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Fitting the two‐compartment model in DCE‐MRI by linear inversion
Author(s) -
Flouri Dimitra,
Lesnic Daniel,
Sourbron Steven P.
Publication year - 2016
Publication title -
magnetic resonance in medicine
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.696
H-Index - 225
eISSN - 1522-2594
pISSN - 0740-3194
DOI - 10.1002/mrm.25991
Subject(s) - weighting , non linear least squares , least squares function approximation , noise (video) , linear model , computer science , algorithm , mathematics , statistics , estimation theory , artificial intelligence , physics , estimator , acoustics , image (mathematics)
Purpose 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. Methods 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. Results 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. Conclusion 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.