Patent ID: 7548062

Claim:
A method of performing a three dimensional magnetic resonance imaging (MRI), comprising: using sampling requirements to define a three dimensional cone trajectory differential equation; solving the three dimensional cone differential equation to obtain a three dimensional cone trajectory starting from a curvature starting point spaced apart from an origin; performing a search for a border success by performing a plurality of cycles, comprising: selecting a point on the three dimensional cone trajectory after the curvature starting point; working backward from the curvature starting point to reduce twist; providing a failure value if it is determined that when the twist reaches zero it is not possible to return to the origin at a final velocity of zero while meeting system constraints; and providing a success value if it is determined that when the twist reaches zero it is possible to return to the origin at a final velocity of zero while meeting system constraints; performing a plurality of cycles, wherein each cycle comprises: applying a magnetic resonance image excitation; and scanning along the calculated three dimensional cone trajectory and acquiring a readout; producing a three dimensional image from the readout of the plurality of cycles.