A continuous representation of heart rate

Analysis of heart rate variability (HRV) often requires a continuous representation of the inherently discrete heart rate measurement. In combination with a suitable cardiac pacemaker model, e.g. the integral pulse frequency modulator (IPFM), the cardiac event series can be considered as an irregular sampling of a continuous input to the pacemaker model, m(t). Continuous representation of heart rate can thus be achieved by a reconstruction of the input function m(t) from the cardiac event series. Two such representations of the heart rate, the instantaneous heart rate (IHR) and the low pass filtered event series (LPFES), have previously been assumed to be consistent with the IPFM model. Simulations show, however, that the LPFES actually is not consistent with the model. The IHR representation, although consistent with the model, suffers from discontinuities which are both unphysiological and inadequate for subsequent signal processing. A solution to the problem has been developed by introducing M(t), the continuous integral of m(t). The samples of M(t) are specified by the cardiac event series and continuous representation of M(t) is achieved by cubic spline interpolation. The input to the cardiac pacemaker model m(t), or in other words, the representation of the heart rate is given by the derivative of M(t).