Diffusion-weighted MRI using multiple b-values and constant echo time

1. A method for acquiring diffusion-weighted images, the method comprising:

selecting a first set of diffusion gradient vectors, each of diffusion gradient vectors in the first set having a constant gradient strength and corresponding to a first non-zero b-value, wherein the directions of the diffusion gradient vectors in the first set are distributed on a surface of a first sphere having a first radius;

defining a cube of constant echo image time (TE) that encloses the first sphere, wherein the cube of constant TE comprises faces and edges, and a volume inside the cube of constant TE defines a volume within which any diffusion gradient vector located therein can be applied without increasing TE; and

selecting a second set of diffusion gradient vectors, each of the diffusion gradient vectors in the second set being located within the cube of constant TE, wherein at least one of the diffusion gradient vectors in the second set corresponds to a second non-zero b-value different from the first non-zero b-value,

wherein at least one diffusion gradient vector in the second set extends to a face of the cube of constant TE without also extending to an edge of the cube of constant TE, and/or at least one diffusion gradient vector in the second set extends to a point within the cube of constant TE without extending to a face or an edge of the cube of constant TE; and

acquiring the diffusion-weighted images using a gradient encoding scheme including the gradients corresponding to each of the diffusion gradient vectors in the first and second sets.

2. The method of claim 1 , wherein each of the diffusion gradient vectors in the second set extends to one of the faces of the cube of constant TE.

3. The method of claim 1 , wherein each of the diffusion gradient vectors in the second set extends to a point within the cube of constant TE without extending to a face or an edge of the cube of constant TE.

4. The method of claim 1 , wherein the diffusion gradient vectors in the first set of diffusion gradient vectors are uniformly distributed on the surface of the first sphere.

5. The method of claim 1 , wherein selecting the second set of diffusion gradient vectors comprises:

defining a second sphere having a second radius larger than the first radius;

specifying a plurality of diffusion gradient vectors having directions distributed on a surface of the second sphere;

projecting each of the diffusion gradient vectors having directions distributed on the surface of the second sphere to a face or an edge of the cube of constant TE; and

including the projected diffusion gradient vectors in the second set.

6. The method of claim 5 , wherein selecting the second set of diffusion gradient values comprises: defining a third sphere having a third radius smaller than the first radius; and

including in the second set, a plurality of diffusion gradient vectors having directions distributed on a surface of the third sphere.

7. The method of claim 6 , wherein the first radius, the second radius, and the third radius are uniformly spaced.

8. The method of claim 6 , wherein the first radius, the second radius, and the third radius are exponentially spaced.

9. The method of claim 5 , wherein the second non-zero b-value is determined by multiplying the first non-zero b-value by a first value, and wherein defining the second sphere comprises defining the second sphere based, at least in part, on the second non-zero b-value.

10. The method of claim 1 , wherein the first non-zero b-value is in the range 800 s/mm 2 to 1200 s/mm 2 .

11. The method of claim 1 , wherein the second non-zero b-value is in the range 2000 s/mm 2 to 4000 s/mm 2 .

12. The method of claim 1 , wherein at least one first diffusion gradient vector in the second set extends to a face of the cube of constant TE without also extending to an edge of the cube of constant TE and at least one second diffusion gradient vector in the second set extends to a point within the cube of constant TE without extending to a face or an edge of the cube of constant TE.

13. A magnetic resonance imaging (MRI) apparatus, comprising:

a main magnetic field coil;

a plurality of gradient magnetic field coils; and

at least one computer processor programmed with a plurality of instructions that, when executed by the at least one computer processor, perform a method of operating the MRI apparatus to acquire diffusion-weighted images, the method comprising:

selecting a first set of diffusion gradient vectors, each of diffusion gradient vectors in the first set having a constant gradient strength and corresponding to a first non-zero b-value, wherein the directions of the diffusion gradient vectors in the first set are distributed on a surface of a first sphere having a first radius;

defining a cube of constant echo image time (TE) that encloses the first sphere, wherein the cube of constant TE comprises faces and edges, and a volume inside the cube of constant TE defines a volume within which any diffusion gradient vector located therein can be applied without increasing TE; and

selecting a second set of diffusion gradient vectors, each of the diffusion gradient vectors in the second set being located within the cube of constant TE, wherein at least one of the diffusion gradient vectors in the second set corresponds to a second non-zero b-value different from the first non-zero b-value,

wherein at least one diffusion gradient vector in the second set extends to a face of the cube of constant TE without also extending to an edge of the cube of constant TE, and/or at least one diffusion gradient vector in the second set extends to a point within the cube of constant TE without extending to a face or an edge of the cube of constant TE; and

acquiring the diffusion-weighted images using a gradient encoding scheme including the gradients corresponding to each of the diffusion gradient vectors in the first and second sets.

14. The magnetic resonance apparatus of claim 13 , wherein at least one first diffusion gradient vector in the second set extends to a face of the cube of constant TE without also extending to an edge of the cube of constant TE and at least one second diffusion gradient vector in the second set extends to a point within the cube of constant TE without extending to a face or an edge of the cube of constant TE.

15. The magnetic resonance apparatus of claim 13 , wherein each of the diffusion gradient vectors in the second set extends to one of the faces of the cube of constant TE without also extending to and edge of the cube of constant TE.

16. The magnetic resonance apparatus of claim 13 , wherein each of the diffusion gradient vectors in the second set extends to a point within the cube of constant TE without extending to a face or an edge of the cube of constant TE.

17. The magnetic resonance apparatus of claim 13 , wherein the diffusion gradient vectors in the first set are uniformly distributed on the surface of the first sphere.

18. The magnetic resonance apparatus of claim 13 , wherein selecting the second set of diffusion gradient vectors comprises:

defining a second sphere having a second radius larger than the first radius;

specifying a plurality of diffusion gradient vectors having directions distributed on a surface of the second sphere;

projecting each of the diffusion gradient vectors having axial directions distributed on the surface of the second sphere to a face or an edge of the cube of constant TE; and

including the projected diffusion gradient vectors in the second set.

19. The magnetic resonance apparatus of claim 18 , wherein selecting the second set of diffusion gradient values comprises:

defining a third sphere having a third radius smaller than the first radius and the second radius; and

including in the second set, a plurality of diffusion gradient vectors having axial directions distributed on a surface of the third sphere.

20. The magnetic resonance apparatus of claim 18 , wherein the second non-zero b-value is determined by multiplying the first non-zero b-value by a first value, and wherein defining the second sphere comprises defining the second sphere based, at least in part, on the second non-zero b-value.