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Propagation of error from parameter constraints in quantitative MRI: Example application of multiple spin echo T 2 mapping
Author(s) -
Lankford Christopher L.,
Does Mark D.
Publication year - 2018
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.26713
Subject(s) - flip angle , constraint (computer aided design) , echo (communications protocol) , spin echo , nuisance parameter , mean squared error , variance (accounting) , algorithm , noise (video) , computer science , function (biology) , accuracy and precision , statistics , mathematics , magnetic resonance imaging , image (mathematics) , artificial intelligence , estimator , biology , business , radiology , medicine , computer network , geometry , accounting , evolutionary biology
Purpose Quantitative MRI may require correcting for nuisance parameters which can or must be constrained to independently measured or assumed values. The noise and/or bias in these constraints propagate to fitted parameters. For example, the case of refocusing pulse flip angle constraint in multiple spin echo T 2 mapping is explored. Methods An analytical expression for the mean‐squared error of a parameter of interest was derived as a function of the accuracy and precision of an independent estimate of a nuisance parameter. The expression was validated by simulations and then used to evaluate the effects of flip angle (θ) constraint on the accuracy and precision ofT ⁁ 2for a variety of multi‐echo T 2 mapping protocols. Results Constraining θ improvedT ⁁ 2precision when the θ‐map signal‐to‐noise ratio was greater than approximately one‐half that of the first spin echo image. For many practical scenarios, constrained fitting was calculated to reduce not just the variance but the full mean‐squared error ofT ⁁ 2 , for bias inθ ⁁ ≲ 6 % . Conclusion The analytical expression derived in this work can be applied to inform experimental design in quantitative MRI. The example application to T 2 mapping provided specific cases, depending on θ ⁁ accuracy and precision, in which θ ⁁ measurement and constraint would be beneficial toT ⁁ 2variance or mean‐squared error. Magn Reson Med 79:673–682, 2018. © 2017 International Society for Magnetic Resonance in Medicine.