Impact of the Endocardium in a Parameter Optimization to Solve the Inverse Problem of Electrocardiography

Abstract

Electrocardiographic imaging aims at reconstructing cardiac electrical events from electrical signals measured on the body surface. The most common approach relies on the inverse solution of the Laplace equation in the torso to reconstruct epicardial potential maps from body surface potential maps. Here we apply a method based on a parameter identification problem to reconstruct both activation and repolarization times. From an ansatz of action potential, based on the Mitchell-Schaeffer ionic model, we compute body surface potential signals. The inverse problem is reduced to the identification of the parameters of the Mitchell-Schaeffer model. We investigate whether solving the inverse problem with the endocardium improves the results or not. We solved the parameter identification problem on two different meshes: one with only the epicardium, and one with both the epicardium and the endocardium. We compared the results on both the heart (activation and repolarization times) and the torso. The comparison was done on validation data of sinus rhythm and ventricular pacing. We found similar results with both meshes in 6 cases out of 7: the presence of the endocardium slightly improved the activation times. This was the most visible on a sinus beat, leading to the conclusion that inclusion of the endocardium would be useful in situations where endo-epicardial gradients in activation or repolarization times play an important role.

Pacemaking function of two simplified cell models

“…Another well-known disadvantage of the phenomenological models like pAP-AP and pCN-CN is their limited ability to represent action potential morphology under varying physiological conditions, e.g., the effect of variation of concentration of particular ions, which is necessary for simulations of complex cardiac diseases such as ion channelopathies. However, the utilization of the considered pacemaker models can be beneficial for the development of simplified real-time simulation systems (e.g., personalized medicine [ 30 , 31 ] and inverse cardiac modeling [ 32 ]), deep learning [ 43 ], as well as for medical device testing platforms [ 44 , 46 ]. The simplified models can also be used in preliminary simulation setups for hypothesis testing and verification, as well as model design and tuning before implementing complex and computationally expensive ion-channel models [ 34 ].…”

Pacemaking function of two simplified cell models

“…The utilization of the considered pacemaker models can be beneficial for the development of simplified real-time simulation systems (e.g. personalized medicine [24,25] and inverse cardiac modeling [26]), deep learning [37], as well as for medical device testing platforms [38,52].…”

“…The utilization of the considered pacemaker models can be beneficial for the development of simplified real-time simulation systems (e.g., personalized medicine [30,31] and inverse cardiac modeling [32]), deep learning [43], as well as for medical device testing platforms [44,46]. The simplified models can also be used in preliminary simulation setups for hypothesis testing and verification, as well as model design and tuning before implementing complex and computationally expensive ion-channel models [34].…”

“…The disadvantage of other simplified models simulating both pacemaker and non-pacemaker action potentials of cardiac cells like VCD, Morris-Lecar, and their modifications is the significant number of parameters that limit the areas of their utilization. On the other hand, computationally lightweight models such as AP, MS, and CN are being successfully used for the solution of the cardiac inverse problem and building patient-specific models [30][31][32][33]. The MS model, however, is known to have some stability problems [19].…”