To address these difficulties, methods derived from various energy minimization formulations in the forms of partial differential equations (PDEs) have been extensively studied and widely used, offering a unified framework which combines knowledge from physically/mathematically motivated regularization, image-based/derived data, representation and computation theory. However, in the presence of the limitations of the existing imaging techniques such as image noise, intensity inhomogeneity, etc, the complexity of the cardiac dynamics and the lack of unambiguous reference landmarks within the myocardium, it remains challenging to robustly and reliably solve these problems. The development of cardiac image analysis algorithms to assess the regional function of the heart constitutes a promising strategy for evaluating normal and abnormal cardiac physiology and mechanics –. The proposed framework has minimal consistency constraints, handling large deformation and material discontinuities are simple and efficient, and it provides a way to avoid the complicated meshing procedures while preserving the accuracy with a relatively small number of nodes. Results showed that the error of our framework against the ground truth was 0.1189 ± 0.0672 while the error of the traditional FEM was 0.1793 ± 0.1166.
We evaluate the performance of meshfree representation on a synthetic heart data and an in-vivo cardiac MRI image sequence. In our implementation, as element-free Galerkin method can efficiently build a meshfree representation using its shape function with moving least square fitting, we apply this meshfree method to handle large deformation or inhomogeneity for solving cardiac segmentation and motion tracking problems.
In this paper, we adopt the idea of meshfree representation into cardiac medical image analysis in order to overcome the difficulties caused by large deformation and inhomogeneous materials of the heart.
Therefore, meshfree method can conveniently process the numerical computation inside interested domains with large deformation or inhomogeneity. The prominent advantage of meshfree method, is the way to build the representation of computational domain, based on the nodal points without any explicit meshing connectivity.
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