Analysis of the QT-RR variability interactions using the NARMAX model

In this paper a new approach is used in order to evaluate and quantify the interactions between the QT and RR intervals. This is achieved after the identification of the RR and QT series with a hybrid model (the non-linear autoregressive moving average with exogenous input (NARMAX)). This identification follows two steps: the first is a linear parametric identification corresponding to the MA model, whereas the second is a non-linear identification using the NARX model. The power spectral density PSD of RR and QT is computed by using the monovariate part of this model (MA model). The QT-related RR series is obtained by using the bivariate part corresponding to the NARX model and its PSD is determined by using the autoregressive method. Then a cross-spectral and the coherence function were determined in order to confirm the obtained results. Different heart pathology cases were selected to evaluate the approach: the normal case, the cases which represent long QT intervals and some other cases which represent short QT intervals. They were taken from the MIT BIH database. The results show that every case illustrates two frequencies; the first in the low frequency band LF and the second in the high frequency band HF. In the normal case and long QT interval cases, the LF was predominating in the QT, RR and in QT-related RR power spectral density PSD. In the short QT interval cases the HF was much larger in all cases. The obtained results were compared to the poincaré plot method which confirms it; however, the NARMAX model can distinguish between normal and pathologic cases with a great precision (p < 0.001). In addition, the QT variability index QTVI is computed and represented by a box plot which expresses the relationship between QT and RR intervals. The QTVI shows a large variability in the short QT interval cases, whereas it shows a small and a negative variability in the long QT interval case.