# Estimate parameters in Inversion Recovery MRI experiments mixture model for non-fluid voxel The Inversion Recovery MRI signal in non-fluid voxel follows is modeled as a mixture of a fluid and a solid compartment. ```r estimateIRsolid(IRfluidobj, TEScale = 100, dataScale = 1000, verbose = TRUE, lower = c(0, 0, 0), upper = c(0.95, 2, 2)) ``` ## 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. ## 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%2:3`using results from function `estimateIRfluid`. ## Returns 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`. ## References J. Polzehl and K. Tabelow (2023), Magnetic Resonance Brain Imaging: Modeling and Data Analysis Using R, 2nd Edition, Chapter 7, Springer, Use R! Series. . J. Polzehl and K. Tabelow (2023), Magnetic Resonance Brain Imaging - Modeling and Data Analysis Using R: Code and Data. . ## Author(s) Karsten Tabelow tabelow@wias-berlin.de J\"org Polzehl polzehl@wias-berlin.de ## See Also `estimateIRfluid`, `estimateIR`, `estimateIRsolidfixed`,`smoothIRSolid` ## Examples ```r ## runs about 7 seconds dataDir0 <- system.file("extdataIR", package = "qMRI") dataDir <- tempdir() library(oro.nifti) library(qMRI) segm <- readNIfTI(file.path(dataDir0,"Brainweb_segm")) Sf <- 900 Rf <- 0.000285 Sgm <- 400 Rgm <- 0.00075 fgm <- .15 Swm <- 370 Rwm <- 0.0011 fwm <- .05 InvTimes0 <- c(100, 200, 400, 600, 800, 1200, 1600, 2000, 2500, 3000, 3500, 4000, 4500, 5000, 6000, 15000) nTimes <- length(InvTimes0) sigma <- 40 ## generate IR signal IRdata <- generateIRData(segm, c(Sf,Rf), c(fgm,Rgm,Sgm), c(fwm,Rwm,Swm), InvTimes0, sigma) for(i in 1:9) writeNIfTI(as.nifti(IRdata[i,,,]), file.path(dataDir,paste0("IR0",i))) for(i in 10:nTimes) writeNIfTI(as.nifti(IRdata[i,,,]), file.path(dataDir,paste0("IR",i))) ## generate IRdata object t1Files <- list.files(dataDir,"*.nii.gz",full.names=TRUE) segmFile <- file.path(dataDir0,"Brainweb_segm") IRdata <- readIRData(t1Files, InvTimes0, segmFile, sigma=sigma, L=1, segmCodes=c("CSF","GM","WM")) ## estimate fluid setCores(2) # parallel mode using 2 threads IRfluid <- estimateIRfluid(IRdata, method="NLR", verbose=FALSE) cat("Estimated parameters Sf:", IRfluid$Sf, " Rf:", IRfluid$Rf, "\n") ## estimate solid IRmix <- estimateIRsolid(IRfluid, verbose=FALSE) ```

estimateIRsolid function