title: Fitting the two-compartment model in DCE-MRI by linear inversion.
abstract: Model fitting of dynamic contrast-enhanced-magnetic resonance imaging-MRI data with nonlinear least squares (NLLS) methods is slow and may be biased by the choice of initial values. The aim of this study was to develop and evaluate a linear least squares (LLS) method to fit the two-compartment exchange and -filtration models.
  
  
  
  A second-order linear differential equation for the measured concentrations was derived where model parameters act as coefficients. Simulations of normal and pathological data were performed to determine calculation time, accuracy and precision under different noise levels and temporal resolutions. Performance of the LLS was evaluated by comparison against the NLLS.
  
  
  
  The LLS method is about 200 times faster, which reduces the calculation times for a 256 × 256 MR slice from 9 min to 3 s. For ideal data with low noise and high temporal resolution the LLS and NLLS were equally accurate and precise. The LLS was more accurate and precise than the NLLS at low temporal resolution, but less accurate at high noise levels.
  
  
  
  The data show that the LLS leads to a significant reduction in calculation times, and more reliable results at low noise levels. At higher noise levels the LLS becomes exceedingly inaccurate compared to the NLLS, but this may be improved using a suitable weighting strategy. Magn Reson Med 76:998-1006, 2016. © 2015 Wiley Periodicals, Inc.
authors.affiliation: Division of Biomedical Imaging, University of Leeds, Leeds, LS2 9JT, UK.|Department of Applied Mathematics, University of Leeds, Leeds, LS2 9JT, UK.
authors.forename: Dimitra
authors.initials: D
authors.lastname: Flouri
authors.affiliation: Department of Applied Mathematics, University of Leeds, Leeds, LS2 9JT, UK.
authors.forename: Daniel
authors.initials: D
authors.lastname: Lesnic
authors.affiliation: Division of Biomedical Imaging, University of Leeds, Leeds, LS2 9JT, UK.
authors.forename: Steven P
authors.initials: SP
authors.lastname: Sourbron
mesh_terms: D000465:Algorithms; D003198:Computer Simulation; D003287:Contrast Media / Q000493:pharmacokinetics*; D006801:Humans; D007089:Image Enhancement / Q000379:methods; D007090:Image Interpretation, Computer-Assisted / Q000379:methods*; D007668:Kidney / Q000000981:diagnostic imaging* / Q000378:metabolism*; D016018:Least-Squares Analysis; D016014:Linear Models; D008279:Magnetic Resonance Imaging / Q000379:methods*; D008954:Models, Biological; D009716:Numerical Analysis, Computer-Assisted; D015203:Reproducibility of Results; D012680:Sensitivity and Specificity
chemical_list: D003287:Contrast Media
keywords: Dynamic Contrast-Enhanced Magnetic Resonance Imaging; linear least squares; non-linear least-squares; tracer-kinetics; two-compartment model