An improved method for susceptibility and radius quantification of cylindrical objects from MRI

A new method is developed to measure the magnetic susceptibilities and radii of small cylinder-like objects at arbitrary orientations accurately. This method for most biological substances only requires a standard gradient echo sequence with one or two echo times, depending on the orientation of an object relative to the main magnetic field. For objects oriented at the magic angle, however, this method is not applicable. As a byproduct of this method, the cross-sectional area as well as signals inside and outside the object can be determined. The uncertainty of each measurement is estimated from the error propagation method. Partial volume, dephasing, and phase aliasing effects are naturally included in the equations of this method. A number of simulations, phantom, and pilot in-vivo human studies are carried out to validate the theory. When the maximal phase value at the boundary of a given cylindrical object is larger than 3 radians, and the phase inside the object is more than 1 radian, the susceptibility can be accurately quantified within 15%. The radius of the object can be determined to subpixel accuracy. This is the case when the signal-to-noise ratio inside the object is about 6:1 or higher and the radius of the object is about one pixel or larger. These conditions are realistic when considering medullary and pial veins for example.