qMRI (version 1.2.7)

estimateIRfluid: Estimate parameters in Inversion Recovery MRI experiments model for CSF voxel

Description

The Inversion Recovery MRI signal in voxel containing only CSF follows is modeled as $S_InvTime = par[1] * abs( 1 - 2 * exp(-InvTime*par[2]) )$ dependings on two parameters. These parameters are assumed to be tissue (and scanner) dependent.

Usage

estimateIRfluid(IRdataobj, TEScale = 100, dataScale = 1000,
method = c("NLR", "QL"), varest = c("RSS", "data"),
verbose = TRUE, lower = c(0, 0), upper = c(2, 2))

Value

List of class IRfluid with components

IRdata

4D array containing the IRMRI data, first dimension refers to inversion times

InvTimes

vector of inversion times

segm

segmentation codes, 1 for CSF, 2 for GM, 3 for WM, 0 for out of brain

sigma

noise standard deviation, if not specified estimated fron CSF areas in image with largest inversion time

L

effective number of coils

Sf

Global estimate of maximal fluid signal

Rf

Global estimate of fluid relaxation rate

Sx

Array of maximal signals

Rx

Array of relaxation rates

sigma

Array of provided or estimated noise standard deviations

Convx

Array of convergence indicators

method

"NLS" for nonlinear regression or "QL" for quasi likelihood.

varest

Method used for variance estimation

The arrays only contain entries for fluid voxel.

Arguments

IRdataobj

Object of class "IRdata" as generated by function readIRData.

TEScale

Internal scale factor for Echo Times. This influences parameter scales in numerical calculations.

dataScale

Internal scale factor for MR signals. This influences parameter scales in numerical calculations.

method

Either "NLS" for nonlinear least squares (ignores Rician bias) or "QL" for Quasi-Likelihood. The second option is more accurate but requires additional information and is computationally more expensive.

varest

Method to, in case of method="QR", estimate sigmaif not provided. Either from residual sums of squares ("RSS") or MR signals ("data") using function varest from package aws. Only to be used in case that no image registration was needed as preprocessing.

verbose

Logical. Provide some runtime diagnostics.

lower

Lower bounds for parameter values.

upper

Upper bounds for parameter values.

Author

Karsten Tabelow
J\"org Polzehl

Details

The Inversion Recovery MRI signal in voxel containing only CSF follows is modeled as $S_InvTime = par[1] * abs( 1 - 2 * exp(-InvTime*par[2]) )$ dependings on two parameters. These parameters are assumed to be tissue (and scanner) dependent.

See Also

estimateIR, estimateIRsolid, estimateIRsolidfixed,smoothIRSolid

Examples

##---- Should be DIRECTLY executable !! ----
##-- ==>  Define data, use random,
##--	or do  help(data=index)  for the standard data sets.

## The function is currently defined as
function (IRdata, InvTimes, segments, TEScale = 100, dataScale = 1000, 
    method = c("NLR", "QL"), sigma = NULL, L = 1, maxR2star = 50, 
    varest = c("RSS", "data"), verbose = TRUE, lower = c(0, 0), 
    upper = c(2, 2)) 
{
    mask <- segments == 1
    nvoxel <- sum(mask)
    ntimes <- length(InvTimes)
    itmin <- order(InvTimes)[1]
    itmax <- order(InvTimes)[ntimes]
    InvTimes[InvTimes == Inf] <- 50 * max(InvTimes[InvTimes != 
        Inf])
    dimdata <- dim(IRdata)
    if (dimdata[1] != ntimes) 
        stop("estimateIRfluid: incompatible length of InvTimes")
    if (any(dimdata[-1] != dim(mask))) 
        stop("estimateIRfluid: incompatible dimension of segments")
    InvTimesScaled <- InvTimes/TEScale
    npar <- 2
    Rx <- Sx <- Conv <- array(0, dim(mask))
    isConv <- array(0, nvoxel)
    isThresh <- array(FALSE, nvoxel)
    modelCoeff <- array(0, c(npar, nvoxel))
    if (varest[1] == "data") {
        if (verbose) 
            cat("estimating variance maps from data\n")
        ind <- (InvTimes == max(InvTimes))[1]
        ddata <- IRdata[ind, , , ]
        shat <- aws::awsLocalSigma(ddata, steps = 16, mask = (segments == 
            1), ncoils = 1, hsig = 2.5, lambda = 6, family = "Gauss")$sigma
        dim(shat) <- dimdata[-1]
        shat <- shat[segments == 1]
        shat[shat == 0] <- quantile(shat, 0.8)
        shat <- shat
        if (is.null(sigma)) 
            sigma <- median(shat)
        else shat <- NULL
    }
    if (method[1] == "QL") {
        if (is.null(sigma)) {
            method <- "NLR"
            warning("estimateIRfluid: method QL needs sigma estimated or supplied")
        }
        sig <- sigma/dataScale
        CL <- sig * sqrt(pi/2) * gamma(L + 0.5)/gamma(L)/gamma(1.5)
    }
    dim(IRdata) <- c(dimdata[1], prod(dim(segments)))
    IRdataFluid <- IRdata[, segments == 1]
    thetas <- matrix(0, 2, nvoxel)
    thetas[1, ] <- IRdataFluid[itmax, ]/dataScale
    thetas[2, ] <- -log((IRdataFluid[itmin]/dataScale + thetas[1, 
        ])/2)/InvTimes[itmin] * TEScale
    if (verbose) {
        cat("Start estimation in", nvoxel, "voxel at", format(Sys.time()), 
            "\n")
        pb <- txtProgressBar(0, nvoxel, style = 3)
    }
    for (xyz in 1:nvoxel) {
        ivec <- IRdataFluid[, xyz]/dataScale
        th <- thetas[, xyz]
        res <- if (method[1] == "NLR") 
            try(nls(ivec ~ IRhomogen(par, InvTimesScaled), data = list(InvTimesScaled), 
                start = list(par = th), control = list(maxiter = 200, 
                  warnOnly = TRUE)), silent = TRUE)
        else try(nls(ivec ~ IRhomogenQL(par, InvTimesScaled, 
            CL, sig, L), data = list(InvTimesScaled, CL = CL, 
            sig = sig, L = L), start = list(par = th), control = list(maxiter = 200, 
            warnOnly = TRUE)), silent = TRUE)
        if (class(res) != "try-error") {
            thhat <- coef(res)
            outofrange <- any(thhat != pmin(upper, pmax(lower, 
                thhat)))
        }
        if (class(res) == "try-error" || outofrange) {
            th <- pmin(upper, pmax(lower, th))
            res <- if (method[1] == "NLR") 
                try(nls(ivec ~ IRhomogen(par, InvTimesScaled), 
                  data = list(InvTimes = InvTimesScaled), start = list(par = th), 
                  algorithm = "port", control = list(maxiter = 200, 
                    warnOnly = TRUE), lower = lower, upper = upper), 
                  silent = TRUE)
            else try(nls(ivec ~ IRhomogenQL(par, InvTimesScaled, 
                CL, sig, L), data = list(InvTimesScaled = InvTimesScaled, 
                CL = CL, sig = sig, L = L), start = list(par = th), 
                algorithm = "port", control = list(maxiter = 200, 
                  warnOnly = TRUE), lower = lower, upper = upper), 
                silent = TRUE)
        }
        if (class(res) != "try-error") {
            sres <- if (varest[1] == "RSS") 
                getnlspars(res)
            else getnlspars2(res, shat[, xyz], sind)
            isConv[xyz] <- as.integer(res$convInfo$isConv)
            modelCoeff[, xyz] <- sres$coefficients
        }
        if (verbose) 
            if (xyz%/%1000 * 1000 == xyz) 
                setTxtProgressBar(pb, xyz)
    }
    Rx[mask] <- modelCoeff[2, ]
    Sx[mask] <- modelCoeff[1, ]
    Conv[mask] <- isConv
    Sf <- median(modelCoeff[1, ], na.rm = TRUE)
    Rf <- median(modelCoeff[2, ], na.rm = TRUE)
    if (verbose) {
        close(pb)
        cat("Finished estimation", format(Sys.time()), "\n", 
            "Sf", Sf, "Rf", Rf, "\n")
    }
    list(Sf = Sf, Rf = Rf, Sx = Sx, Rx = Rx, sigma = sigma, Conv = Conv)
  }