation and the data resolution is similar to our data sets, this value does not need to be changed. When the segmentation target is of larger pixel number, such as in the case of data with higher resolution or target tissue of larger area, the value of threshold $T$ will have less effect to the results.

Table 4 The parameters in the proposed method

Fig. 7

Effect of threshold T

The rest of four parameters do not have significant effect to the results in relative large value ranges. We have recorded the DSC of myocardium with weighting parameter $\gamma$ doubling from 0.005 to 0.64, as illustrated in Fig. 8. The highest average DSC is achieved when $\gamma$ is set at 0.01, but the paired t test shows that no significant difference (p < 0.05) exists between the $\gamma$ value of 0.01 and the rest. This demonstrates that the change of parameter $\gamma$ in a relatively large range (from 0.005 to 0.64) does not have a great effect on the final segmentation results. When the value of parameter $\gamma$ is small, such as 0.005, insufficient shape information is imposed and the performance of the method becomes less stable, where the DSC standard deviation is larger. When parameter $\gamma$ is set at a large value, such as 0.64, the imposed constraint may limit the flexibility of the algorithm, which results in a poorer fitting of the results to the image intensity.

Fig. 8

Effect of weighting parameter γ

The sparse representation-based model is able to select the proper shape templates from the dictionary to model the myocardium shape. However, as the size of the dictionary increase, the computation time will also increase. So we proposed to build the target-specific dictionary, where a threshold of DSC is used to remove some irrelevant shape templates and reduce the size of the dictionary. The shape repository used in this study is relative small, so we choose a low threshold of 30%. In this study, with the shape template repository built with 201 slices from the Challenge data set, a threshold below 50% does not have effect to the accuracy of results. And with a threshold of 60%, a DSC of 73.15 ± 8.50% is achieved. When the threshold is further increased, for some slices, no shape templates will be kept or the reserved number is too small to give enough flexibility modeling the actual myocardium shape. In the clinical practice, in order to reduce the computation time, the value can be set higher (such as 50–60%). Also, if the shape repository is large and has a good variety of shape characters, a higher value should be set.

The parameter λ in the sparse representation-based shape model controls the level of sparsity. When the parameter λ is larger, the nonzero elements in the vector $\varvec{w}$ will be less. This means that less templates in $D_{r}$ will be effective in representing the myocardium. In this study, the value of λ changing between 0.1–1 does not have significantly effect to the results.

Another free parameter is $\beta$ in the Gaussian weighting function. When the value of $\beta$ increases, the sensitivity of the random walks method to the intensity contrast increases. In our empirical observations, when the value of $\beta$ is sufficiently large, changing $\beta$ in a large range does not affect the results. In our experiment, the square gradients are normalized to the interval of [0, 1], and good results can be achieved when $\beta > 100$. In a relevant work [31], a careful study of the effect of $\beta$ was undertaken, and a similar trend was found.