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#' Interpolates the given TAC to perform the correlation.
#'
#' This interpolation process (actually, an extrapolation) is needed to convert
#' the given TAC into a signal with frames of equal length. This length is the
#' minimum frame length for the given study.
#'
#' @param tac The TAC to be interpolated.
#' @param time.start Initial acquisition time for each frame.
#' @param time.end Final acquisition time for each frame.
#' @param interpolation.type Interpolation type. 1 for linear, 2 for "natural"
#' splines. Defaults to 1.
#'
#' @return A list containing \code{tsample}, the sampling time vector and the
#' \code{y}, the interpolated TAC.
interpolate.tac <- function(tac, time.start, time.end,
interpolation.type = 1) {
# Initial condition is 0 for both the TAC and the time.end values
tac0 <- c(0, tac)
time.end0 <- c(0, time.end)
# Compute frame length for next step
frame.length <- time.end - time.start
# The time.vector variable divides all the frames into the minimum
# time length unit, which is a second (1/60 minutes).
time.vector <- seq(0, max(time.end), 1/60)
# Interpolate according to user selection
if (interpolation.type == 1)
tac.inter <- approx(time.end0, tac0, xout = time.vector, rule = 2)
else if (interpolation.type == 2)
tac.inter <- spline(time.end0, tac0, xout = time.vector,
method = "natural")
return(list(tsample = time.vector, y = tac.inter$y))
}
#' Actual interpolation.
#'
#' Typically used after \code{\link{interpolate.tac}}. This is just a simplified
#' call to the \code{\link{approx}} function.
#'
#' @param tac The extrapolated TAC to interpolate
#' @param tsample The sampling points used in the original extrapolation.
#' @param time.points The new time points for which the signal is desired.
#'
#' @return The new interpolated TAC.
revinterpolate.tac <- function(tac, tsample, time.points) {
approx(tsample, tac, xout = time.points, rule = 2)$y
}
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