MRI edge enhancement as a diffusive discord of spin phase structure

The enhancement of magnetic resonance image intensity near impermeable boundaries can be nicely described by a new approach where the diffusional spin echo attenuation is linked to the correlation function of molecular motion. In this method the spin phase structure created by the applied gradient is considered to be a composition of plane waves with the wave vectors representing feasible momentum states of a particle in confinement. The enhancement of edges on the magnetic resonance images (MRI) comes out as a discord of plane waves due to particle motion. It results from the average of the wave phase by using the cumulant expansion in the Gaussian approximation. The acquired analytical expression describes the MRI signal space distribution where the enhancement of edges depends on the intensity and the duration of gradient sequence as well as on the length of the mean squared particle displacement in restricted geometry. This new method works well with gradients of general waveform and is, therefore, suitable for imaging sequences where finite or even modulated gradients are usually used.