Limits...
A geometrical approach for automatic shape restoration of the left ventricle.

Tan ML, Su Y, Lim CW, Selvaraj SK, Zhong L, Tan RS - PLoS ONE (2013)

Bottom Line: The goal of the optimization is to achieve a smooth epicardial shape by iterative in-plane and through-plane translation of vertices in the LV model.In the 20 in vivo patient-specific models, the results show that our method is able to restore the shape of LV models without altering the general shape of the model.The magnitudes of in-plane translations are also consistent with existing registration techniques and experimental findings.

View Article: PubMed Central - PubMed

Affiliation: Geometrical Modelling, Institute of High Performance Computing, ASTAR, Singapore, Singapore. tanml@ihpc.a-star.edu.sg

ABSTRACT
This paper describes an automatic algorithm that uses a geometry-driven optimization approach to restore the shape of three-dimensional (3D) left ventricular (LV) models created from magnetic resonance imaging (MRI) data. The basic premise is to restore the LV shape such that the LV epicardial surface is smooth after the restoration and that the general shape characteristic of the LV is not altered. The Maximum Principle Curvature (k1) and the Minimum Principle Curvature (k2) of the LV epicardial surface are used to construct a shape-based optimization objective function to restore the shape of a motion-affected LV via a dual-resolution semi-rigid deformation process and a free-form geometric deformation process. A limited memory quasi-Newton algorithm, L-BFGS-B, is then used to solve the optimization problem. The goal of the optimization is to achieve a smooth epicardial shape by iterative in-plane and through-plane translation of vertices in the LV model. We tested our algorithm on 30 sets of LV models with simulated motion artifact generated from a very smooth patient sample, and 20 in vivo patient-specific models which contain significant motion artifacts. In the 30 simulated samples, the Hausdorff distances with respect to the Ground Truth are significantly reduced after restoration, signifying that the algorithm can restore geometrical accuracy of motion-affected LV models. In the 20 in vivo patient-specific models, the results show that our method is able to restore the shape of LV models without altering the general shape of the model. The magnitudes of in-plane translations are also consistent with existing registration techniques and experimental findings.

Show MeSH
Constraint in the z axis.(a) Angle  between vertex normal  and the -axis, and the impact on volume change due to translation, (b) LV epicaridal surface modified by the free-form deformation process.
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pone-0068615-g004: Constraint in the z axis.(a) Angle between vertex normal and the -axis, and the impact on volume change due to translation, (b) LV epicaridal surface modified by the free-form deformation process.

Mentions: In Figure 4(a), we illustrate the impact of on the volume of the LV mesh with respect to the vertical shift of the vertices. Two vertices and on the same contour are such that >. Given the same allowance of vertical shift such that their new positions become and , we observed that the deviation of from the original surface of the mesh is greater than , indicating that when is smaller, the resulting volume change due to the vertical vertex shift is larger. Therefore, the function in Equation (14) is used to constrain the vertices such that if there is greater deviation between the vertex normal from the SA-plane (i.e., is small), the allowable vertical translation in the -direction will be less. This will prevent unduly large change in the volume of the restored mesh. Figure 4(b) illustrates an LV epicardial surface modified by the free-form deformation process.


A geometrical approach for automatic shape restoration of the left ventricle.

Tan ML, Su Y, Lim CW, Selvaraj SK, Zhong L, Tan RS - PLoS ONE (2013)

Constraint in the z axis.(a) Angle  between vertex normal  and the -axis, and the impact on volume change due to translation, (b) LV epicaridal surface modified by the free-form deformation process.
© Copyright Policy
Related In: Results  -  Collection

Show All Figures
getmorefigures.php?uid=PMC3716701&req=5

pone-0068615-g004: Constraint in the z axis.(a) Angle between vertex normal and the -axis, and the impact on volume change due to translation, (b) LV epicaridal surface modified by the free-form deformation process.
Mentions: In Figure 4(a), we illustrate the impact of on the volume of the LV mesh with respect to the vertical shift of the vertices. Two vertices and on the same contour are such that >. Given the same allowance of vertical shift such that their new positions become and , we observed that the deviation of from the original surface of the mesh is greater than , indicating that when is smaller, the resulting volume change due to the vertical vertex shift is larger. Therefore, the function in Equation (14) is used to constrain the vertices such that if there is greater deviation between the vertex normal from the SA-plane (i.e., is small), the allowable vertical translation in the -direction will be less. This will prevent unduly large change in the volume of the restored mesh. Figure 4(b) illustrates an LV epicardial surface modified by the free-form deformation process.

Bottom Line: The goal of the optimization is to achieve a smooth epicardial shape by iterative in-plane and through-plane translation of vertices in the LV model.In the 20 in vivo patient-specific models, the results show that our method is able to restore the shape of LV models without altering the general shape of the model.The magnitudes of in-plane translations are also consistent with existing registration techniques and experimental findings.

View Article: PubMed Central - PubMed

Affiliation: Geometrical Modelling, Institute of High Performance Computing, ASTAR, Singapore, Singapore. tanml@ihpc.a-star.edu.sg

ABSTRACT
This paper describes an automatic algorithm that uses a geometry-driven optimization approach to restore the shape of three-dimensional (3D) left ventricular (LV) models created from magnetic resonance imaging (MRI) data. The basic premise is to restore the LV shape such that the LV epicardial surface is smooth after the restoration and that the general shape characteristic of the LV is not altered. The Maximum Principle Curvature (k1) and the Minimum Principle Curvature (k2) of the LV epicardial surface are used to construct a shape-based optimization objective function to restore the shape of a motion-affected LV via a dual-resolution semi-rigid deformation process and a free-form geometric deformation process. A limited memory quasi-Newton algorithm, L-BFGS-B, is then used to solve the optimization problem. The goal of the optimization is to achieve a smooth epicardial shape by iterative in-plane and through-plane translation of vertices in the LV model. We tested our algorithm on 30 sets of LV models with simulated motion artifact generated from a very smooth patient sample, and 20 in vivo patient-specific models which contain significant motion artifacts. In the 30 simulated samples, the Hausdorff distances with respect to the Ground Truth are significantly reduced after restoration, signifying that the algorithm can restore geometrical accuracy of motion-affected LV models. In the 20 in vivo patient-specific models, the results show that our method is able to restore the shape of LV models without altering the general shape of the model. The magnitudes of in-plane translations are also consistent with existing registration techniques and experimental findings.

Show MeSH