much less successful with permanent and persistent AF (PeAF). ... of atrial electrical activity can guide more effective treatment of patients with PeAF and that.
Reconstructing atrial fibrillation: New inverse method for intracardiac electro-anatomic mapping J. Chamorro-Servent1, B. H. Smaill1,2, 1Auckland Bioengineering Institute, 2Physiology, The University of Auckland, New Zealand
Atrial fibrillation (AF) is a common heart rhythm disorder associated with increased risk of stroke and impaired quality of life. Percutaneous catheter ablation has proved effective in reversing drug-resistant paroxysmal AF, but has been much less successful with permanent and persistent AF (PeAF). There is evidence that real-time 3D electroanatomic mapping of atrial electrical activity can guide more effective treatment of patients with PeAF and that improved mapping systems are needed for this purpose. Limitations of the current contact catheter mapping systems are that electrodes may not be uniformly distributed across the atrial wall and a large fraction of them usually do not contact the wall. To improve this, our group is developing an inverse mapping method that will enable high-resolution potentials on the inner surface of the atria to be computed from potentials measured at multiple electrodes located on the splines of a non-contact open basket catheter positioned inside the atrial chamber. Accurate low cost forward and inverse solution methods are required to provide precise real-time or near realtime electro-anatomic maps. The cardiac inverse relies on the fact that Laplace’s law holds throughout the domain of interest. Traditionally, the forward problem has been reduced to cardiac and measurement surfaces by applying Green’s 2nd theorem and discretised using the boundary element method (BEM). BEM is inherently accurate, but meshing of heart and measurement surfaces can be time-consuming. Furthermore, precise estimates of surface normals are required, while singularities adjacent to the surfaces in the fundamental basis function used can introduce artifact. Meshless methods (MMs) have been developed in other fields to overcome them. MMs provide simpler alternative to BEM. The method of fundamental solution (MFS) is a MMs that has been used in various applications to solve partial differential equations, including Electrocardiographic imaging (ECGI). In MFS, the potential is expressed as summation over a discrete set of virtual point sources placed outside the domain of interest. The basis function used is the Laplace fundamental solution. With ECGI, the potential gradients normal to the body surface can be set to zero because there is no flux across it. This is not the case with ICEI. However, the open nature of our catheter allows us to calculate the potentials inside, which will serve as indirect “flux” without needing to calculate the reel flux to solve MFS. It is well-known that optimal placement of the virtual source points poses a difficulty for MFS implementation. But, as far as we are aware, there have not been attempts to optimise source node placement, although this has proved useful in other fields. Singular value analysis (SVA) and Picard’s condition provide a means of investigating the relationship between outputs and inputs and to determine the number of independent source values that can be identified from noisy measurement data. These techniques have been previously used in tomography imaging to optimize the experimental setups. We present here a MFS applied to our non-contact intracardiac electrical imaging (ICEI). We apply SVA and Picard’s condition to study node placement, number and measurements of internal measurements sites, their distance from the external boundary and the degrees of freedom in the solution set. In comparison with BEM, MFS is easier to implement, as accurate, more robust, and much more efficient. Solution times are the order of seconds compared with minutes for an equivalent BEM solution. Besides, in MFS the determination of an approximation to the solution at a point in the interior of the domain of the problem only requires an evaluation of the approximate solution. This simplifies our problem since we do not need to solve it by quadrature or by using another forward problem method requiring discretization of the catheter domain. Finally, we have demonstrated that reducing the number of source nodes to better match the degrees of freedom of measured potential distributions improves the efficiency and robustness of inverse solution. Similarly, adaptative node placement based on the position of the catheter inside the atria improves also the efficiency. In conclusion, an accurate node placement improves the efficiency and robustness of the fast MFS method.
