qMRI (version 1.2.7)

estimateIRsolid: Estimate parameters in Inversion Recovery MRI experiments mixture model for non-fluid voxel

Description

The Inversion Recovery MRI signal in non-fluid voxel follows is modeled as a mixture of a fluid and a solid compartment.

Usage

estimateIRsolid(IRfluidobj, TEScale = 100, dataScale = 1000,
verbose = TRUE, lower = c(0, 0, 0), upper = c(0.95, 2, 2))

Value

List of class IRmixed 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

fx

Array of fluid proportions

Sx

Array of maximal signals

Rx

Array of relaxation rates

Sf

Global estimate of maximal fluid signal

Rf

Global estimate of fluid relaxation rate

ICovx

Covariance matrix of estimates fx, Sx and Rx.

sigma

Array of provided or estimated noise standard deviations

Convx

Array of convergence indicators

rsdx

Residual standard deviations

method

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

varest

Method used for variance estimation

The arrays contain entries for all voxel with segments%in%1:3.

Arguments

IRfluidobj

Object of class "IRfluid" as generated by function estimateIRfluid.

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.

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 non-fluid voxel follows is modeled as a mixture of a fluid and a solid compartment. The function calculates estimates of the maximum signal and recovery rate for the solid compartment and a mixture coefficient (proportion of fluid) for all voxel with segment%in%2:3using results from function estimateIRfluid.

See Also

estimateIRfluid, estimateIR, 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, Sfluid, Rfluid, TEScale = 100, 
    dataScale = 1000, method = c("NLR", "QL"), sigma = NULL, 
    L = 1, maxR2star = 50, varest = c("RSS", "data"), verbose = TRUE, 
    lower = c(0, 0, 0), upper = c(0.95, 2, 2)) 
{
    mask <- segments > 1
    nvoxel <- sum(mask)
    ntimes <- length(InvTimes)
    InvTimes[InvTimes == Inf] <- 50 * max(InvTimes[InvTimes != 
        Inf])
    dimdata <- dim(IRdata)
    if (dimdata[1] != ntimes) 
        stop("estimateIRsolid: incompatible length of InvTimes")
    if (any(dimdata[-1] != dim(mask))) 
        stop("estimateIRsolid: incompatible dimension of segments")
    InvTimesScaled <- InvTimes/TEScale
    npar <- 3
    fx <- Rx <- Sx <- rsdx <- array(0, dim(mask))
    ICovx <- array(0, c(3, 3, prod(dim(mask))))
    Convx <- array(0, dim(mask))
    fx[segments == 1] <- 1
    Rx[segments == 1] <- Rfluid
    Sx[segments == 1] <- Sfluid
    Convx[segments == 1] <- 1
    ICovx[1, 1, segments == 1] <- 1e+20
    ICovx[2, 2, segments == 1] <- 1e+20
    ICovx[3, 3, segments == 1] <- 1e+20
    isConv <- array(FALSE, nvoxel)
    isThresh <- array(FALSE, nvoxel)
    modelCoeff <- array(0, c(npar, nvoxel))
    invCov <- array(0, c(npar, npar, nvoxel))
    rsigma <- array(0, nvoxel)
    if (method[1] == "QL") {
        if (is.null(sigma)) {
            method <- "NLR"
            warning("estimateIRsolid: method QL needs sigma estimated from fluid 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)))
    IRdataSolid <- IRdata[, mask]
    thetas <- matrix(0, 3, nvoxel)
    thetas[3, ] <- IRdataSolid[(1:ntimes)[InvTimes == max(InvTimes)][1], 
        ]/dataScale
    thetas[2, ] <- 1/median(InvTimesScaled)
    thetas[1, ] <- 0.3
    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 <- IRdataSolid[, xyz]/dataScale
        th <- thetas[, xyz]
        res <- if (method[1] == "NLR") 
            try(nls(ivec ~ IRmix2(par, ITS, Sfluid, Rfluid), 
                data = list(ITS = InvTimesScaled, Sfluid = Sfluid, 
                  Rfluid = Rfluid), start = list(par = th), control = list(maxiter = 200, 
                  warnOnly = TRUE)), silent = TRUE)
        else try(nls(ivec ~ IRmix2QL(par, ITS, Sfluid, Rfluid, 
            CL, sig, L), data = list(ITS = InvTimesScaled, Sfluid = Sfluid, 
            Rfluid = Rfluid, 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 ~ IRmix2(par, ITS, Sfluid, Rfluid), 
                  data = list(ITS = InvTimesScaled, Sfluid = Sfluid, 
                    Rfluid = Rfluid), start = list(par = th), 
                  algorithm = "port", control = list(maxiter = 200, 
                    warnOnly = TRUE), lower = lower, upper = upper), 
                  silent = TRUE)
            else try(nls(ivec ~ IRmix2QL(par, ITS, Sfluid, Rfluid, 
                CL, sig, L), data = list(ITS = InvTimesScaled, 
                Sfluid = Sfluid, Rfluid = Rfluid, 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$coefficients
            if (sres$sigma != 0) {
                invCov[, , xyz] <- sres$invCov
                rsigma[xyz] <- sres$sigma
            }
        }
        if (verbose) 
            if (xyz%/%1000 * 1000 == xyz) 
                setTxtProgressBar(pb, xyz)
    }
    if (verbose) {
        close(pb)
        cat("Finished estimation", format(Sys.time()), "\n")
    }
    fx[mask] <- modelCoeff[1, ]
    Rx[mask] <- modelCoeff[2, ]
    Sx[mask] <- modelCoeff[3, ]
    ICovx[, , mask] <- invCov
    dim(ICovx) <- c(3, 3, dim(mask))
    Convx[mask] <- isConv
    rsdx[mask] <- rsigma
    list(fx = fx, Rx = Rx, Sx = Sx, Sf = Sfluid, Rf = Rfluid, 
        ICovx = ICovx, Convx = Convx, sigma = sigma, rsdx = rsdx)
  }