Archive | 2019
Towards the Real-Time Modeling of the Heart
Abstract
Abstract Several studies have been carried out recently with the aim of achieving cardiac modeling of the whole heart for a full heartbeat. However, within the context of the Galerkin method, those simulations have a high computational demand, ranging from 16 to 200 CPUs, and long calculation times, lasting from 1 to 50\xa0h. To solve this problem, this research proposes to make use of a reduced order method called the proper orthogonal decomposition with interpolation (PODI) method to achieve real-time modeling with an adequate level of solution accuracy. The idea behind this method is to first construct a database of precomputed full-scale solutions of the heart s biomechanical and physiological characteristics using the element-free Galerkin method or the finite element method and then project a selected subset of these solutions to a low-dimensional space. Using the moving least square approximation method, an interpolation is carried out for the problem at hand, before the resulting solution is projected back to the original high-dimensional solution space. The research objective to tackle real-time modeling of a patient-specific heart for a full heartbeat is approached in two stages. First, a so-called “time standardization scheme” is developed to synchronize variations in the timeline during the four phases of a full heartbeat cycle. This is necessary due to the fact that time increments are not uniform throughout the simulated heart cycle. The results generated by the proposed cardiac PODI framework exhibit high levels of accuracy and are obtained approximately 2200 times faster than using conventional full-scale modeling. Second, the PODI method is further extended to deal with arbitrary heart anatomies. For this purpose, a method called degrees of freedom standardization (DOFS) is developed. DOFS employs a template mesh onto which all datasets are projected. These standardized dataset fields are used for the actual PODI calculation and the resulting low-order solutions are subsequently projected back to the mesh of the problem at hand. The first template mesh to be considered is a cube mesh. However, it is found to produce results with high errors and nonphysical behavior. The second template mesh used is a heart template. In this case, a preprocessing step is required where a nonrigid transformation based on the coherent point drift method is utilized to transform all heart simulation datasets onto the template heart. The cardiac PODI framework enhanced by the heart template approach generates solutions at computation speeds approximately 80 times faster than using a conventional full-scale method at slightly lower levels of accuracy than above.