Magnetic resonance method and system for quantification of anisotropic diffusion

• US 7,078,897 B2
• Filed: 01/15/2003
• Issued: 07/18/2006
• Est. Priority Date: 01/16/2002
• Status: Active Grant

• Current Assignee: Washington University In St Louis
• Original Assignee: Washington University In St Louis
• Inventors: Yablonskiy, Dmitriy A., Conradi, Mark S., Sukstanskii, Alexander L.
• Primary Examiner(s): Bennett, G. Bradley
• Assistant Examiner(s): COURSON, TANIA C
• Application Number:
  US10/345,010
• Publication Number:
  US 20030160612A1
• Time in Patent Office: 1,280 Days
• Field of Search: 324/307, 324/309, 324/306
• US Class Current: 324/307
• CPC Class Codes: G01R 33/56341 Diffusion imaging

Abstract

An MR method and system of determining elements of the apparent diffusion coefficient tensor in a material with plurality of anisotropic structural units that can be too small to be resolved by direct imaging. MR data is acquired with MR system including pulse sequences, the sequences including imaging or spectroscopy pulse sequences with a series of embedded diffusion-sensitizing gradient waveforms with different gradient strength applied to the material. A nonlinear function of a b-value corresponding to the pulse sequence is defined and the acquired MR data is processed according to defined nonlinear function. Images/maps of the components of the tensor of apparent diffusion coefficients, corresponding to anisotropic structural units, based on the processed MR data, are created. A method of evaluating of the geometrical parameters of lung airways is also described.

Claims

1. A method of acquiring MR images of a subject, wherein each voxel of interest in the subject being imaged contains a plurality of anisotropic structural units that are too small to be resolved by direct imaging of the voxels using an MRI system, said method comprising the steps of:

a. generating MR pulse sequences via the MRI system that generate MR data corresponding to the subject'"'"'s plurality of anisotropic structural units, wherein the sequences include MR imaging or spectroscopy pulse sequences with a series of embedded diffusion-sensitizing gradient waveforms of varying gradient strength that are each characterized by a respective b-value within the individual sequences;

b. acquiring the MR data for each b-value;

c. defining a nonlinear function of the b-value;

d. defining imaging units;

e. fitting the acquired MR data for each of the imaging units containing a plurality of anisotropic structural units to the nonlinear function and thereby determining elements of an apparent diffusion coefficient with respect to each of said plurality of anisotropic structural units in at least one selected direction in the local coordinate system associated with a given one of said anisotropic structural units; and

f. creating MR images based on the elements of the apparent diffusion coefficient in the at least one selected direction in the local coordinate system associated with a given one of said anisotropic structural units contained within the subject being imaged.

2. The method of claim 1 further comprising the step of conducting a diagnostic evaluation of geometrical parameters of the subject'"'"'s plurality of anisotropic structural units based on the acquired MR data.

3. The method of claim 1 wherein the MR pulse sequences include at least one of a spin echo pulse sequence, a gradient echo pulse sequence, and a spectroscopy pulse sequence, applied to the subject being imaged as at least one of a two-dimensional multi-slice multi-gradient pulse sequence, a three-dimensional multi-gradient pulse sequence, and a spectroscopy pulse sequence.

4. The method of claim 1 wherein each b-value is determined by a time-dependent field gradient waveform G(t) such that,

$b={\gamma }^{}$

2 ⁢

∫

0 t ⁢

⁢

ⅆ

t 1 ⁡

[ ∫

0 t 1 ⁢

⁢

ⅆ

t 2 ⁢

G ⁡

( t 2 ) ] 2 ,

where γ

is the gyromagnetic ratio and t is time.

5. The method of claim 1 wherein each of the diffusion-sensitizing gradient waveforms of varying gradient strength comprises a trapezoidal gradient waveform and wherein a general expression for each b-value is

$b={({\gamma }_{}}^{}$

G m ) 2 ⁡

[ δ

2 ⁡

( Δ

- δ

3 ) + τ

⁡

( δ

2 - 2 ⁢

Δ

δ

+ Δ

τ

- 7 6 ⁢

δ

τ

+ 8 15 ⁢

τ

2 ) ] ,

where G_m is the amplitude of the gradient, Δ

is a diffusion time, δ

is a pulse width, and τ

is a gradient ramp up and ramp down time.

6. The method of claim 1 wherein the nonlinear function of the b-value, designated F(b), defines MR signal attenuation in the presence of said diffusion-sensitizing gradients such that

$F$

( b ) = ∫

λ

⁢

⁢

ⅆ

λ

⁢

⁢

p ⁡

( λ

) ⁢

∫

0 π

⁢

sin ⁢

⁢

θ

d ⁢

⁢

θ

⁢

∫

0 2 ⁢

π

⁢

ⅆ

φ

⁢

⁢

P λ

⁡

( θ

, φ

) ⁢

exp ⁢

{ - b ⁡

[ D z ⁡

( λ

, b ) ⁢

cos 2 ⁢

θ

+ sin 2 ⁢

θ

⁡

( D x ⁡

( λ

, b ) ⁢

cos 2 ⁢

φ

+ D y ⁡

( λ

, b ) ⁢

sin 2 ⁢

φ

) ] }

where P_λ

(θ

, φ

) is a distribution function of the orientation of a given subset of the subject'"'"'s plurality of anisotropic structural units within each of said imaging units, characterized by the same parameter λ

;

where p(λ

) is a distribution function of the geometrical parameters of the subject'"'"'s plurality of anisotropic structural units within each of said imaging units; and

where D_x, D_y, D_z are the diagonal elements of the tensor of the apparent diffusion coefficients, characteristic to a given structural unit of the subject'"'"'s plurality of anisotropic structural units, in the local coordinate system associated with a given one of said structural units.

7. The method of claim 1 wherein the nonlinear function of the b-value, designated F(b), for a material having homogeneous orientation distribution of the subject'"'"'s plurality of anisotropic structural units is reduced to

$F$

( b ) = ∫

λ

⁢

⁢

ⅆ

λ

⁢

⁢

p ⁡

( λ

) ⁢

exp ⁡

( - bD AV ) ⁢

exp ⁡

( bD AN 3 ) . 1 4 ⁢

π

⁢

∫

0 2 ⁢

π

⁢

ⅆ

φ

exp ⁡

( - bD AN ⁢

cos 2 ⁢

φ

) ⁢

Φ

⁡

[ ( bD AN - bd AN ⁢

cos ⁢

⁢

2 ⁢

φ

) 1 / 2 ] ( bD AN - bd AN ⁢

cos ⁢

⁢

2 ⁢

φ

) 1 / 2

where Φ

is the error function,

D_AV=⅓

(D_x+D_y+D_z) is the anisotropic structural unit mean diffusivity,

d_AN=½

(D_x+D_y) is the anisotropic structural unit in-plane anisotropy difflisivity, and

D_AN=D_z−

½

(D_x+D_y) is the anisotropic structural unit out-of-plane anisotropy diffusivity.

8. The method of claim 1 further comprising reducing the nonlinear function of the b-value, designated F(b), for materials including similar anisotropic structural units of uniaxial anisotropy (D_x=D_y) to:

$F<br><br>\left(b\right)=\exp <br><br>\left(-{\mathrm{bD}}_{\mathrm{AV}}\right)<br><br>\frac{\sqrt{\mathrm{\pi <br><br>}}}{2}<br><br>\exp <br><br>\left(\frac{{\mathrm{bD}}_{\mathrm{AN}}}{3}\right)·<br><br>\frac{\mathrm{\Phi <br><br>}<br><br>\left(\sqrt{{\mathrm{dD}}_{\mathrm{AN}}}\right)}{\sqrt{{\mathrm{bD}}_{\mathrm{AN}}}}$

where Φ

is the error function,

D_AV=⅓

(D_x+D_y+D_z) is the anisotropic structural unit mean diffusivity, and

D_AN=D_z−

½

(D_x+D_y) is the anisotropic structural unit out-of-plane anisotropy diffusivity.

9. The method of claim 1 wherein the step of creating MR images based on the elements of the apparent diffusion coefficient comprises the steps of creating an MR image corresponding to an anisotropic structural unit mean diffusivity D_AV(x, y, z) based on the fitted acquired MR data, creating an image corresponding to an out-of-plane anisotropy diffusivity D_AN(x, y, z) based on the fitted acquired MR data, and creating an image corresponding to an in-plane anisotropy diffusivity d_AN(x, y, z) based on the fitted acquired MR data.

10. The method of claim 1 wherein each voxel of interest in the subject contains anisotropic structural units comprising a gas in small airways such as the small airways in the lungs of humans and animals that are too small to be resolved by direct MR imaging of the voxels using the MRI system.

11. A method as in claim 1 including further processing the MR data and thereby deriving estimates of dimensions of each of said anisotropic structural units in at least one selected direction.

12. A method as in claim 11 in which the at least one selected direction includes a direction perpendicular to the length of elongated structural units.

13. A method as in claim 11 in which the at least one selected direction includes a direction parallel to the length of elongated structural units.

14. An MRI apparatus acquiring MR images of a material, wherein each voxel of interest within the material contains a plurality of anisotropic structural units that are too small to be resolved by direct imaging of the material'"'"'s voxels using the MRI apparatus, comprising:

a. a magnetic resonance imaging system having a magnetic assembly including a magnet impressing a polarizing magnetic field on the material, a plurality of gradient coils positioned about the material impressing an inhomogeneous magnetic field on the material, a RF transceiver system having an RF coil assembly, and an RF switch controlling the RF transceiver system in order to transmit and receive RF signals to and from the material and acquire MR data from the material;

b. said gradient coils and RF transceiver system selectively applying to the subject MR pulse sequences including MR imaging pulse sequences or spectroscopy pulse sequences with a series of embedded diffusion-sensitizing gradient waveforms of varying gradient strength that are each characterized by a respective b-value within the individual sequences;

c. said RF transceiver system acquiring MR data corresponding to each b-value;

d. a processor containing information defining imaging units and defining a non-linear function of the b-values;

e. said processor being coupled with the RF transceiver system and receiving the MR data acquired thereby and fitting the acquired MR data corresponding to each of the imaging units for the material'"'"'s plurality of anisotropic structural units to the nonlinear function and thereby determining elements of an apparent diffusion coefficient with respect to each of said structural units in at least one selected direction related to an orientation of each of said anisotropic structural units; and

f. said processor further creating MR images of the material based on the elements of the apparent diffusion coefficient in the at least one selected direction related to an orientation of each of said anisotropic structural units contained within the material; and

g. a display coupled to the processor and selectively receiving the created MR images and selectively displaying the received MR images of the apparent diffusion coefficient in the at least one selected direction related to an orientation of each of said anisotropic structural units contained within the material.

15. The apparatus of claim 14 further comprising:

a digitizer coupled with the RF transceiver system and digitizing the RF signals received by the RF coil assembly; and

a memory module coupled with the digitizer and storing the digitized MR signals in an array of raw k-space data; and

said processor rearranging the raw k-space data into separate k-space data arrays for each of the MR images, processing each of the separate k-space data arrays and thereby creating said MR images.

16. The apparatus of claim 14 wherein each voxel of interest within the material comprises a gas in small airways such as the small airways within the lungs of humans and animals that are too small to be resolved by direct imaging of the voxels by the MRI apparatus.

17. A system acquiring MR images of a subject, wherein each voxel of interest in the subject contains a plurality of anisotropic structural units that are too small to be resolved by direct imaging of the voxels with the system, comprising:

a. an MR pulse sequence generator generating a series of MR pulse sequences including MR imaging pulse sequences or spectroscopy pulse sequences, said pulse sequences including embedded diffusion-sensitizing gradients of varying gradient strength, said diffusion-sensitizing gradient being characterized by a parameter that is different for different ones of said MR pulse sequences;

b. an MR data acquisition system acquiring MR data from the subject generated in response to said MR pulse sequences, said MR data acquisition system including a memory storing the acquired MR data;

c. a processor containing information defining imaging units and defining a non-linear function of the parameter characterizing the diffusion-sensitizing gradients;

d. said processor being coupled with the MR data acquisition system and receiving the MR data acquired thereby and fitting the acquired MR data that corresponds to each of the imaging units to the nonlinear function and thereby determining elements of an apparent diffusion coefficient with respect to each of the anisotropic structural units in at least one selected direction related to an orientation of each of said anisotropic structural units; and

e. said processor reconstructing MR images of the subject based on the elements of the apparent diffusion coefficient in the at least one selected direction related to an orientation of each of said anisotropic structural units contained within the subject; and

f. a display coupled to the processor and selectively receiving the created MR images and selectively displaying the received MR images of the apparent diffusion coefficient in the at least one selected direction related to an orientation of each of said anisotropic structural units contained within the subject.

18. The system of claim 17 wherein the MR pulse sequences include at least one of a two-dimensional multi-slice multi-gradient pulse sequence, a three-dimensional multi-gradient pulse sequence, and a spectroscopy pulse sequence.

19. The system of claim 17 wherein the parameter of the diffusion-sensitizing gradients is a b-value, the non-linear function is a nonlinear function of a b-value, and the b-value is determined by a field gradient waveform G(t) such that,

$b={\gamma }^{}$

2 ⁢

∫

0 t ⁢

ⅆ

t 1 ⁡

[ ∫

0 t i ⁢

ⅆ

t 2 ⁢

G ⁡

( t 2 ) ] 2 ,

where γ

is the gyromagnetic ratio and t is time.

20. The system of claim 17 wherein the diffusion-sensitizing gradients comprise a trapezoidal gradient waveform and wherein a general expression for the b-value is

$b={(\gamma }^{}$

⁢

⁢

G m ) 2 ⁡

[ δ

2 ⁡

( Δ

- δ

3 ) + τ

⁡

( δ

2 - 2 ⁢

Δ

δ

+ Δ

τ

- 7 6 ⁢

δ

τ

+ 8 15 ⁢

τ

2 ) ] ,

where G_m is the amplitude of the gradient, Δ

is a diffusion time, δ

is a pulse width, and τ

is a gradient ramp up and ramp down time.

21. The system of claim 17 wherein the nonlinear function is designated F(b) and defines MR signal attenuation in the presence of said diffusion-sensitizing gradients such that

$\begin{array}{c}F\end{array}$

( b ) = ∫

λ

⁢

ⅆ

λ

⁢

⁢

p ⁡

( λ

) ⁢

∫

0 π

⁢

sin ⁢

⁢

θ

⁢

ⅆ

θ

⁢

∫

0 2 ⁢

π

⁢

ⅆ

φ

⁢

⁢

P λ

⁡

( θ

, φ

) ⁢

exp ⁢

{ - b ⁡

[ D z ⁡

( λ

, b ) ⁢

cos 2 ⁢

θ

+ sin 2 ⁢

θ

⁡

( D x ⁡

( λ

, b ) ⁢

cos 2 ⁢

φ

+ D y ⁡

( λ

, b ) ⁢

sin 2 ⁢

φ

) ] }

where P_λ

(θ

, φ

) is a distribution function of the orientation of a given subset of the subject'"'"'s plurality of anisotropic structural units within each of said imaging units, characterized by the same parameter λ

;

where p(λ

) is a distribution function of the geometrical parameters of the subject'"'"'s plurality of anisotropic structural units within each of said imaging units; and

where D_x, D_y, D_x are the diagonal elements of the tensor of the apparent diffusion coefficients in the local coordinate system associated with a given one of said anisotropic structural units in the subject.

22. The system of claim 17 wherein the nonlinear function is designated F(b) for a subject having homogeneous orientation distribution of the subject'"'"'s structural units is reduced to

$F$

( b ) = ∫

λ

⁢

ⅆ

λ

⁢

⁢

p ⁡

( λ

) ⁢

exp ⁡

( - bD AV ) ⁢

exp ⁡

( bD AN 3 ) ·

·

1 4 ⁢

π

⁢

∫

0 2 ⁢

π

⁢

ⅆ

φ

exp ⁡

( - bD AN ⁢

cos 2 ⁢

φ

) ⁢

Φ

⁡

[ ( bD AN - bd AN ⁢

⁢

cos ⁢

⁢

2 ⁢

⁢

φ

) 1 / 2 ] ( bD AN - bd AN ⁢

cos ⁢

⁢

2 ⁢

φ

) 1 / 2

where Φ

is the error function,

$\begin{array}{c}{D}_{\mathrm{AV}}=<br><br>\frac{1}{3}<br><br>\left(D_x=D_y+D_z\right)<br><br><br><br>\mathrm{is}<br><br><br><br>\mathrm{the}<br><br><br><br>\mathrm{anisotropic}<br><br><br><br>\mathrm{structural}<br><br><br><br>\mathrm{unit}\\ <br><br>\mathrm{mean}<br><br><br><br>\mathrm{diffusivity},\\ d_{\mathrm{AN}}=<br><br>\frac{1}{2}<br><br>\left(D_x-D_y\right)<br><br><br><br>\mathrm{is}<br><br><br><br>\mathrm{the}<br><br><br><br>\mathrm{anisoptropic}<br><br><br><br>\mathrm{structural}<br><br><br><br>\mathrm{unit}\\ <br><br>\mathrm{in}<br><br>\text{-}<br><br>\mathrm{plane}<br><br><br><br>\mathrm{anisotropy}<br><br><br><br>\mathrm{diffusivity},<br><br>\mathrm{and}\\ D_{\mathrm{AN}}=<br><br>D_z-\frac{1}{2}<br><br>\left(D_x+D_y\right)<br><br><br><br>\mathrm{is}<br><br><br><br>\mathrm{the}<br><br><br><br>\mathrm{anisotropic}<br><br><br><br>\mathrm{structural}<br><br><br><br>\mathrm{unit}\\ <br><br>\mathrm{out}<br><br>\text{-}<br><br>\mathrm{of}<br><br>\text{-}<br><br>\mathrm{plane}<br><br><br><br>\mathrm{anisotropy}<br><br><br><br>\mathrm{diffusivity}.\end{array}$

23. The system of claim 17 wherein the nonlinear function is designated F(b) for a subject including similar structural units of uniaxial anisotropy (D_x=D_y) and is reduced to:

$F<br><br>\left(b\right)=\exp <br><br>\left(-{\mathrm{bD}}_{\mathrm{AV}}\right)<br><br>\frac{\sqrt{\mathrm{\pi <br><br>}}}{2}<br><br>\exp <br><br>\left(\frac{{\mathrm{bD}}_{\mathrm{AN}}}{3}\right)·<br><br>\frac{\mathrm{\Phi <br><br>}<br><br>\left(\sqrt{{\mathrm{bD}}_{\mathrm{AN}}}\right)}{{\mathrm{bD}}_{\mathrm{AN}}}$

where Φ

is the error function,

D_AV=⅓

(D_x+D_y+D_z) is the anisotropic structural unit mean diffusivity, and

D_AN=D_z−

½

(D_x+D_y) is the anisotropic structural unit out-of-plane anisotropy diffusivity.

24. The system of claim 17 wherein said processor reconstructing MR images of the subject based on the elements of the apparent diffusion coefficient reconstructs an image corresponding to an anisotropic structural unit mean diffusivity D_AV(x, y, z) based on the fitted MR data, an image corresponding to an out-of-plane anisotropy diffusivity D_AN(x, y, z) based on the fitted MR data, and an image corresponding to an in-plane anisotropy diffusivity d_AN(x, y, z) based on the fitted MR data.

25. The system of claim 17 wherein each voxel of interest in the subject contains structural units comprising a gas in small airways such as the small airways in the lungs of humans and animals that are too small to be resolved by direct imaging of the voxels with the system.

26. An MRI method for acquiring MR images of a material, wherein each voxel of interest in the material contains a plurality of anisotropic structural units that are too small to be resolved by direct imaging of the voxels using a magnetic resonance imaging system having a magnetic assembly including a magnet to impress a polarizing magnetic field on the material, a plurality of gradient coils positioned about the subject to impress an inhomogeneous magnetic field on the material, a RF transceiver system having an RF coil assembly, and an RF switch responsive to a pulse module controlling the RF transceiver system to transmit and receive RF signals to and from the material to acquire MR data containing information for MR images of the material, the MRI method comprising the steps of:

a. acquiring multiple sets of MR data from the RF transceiver system in response to MR pulse sequences that include difftision-sensitizing gradients, wherein the diffusion-sensitizing gradient differ from one of said MR pulse sequences to another;

b. determining a signal intensity for each set of the acquired MR data;

c. fitting the determined signal intensity for each set of MR data to a nonlinear function of a parameter related to said diffusion-sensitizing gradients;

d. determining elements of an apparent diffusion coefficient with respect to each of said anisotropic structural units contained in said material for the fitted MR data in at least one selected direction related to an orientation of each of said anisotropic structural units contained in said material;

e. reconstructing MR images of the material based on the determined elements of the apparent diffusion coefficient for the fitted MR data in the at least one selected direction related to an orientation of each of said anisotropic structural units contained in said material; and

f. selectively displaying the reconstructed MR images of the material.

27. The method of claim 26 further comprising the steps of:

a. digitizing the determined signal intensity for each set of the acquired MR data;

b. storing the digitized signal intensity for each set of the acquired MR data in a memory as an array of raw k space data;

c. rearranging the raw k-space data into separate k-space data arrays for each MR image of the subject to be reconstructed; and

d. processing each separate k-space data array to reconstruct the MR images of the subject.

28. The method of one of claim 26 or 27 wherein each voxel of interest in the material comprises a gas in small airways such as the small airways in the lungs of humans and animals that are too small to be resolved by direct imaging of the voxels with said system.

29. A method as in claim 26 including further processing the MR data and thereby estimating radial dimensions of said structural units.

30. A method comprising:

a. acquiring MR data of a subject, wherein each voxel of interest in the subject contains anisotropic structural units that are too small to be imaged directly with MRI of the voxels, using a number of MR pulse sequences, wherein;

i. at least some of said MR pulse sequences include diffusion-sensitizing gradients; and

ii. said included diffusion-sensitizing gradients are different for each of the corresponding gradients applied in each of the number of said pulse sequences;

b. defining an array of image pixels;

c. estimating several pixel values for each of the defined image pixels by fitting the acquired MR data to a non-linear function relating a parameter of said diffusion-sensitizing gradients to the acquired MR data, wherein each of the several pixel values for a given one of said image pixels is estimated by fitting MR data for a respective one of said MR pulse sequences to said non-linear function;

d. deriving estimates of parameters related to the diffusion of fluids in the subject in at least one selected direction related to the orientation of each of said anisotropic structural units contained in said subject that are too small to be imaged directly with MRI of the voxels, using the pixel image data; and

e. selectively storing or displaying images of selected distributions in the subject of said parameters related to said diffusion of fluids in the subject in said at least one selected direction.

31. A system comprising:

a. an MRI magnet and data acquisition unit providing MR data of a subject, wherein each voxel of interest in the subject contains a plurality of anisotropic structural units that are too small to be imaged directly with MRI of the voxels with said system, said data acquisition unit providing said MR data of the subject by applying to the subject a number of MR pulse sequences, wherein;

i. at least some of the number of said MR pulse sequences include diffusion-sensitizing gradients; and

ii. said included diffusion-sensitizing gradients are different for each of the corresponding grandients applied in each of the number of said pulse sequences;

b. an MRI image processor containing information defining an array of image pixels and converting the acquired MRI data to pixel image data corresponding to each of the image pixels and thereby estimating several pixel values corresponding to each of the image pixels, each of the pixel values corresponding to any one of said image pixels pertaining to a respective one of the pulse sequences;

c. a diffusion calculator that processes the several pixel values corresponding to each of the image pixels according to a non-linear relationship of the pixel values and parameters related to diffusion of fluids in the subject at each of said anisotropic structural units in at least one selected direction and thereby deriving estimates of directional diffusion of the fluids in the subject at respective locations in the subject;

d. a diffusion image processor processing said estimates of directional diffusion into at least one image of the values, at selected locations in the subject, of the diffusion in at least one selected direction relative to an orientation of each of said anisotropic structural elements; and

e. selectively storing and/or displaying said at least one image of the diffusion at each of said anisotropic structural units.