Nonlinear least squares fitting for variable flip angle T1 estimation

Paul Kinchesh, Philip D Allen, Michael Brady, Sean C Smart

Cancer Research UK and Medical Research Council Oxford Institute for Radiation Oncology, 
Department of Oncology, University of Oxford, Oxford, United Kingdom

Summary

The source code presented enables a fast nonlinear least squares fit for T1 estimation using 
a robust and efficient version of the Levenberg-Marquardt minimization algorithm provided 
by a derivative solver in the Gnu Scientific Library (GSL, http://www.gnu.org/software/gsl/).

Input data are variable flip angle (VFA) '.nii' data and (optionally) a processed actual flip angle 
imaging (AFI) 'nii' data set containing the flip angle (FA) distribution resulting from the prescribed
AFI flip angle. FA maps provide a voxel wise FA correction for the VFA FA prescription during fitting.

Output data are a T1 estimate (T1_VFA.nii), a M0* = Mo.exp(-TE/T2*) estimate (M0_VFA.nii), and 
(optionally) the number of iterations (NIT_VFA.nii).

The 'nii' data are in the NIfTI-1 format, http://nifti.nimh.nih.gov/
ImageJ is a suitable viewer, http://imagej.nih.gov/ij/

Usage: niiT1vfa [-f FA1,..,FAn] [-r TR] [-m maxT1] [-t thr]
                [-a AFI.nii] [-p AFIflip] [-s] VFA.nii
         VFA.nii is the file containing the VFA data
         Options:
           [-f FA1,FA2,..,FAn] specify flip angles
           [-r TR]             specify TR/s (default 0.0028 s)
           [-m maxT1]          maximum T1/s (default 10.0 s)
           [-t thr]            threshold (default automatic)
           [-a AFI.nii]        use AFI FA file to correct prescribed FAs
           [-p AFIflip]        prescribed AFI flip/deg (default 64 deg)
           [-s]                generate T1 & iteration stats
         Output:
           T1_VFA.nii          T1 estimate
		   M0_VFA.nii          M0* estimate, M0* = Mo.exp(-TE/T2*)
           NIT_VFA.nii         Number of iterations (-s option only) 
		   
The nonlinear least squares fitting routine presented can be used on the VFA data published at
http://dx.doi.org/10.5287/bodleian:a4awG5r7R which presents four complete in vivo data sets for:
Whole Body T1 Mapping of Small Animals using Prospective Gating and Variable Flip Angle Imaging. 

Funding

This work was supported financially by Cancer Research UK (CRUK grants C5255/A12678, C2522/A10339), 
the Engineering and Physical Sciences Research Council (EPSRC grant C2522/A10339) and 
the Medical Research Council Unit Grant for the Oxford Institute for Radiation Oncology.

Files in Repository

niiT1vfa.tar.gz: Nonlinear least squares fitting source code (gzipped tarfile).
niiT1vfa.zip:    Nonlinear least squares fitting source code (zipped file).
INSTALL.txt:     Nonlinear least squares fitting INSTALL file.