tailieunhanh - New Developments in Biomedical Engineering 2011 Part 5

Tham khảo tài liệu 'new developments in biomedical engineering 2011 part 5', kỹ thuật - công nghệ, cơ khí - chế tạo máy phục vụ nhu cầu học tập, nghiên cứu và làm việc hiệu quả | 152 New Developments in Biomedical Engineering Recently mesh adaptation methods have been introduced to reduce the size of the spatial mesh as well as the computational time. This method consists in locating finer mesh cells near the depolarisation-repolarization front position while a coarser mesh is used away from the front. In the context of isotropic unstructured meshes the reader is referred to Cherry et al. 2003 Colli Franzone et al. 2006 and Trangenstein Kim 2004 for more details. However for two and three dimensional anisotropic mesh adaptation where mesh cells are elongated along a specified direction the reader is referred to Belhamadia 2008a b Belhamadia et al. 2009 . The scope of this book chapter is to present the recent adaptive technique introduced in Bel-hamadia 2008a b for simulating the two-dimensional cardiac electrical activity. The method proposed reduces greatly the size of the spatial mesh as well as the computational time. Also an accurate prediction of the depolarization and repolarization fronts is obtained showing the advantages of the proposed method. This work is organized as follows. Section 2 presents a brief description of the bidomain and monodomain models with Aliev-Panfilov ion kinetics. Also the finite element discretization for these models are presented. Section 3 is devoted to a description of the time-dependent adaptive strategy while the last section presents two-dimensional numerical results representing the re-entrant waves. 2. Mathematical Models The bidomain and modomain models will be now presented. The first model consists of a nonlinear partial differential equation for the transmembrane potential Vm coupled with an elliptic one for the extracellular potential pe as well as an ordinary differential equation for at least one variable representing the ionic currents. This system of equations takes the following form V V- GiVVm V GiV pe lion Vm W V Gi Ge V pe V GiVVm 1 . g Vm W where Gi and Ge are the symmetric intra- .