#
Surface Mesh Reconstruction from Cardiac MRI Contours^{ †}

^{*}

^{†}

## Abstract

**:**

## 1. Introduction

- Development of a surface reconstruction method capable of dealing with non-parallel, cross-sectional, sparse, heterogeneous, and non-coincidental contours,
- Use of our technique on the surfaces of the left ventricle as well as on the right ventricle,
- Evaluation of our method on several realistic shapes generated from a statistical shape model, as well as on real data data consisting of normal and abnormal pathologies.

#### State of the Art

## 2. Materials and Methods

#### 2.1. Synthetic and Real Data

**b**are a set of parameters that, when applied to $\mathsf{\Phi}$ along with the rigid transformation model $\mathcal{T}$, generate a new shape. The error metric d is the contour-to-mesh distance. For each of the contours, the shape model with the minimum contour-to-mesh distance was obtained, and a set of spatially consistent contours were generated by slicing the mesh at the same planes as the CMR acquired contour planes. Figure 1 shows an example of such a mesh.

#### 2.2. Initial Meshes

#### 2.3. Mesh Deformation

## 3. Results

#### 3.1. Simulation of CMR Acquisitions

#### 3.2. Synthetic Data

#### 3.2.1. Short Axis Contours

#### 3.2.2. Short Axis and Long Axis Contours

#### 3.2.3. Non-Parallel, Non-Coincidental Contours

#### 3.3. CMR Acquired Data

## 4. Discussion

## 5. Conclusions

## Acknowledgments

## Author Contributions

## Conflicts of Interest

## Abbreviations

MRI | Magnetic resonance imaging |

CMR | Cardiac magnetic resonance |

SAX | Short axis slice |

LAX | Long axis slice |

TPS | Thin plate spline |

SSM | Statistical shape model |

## Appendix A. Illustration of Extreme Cases

**Figure A1.**Illustration of resulting meshes for different extreme sets of parameters in the exploration and tuning of the parameters experiment. The color along the contours represents the distance to the resulting mesh. See the main text in Appendix A for comments on the different panels.

## Appendix B. Simulation of CMR Acquisitions

**Figure A2.**Resulting output mesh using our methodology on simulated CMR acquired contours (see Section 3.1). The figure shows the various shapes of the 40 generated meshes.

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**Figure 1.**An example of the SSM of the left ventricle epicardium and right ventricle endocardium fitted to real contours. The dark blue contours represent the real contours. The green contours represent the synthetic contours generated by slicing the SSM at the same spatial pose of the CMR acquired contour planes.

**Figure 2.**Overall pipeline for generating a surface mesh from contours illustrated on left epicardial contours. (

**a**) the input contours; (

**b**) tubular initial mesh with its vertices equally spaced along the contours; (

**c**) the initial mesh after the Laplacian smoothing and showing the attractor points on the contours, with a visual illustration of their connections pulling the mesh; (

**d**) the resulting mesh after several small deformations towards the attractor points; (

**e**) the mesh after having undergone the process of subdivision, smoothing and decimation; (

**f**) the resulting mesh, after several iteration of steps (

**d**,

**e**).

**Figure 3.**Parallel Coordinate graph showing the different combinations of parameters giving the minimum average, median, and min mesh to mesh distance, as well as the number of triangles generated. The red lines represent the selected bands for the y-axis. The highlighted blue lines represent the parameters that have generated meshes that satisfies the selected criteria. The faded lines represent every parameter permutation and their respective evaluation metrics. There are 3440 permutations. The fifth to seventh y-axis represent the mean, median and min mesh-to-mesh error distances in mm, between the ground truth meshes and the generated meshes given the respective parameters.

**Figure 4.**(

**a**) the ground truth surface (left epicardium of the mean shape of the SSM) and the synthesized contours in red; (

**b**) our resulting mesh given the red contours; (

**c**) the surface-to-mesh distance error (in mm). The resulting mesh has been clipped at the level of the most basal contour.

**Figure 5.**Impact of increasing the number of SAX contours on the error distance between the generated mesh and the ground truth surface.

**Figure 6.**The effect of increasing the amount of left epicardial LAX contours have on the error distance between the generated mesh and the ground truth mesh. Top to bottom: 1–8 LAX slices added, successively. Each LAX added is a rotated version of the first LAX shown in the first row, first column. Rotations were generated as per the following: 90, 45, 135, 22.5, 157.5, 112.5, 67.5 degrees, respectively.

**Figure 7.**Distance map from the resulting geometrical mesh to the simulated cardiac input data. The contours were transformed by small out of plane rotations and translations. The left panel shows the resulting left ventricular epicardial mesh, and the right panel shows the right ventricular endocardial mesh. The distance errors represent the contour-to-mesh distances.

**Figure 9.**Example of resulting surface meshes generated from (

**a**) contours for a normal case, and (

**b**) contours belonging to a severe abnormal anatomy. The left panel shows surface meshes for the left endocardial (in red) and epicardial (in blue) ventricle as well as the right epicardial ventricle (in orange). The right panel shows surface meshes for the left endocardial (in red) and epicardial (in blue) ventricle.

**Figure 10.**Endocardial contour-to-mesh distance having built the mesh with the entire set of contours (labelled $OM$, which stands for “Original Mesh”, in blue) and excluded contour-to-mesh distance having built the mesh without the excluded contour (labelled $CM$, which stands for “Computed Mesh”, in red).

**Figure 11.**Contour-to-mesh distances for all 24 cases, having built the meshes without the respectively excluded contour. Each error bar represents the distribution of distances for each of the respective statistical measurement. Each square represents the mean of each statistical measure, with the upper and lower notches representing the minimum and maximum values, respectively.

**Top**: epicardial contour-to-mesh distances;

**bottom**: endocardial contour-to-mesh distances. The y-axis represents the contour index. 1–2 represent the LAX, 3–11 represent the apex to the base, respectively.

**Table 1.**Table depicting the mesh-to-mesh distances (in mm) between the ground truth surface meshes and our generated meshes for 40 different geometries.

Measure | Epicardium (mm) | Endocardium (mm) | Right Ventricle (mm) |
---|---|---|---|

Mean | 0.12 | 0.14 | 0.29 |

Median | 0.09 | 0.09 | 0.22 |

Max | 1.11 | 1.29 | 3.34 |

Min | 1.35 $\times {10}^{-5}$ | 2.04 $\times {10}^{-5}$ | 7.49 $\times {10}^{-5}$ |

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**MDPI and ACS Style**

Villard, B.; Grau, V.; Zacur, E.
Surface Mesh Reconstruction from Cardiac MRI Contours. *J. Imaging* **2018**, *4*, 16.
https://doi.org/10.3390/jimaging4010016

**AMA Style**

Villard B, Grau V, Zacur E.
Surface Mesh Reconstruction from Cardiac MRI Contours. *Journal of Imaging*. 2018; 4(1):16.
https://doi.org/10.3390/jimaging4010016

**Chicago/Turabian Style**

Villard, Benjamin, Vicente Grau, and Ernesto Zacur.
2018. "Surface Mesh Reconstruction from Cardiac MRI Contours" *Journal of Imaging* 4, no. 1: 16.
https://doi.org/10.3390/jimaging4010016