Determination of stimulation threshold in a 3D model of a pacemaker
Résumé
We present a 3D model which computes the threshold of a pacemaker, i.e. the minimal electrical energy required for a pacemaker stimulation to elicit action potentials throughout the heart muscle. This model was developed during the SimCardioTest European project on in-silico techniques for cardiac medicine. More precisely, a pacemaker device behaves like a pulse generator that locally applies a current to the heart for a short duration via leads inserted in the heart cavities. If sufficient, the delivered energy triggers an action potential in the heart. In that case, the device is said to capture. In the pulse amplitude-duration plane, capturing and non-capturing regions are delimited by the energy threshold curve. To preserve the pacemaker battery, it is necessary to stimulate at the minimal energy that captures. Hence, being able to predict the threshold curve contributes to lead design improvement, capture optimization and the increase of device lifetime. We introduce a new 3D computational model that couples through boundary conditions the cardiac bidomain equations, embedded in a bath, to a model based on an electrotechnic equivalent schematic of the pulse generator and pacemaker leads. These conditions model the capacitive and resistive effects of the metal-tissue interface during pacing. Such an interface model is of paramount importance to evaluate the energy actually delivered to the tissue. For each pulse amplitude and duration, capture is considered achieved if the volume of excited tissue increases during the 10 ms after the pulse ends. Afterwards, the threshold curve is built by dichotomy. Model solutions are approximated with a finite element method, on a given mesh of the cardiac domain and leads, with a fixed time step. We use an iterative method to solve the linear system which arises at each time step. We will show results of the software quality assurance, and numerical convergence verification procedures, which were designed following the ASME V&V40 guidelines. We will notably present convergence of the solution and accuracy of the threshold curve with respect to mesh size, time step, and stopping criteria for the iterative solver.
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