Quality Metrics for High Order Meshes: Analysis of the Mechanical Simulation of the Heart Beat

Abstract

The quality of a computational mesh is an important characteristic for stable and accurate simulations. Quality depends on the regularity of the initial mesh, and in mechanical simulations it evolves in time, with deformations causing changes in volume and distortion of mesh elements. Mesh quality metrics are therefore relevant for both mesh personalization and the monitoring of the simulation process. This work evaluates the significance, in meshes with high order interpolation, of four quality metrics described in the literature, applying them to analyse the stability of the simulation of the heart beat. It also investigates how image registration and mesh warping parameters affect the quality and stability of meshes. Jacobian-based metrics outperformed or matched the results of coarse geometrical metrics of aspect ratio or orthogonality, although they are more expensive computationally. The stability of simulations of a complete heart cycle was best predicted with a specificity of 61%, sensitivity of 85%, and only nominal differences were found changing the intra-element and per-element combination of quality values. A compromise between fitting accuracy and mesh stability and quality was found. Generic geometrical quality metrics have a limited success predicting stability, and an analysis of the simulation problem may be required for an optimal definition of quality.

An automatic service for the personalization of ventricular cardiac meshes

“…For a detailed analysis of this compromise in the simulation of cardiac mechanics, the reader is referred to Lamata et al . [22]. This section reports the effect of the selection of the LoD parameter ruling the registration process in the meshing service.…”

“…Mesh quality ( Q ) is characterized by the Jacobian ratio, previously identified to be the quality metric with the best compromise between performance versus computational cost in the prediction of simulation stability [22]. This metric analyses the transformation from local to global coordinates, measuring the homogeneity of each volume differential.…”

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Figure 6.Impact of the choice of the LoD in geometrical accuracy (lines with crosses), characterized by the average fitting error (see equation (3.1)), and mesh quality (lines with circles), characterized by the Jacobian ratio (see equation (3.2)), in the two average anatomies (A1, A2). Horizontal dashed line is the empirical threshold of mesh quality [22]. (Online version in colour.

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Guest Editorial Special Issue on Medical Imaging and Image Computing in Computational Physiology

“…The method was used to assess local aneurysmal hemodynamics after coiling using computational fluid dynamics. Lamata et al [28] explored various mesh quality criteria for cardiac simulations. They stressed that generic geometrical quality metrics have limited success in predicting stability, and an analysis of the simulation problem may be required for an optimal definition of quality.…”

Three-dimensional Multiscale Modelling and Simulation of Atria and Torso Electrophysiology

“…Thanks to the high quality and regularity of the mesh, the stability of numerical computations is guaranteed (Lamata et al 2013). …”