Some considerations on the IPFM model for the heart rate variability analysis

Abstract

The IntroductionIt is commonly admitted that the IPFM model is a possible model for the generation of the R waves time occurrences. The use of the outputs ¢ ¥ £ s for the frequency analysis of the heart rate variability has been studied in detail in several papers. The latest [1], [2] gives some recommendation in using these outputs in order to reduce or cancel the distortion of the spectrum. The problem of the choice for the model input is not usually addressed and is simplified using a single or a sum of cosines but not a real physiological signal, the respiration for instance. Since the Respiratory Sinus Arrhytmia (RSA) is one of the most important component of the heart rate variability it is straightforward that effort should be made in taking the respiration as an input of the model. In the last CinC we have proposed [3] a model for the generation of the R waves:(1)is an external modulation. It will be shown in the following paper that similarly to the IPFM model a time occurrences generator, called PFM model, can be deduced from the expression (1). The condition for the correct use of the heart period signal defined aswill be also given. The aim of this communication is to compare these two models regarding their ability to mimic the RSA when a real or a synthetic respiration signal is used as the input of the model. It has been shown that the repetitive pattern of the RSA can exhibit different shapes [4] depending on the subjects and experimental conditions. These shapes could be compared to arch or inverted arch and will be designated consequently. Since this shape analysis is a step forward compared to classical frequency analysis we will check whether the PFM or the IPFM can exhibit these patterns under some artificial experimental conditions. We will close this communication presenting a real case. This case compares the outputs obtained from the two models, using the recorded respiration volume as the input, to the measured heart period signal from the real ECG signal. Models definitions and propertiesStarting from the R-waves generator defined by (1) and assuming that the maximum of with. The proposed solution of this equation is:This is an approximated solution in the simple case that the modulating function is a single cosine. It can be shown that it is an acceptable solution when the condition:is verified. From (3) the heart period signal can be calculated byand is finally:We can state that if the model proposed in (1) synthesize a real ECG (R-waves), the deduced @ R S

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