Closed-loop vagus nerve stimulation for heart rate control evaluated in the Langendorff-perfused rabbit heart

Figure 1. Overview of the stimulation paradigm and the control strategy implementation. (a) Cardiac-synchronized stimulation, as is defined by its five main parameters: current amplitude, C, pulse width, PW, frequency, F, number of pulses per burst, NP, and stimulation onset delay, D, electrocardiogram (ECG), stimulation signal (STIM). (b) Block diagram of the proportional-integral controller as used during in-silico development. Reference heart rate, HRref, measured heart rate, HR(t), integral gain, Ki, proportional gain, Kp, calculated error, e(t), current amplitude, C(t).

Figure 2. Overview of the experimental setup. (a) Isolated heart preparation with needle electrodes inserted into the vagus nerve for stimulation and wire electrodes inserted into the base of the right atrium to measure the electrocardiogram. (b) Zoomed-in image of the needle electrodes inserted into the vagus nerve next to the superior cardiac branch with the cathode caudal and the anode cephalad. (c) Schematic overview of the hardware-in-the-loop implementation of the control strategy. Reference heart rate, HRref, measured heart rate, HR(t), calculated error, e(t), current amplitude, C(t), control voltage for the isolated stimulator Vc(t).

Figure 3. Contour plots of average performance indicators for the whole virtual study population in parameter space (Kp, Ki) for (a) continuous stimulation and (b) cardiac-synchronized stimulation. Initial gain combinations found based on single individual simulation are depicted as point marker and optimized gain combination selected on virtual population are depicted as triangle marker. The acceptable limits for all performance indicators are highlighted by the black contour lines. In the panels where no black contour line is visible, the entire parameters space is part of the optimal domain.

Figure 4. Exemplary heart rate response along with the corresponding stimulation signals for a step reduction of 20 bpm from baseline for (a) Kp = 0.01, Ki = 0.05 and (b) Kp = 0.008, Ki = 0.01 using the continuous control strategy, and for (c) Kp = 0.001, Ki = 0.005 and (d) Kp = 0.0005, Ki = 0.003 using the cardiac-synchronized control strategy recorded in one isolated heart. Overview of the strategy performance on the whole study population as quantified by (e) the cost function, (f) rise time, (g) steady-state error, and (h) percentual overshoot for the initial and optimized controller gains. Differences in the mean performance indicators were tested using a two-tailed Student-t test.