# Portable Sensor System for Registration, Processing and Mathematical Analysis of PPG Signals
## 2 Portable Sensor System for Registration, Processing and Analysis of PPG Signals
### Preprocessing and Mathematical Methods for PRV Analysis
#### 2.3.3 Module for Mathematical Analysis of PRV  
The mathematical analysis of PRV is performed by applying linear and nonlinear methods. The linear methods for analysis are Time-Domain and Frequency-Domain. In this article are used the following nonlinear methods for analysis: Poincare plots, Rescaled Range Plot (R/S), DFA (Detrended Fluctuation Analysis), MFDFA (MultiFractal Detrended Fluctuation Analysis), Approximate Entropy, and Sample Entropy. Time-Domain analysis is very commonly used in cardiology due to the boundaries of norm-pathology being known according to the standard introduced [50]. The following parameters are determined in the Time-Domain: the mean of normal-to-normal intervals (MeanNN), the mean of heart rate (MeanHR); the standard deviation of normal-to-normal intervals (SDNN), standard deviation of the averages normal-to-normal time intervals (SDANN), the ratio of pairs of successive normal-to-normal intervals differing more than 50 ms (pNN50), the square root of the mean of the sum of the squares of successive differences between normal-to-normal intervals (RMSSD), and the mean of the standard deviations of all normal-to-normal intervals (SDIndex). Table 1 presents the formulas for the most commonly used parameters in the time domain. In the Frequency-Domain, studies are conducted in three main ranges (Table 2): Very Low Frequency domain; Low Frequency domain; and, High Frequency domain. The Very Low Frequency \begin{table}
\begin{tabular}{c c} \hline \hline
**Parameter** & **Formula** \\ \hline SDNN[ms] & \\ SDANN[ms] & \\ SDIndex[ms] & \\ RMSSD[ms] & \\ pNN50[\%] & \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Commonly used Time-Domain parameters [50]. domain refers to the mechanisms of the nervous system that are responsible for the long-term regulation of the human body; Low Frequency domain is related to the sympathetic nervous system, while also taking the influence of the parasympathetic nervous system into account; High Frequency domain corresponds to parasympathetic influences and it takes the influence of respiratory processes into account. Sympathetic cardiac control of the nervous system operates at frequencies lower than 0.15 Hz (0.01-0.15 Hz, Low Frequency) domain, accelerates cardiac activity, narrows blood vessels, raises blood pressure, widens the airways in the lungs, widens the pupil of the the eye, reduces the activity of the digestive system, raises the temperature, and mobilizes the whole body. Parasympathetic modulation, including humoral factors, gender and age, is also affected here. The parasympathetic heart control of the nervous system operates at frequencies up to 0.4 Hz (from 0.15 to 0.4 it is High Frequency domain) and it modulates the activity of the human body by slowing the heart activity, thus lowering blood pressure (generally its activity is the opposite of the sympathetic one). A non-parametric Welch periodogram method [51], which is suitable for cardiac biomedical data, was used for determining the spectral components. In this method, the obtained individual periodograms for overlapping individual data blocks are averaged to produce the final periodogram. The power spectral density (PSD) of the PRV data series is determined while using the Welch Periodogram method. The Frequency-Domain analysis is also standardized, with the limits of norm-pathology being known, thus making it a preferred method. The introduction in recent years of the non-linear methods of PRV analysis has allowed for an additional assessment of the qualitative and quantitative characteristics of PRV and it has expanded the scope for clinical interpretation. These methods are not standardized, but they are in the process of active research and they provide additional information on the \"chaotic\" dynamics of PP interval series. When compared to linear analysis methods, nonlinear methods allow for new, additional estimates to be obtained that give an idea of the nonlinear, dynamic processes in the studied signals.