Section 2.1 describes the operation of SDCP, which is the basis of the proposed RR-SDCP presented in Sect. 2.2. The subsequent Sects. 2.3–2.5 describe the simulation setup, the input data preparation and the data analysis that was employed for the performance evaluation of RR-SDCP, respectively.

2.1 Synchronous duty-cycling communication protocol: SDCP

Figure 1 illustrates the communication protocol implemented in this work, which is based on the concept of synchronous transceiver duty-cycling outlined in [9]. The main principle is to restrict communication to short periodic windows, allowing the LLPMs to save power by turning off their transceivers in the intervening sleep periods. The window interval during the alert period of the LLPMs is equal to the sensed AV-delay \(t_\). More frequent communication is not required from a physiological point of view. During the refractory period following ventricular activation, the window interval is temporarily increased to an integer multiple of \(t_\). Inter-device communication is organized based on a request-response protocol, with the ALLPM and the ventricular LLPM (VLLPM) as the primary and subordinate devices, respectively. A communication cycle is thus always initiated by a request of the ALLPM and is followed by the response of the VLLPM. In detail, the ALLPM sends a pacing trigger and the corresponding pacing delay \(t_\) to the VLLPM in the next communication window after a sensed or paced P-wave. The VLLPM immediately responds in one of two ways, depending on whether it detected a late-cycle premature ventricular contraction (PVC) in the previous sleep period. In the more typical case without late-cycle PVC, the pacing command is simply acknowledged and executed. In the second case, the VLLPM responds by rejecting the pacing command to prevent pacing onto the T-wave. In addition, the VLLPM adds the elapsed time that has passed since the detection of the PVC to the response message. This enables the ALLPM to retrospectively reset its lower-rate counter such that the next pacing pulse would be delivered after a preset time delay relative to the PVC, which is the typical PVC response of conventional dual-chamber PMs [10]. In this work, a PVC is considered as late-cycle if the next sensed or paced P-wave occurs within a timeframe shorter than the post-ventricular atrial refractory period (PVARP), which is a fundamental setting of dual-chamber PMs [10].

2.2 Rate-responsive window scheduling: RR-SDCPFig. 2

a Block diagram implementation and b timing diagram of rate-responsive window scheduling algorithm (RR-SDCP)

The goal of the RR-SDCP algorithm is to provide a fixed number of available communication windows \(n_\) per cardiac cycle. This requires that the sleep interval after an active window is dynamically adjusted based on the momentary heart rate.

Figure 2a shows the block diagram of the proposed window scheduling algorithm. A timer generates periodic pulses at the minimum required window interval given by \(t_\), which are processed by the subsequent window selection logic (WSL). The WSL decides for each timer pulse whether the rest of the communication system is activated, i.e. if there is an available communication window.

As illustrated in Fig. 2b, the WSL follows a cyclic operation, where cycle boundaries are marked by active communication windows. In each cycle, the first \(n_\) timer pulses do not result in available communication windows, referred to as skipped windows. After that, communication windows are made available at an interval of \(t_\) until inter-device communication occurs and the cycle is complete. During each cycle, the state variable \(n_\) is updated based on the difference \(\Delta n_[k]=n_[k]-n_\), where \(n_[k]\) represents the number of available windows in cycle k and \(n_\) denotes the target value. The update algorithm tries to regulate \(\Delta n_[k]\) to zero, by adjusting \(n_\) in the next cycle accordingly, i.e. \( n_[k+1]=n_[k]+\Delta n_[k]\). The update is thereby given by

$$\begin \Delta n_[k] = -1 & \Delta n_[k]<0, \\ 0 & \Delta n_[k]=0, \\ s_[k] & \Delta n_[k]>0, \\ \end\right. } \end$$

(1)

where the positive increment \(s_[k]\) is calculated by averaging the last \(n_\) cycles according to,

$$\begin \begin s_[k]&=\left\lfloor \frac}\sum \limits _^-1} sign(\Delta n_[k-i]) \right\rfloor \\&= +1 & \Delta n_>0 \text n_ \text ,\\ 0 & \text \end\right. } \end \end$$

(2)

While negative deviations of \(n_\) from the setpoint immediately decrement \(n_\) in the next cycle, positive deviations need to consistently persist over \(n_\) cycles, before \(n_\) is incremented. This asymmetry (assuming \(n_>1\)) reflects the heart rate profile during intense physical activity, where heart rate quickly increases at the onset of exercise but decelerates more slowly after activity ends [10].

To ensure overlapping communication windows, \(n_[k]\) must be synchronized between the two LLPMs. The ALLPM calculates the update \(\Delta n_\) immediately after detecting a P-Wave and appends it to each pacing request message. This approach only increases the message size by a maximum of two bits, while allowing the VLLPM to infer \(n_[k]\) by accumulating updates.

2.3 Simulation model

The performance of the RR-SDCP algorithm was analyzed by system-level simulations in Simulink (MathWorks, USA), based on functional models of the relevant LLPM components. The pacing units were modeled by implementing the dual-chamber timing cycles listed in Table 1 [10]. Each model featured a sense input for detecting the intrinsic electric activity of the respective cardiac chamber and a pacing output for stimulation. Inputs and outputs were were represented as 1-bit digital signals. The ALLPM model featured an additional mode_switch input. When set to logic high, the system effectively operates as a single-chamber ventricular pacemaker, i.e. the ALLPM will both, withhold pacing and not trigger ventricular pacing in response to a sensed atrial event.

The two LLPMs synchronize their activity by exchanging communication messages according to RR-SDCP outlined in Sects. 2.1 and 2.2. Each message consists of two header bits, specifying the type of the request or response message and a variable-sized payload. Table 2 lists the message types and their payload size \(n_\). The last column depicts the total number of bits \(n_\) required for actual physical data transmission. Thereby, \(n_\) was calculated by adding \(n_\) to an estimated number of eight overhead bits, including the message header and additional bits for packet synchronization, preamble and parity information.

For comparison to existing LLPMs, functional models of the AVEIR™ DR and the Micra™ AV were implemented based on their device manuals [7, 11]. The main difference of the AVEIR™ DR, which is also a dual-chamber system, is that inter-device communication is possible at any time. Consequently, a sensed P-Wave or PVC is instantaneously communicated by the ALLPM or VLLPM, respectively, to start the corresponding timing cycle in the other device. The Micra™ AV, a single-chamber ventricular LLPM, achieves AV-synchrony through remote mechanical sensing of the atrial contraction, which occurs with a delay compared to electrical sensing of the P-Wave in the atrium. [12, 13]. To account for this delay, the atrial sense input was delayed by 100 ms before being applied to the model [14].

The pacemaker settings for each model were set to the default values of the corresponding commercial device as listed in Table 1. The parameters for the RR-SDCP model were set to the same values as for the AVEIR™ DR.

Table 1 Implemented timing cycles and parameter values used in simulationsTable 2 Message types exchanged between the two LLPMs and the number of bits \(n_\) and \(n_\) required to represent the payload and the complete message, respectively2.4 Data preparation

The sensing input for the simulation model, i.e. intrinsic electrical activity of the heart, was derived from human ECG recordings of the MIT-BIH arrhythmia database, freely available through PhysioNet [15, 16]. Each record in [15] provides QRS-complex annotations obtained from MLII and V1 (or V2/V5 for certain records) ECG leads. The selected subset included all 12 recordings with available P-wave annotations through [17]. Each beat annotation timeseries was transformed into a digital signal by generating a unit-duration pulse at the specified time for each annotated beat. To represent a typical pacemaker scenario, a complete AV-block was artificially induced, by removing all normal QRS-complexes from the ventricular channel. Beats labeled as PVCs were retained, as these may commonly occur in pacemaker patients. The mode_switch input of the ALLPM was derived from the rhythm annotations. Specifically, mode_switch was set to 1 during episodes of supraventricular tachycardias (SVTA) and to 0 during all other rhythms. Table 3 summarizes the characteristics of the input data.

Table 3 Signal statistics of ECG records from MIT-BIH arrhythmia database that were used as simulation inputs2.5 Data analysis

Data analysis was performed in Matlab R2022b (MathWorks, USA) based on the recorded simulation outputs (i.e. not derived from implanted devices), which included the two pacing outputs and the communication signals (active window, message type and payload).

2.5.1 AV-synchrony and communication resources

AV-synchrony was evaluated for each ventricular beat in the VLLPM alert period. A beat was considered as AV-synchronous if preceded by a P-wave within a time interval of 80–200 ms. The lower limit was motivated as there needs to be a minimum delay between atrial and ventricular activation for the atrial kick to effectively contribute to the cardiac output [10]. The upper limit matches the paced AV-delay, which is the longest expected AV-interval for proper dual-chamber operation with the settings in Table 1. The AV-synchrony ratio was then calculated as

$$\begin R_=\frac}}, \end$$

(3)

where \(n_\) and \(n_\) represent the number of total and AV-synchronous QRS-complexes, respectively.

Communication resources were evaluated by recording the average frequency of communication windows \(f_\) and the average number of bits transmitted per second \(r_\), given by

$$\begin r_=\frac}\sum _^} n_, \end$$

(4)

where \(n_\) is the number of bits contained in message i (cf. Table 2), \(n_\) the total number of transmitted messages and \(t_\) the total duration of the simulation run.

2.5.2 Transceiver current estimation

The transceiver current is the sum of the average currents of the receiver and the transmitter. The receiver current was estimated by combining the simulation results of the communication resources with the electrical performance of the receiver prototype shown in Table 4. This receiver design was specially developed for SDCP-based LLPM synchronization and implemented as an application-specific-integrated-circuit in earlier work by the authors [9]. The average receiver current was calculated as

$$\begin I_=I_d_=I_\frac}\sum _t_, \end$$

(5)

where \(I_\) represents the current consumption in active mode, \(d_\) the average duty-cycle and \(t_\) the duration of the i-th window. The window duration \(t_\) depends on whether a message was received in the given window and is calculated as follows: each window has a minimum duration of \(t_\) to guarantee a sufficiently long listening time for message detection. This idle window duration is imposed by the hardware implementation (cf. [9] for details) and was set to \(t_=400\) \(\mu \)s and \(t_=270\) \(\mu \)s for the VLLPM and ALLPM, respectively. In case of an incoming message, the minimum window length is increased by the message duration \(t_\), i.e. \(t_=t_+t_\), with \(t_=n_/f_\), where \(n_\) is the number of received bits and \(f_\) the communication data rate.

Transmitter consumption is mainly influenced by the current level sent through the communication channel. It must be high enough to ensure the receiver detects the input signal above its sensitivity threshold. Thus, the average transmitter output current was approximated by,

$$\begin I_=\frac}R_}\frac}, \end$$

(6)

where \(V_\) is the receiver sensitivity (cf. Table 4), \(G_\) the channel attenuation and \(R_\) the transmitter inter-electrode impedance. Parameter values of \(G_=-66\) dB and \(R_=400~\Omega \) representing typical intracardiac characteristics were used [6, 8, 18, 19].

Table 4 Measured electrical characteristics of the receiver in [9] that were used for transceiver current estimation