A Biologically Motivated Phase-Offset to the Piecewise-Linear Model of Instantaneous Heart-Rate Interpolation

This paper formalizes the general theory of instantaneous heart-rate (IHR) interpolation from electrocardiogram RR-intervals. This paper also introduces a novel extension to the current basic piecewise-linear interpolation method which allows the discontinuity of the IHR interpolation to be offset from the R-wave. Thus an entire heart cycle can be modelled with a constant IHR. This phase-offset piecewise-linear IHR interpolation model is derived from the general theory of IHR interpolation and results are demonstrated on some true recorded RR-sequences. Recursive and batch matrix forms are derived. Stable solutions can be found for any offset not equal to n radians, though the IHR calculated with a nonzero offset has a significant change to the HRV statistics. Applications of this method to the synthesis of ECG with natural heart-rate variability are also discussed