Magnetic resonance imaging concepts

1. A method of acquiring time-resolved, three-dimensional, gradient echo magnetic resonance imaging data from a tissue, the method comprising:

(a) defining, in a k x -k y plane in k-space, a set of interleaved spiral trajectories, the number of spiral trajectories S being equal to n times m where n and m are positive integers, such that each spiral trajectory is associated with a distinct azimuthal angle in the k x -k y plane and the distinct azimuthal angles are spaced about a range of 360 degrees and there are n groups of m different spiral trajectories;

(b) defining an ordered plurality of distinct k z values along an axis perpendicular to the k x -k y plane in k-space, where the number of k z values defined is N z ;

(c) for a first spiral trajectory in a first group of m different spiral trajectories associated with the first azimuthal angle, applying a radiofrequency pulse to the tissue and collecting k-space data sampled along the first spiral trajectory at a first of the plurality of k z values;

(d) repeating step (c) N z repetitions, once at each of the plurality of distinct k z values;

(e) repeating step (d) for each remaining spiral trajectory in the first group of m different spiral trajectories and associating the data collected in steps (c)-(d) with a first of a plurality of n different times; and

(f) repeating steps (c)-(e) for each of the n different groups of m spiral trajectories, thereby collecting data associated with n different times, respectively, and collecting data associated with all S spiral trajectories;

wherein the data is sampled along the spiral trajectories so that the data is oversampled with constant density at the center of k-space and undersampled with variable density at the edge of k-space.

2. The method of claim 1 wherein:

the distinct azimuthal angles are evenly spaced about a range of 360 degrees in increments of 360/S degrees of azimuth;

the group of m spiral trajectories in step (e) are evenly spaced in increments of (360/S)*m degrees of azimuth;

in step (f), the group of m spiral trajectories in each repetition of step (e) are spaced from the group of m spiral trajectories in the previous repetition of step (e) by an increment of 360/S degrees of azimuth; and

the plurality of times associated with the repetitions of steps (c) and (d) are evenly spaced in time.

3. The method of claim 1 further comprising:

(g) associating the data collected in step (f) with a first image frame; and

(h) repeating step (e) for the first group of m spiral trajectories;

(i) associating the data collected in step (h) and data collected in the previous n−1 repetitions of step (e) with a second image frame.

4. The method of claim 1 further comprising:

(j) carrying out step (f) prior to the introduction of a contrast agent into the tissue thereby forming a background mask;

(k) repeating step (f) after the arrival of contrast agent in the tissue;

(l) subtracting the background mask from the data collected in step (k).

5. The method of claim 1 wherein the magnetic resonance imaging data is spoiled gradient echo contrast-enhanced, magnetic resonance angiography data.

6. The method of claim 1 wherein all the data is collected using the echo time.

7. The method of claim 1 further comprising:

(m) generating an image from the data collected in step (f).

8. The method of claim 7 wherein step (m) further comprises off-resonance correction.

9. The method of claim 1 , wherein the center of k-space is 30% oversampled.

10. The method of claim 9 , wherein the edge of k-space is 30% undersampled.

11. The method of claim 1 , wherein each spiral trajectory has a radius at the center of k space that increases linearly with azimuth angle, so that sampling at the center of k space has constant density.

12. The method of claim 11 , wherein the radius at the edge of k space increases quadratically with azimuth angle.

13. The method of claim 1 , wherein the radius at the edge of k space increases quadratically with azimuth angle.