A General Solution for Transverse Signal Decay Under the Weak Field Approximation: Theory and Validation with Spherical Perturbers
Avery J.L. Berman1,2 and Bruce Pike2
1Montreal Neurological Institute, McGill University, Montreal, QC, Canada, 2Department of Radiology and Hotchkiss Brain Institute, University of Calgary, Calgary, AB, Canada
This study presents a closed-form analytical
solution that describes transverse signal relaxation using the weak field
approximation (WFA). The closed-form solution (CFS) fully describes the net
signal dynamics under any train of 180° refocusing pulses, and we show that it
is in close agreement with a commonly employed mono-exponential expression of
the WFA. We compared the CFS to simulations from a medium containing spherical
perturbers, with a focus on modelling red blood cells. The CFS and simulations
were in close agreement but the results systematically varied depending on
whether or not the spheres were allowed to overlap. This theory can be
applied in areas such as tissue iron imaging or relaxometry of blood.
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