# Impact of Heart Rate Fragmentation on the Assessment of Heart Rate Variability +
## 2 Methods
### Data Analysis  
We analyzed the conventional time- and frequency-domain HRV metrics according to the recommended standard [3] using custom-made software validated with simulated R-R interval data including HRV components of known amplitude and frequency. Briefly, from the ECG data, the time series of NN intervals, \(\{NN_{i}\}=\{tN_{i}-tN_{i-1}\}\), where \(tN_{i}\) represents the time of occurrence of the \(i^{th}\) normal sinus beat were derived. Mean HR was calculated from the average of \(NN_{i}\) over 24 h. For the time domain HRV metrics, SDNN was computed as 24 h standard deviation of \(NN_{i}\), rMSSD as the root of mean square of successive difference of \(NN_{i}\). For the frequency domain metrics, \(\{NN_{i}\}\) time series were interpolated by a horizontal step function, resampled at 2 Hz, filtered with a Hanning window, and converted into frequency domain by Fast Fourie transformations (FFT). The power spectral density was integrated for the power within ultra-low frequency (ULF, <0.0033 Hz), very-low frequency (VLF, 0.0033-0.04 Hz), low frequency (LF, 0.04-0.15 Hz), and high frequency (HF, 0.15-0.40 Hz) bands, respectively. The power of ULF, VLF, LF, and HF was transformed into natural logarithmic values to normalize the distributions.  
We also calculate LF/HF as LF-to-HF power ratio. Additionally, we calculated the power of very-high frequency component (VHF, 0.4-1.0 Hz) to detect high frequency HRF such as the alternation of NN interval every beat.  
As the indicator of HRF, we calculated the percentage of inflection points (PIP) [5] and the distributions of the symbolic dynamical patterns (words) of NN interval sequence [6]. First, from the \(\{NN_{i}\}\), the time series of the differences between consecutive NN intervals, \(\{\Delta NN_{i}\}=\{NN_{i}-NN_{i-1}\}\), were derived. Second, \(\{\Delta NN_{i}\}\) were converted into a ternary symbolic sequence as follows: \"A\" (acceleration) if \(\Delta NN_{i}\leq-8\ ms\), \"N\" (no change) if \(-8\ ms<\Delta NN_{i}<8\ ms\), and \"D\" (deceleration) if \(\Delta NN_{i}\geq 8\ ms\), where \(\pm\) 8 ms was used for threshold taking 125 Hz sampling frequency of the Holter ECG into consideration (1000 ms/125 Hz = 8 ms). Third, the hard inflection point was defined as the point where \(\Delta NN_{i}\) changed from \"A\" to \"D\", or \"D\" to \"A\". The soft inflection point was defined as the point where \(\Delta NN_{i}\) changed from \"N\" to \"A\", \"N\" to \"D\", \"A\" to \"N\", or \"D\" to \"N\". Fourth, the hard PIP (PIPh) and soft PIP (PIPs) were calculated as the percentage of hard and soft inflection points to all points connecting two consecutive NN intervals, respectively.  
The symbolic dynamical patterns were analyzed as the word of length four that was consisted of the ternary symbols of four consecutive \(\Delta\)NN. The words were categorized depending on the type (hard, soft, or mixed) and number (0-3) of inflection points in the sequence of \(\Delta\)NN [6]. For example, sequence \"DDAD\" is categorized as \"Wh2\" because it includes two hard inflection points, \"DNAN\" as \"Ws3\" because it includes three soft inflection points, and \"DDAN\" as \"Wm2 because it includes two mixed (hard and soft) inflection points. Table 1 shows the entire picture of the word classification. The percentage of each category of words for all observed words during 24 h was calculated.