Determining the form of RF pulses for selective excitation in magnetic resonance imaging

摘要

The invention relates to a magnetic resonance method involving the generation of high-frequency pulses and magnetic gradients (gx, gy, gz) for the selective excitation of an object to be examined. According to the invention, the magnetic resonance method is characterized in that a magnetic resonance signal s(t) according to the following signal equation is generated:;s⁡(t)=∫V⁢m(rr,T)⁢exp⁡[t⁢/⁢T2]⁢exp⁡[ⅈ⁢⁢t⁢⁢ωs]⁢exp⁡[-ⅈ⁢⁢kr⁡(T-t)·rr]⁢⁢ⅆ3⁢r
wherein stands for a desired transversal magnetization after the selective excitation, t stands for a time, {right arrow over (r)} stands for a position vector and T stands for a duration of a pulse, and whereby s(t) stands for a magnetic resonance signal, V stands for a volume that is to be examined, T2 stands for a transversal relaxation time, and ωs stands for a shift of the resonance frequency. The invention also relates to a nuclear spin tomograph for carrying out the magnetic resonance method.

主权项

1. A magnetic resonance method involving the generation of high-frequency pulses and magnetic gradients (gx, gy, gz) for the selective excitation of an object that is to be examined, whereby the magnetic resonance method comprises the following steps:
providing a transversal magnetization m({right arrow over (r)}, T) which is described bym(r->,T)=ⅈγ⁢⁢m0⁢exp⁡[-T⁢/⁢T2]⁢exp⁡[-ⅈ⁢⁢T⁢⁢ωs]⁢∫0T⁢exp⁡[t⁢/⁢T2]⁢exp⁡[ⅈ⁢⁢t⁢⁢ωs]⁢b1⁡(t)⁢exp[ⅈ⁢⁢k->⁡(t)·r->]⁢⁢ⅆtwherein i stands for an imaginary unit, γ stands for a gyromagnetic ratio, m0 stands for an equilibrium magnetization, t stands for a time, {right arrow over (r)}; stands for a position vector and T stands for a duration of a pulse, T2 stands for a transversal relaxation time, ωs stands for a shift of the resonance frequency, b1(t) stands for a high-frequency pulse, and {right arrow over (k)}(t) stands for a vector of the k-space trajectory that is given by the magnetic gradients,
determining the high-frequency pulse by means of a signal equation s(t) according to:s⁡(t)=∫V⁢m(r->,T)⁢exp⁡[t⁢/⁢T2]⁢exp⁡[ⅈ⁢⁢t⁢⁢ωs]⁢exp⁡[-ⅈ⁢⁢k->⁡(T-t)·r->]⁢⁢ⅆ3⁢rwherein V stands for a volume that is to be examined, so that, except for factors, the high-frequency pulse is obtained as:b1⁡(t)=J⁡(t)ⅈγ⁢⁢m0⁢s⁡(T-t)wherein J(t) is a Jacobi determinant that, under the premise of the bijectivity of k(t) onto a value range of t, yields the dependence of the coordinate transformation between the time parameterization and the k-space parameterization,
using the high-frequency pulse to excite the volume that is to be examined, detecting the measured signal generated by the high-frequency pulse in the volume that is to be examined, and evaluating the measured signal.