title: Characterizing magnetic resonance signal decay due to Gaussian diffusion: the path integral approach and a convenient computational method.
abstract: 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, theb-value andb-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 (MCF) 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.
authors.affiliation: Department of Physics, Bođaziçi University, Bebek, Ýstanbul, Turkey; Department of Radiology, Brigham and Women's Hospital, Harvard Medical School, Boston, MA, USA.
authors.forename: Evren
authors.initials: E
authors.lastname: Özarslan
authors.affiliation: Department of Radiology, Brigham and Women's Hospital, Harvard Medical School, Boston, MA, USA.
authors.forename: Carl-Fredrik
authors.initials: CF
authors.lastname: Westin
authors.affiliation: Department of Biochemistry and Molecular Biology, University of Florida, Gainesville, FL, USA.
authors.forename: Thomas H
authors.initials: TH
authors.lastname: Mareci
keywords: Bloch-Torrey; anisotropy; diffusion; free diffusion; general gradient waveform; generalized; microstructure; multiple propagator; path integral