Fig 1.
Proposed closed-loop control system, based on a fully-connected state transition model (STM).
The system consists of three components: a real-time control application, a neuromodulator prototype and a sheep used for animal experimentation. An intracardiac electrogram (EGM) is obtained via a cardiac lead implanted into the right ventricle of the sheep, analogically processed by the neuromodulator, and acquired via the analog to digital converter into the real-time control application. R-wave instants are detected and used for calculating a Weighted Moving Average of the RR intervals WMARR(b), which will be used as control variable. An error ϵ is obtained from the difference between the target (RRT) and WMARR(b). The STM-based controller estimates a new set of VNS parameters Si, minimizing ϵ. VNS is triggered synchronously to the R-wave, with the new set of parameters Si, to deliver VNS to the right vagus nerve of the sheep. VNS with these new parameters will modify the acquired EGM and a weighted moving average of the new RR interval is computed, closing the loop.
Fig 2.
Typical vagus nerve stimulation pattern (solid line), synchronized with the cardiac activity (dashed line).
The controller can modulate the following VNS parameters: number of pulses (Pnpulses), the interpulse period (Pipp, ms), delay (Pdel, ms), current amplitude (Pcur, mA), and pulse width (Ppw, ms).
Fig 3.
a) Partially-connected state transition model of N + 1 states. The current state (CS(b) = Si) may transit to a neighbor state (Si-1 or Si+1) or stay at the same state (Si). All states are connected to state S0, which turns off VNS. b) Fully-connected state-transition model of N + 1 states. The current state (CS(b) = Si) may transit to any state (Si-k or Si+k) or stay at the same state (Si). All states are connected with all the states including the state S0, which turns off VNS.
Fig 4.
The STA determines the optimal VNS parameters Si minimizing the value ϵ, which represents the difference between the target RR and WMARR(b). Variable i is bounded between 0 and N. Parameter E defines the acceptable level of error on ϵ.
Fig 5.
Example output of the training phase for a particular sheep and N = 30.
Top panel: ΔRRi as a function of sorted states. Bottom panel: Colormap of the normalized VNS parameters associated with each state, expressed as percentage of their corresponding range values.
Fig 6.
Performance indicators of three STM-based controllers.
P10 is a partially-connected STM-based controller of N = 10 states, evaluated on 6 sheep for 13 different targets. P30 is a partially- connected STM-based controller of N = 30 states, evaluated on 7 sheep for 10 different targets. F30 is a fully-connected STM-based controller of N = 30 states evaluated on the same 7 sheep for the same 10 targets. The three controllers were used on sheep anesthetized by etomidate. Most of the sheep used in the experimental protocol P10 are different from the sheep used in the control tests of the P30 and F30 controllers. The sheep involved in the P30 and F30 protocols were the same. p-values are calculated between the three controllers. In the box plots, the dotted lines represent a Wilcoxon unpaired test and the solid line represents a Wilcoxon paired test. * denotes P < 0.05, and ** denotes P < 0.01.
Table 1.
P10 vs P30.
Fig 7.
The top of the figure shows the WMARR response when P10 (dotted line) and P30 (solid line) controllers are used to regulate RR to 600 ms. The middle shows the dynamics of the P30. The bottom shows the dynamics of the P10 controller.
Fig 8.
The top panel of the figure shows the WMARR response when the P30 (dotted line) and F30 (solid line) controllers are used to regulate RR to 700 ms. The bottom panel shows the dynamics of the P30 (dotted line) and F30 (solid line) controllers.