title: Spin dephasing in a magnetic dipole field around large capillaries: Approximative and exact results.
abstract: We present an analytical solution of the Bloch-Torrey equation for local spin dephasing in the magnetic dipole field around a capillary and for ensembles of capillaries, and adapt this solution for the study of spin dephasing around large capillaries. In addition, we provide a rigorous mathematical derivation of the slow diffusion approximation for the spin-bearing particles that is used in this regime. We further show that, in analogy to the local magnetization, the transverse magnetization of one MR imaging voxel in the regime of static dephasing (where diffusion effects are not considered) is merely the first term of a series expansion that constitutes the signal in the slow diffusion approximation. Theoretical results are in agreement with experimental data for capillaries in rat muscle at 7T.
authors: Heidelberg University Hospital, INF 400, D-69120 Heidelberg, Germany; German Cancer Research Center, INF 280, D-69120 Heidelberg, Germany. Electronic address: felix.kurz@med.uni-heidelberg.de.
authors: F T
authors: FT
authors: Kurz
authors: German Cancer Research Center, INF 280, D-69120 Heidelberg, Germany.
authors: L R
authors: LR
authors: Buschle
authors: University of Würzburg, Am Hubland, D-97074 Würzburg, Germany.
authors: T
authors: T
authors: Kampf
authors: German Cancer Research Center, INF 280, D-69120 Heidelberg, Germany.
authors: K
authors: K
authors: Zhang
authors: German Cancer Research Center, INF 280, D-69120 Heidelberg, Germany.
authors: H P
authors: HP
authors: Schlemmer
authors: Heidelberg University Hospital, INF 400, D-69120 Heidelberg, Germany.
authors: S
authors: S
authors: Heiland
authors: Heidelberg University Hospital, INF 400, D-69120 Heidelberg, Germany.
authors: M
authors: M
authors: Bendszus
authors: Heidelberg University Hospital, INF 400, D-69120 Heidelberg, Germany; German Cancer Research Center, INF 280, D-69120 Heidelberg, Germany.
authors: C H
authors: CH
authors: Ziener
mesh_terms: D000818:Animals; D002196:Capillaries / Q000000981:diagnostic imaging*; D004058:Diffusion; D060526:Magnetic Fields; D008279:Magnetic Resonance Imaging; D018482:Muscle, Skeletal / Q000098:blood supply*; D051381:Rats
keywords: Diffusion dephasing; Modeling of MR signal; Static dephasing; Susceptibility contrast; Transverse relaxation