Doppler shift during overdrive pacing of spiral waves. Prediction of the annihilation site

• Induced drift of spiral waves can be perceived by detectors using the Doppler effect. • The classical Doppler formula helps estimate the speed of induced drift in 2D media. • A drifting spiral wave’s core follows a path approximately in the area of lowered period. • The area of low period is manifest early, usually after 2 or 3 spiral wave rotations. • The Doppler effect for excitation waves can be used in anti-tachycardia treatment. Spiral waves of electrical excitation can occur in the heart in cases of dangerous arrhythmias. Low-voltage cardioversion is a treatment method that aims to induce drift and annihilation of the spiral waves. Drift of wave sources causes Doppler shift but it has not been studied for the waves that are interacting with plane wave trains in excitable media. In our numerical research, we made 2D and 3D solitary spiral waves drift by external pacing and studied the Doppler shift using detectors at the tissue boundary. We examined spiral waves with a circular core and meandering waves and tried various external stimulation periods. We observed that the period of the source in the direction of the drift decreased, which could be described quite precisely in 2D by the classical Doppler shift formula. Moreover, the boundary annihilation site of the spiral can be accurately predicted as the location where the minimal period at the boundary is measured.