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Novel Atlas of Fiber Directions Built From Ex Vivo DT images of Porcine Hearts
Mia Mojica1, Mihaela Pop2, Maxime Sermesant3, and Mehran Ebrahimi1

1University of Ontario Institute of Technology, Oshawa, ON, Canada, 2Sunnybrook Research Institute, Toronto, ON, Canada, 3INRIA Sophia Antipolis, Sophia Antipolis, France

### Synopsis

In this study we successfully created the first high-resolution cardiac Diffusion Tensor (DT) imaging-based fiber atlas from porcine hearts. Furthermore, we laid the foundation of a framework for building a statistical cardiac atlas by computing an average cardiac geometry from a small database (N=8) of explanted porcine hearts without the need for selecting landmarks, transforming the diffusion tensors of subjects, and obtaining the associated average DT field and fiber architecture. The fiber atlas can be used for personalized electro-mechanical simulations of cardiac function (in anisotropic models when DT data is not available), and aid in diagnosis or therapy guidance procedures.

### Introduction

Cardiac MR image-based predictive models integrating statistical atlases of heart anatomy and fiber orientations can aid in better diagnosis of cardiovascular disease, a major cause of death worldwide. Such atlases have been built from diffusion tensor (DT) imaging of various species: rat, dog, and human heart1,2,3, and can be used for personalized computational electro-mechanical studies where the DTI data is not available, to help with diagnosis and therapy guidance interventions. Here, we propose a framework for constructing a statistical fiber atlas from high resolution ex vivo DT images of porcine hearts, by first computing an average geometry and then obtaining directional information of diffusion tensors linked to the reference frame of the transformed subjects (i.e., hearts).

### Methods

A diagram of the workflow is presented in Figure 1. First, the diffusion-weighted (DW) MRI studies were performed on a dedicated 1.5T GE Signa Excite scanner using a small database of $N=8$ explanted healthy pig hearts, with approval from our institute. In the current study, we used the following MR parameters: TE=35 ms, TR=700 ms, ETL=2, b=0 for the unweighted MR images, and b=500 s/mm2 when the seven diffusion gradients were applied, respectively4. Image resolution was ~0.5x0.5x1.6 mm.

The geometries of the 3D anatomical volumes $T_i ~(i = 1,\ldots,N)$ were first normalized to generate a mean cardiac volume. This was done through an iterative groupwise registration scheme. At every groupwise iteration, all the subjects were registered to the current reference volume via multilevel nonparametric registration5. The resulting transformations from the pairwise registration step were used to update the reference geometry $I_{\text{mean}}^{n}$.

The diffusion tensors associated with each subject were subsequently transformed using the transformations aligning the subjects to the average geometry; this was done to project the tensors onto a common reference frame, which would ultimately enable us to extract tensor statistics for the population. We used a Finite Strain reorientation method to transform the tensors. Given a deformation field $y$, the rotation component of the local affine transformation given by $A = I + \nabla y$ was used to reorient the tensor at every voxel. It was obtained by solving for $R$ in the polar decomposition of $A$: $A = RU$, while the reoriented tensor $A(D)$ was given by $A(D) = RDR^T$. Finally, we used the Log-Euclidean metric to calculate the average diffusion tensor field $\overline{D}_\text{log}(X)$: $\overline{D}_\text{log}(X) = \exp\left[\displaystyle\frac{1}{N}\sum_{i=1}^{N}\log\left(D_i\left(X\right)\right)\right]$, where $D_i(X)$ refers to the reoriented tensor of the $i^\text{th}$ subject.

### Results and Discussion

The groupwise registration algorithm took only 8 iterations until it converged to the stable average geometry shown in Figure 2(a). The error evolution of the groupwise algorithm (measured in terms of change in average intensity values between consecutive reference geometries) is shown in Figure 2(b). In Figure 3, we present the average tensor field and the results of the Finite Strain reorientation method. Note that the geometric features and the local orientation of the diffusion tensor fields were preserved. This makes Finite Strain an ideal method for inter-subject DT-MRI registration3.

The average cardiac fiber architecture is shown in Figure 4 in three views: anterior (A), posterior (P), and lateral (L). Fiber tractography was performed on the average DT field using MedInria (http://med.inria.fr) to find the end-to-end pathway of the principal direction of diffusion given by the first eigenvector of the diffusion tensors.

### Conclusions and Future Work

We successfully created the first cardiac fiber atlas for porcine hearts. In addition, we laid the foundation of a framework for building a statistical cardiac atlas by computing an average cardiac geometry from a small database without the need for selecting landmarks, transforming the diffusion tensors of the subjects, and obtaining the associated average diffusion tensor field and cardiac fiber architecture. The next step will be to compute tensor statistics to better understand the underlying fiber and laminar sheet structure and to use the fiber atlas for electro-mechanical simulations to predict cardiac function.

### Acknowledgements

This work was supported in part by an NSERC Discovery grant and Deborah Saucier Early Researcher Award for Dr. Mehran Ebrahimi, and an Inria - Associated team grant for Drs. Mihaela Pop and Maxime Sermesant. Mia Mojica is supported by an Ontario Trillium Scholarship (OTS).

### References

1. Piuze, E., et al. Atlases of cardiac fiber differential geometry. In International Conference on Functional Imaging and Modeling of the Heart, pages 442–449. Springer, 2013.

2. Lombaert H., et al. Human atlas of the cardiac fiber architecture: study on a healthy population. IEEE transactions on medical imaging, 31(7):1436–1447, 2012.

3. Peyrat, J.M., et al. A computational framework for the statistical analysis of cardiac diffusion tensors: application to a small database of canine hearts. IEEE transactions on medical imaging, 26(11):1500–1514, 2007.

4. Pop, M., et al. Quantification of fibrosis in infarcted swine hearts by ex vivo late gadolinium-enhancement and diffusion-weighted MRI methods. Physics in medicine and biology, 58(15):5009, 2013

5. Modersitzki, J. FAIR: Flexible algorithms for image registration, volume 6. SIAM, 2009

### Figures

Figure 1: Workflow diagram for building a statistical porcine cardiac atlas. DW images were acquired, and then an average cardiac geometry was constructed through groupwise registration. The diffusion tensors for each heart were reoriented and averaged to compute a cardiac fiber atlas.

Figure 2: Results of the groupwise registration. (a) 3D and axial views of the computed average geometry, (b) the rate of convergence of the groupwise scheme was measured in terms of the average change in intensity values between successive reference volumes. The groupwise registration algorithm terminates when either the maximum number of iterations (n = 10) is reached, or when there is no significant improvement in the average change in intensity values, i.e. when $\dfrac{\text{mean}\left(|I_{\text{mean}}^{n+1} - I_{\text{mean}}^{n}|\right)}{\text{mean}\left(|I_{\text{mean}}^{n} - I_{\text{mean}}^{n-1}|\right)}>0.05$.

Figure 3: Tensor Reorientation and Averaging. (Top) The original tensors of one of the subjects and (Bottom) the average DT field. The local orientation of the tensors were preserved by the Finite Strain reorientation method. The tensors are red when the primary eigenvector is oriented along the direction of the x-coordinates, green along the direction of the y-coordinates, and blue along the direction of the z-coordinates.

Figure 4: Fiber Tractography. Cardiac fiber atlas obtained by tracking the end-to-end pathway of the principal direction of diffusion at every voxel. As indicated by the cube in the bottom left, the fibers are red when the primary eigenvector is oriented along the direction of the x-coordinates, green along the direction of the y-coordinates, and blue along the direction of the z-coordinates.

Proc. Intl. Soc. Mag. Reson. Med. 27 (2019)
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