Rapid method of optimal gradient waveform design for MRI

• US 6,020,739 A
• Filed: 04/25/1997
• Issued: 02/01/2000
• Est. Priority Date: 04/25/1997
• Status: Expired due to Term

• Current Assignee: Board of Trustees of the Leland Stanford Junior University (Stanford Management Co.)
• Original Assignee: Board of Trustees of the Leland Stanford Junior University (Stanford Management Co.)
• Inventors: Meyer, Craig H., Pauly, John M.
• Primary Examiner(s): Oda, Christine K.
• Assistant Examiner(s): Shrivastav, Brij B.
• Application Number:
  US08/845,343
• Time in Patent Office: 1,012 Days
• Field of Search: 324/309, 324/307, 324/300, 324/310, 324/311, 324/312, 324/313, 324/314, 324/318, 324/322
• US Class Current: 324/309
• CPC Class Codes: G01R 33/4824 using a non-Cartesian trajectory

Abstract

Spiral gradient design for a k-space trajectory using gradient amplifier parameters includes first determining an angle between a given gradient, g_n, and the next gradient, g_n+1, and then determining the magnitude of |g_n+1 | based on gradient constraints represented by a circle or other shape surrounding and offset from the distal end of g_n, where g_n+1 extends along <g_n+1 to the farthest intersection thereof with the circle.

Claims

1. A method of spiral gradient design for a k-space trajectory in magnetic resonance imaging, k(τ

)=Aπ

eⁱω

t where τ and

ω

can be functions of time, and where a discrete-time gradient waveform is g_n, comprising the steps of;

a) determining the angle between a given gradient sample g_n and the next gradient sample g_n+1, and

b) determining the magnitude of |g_n+1 | using permissible change based on constraints of the magnetic resonance imaging system.

2. A method of spiral gradient design for a k-space trajectory in magnetic resonance imaging, k(τ

)=Aτ

eⁱω

τ

where τ and

ω

can be functions of time and where a discrete-time gradient waveform is g_n and the discrete-time k_n ==Σ

ⁿ_i=o g_i, assuming a series inductor-resistor (LR) gradient circuit model and using the gradient circuit parameters ##EQU5## the steady-state gradient amplitude with a maximum voltage V applied, and ##EQU6## the maximum step in gradient amplitude possible starting from an amplitude of zero, said method comprising the steps of;

a) determining the angle,∠

, between a given gradient sample g_n and the next gradient sample g_n+1 by evaluating the first derivative of k(τ

) at the current value of τ and

obtaining ##EQU7## b) determining the magnitude of |g_n+1 | based on gradient constraints represented by a circle of radius, S ##EQU8## surrounding and offset from the distal end of g_n, where |g_n+1 | extends along ∠

g_n+1 to the farthest intersection thereof with said circle.

3. The method as defined by claim 2 wherein an offset of the circle from the distal end of g_n is due to voltage drop across the resistor, R, in the gradient circuit model.

4. The method as defined by claim 2 wherein the gradient circuit model is a constant voltage design with the center of the circle offset from the tip of g_n.

5. The method as defined by claim 4 wherein ##EQU9## Δ

θ

=angle between g_n and g_n+1.

6. A method of spiral gradient design for a k-space trajectory in magnetic resonance imaging, k(τ

)=Aτ

eⁱω

τ

where τ and

ω

can be functions of time and where a discrete-time gradient waveform is g_n and the discrete-time k_n =Σ

ⁿ_i=0 g_i, assuming a gradient model with a maximum slew rate and a maximum gradient amplitude, said method comprising the steps of;

a) determining the angle, ∠

, between a given gradient sample g_n and the next gradient sample g_n+1 by evaluating the first derivative of k(τ

) at the current value of τ and

obtaining ##EQU10## b) determining the magnitude of |g_n+1 | based on gradient constraints represented by a maximum slew rate, S, and a maximum gradient amplitude, G, where S is the radius of a circle centered at the distal end of g_n.

7. The method as defined by claim 6 wherein the gradient circuit model is constant-slew design with the center of the circle at the tip of g_n.

8. The method as defined by claim 7 wherein ##EQU11## Δ

θ

=angle between g_n and g_n+1.