Analysis Functions of Respiratory Data

Description

Provides functions for the complete analysis of respiratory data. Consists of a set of functions that allow to preprocessing respiratory data, calculate both regular statistics and nonlinear statistics, conduct group comparison and visualize the results. Especially, Power Spectral Density ('PSD') (A. Eke (2000) <doi:10.1007/s004249900135>), 'MultiScale Entropy(MSE)' ('Madalena Costa(2002)' <doi:10.1103/PhysRevLett.89.068102>) and 'MultiFractal Detrended Fluctuation Analysis(MFDFA)' ('Jan W.Kantelhardt' (2002) <doi:10.1016/S0378-4371(02)01383-3>) were applied for the analysis of respiratory data.

Details

The R package RespirAnalyzer contains functions for analyzing respiratory data.

Author(s)

Xiaohua Douglas Zhang [aut, cph], Teng Zhang [aut], Xinzheng Dong [aut, cre]

Maintainer: Xinzheng Dong <dong.xinzheng@foxmail.com>

References

Zhang T, Dong X, Chen C, Wang D, Zhang XD. RespirAnalyzer: an R package for continuous monitoring of respiratory signals.

Examples

# load Data from TestData dataset
data("TestData")
Seriesplot.fn(Data[1:2000,1],Data[1:2000,2],points=FALSE,
              xlab="Time(s)",ylab="Respiratory")
Fs=50 ## sampling frequency is 50Hz
Peaks <- find.peaks(Data[,2],Fs,lowpass=TRUE,freq=1,MovingAv=FALSE,
                    W=FALSE,filter=TRUE,threshold=0.05)
points(Data[Peaks[2:13,1],1],Data[Peaks[2:13,1],2],col=2)
PP_interval <- diff(Peaks[,1])/Fs
Seriesplot.fn(1:length(PP_interval),PP_interval,points=FALSE,xlab="Count",
          ylab="Inter-breath Interval(s)")
#### Moving Average
W <- FS <- 50
Data[,3] <- MovingAverage(Data[,2],W)
Seriesplot.fn(Data[1:2000,1],Data[1:2000,2],points=FALSE,
              xlab="Time(s)",ylab="Respiratory")
lines(Data[1:2000,1],Data[1:2000,3],col=2)
#### Low pass filter
bf <- signal::butter(2, 2/Fs, type="low")
Data[,4] <- signal::filtfilt(bf,Data[,2])
Seriesplot.fn(Data[1:2000,1],Data[1:2000,2],points=FALSE,
              xlab="Time(s)",ylab="Respiratory")
lines(Data[1:2000,1],Data[1:2000,4],col=2)
#### entropy of  rawdata
scale_raw <- seq(1,90,2)
MSE <-  MSE(Data$V2[seq(1,100000,2)], tau=scale_raw, m=2, r=0.15, I=40000)
Seriesplot.fn(MSE$tau ,MSE$SampEn,points=TRUE,
              xlab="Scale",ylab="Sample entropy")
#### entropy of IBI
scale_PP <- 1:10
MSE <-  MSE(PP_interval, tau=scale_PP, m=2, r=0.15, I=40000)
Seriesplot.fn(MSE$tau ,MSE$SampEn,points=TRUE,
              xlab="Scale",ylab="Sample entropy")

#### PSD analysis
LowPSD(PP_interval, plot=TRUE,min=1/64, max=1/2)
#### MFDFA
exponents=seq(3, 9, by=1/4)
scale=2^exponents
q=-10:10
m=2
Result <- MFDFA(PP_interval, scale, m, q)
MFDFAplot.fn(Result,scale,q,model = TRUE)
#### fit.model
Coeff <- fit.model(Result$Hq,q)
Coeff
Para<- -log(Coeff)/log(2);Para[3]=Para[1]-Para[2]
names(Para)<-c("Hmax","Hmin","i÷H")
Para

#### Individualplot
data("HqData")
PP_Hq <- HqData
filenames <- row.names(PP_Hq)
q=-10:10
ClassNames <- c(substr(filenames[1:19], start = 1, stop = 3),
                substr(filenames[20:38], start = 1, stop = 5))
Class <- unique(ClassNames)
col_vec <- rep(NA, nrow(PP_Hq) )
pch_vec <- rep(16, nrow(PP_Hq) )
for( i in 1:length(Class) ) { col_vec[ ClassNames == Class[i] ] <- i }
Individualplot.fn(q,PP_Hq,Name=Class,col=col_vec,pch=pch_vec, xlab="q",ylab="Hurst exponent")
legend("topright", legend=paste0(Class, "(N=", table( ClassNames ), ")"),
      col=1:4, cex=1, lty=1, pch=16)

#### Groupplot
data("HqData")
PP_Hq <- HqData
filenames <- row.names(PP_Hq)
q <- -10:10
ClassNames <- c(substr(filenames[1:19], start = 1, stop = 3),
                substr(filenames[20:38], start = 1, stop = 5))
Class <- unique(ClassNames)
for (i in 1:length(q)){
  Data <- GroupComparison.fn(PP_Hq[,i],ClassNames)
  Result_mean_vec <- Data[,"Mean"]
  Result_sd_vec <- Data[,"SE"]
  if( i == 1 ) {
    Result_mean_mat <- Result_mean_vec
    Result_sd_mat <- Result_sd_vec
  } else {
    Result_mean_mat <- rbind(Result_mean_mat, Result_mean_vec)
    Result_sd_mat <- rbind(Result_sd_mat, Result_sd_vec)
 }
}
Groupplot.fn (q[1:10],Result_mean_mat[1:10,],Class,errorbar = Result_sd_mat[1:10,],
              xRange = NA, yRange = NA, col = NA, pch = rep(16,4), Position = "topright",
              cex.legend = 1, xlab="q",ylab="Hurst exponent",main = "")
Groupplot.fn (q[11:21],Result_mean_mat[11:21,],Class,errorbar = Result_sd_mat[11:21,],
              xRange = NA, yRange = NA, col = NA, pch = rep(16,4), Position = "topright",
              cex.legend = 1, xlab="q",ylab="Hurst exponent",main = "")

An example of respiratory data

Description

The respiratory data of a healthy people.

Details

This is an data to be included in my package

Source

Fantasia Database, PhysioNet

References

"https://doi.org/10.13026/C2RG61"

Function to calculate the statistics for each Group

Description

function to calculate the statistics for each Group: Number of Samples, mean, standard deviation (SD), standard error (SE), median, confident interval, p-value of ANOVA

Usage

GroupComparison.fn(Data, GroupName, na.rm = TRUE, conf.level = 0.95)

Arguments

Value

a dataframe for the statistics for each Group. Number of Samples, mean

standard deviation (SD), median, upper and lower bounds of CI, p-value of ANOVA

References

Zhang T, Dong X, Chen C, Wang D, Zhang XD. RespirAnalyzer: an R package for continuous monitoring of respiratory signals.

Examples

data("HqData")
PP_Hq <- HqData
filenames <- row.names(PP_Hq)
q <- -10:10
ClassNames <- c(substr(filenames[1:19], start = 1, stop = 3),
                substr(filenames[20:38], start = 1, stop = 5))
Class <- unique(ClassNames)
Data <- GroupComparison.fn(PP_Hq[,1],ClassNames)
Data

Function to plot the mean and error bar by group

Description

function to plot the mean and error bar of sample entropy or the MFDFA results by group

Usage

Groupplot.fn(
  x,
  Average,
  GroupName,
  errorbar = NA,
  xRange = NA,
  yRange = NA,
  col = NA,
  pch = NA,
  Position = "topright",
  cex.legend = 0.75,
  xlab = "",
  ylab = "",
  main = ""
)

Arguments

Value

No value returned

References

Zhang T, Dong X, Chen C, Wang D, Zhang XD. RespirAnalyzer: an R package for continuous monitoring of respiratory signals.

Examples

data("HqData")
PP_Hq <- HqData
filenames <- row.names(PP_Hq)
q <- -10:10
ClassNames <- c(substr(filenames[1:19], start = 1, stop = 3),
                substr(filenames[20:38], start = 1, stop = 5))
Class <- unique(ClassNames)
for (i in 1:length(q)){
  Data <- GroupComparison.fn(PP_Hq[,i],ClassNames)
  Result_mean_vec <- Data[,"Mean"]
  Result_sd_vec <- Data[,"SE"]
  if( i == 1 ) {
    Result_mean_mat <- Result_mean_vec
    Result_sd_mat <- Result_sd_vec
  } else {
    Result_mean_mat <- rbind(Result_mean_mat, Result_mean_vec)
    Result_sd_mat <- rbind(Result_sd_mat, Result_sd_vec)
 }
}
Groupplot.fn (q[1:10],Result_mean_mat[1:10,],Class,errorbar = Result_sd_mat[1:10,],
              xRange = NA, yRange = NA, col = NA, pch = rep(16,4), Position = "topright",
              cex.legend = 1, xlab="q",ylab="Hurst exponent",main = "")
Groupplot.fn (q[11:21],Result_mean_mat[11:21,],Class,errorbar = Result_sd_mat[11:21,],
              xRange = NA, yRange = NA, col = NA, pch = rep(16,4), Position = "topright",
              cex.legend = 1, xlab="q",ylab="Hurst exponent",main = "")

The Hurst exponent of respiratory data

Description

The Hurst exponent extracted from the MFDFA result of respiratory data.

Details

This is an data to be included in my package

Source

Fantasia Database, PhysioNet

References

"https://doi.org/10.13026/C2RG61"

Function to plot multiscale entropy or MFDFA results by individual.

Description

function to plot multiscale entropy or MFDFA results by individual.

Usage

Individualplot.fn(
  x,
  y,
  Name = NA,
  xRange = NA,
  yRange = NA,
  col = NA,
  pch = NA,
  Position = "topright",
  cex.legend = 0.75,
  xlab = "",
  ylab = "",
  main = ""
)

Arguments

Value

No value returned

References

Zhang T, Dong X, Chen C, Wang D, Zhang XD. RespirAnalyzer: an R package for continuous monitoring of respiratory signals.

Examples

data("HqData")
PP_Hq <- HqData
filenames <- row.names(PP_Hq)
q=-10:10
ClassNames <- c(substr(filenames[1:19], start = 1, stop = 3),
                substr(filenames[20:38], start = 1, stop = 5))
Class <- unique(ClassNames)
col_vec <- rep(NA, nrow(PP_Hq) )
pch_vec <- rep(16, nrow(PP_Hq) )
for( i in 1:length(Class) ) { col_vec[ ClassNames == Class[i] ] <- i }
Individualplot.fn(q,PP_Hq,Name=Class,col=col_vec,pch=pch_vec, xlab="q",ylab="Hurst exponent")
legend("topright", legend=paste0(Class, "(N=", table( ClassNames ), ")"),
      col=1:4, cex=1, lty=1, pch=16)

Function to calculate the power spectral density (PSD)

Description

function to calculate the power spectral density (PSD) of a time series. Methods derived from A. Eke (2000) "Physiological time series: distinguishing fractal noises from motions" <doi:10.1007/s004249900135>.

Usage

LowPSD(series, plot = TRUE, min = 1/8, max = 1/2)

Arguments

Value

a value of spectral exponent(beta) which the the slope of the of the fitting line on plot of log power vs. log frequency

References

Zhang T, Dong X, Chen C, Wang D, Zhang XD. RespirAnalyzer: an R package for continuous monitoring of respiratory signals.

Examples

data("TestData")
Fs <- 50
Peaks <- find.peaks(Data[,2],Fs,lowpass=TRUE,freq=1,MovingAv=FALSE,
                    W=FALSE,filter=TRUE,threshold=0.05)
PP_interval=diff(Peaks[,1])/Fs
LowPSD(series=PP_interval,plot=TRUE,min=1/64, max=1/2)

MultiFractal Detrended Fluctuation Analysis

Description

Applies the MultiFractal Detrended Fluctuation Analysis (MFDFA) to time series.

Usage

MFDFA(tsx, scale, m, q)

Arguments

Value

A list of the following elements:

• Hq q-order Hurst exponent.

• tau_q Mass exponent.

• hq Holder exponent.

• Dq singularity dimension.

• Fqi q-order fluctuation function.

• line linear fitting line of fluctuation function.

References

Zhang T, Dong X, Chen C, Wang D, Zhang XD. RespirAnalyzer: an R package for continuous monitoring of respiratory signals.

Examples

data("TestData") # load Data from TestData dataset
Fs <- 50
Peaks <- find.peaks(Data[,2],Fs,lowpass=TRUE,freq=1,MovingAv=FALSE,
                    W=FALSE,filter=TRUE,threshold=0.05)
head(Peaks)
PP_interval <- diff(Peaks$PeakIndex)/Fs
## Computing Multifractal
exponents=seq(3, 9, by=1/4)
scale=2^exponents
q=-10:10
m=2
Result <- MFDFA(PP_interval, scale, m, q)
Coeff <- fit.model(Result$Hq,q)
print(Coeff)
Para<- -log(Coeff)/log(2)
Para[3]=Para[1]-Para[2]
names(Para)<-c("Hmax","Hmin","DeltaH")
Para

PP_Hq <- Result$Hq
PP_hq <- Result$hq
PP_Dq <- Result$Dq
PP_Para <-Para

Function to plot the results of MFDFA analysis

Description

function to plot the results of MFDFA analysis: q-orde fluctuation function, Hurst exponent,mass exponent and multifractal spectrum. The fitting result of binomial multifratcal model can be also shown by the fitting line

Usage

MFDFAplot.fn(
  Result,
  scale,
  q,
  cex.lab = 1.6,
  cex.axis = 1.6,
  col.points = 1,
  col.line = 1,
  lty = 1,
  pch = 16,
  lwd = 2,
  model = TRUE,
  cex.legend = 1
)

Arguments

Value

No value returned

References

Zhang T, Dong X, Chen C, Wang D, Zhang XD. RespirAnalyzer: an R package for continuous monitoring of respiratory signals.

Examples

data("TestData")
Fs=50 ## sampling frequency is 50Hz
Peaks <- find.peaks(Data[,2],Fs,lowpass=TRUE,freq=1,MovingAv=FALSE,
                    W=FALSE,filter=TRUE,threshold=0.05)
PP_interval=diff(Peaks[,1])/Fs
exponents=seq(3, 9, by=1/4)
scale=2^exponents
q=-10:10
m=2
Result <- MFDFA(PP_interval, scale, m, q)
MFDFAplot.fn(Result,scale,q)

Function to compute the multiscale entropy(MSE)

Description

function to perform a multiscale entropy (MSE) analysis of a regularly spaced time series. Return the results as an R data frame. Methods derived from Madalena Costa(2002) "Multiscale entropy analysis of complex physiologic time series" <doi:10.1103/PhysRevLett.89.068102>.

Usage

MSE(x, tau, m, r, I)

Arguments

Value

A data frame with with one row for each combination of 'tau', 'm' and 'rSD'. Columns are "tau", "m", "rSD", and "SampEn" (the calculated sample entropy). The data frame will also have an attribute "SD", the standard deviation of 'x'. rSD = r*sd(y)

References

Zhang T, Dong X, Chen C, Wang D, Zhang XD. RespirAnalyzer: an R package for continuous monitoring of respiratory signals.

Examples

data("TestData") # load Data from TestData dataset
oldoptions <- options(scipen=999)
Fs <- 50 # sampling frequency
scale_raw <- seq(1,90,by=2)
MSER <-  MSE(Data[1:10000,2], tau=scale_raw, m=2,
            r=0.15, I=40000)
print(MSER)
options(oldoptions)

Function to calculate Moving Average of a series

Description

function to calculate Moving Average of a series

Usage

MovingAverage(y, W)

Arguments

Value

A new numeric vector after calculate the moving average.

References

Zhang T, Dong X, Chen C, Wang D, Zhang XD. RespirAnalyzer: an R package for continuous monitoring of respiratory signals.

Examples

data("TestData")
W <- 50
y <- MovingAverage(Data[,2],W)

Function to plot series data

Description

function to plot series data. including Respiration data and Peak-to-Peak intervals series.

Usage

Seriesplot.fn(
  x,
  y,
  xRange = NA,
  yRange = NA,
  points = TRUE,
  pch = 1,
  col.point = 1,
  cex.point = 1,
  line = TRUE,
  lty = 1,
  col.line = 1,
  lwd = 1,
  xlab = "x",
  ylab = "y",
  main = ""
)

Arguments

Value

No value return

References

Zhang T, Dong X, Chen C, Wang D, Zhang XD. RespirAnalyzer: an R package for continuous monitoring of respiratory signals.

Examples

data("TestData")
oldpar <- par(mfrow=c(1,2))
Seriesplot.fn(Data[1:10000,1],Data[1:10000,2],points=FALSE,xlab="Time(s)",ylab="Respiration")
Fs=50 ## sampling frequency is 50Hz
Peaks <- find.peaks(Data[,2],Fs,lowpass=TRUE,freq=1,MovingAv=FALSE,
                    W=FALSE,filter=TRUE,threshold=0.05)
PP_interval=diff(Peaks[,1])/Fs
Seriesplot.fn(1:length(PP_interval),PP_interval,points=FALSE,xlab="Count",ylab="Interval(s)")
par(oldpar)

Function to find the peak-to-peak intervals of a respiratory signal.

Description

function to find the peak-to-peak intervals of a respiratory signal.

Usage

find.peaks(
  y,
  Fs,
  lowpass = TRUE,
  freq = 1,
  MovingAv = FALSE,
  W = FALSE,
  filter = TRUE,
  threshold = 0.2
)

Arguments

Value

a dataframe for the information of peaks. "PeakIndex" is the position of the peaks and "PeakHeight" is the height of the peaks

References

Zhang T, Dong X, Chen C, Wang D, Zhang XD. RespirAnalyzer: an R package for continuous monitoring of respiratory signals.

Examples

data("TestData") # load Data from TestData dataset
Fs=50 ## sampling frequency is 50Hz
Peaks <- find.peaks(Data[,2],Fs,lowpass=TRUE,freq=1,MovingAv=FALSE,
                    W=FALSE,filter=TRUE,threshold=0.05)
Peaks

Function to fit the MFDFA result with the extended binomial multifractal model.

Description

function to fit the result of Multifractal detrended fluctuation analysis (MFDFA) with the extended binomial multifractal model. Return the results as a vector which contain the parameters of the model and the goodness of fit

Usage

fit.model(Hq, q)

Arguments

Value

a vector for fitting parameters."a" and "b" is the coefficients of the extended binomial multifractal model. "Goodness" is the goodness of fit

References

Zhang T, Dong X, Chen C, Wang D, Zhang XD. RespirAnalyzer: an R package for continuous monitoring of respiratory signals.

Examples

data("TestData") # load Data from TestData dataset
Fs=50 ## sampling frequency is 50Hz
Peaks=find.peaks(Data[,2],Fs)
PP_interval=diff(Peaks[,1])/Fs
exponents=seq(3, 8, by=1/4)
scale=2^exponents
q=-10:10
m=2
Result <- MFDFA(PP_interval, scale, m, q)
Coeff <- fit.model(Result$Hq,q)
Coeff