دانلود رایگان مقاله شبیه سازی با استفاده از شبکه هرمیت مکعب با گره برای مدل سازی ایزوهندسی

Abstract

Cubic Hermite hexahedral finite element meshes have some well-known advantages over linear tetrahedral finite element meshes in biomechanical and anatomic modeling using isogeometric analysis. These include faster convergence rates as well as the ability to easily model rule-based anatomic features such as cardiac fiber directions. However, it is not possible to create closed complex objects with only regular nodes; these objects require the presence of extraordinary nodes (nodes with 3 or >=5 adjacent elements in 2D) in the mesh. The presence of extraordinary nodes requires new constraints on the derivatives of adjacent elements to maintain continuity. We have developed a new method that uses an ensemble coordinate frame at the nodes and a local-to-global mapping to maintain continuity. In this paper, we make use of this mapping to create cubic Hermite models of the human ventricles and a four-chamber heart. We also extend the methods to the finite element equations to perform biomechanics simulations using these meshes. The new methods are validated using simple test models and applied to anatomically accurate ventricular meshes with valve annuli to simulate complete cardiac cycle simulations.

8. Conclusions

We have developed a method by which we can perform cardiac biomechanics simulations on cubic-Hermite meshes with extraordinary nodes. These meshes are capable of representing complex geometries with fewer elements. This reduces the computational time since computing the element stiffness matrix for each element is the most computationally intensive operation in higher-order finite element analysis. In addition, locally varying quantities such as the fiber direction have been incorporated into these meshes. Using our method, meshes with locally varying properties can be generated and hence, this method can be used to model complex materials such as the muscle tissue. Compact cubic Hermite meshes are ideally suited for patient-specific cardiac modeling. Since these meshes have fewer degrees of freedom, they can be used to create template meshes from population averaged cardiac dimensions. These template meshes can then be modified using image registration algorithms to create patient-specific cardiac meshes from images obtained using computed tomography (CT) or magnetic resonance (MR) automatically. Since creating an anatomically accurate patient-specific mesh is the most tedious and time-consuming step of the process, using these meshes can significantly reduce the total time for patient-specific modeling. The finite element method used in this paper only rely on C0 continuity of geometry and dependent variables between the elements for mechanics simulations. However, the methods used for constructing the cubic-Hermite finite element mesh and the local-to-global mapping are more general and can be used to enforce higher order G1 continuity by modifying the twice-subdivided mesh suitably. Enforcing high-order continuity might help reduce the total DOFs in the analysis and might improve convergence by requiring fewer iterations to reach a converged solution. Using anatomically accurate heart models for biomechanics simulations will enable modeling of complex interactions that were not previously possible with ventricular models that do not include the valve plane. One example is to model mitral valve regurgitation by linking it to changes in the mitral valve annuli during the heart cycle. The four-chamber mesh can be used to model the effect of atrial geometry on the heart function. Anatomically accurate boundary conditions can be imposed on the cardiac geometry, resulting in the model replicating the motion of the cardiac walls and the valve plane accurately during the cardiac cycle.