Open AccessCharacterizing magnetic resonance signal decay due to gaussian diffusion: The path integral approach and a convenient computational method
Author(s) -
Özarslan Evren,
Westin CarlFredrik,
Mareci Thomas H.
Publication year - 2015
Publication title -
concepts in magnetic resonance part a
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.229
H-Index - 49
eISSN - 1552-5023
pISSN - 1546-6086
DOI - 10.1002/cmr.a.21354
Subject(s) - waveform , diffusion mri , diffusion , gaussian , signal (programming language) , computation , pulse (music) , path (computing) , algorithm , physics , mathematical analysis , mathematics , nuclear magnetic resonance , computer science , magnetic resonance imaging , optics , medicine , quantum mechanics , voltage , detector , radiology , programming language , thermodynamics
The influence of Gaussian diffusion on the magnetic resonance signal is determined by the apparent diffusion coefficient (ADC) and tensor (ADT) of the diffusing fluid as well as the gradient waveform applied to sensitize the signal to diffusion. Estimations of ADC and ADT from diffusion‐weighted acquisitions necessitate computations of, respectively, the b ‐value and b‐matrix associated with the employed pulse sequence. We establish the relationship between these quantities and the gradient waveform by expressing the problem as a path integral and explicitly evaluating it. Further, we show that these important quantities can be conveniently computed for any gradient waveform using a simple algorithm that requires a few lines of code. With this representation, our technique complements the multiple correlation function method commonly used to compute the effects of restricted diffusion, and provides a consistent and convenient framework for studies that aim to infer the microstructural features of the specimen. © 2015 Wiley Periodicals, Inc. Concepts Magn Reson Part A 44A: 203–213, 2015.