R/SingleVoxelFFBS.R

In BayesDLMfMRI: Statistical Analysis for Task-Based Fmri Data

#' @name SingleVoxelFFBS
#' @title SingleVoxelFFBS
#' @description
#' \loadmathjax
#' This function is used to perform an activation analysis for single voxels based on the FFBS algorithm.
#' @references
#' \insertRef{CARDONAJIMENEZ2021107297}{BayesDLMfMRI}
#' 
#' \insertRef{cardona2021bayesdlmfmri}{BayesDLMfMRI}
#' @details
#' This function allows the development of an activation analysis for single voxels. A multivariate dynamic linear model is fitted to a cluster of voxels, with its center at location (i,j,k), in the way it is presented in \insertCite{CARDONAJIMENEZ2021107297}{BayesDLMfMRI}.
#' @param posi.ffd  the position of the voxel in the brain image.
#' @param covariates a data frame or matrix whose columns contain the covariates related to the expected BOLD response obtained from the experimental setup.
#' @param ffdc a 4D array (\code{ffdc[i,j,k,t]}) that contains the sequence of MRI images that are meant to be analyzed. \code{(i,j,k)} define the position of the observed voxel at time t.
#' @param m0 the constant prior mean value for the covariates parameters and common to all voxels within every neighborhood at \code{t=0} (\code{m=0} is the default value when no prior information is available). For the case of available prior information, \code{m0} can be defined as a \mjseqn{p\times q} matrix, where \mjseqn{p} is the number of columns in the covariates object and \mjseqn{q} is the cluster size.
#' @param Cova a positive constant that defines the prior variances for the covariates parameters at \code{t=0} (\code{Cova=100} is the default value when no prior information is available). For the case of available prior information, \code{Cova} can be defined as a \mjseqn{p\times p} matrix, where \mjseqn{p} is the number of columns in the covariates object.
#' @param delta a discount factor related to the evolution variances. Recommended values between \code{0.85<delta<1}. delta=1 will yield results similar to the classical general linear model.
#' @param S0 prior covariance structure among voxels within every cluster at \code{t=0}. \code{S0=1} is the default value when no prior information is available and defines an \mjseqn{q\times q} identity matrix. For the case of available prior information, \code{S0} can be defined as an \mjseqn{q\times q} matrix, where \mjseqn{q} is the common number of voxels in every cluster.
#' @param n0 a positive hyperparameter of the prior distribution for the covariance matrix \code{S0} at \code{t=0} (\code{n1=1} is the default value when no prior information is available). For the case of available prior information, \code{n0} can be set as \code{n0=np}, where \code{np} is the number of MRI images in the pilot sample.
#' @param N1 is the number of images (\code{2<N1<T}) from the \code{ffdc} array employed in the model fitting. \code{N1=NULL} (or equivalently \code{N1=T}) is its default value, taking all the images in the \code{ffdc} array for the fitting process.
#' @param Nsimu1 is the number of simulated on-line trajectories related to the state parameters. These simulated curves are later employed to compute the posterior probability of voxel activation.
#' @param Cutpos1 a cutpoint time from where the on-line trajectories begin. This parameter value is related to an approximation from a t-student distribution to a normal distribution. Values equal to or greater than 30 are recommended (\code{30<Cutpos1<T}).  
#' @param Min.vol helps to define a threshold for the voxels considered in
#' the analysis. For example, \code{Min.vol = 0.10} means that all the voxels with values
#' below to \code{max(ffdc)*Min.vol} can be considered irrelevant and discarded from the analysis.
#' @param r1 a positive integer number that defines the distance from every voxel with its most distant neighbor. This value determines the size of the cluster. The users can set a range of different \code{r1} values: \mjseqn{r1 = 0, 1, 2, 3, 4}, which leads to \mjseqn{q = 1, 7, 19, 27, 33}, where \mjseqn{q} is the size of the cluster.
#' @return a list containing a vector (Evidence) with the evidence measure of 
#' activation for each of the \code{p} covariates considered in the model, the simulated 
#' online trajectories related to the state parameter, the simulated BOLD responses,
#'  and a measure to examine the goodness of fit of the model \mjseqn{(100 \ast |Y[i,j,k]_t - \hat{Y}[i,j,k]_t |/ \hat{Y}[i,j,k]_t )} for that particular voxel (\code{FitnessV}).
#' @examples 
#'\dontrun{
#' # This example can take a long time to run.
#' fMRI.data  <- get_example_fMRI_data()
#' data("covariates", package="BayesDLMfMRI")
#' res.indi <- SingleVoxelFFBS(posi.ffd = c(14, 56, 40), 
#'                             covariates = Covariates,
#'                             ffdc =  fMRI.data, 
#'                             m0 = 0, Cova = 100, delta = 0.95, S0 = 1, 
#'                             n0 = 1, Nsimu1 = 100, N1 = FALSE, Cutpos1 = 30, 
#'                             Min.vol = 0.10, r1 = 1)
#' 
#' }
#' @export
SingleVoxelFFBS <- function(posi.ffd, covariates, ffdc, m0, Cova, delta, 
                            S0, n0, N1, Nsimu1, Cutpos1, Min.vol, r1){
  
   if(is.logical(N1)) {
    if(N1==FALSE){N1 = dim(covariates)[1]}
   }

   .validate_input(
    covariates=covariates,
    ffdc = ffdc,
    delta=delta,
    n0=n0,
    N1=N1,
    Nsimu1=Nsimu1,
    Cutpos1=Cutpos1,
    Min.vol=Min.vol,
    r1=r1
  )
  
  if(r1 == 0){
    
    posi <- .distanceNeighbors (posi.refer = as.vector(posi.ffd), r1)
    
    #BOLD RESPONSE SERIES IN THE CLUSTER RELATED TO posi
    series.def <- sapply(1:(dim(posi)[1]), function(k){ffdc[posi[k,1], posi[k,2], posi[k,3], ]})
    #CHEKING THE THRESHOLD Min.vol FOR THE MAIN TS: JUST TEMPORAL SERIES ABOVE THE THRESHOLD, DISCARD TEMPORAL SERIES WITH NON-SIGNIFICANT SIGNAL
    if(min(series.def[,1]) < Min.vol){
      return(list(EvidenceJoint = rep(NA, dim(covariates)[2]), EvidenceMargin = rep(NA, dim(covariates)[2]), EvidenLTT = rep(NA, dim(covariates)[2])))}else{
        series.def <- matrix((series.def - mean(series.def))/sd(series.def), ncol=1)
        #PRIOR HYPERPARAMETERS FOR q1=1
        m01   <- matrix(rep(m0, dim(covariates)[2]*dim(series.def)[2]), ncol=1)
        Cova1 <- diag(rep(Cova, dim(covariates)[2]))
        S01 <- diag(rep(S0,dim(series.def)[2]))
        #DISCOUNT FACTORS MATRIX
        delta1 <- sqrt(delta)
        Beta1 <-  diag(1/c(rep(delta1, dim(covariates)[2])))
        
        res <- .Individual_Backwards_Sampling(ffd1 = as.matrix(series.def), Cova = as.matrix(covariates), m0In = m01, c0In = Cova1, 
                                              S0In = S01, beta0In = Beta1, nt0In = n0, NIn = N1, Nsimu = Nsimu1, CUTpos = Cutpos1)
        res  <- list(EvidenceJoint = as.vector(res$Eviden_joint), EvidenceMargin = as.vector(res$Eviden_margin), EvidenLTT=as.vector(res$eviden_lt))
        attr(res, "class") <- "fMRI_single_voxel"
        return(res)
        
      }
  }else{
    #THIS LINE RETURN THE POSITIONS OF EACH VOXEL INSIDE THE CLUSTER GIVEN THE DISTANCE r1
    posi1 <- .distanceNeighbors (posi.refer = as.vector(posi.ffd), r1)
    
    
    aux.pos <- dim(ffdc)[1:3]
    #GOING THROUGH EACH ROW AND CHECKING IF ANY POSITION IS OUTSIDE THE BOUNDS
    row_sub1 <- apply(posi1, 1, function(row, x1){0 < row & row<=x1}, x1=aux.pos)
    posi <- posi1[apply(t(row_sub1), 1, sum)==3, ]
    #BOLD RESPONSE SERIES FOR THE CLUSTER RELATED TO posi
    series <- sapply(1:(dim(posi)[1]), function(k){ffdc[posi[k,1], posi[k,2], posi[k,3], ]})
    #CHEKING THE THRESHOLD Min.vol FOR THE MAIN TS: JUST TEMPORAL SERIES ABOVE THE THRESHOLD, DISCARD TEMPORAL SERIES WITH NON-SIGNIFICANT SIGNAL
    if(min(series[,1]) < Min.vol){return(list(EvidenceJoint = rep(NA, dim(covariates)[2]), EvidenceMargin = rep(NA, dim(covariates)[2]), EvidenLTT = rep(NA, dim(covariates)[2])))}else{
      # IDENTIFYING AND REMOVING TEMPORAL SERIES INSIDE THE CLUSTER WITH ZERO VALUES
      zero.series <- unique(which(series==0, arr.ind = TRUE)[,2]) 
      if(length(zero.series)==0){series.def <- series}else{series.def <- series[,-(zero.series)]}
      #CHECKING THE SIZE OF THE CLUSTER: q=1 or q>1
      #is.vector(series.def)==TRUE THEN q=1 OTHERWISE q>1
      if(is.vector(series.def)){ 
        series.def <- matrix((series.def - mean(series.def))/sd(series.def), ncol=1)
        #PRIOR HYPERPARAMETERS FOR q1=1
        m01   <- matrix(rep(m0, dim(covariates)[2]*dim(series.def)[2]), ncol=1)
        Cova1 <- diag(rep(Cova, dim(covariates)[2]))
        S01 <- diag(rep(S0,dim(series.def)[2]))
        #DISCOUNT FACTORS MATRIX
        delta1 <- sqrt(delta)
        Beta1 <-  diag(1/c(rep(delta1, dim(covariates)[2])))}else{
          series.def <- apply(series.def, 2, function(x){(x-mean(x))/sd(x)})
          #PRIOR HYPERPARAMETERS FOR q1>1
          m01   <- matrix(rep(m0, dim(covariates)[2]*dim(series.def)[2]), ncol=dim(series.def)[2])
          Cova1 <- diag(rep(Cova, dim(covariates)[2]))
          S01 <- diag(rep(S0,dim(series.def)[2]))
          delta1 <- sqrt(delta)
          #DISCOUNT FACTORS MATRIX
          Beta1 <-  diag(1/c(rep(delta1, dim(covariates)[2])))
          
        }
      
      
      
      res <- .Individual_Backwards_Sampling(ffd1 = as.matrix(series.def), Cova = as.matrix(covariates), m0In = m01, c0In = Cova1, 
                                            S0In = S01, beta0In = Beta1, nt0In = n0, NIn = N1, Nsimu = Nsimu1, CUTpos = Cutpos1)
      attr(res, "class") <- "fMRI_single_voxel"
      #EVIDENCE OF ACTIVATION FOR A SINGLE VOXEL TAKING INTO ACCOUNT THE INFORMATION OF THE ENTIRE CLUSTER OF SIZE q
      return(res)
      
      
      
      
      
    }
    
  }
  
  
  
}
#END FUNCTION