A percentile-based coarse graining approach is helpful in symbolizing heart rate variability during graded head-up tilt

Coarse graining of physiological time series such as the cardiac interbeat interval series by means of a symbolic transformation retains information about dynamical properties of the underlying system and complements standard measures of heart rate variability. The transformations of the original time series to the coarse grained symbolic series usually lead to a non-uniform occurrence of the different symbols, i.e. some symbols appear more often than others influencing the results of the subsequent symbolic series analysis. Here, we defined a transformation procedure to assure that each symbol appears with equal probability using a short alphabet {0,1,2,3} and a long alphabet {0,1,2,3,4,5}. The procedure was applied to the cardiac interbeat interval series RRi of 17 healthy subjects obtained during graded head-up tilt testing. The symbolic dynamics is analyzed by means of the occurrence of short sequences (`words') of length 3. The occurrence of words is grouped according to words without variations of the symbols (0V%), one variation (1V%), two like variations (2LV%) and two unlike variations (2UV%). Linear regression analysis with respect to tilt angle showed that for the short alphabet 0V% increased with increasing tilt angle whereas 1V%, 2LV% and 2UV% decreased. For the long alphabet 0V%, and 1V% increased with increasing tilt angle whereas 2LV% and 2UV% decreased. These results were slightly better compared to the results from non-uniform symbolic transformations reflecting the deviation from the mean. In conclusion, the symbolic transformation assuring the appearance of symbols with equal probability is capable of reflecting changes of the cardiac autonomic nervous system during graded head-up tilt. Furthermore, the transformation is independent of the time series' distribution.