System and method for assessing adenosine triphosphate hydrolysis rate using double saturation transfer magnetic resonance imaging and spectroscopy

1. A magnetic resonance imaging (MRI) system comprising:

a magnet system configured to generate a polarizing magnetic field about at least a region of interest (ROI) in a subject arranged in the MRI system;

a plurality of gradient coils configured to apply a gradient field to the polarizing magnetic field;

a radio frequency (RF) system configured to apply an excitation field to the subject and acquire MR image data from a ROI;

a computer system programmed to:

control the plurality of gradient coils and the RF system according to a pulse sequence to acquire data including intrinsic longitudinal relaxation time of phosphocreatine (PCr), T 1,PCr int , acquired using an inversion recovery data acquisition with saturation of a gamma phosphate in adenosine triphosphate (ATPγ);

control the plurality of gradient coils and the RF system according to a pulse sequence to acquire data including an intrinsic longitudinal relaxation time of ATPγ, T 1,ATPγ int , acquired using an inversion recovery data acquisition with both PCr and inorganic phosphate (Pi) saturation;

measure equilibrium magnetization of PCr (M 0,PCr ) and equilibrium magnetization of ATPγ (M 0,ATPγ ) using a relaxed control phosphorous-31 (P-31) spectrum acquired without saturation;

measure steady-state magnetization of PCr (M ss,PCr ) using a P-31 spectrum acquired with ATPγ saturation;

measure steady-state magnetization of ATPγ (M ss,ATPγ ) using a P-31 spectrum acquired with both PCr and Pi saturation; and

calculate an ATP hydrolysis rate using the intrinsic longitudinal relaxation times of PCr and ATPγ, the equilibrium magnetization of PCr and ATPγ, and the steady-state magnetization of PCr and ATPγ.

2. A method for calculating adenosine triphosphate (ATP) hydrolysis rate, the method comprising the steps of:

a) acquiring data including intrinsic longitudinal relaxation time of phosphocreatine (PCr), T 1,PCr int , acquired using an MRI system to perform an inversion recovery data acquisition with saturation of a gamma phosphate in adenosine triphosphate (ATPγ);

b) acquiring data including an intrinsic longitudinal relaxation time, T 1,ATPγ int , of ATPγ acquired using the MRI system to perform an inversion recovery data acquisition with both PCr and inorganic phosphate (Pi) saturation;

c) measuring equilibrium magnetization of PCr (M 0,PCr ) and equilibrium magnetization of ATPγ (M 0,ATPγ ) using a relaxed control phosphorous-31 (P-31) spectrum acquired without saturation using the MRI system;

d) measuring steady-state magnetization of PCr (M ss,PCr ) using a P-31 spectrum acquired with ATPγ saturation using the MRI system;

e) measuring steady-state magnetization of ATPγ (M ss,ATPγ ) using a P-31 spectrum acquired with both PCr and Pi saturation using the MRI system;

calculating with a computer system, an ATP hydrolysis rate using the intrinsic longitudinal relaxation times of PCr and ATPγ, the equilibrium magnetization of PCr and ATPγ, and the steady-state magnetization of PCr and ATPγ; and

g) generating with the computer system, a report indicating at least the ATP hydrolysis rate determined in step f).

3. The method as recited in claim 2 in which step f) includes calculating a forward rate constant of a PCr→ATP reaction and a total rate constant of combined PCr→ATP and Pi→ATP reactions.

4. The method as recited in claim 3 in which the forward rate constant of the PCr→ATP reaction is calculated using a rate equation having the following form:

k

PCr

->

ATP

=

1

T

1

,

PCr

int

·

M

0

,

PCr

-

M

ss

,

PCr

M

ss

,

PCr

.

5. The method as recited in claim 3 in which the total rate constant is calculated using a rate equation having the following form:

k

ATP

,

tot

=

1

T

1

,

ATP

⁢

⁢

γ

int

·

M

0

,

ATP

⁢

⁢

γ

-

M

ss

,

ATP

⁢

⁢

γ

M

ss

,

ATP

⁢

⁢

γ

.

6. The method as recited in claim 3 in which step f) includes calculating the ATP hydrolysis rate by subtracting the forward rate constant of the PCr→ATP reaction from the total rate constant.

7. The method as recited in claim 6 in which the ATP hydrolysis rate is calculated according to:

k

ATP

->

Pi

=

k

ATP

,

tot

-

M

0

,

PCr

M

0

,

ATP

⁢

⁢

γ

⁢

k

PCr

->

ATP

.

8. The method as recited in claim 2 in which the ATP hydrolysis rate calculated in step f) is the ATP hydrolysis rate of at least one of in vivo heart tissue and skeletal muscle tissue.

9. A magnetic resonance imaging (MRI) system comprising:

a magnet system configured to generate a polarizing magnetic field about at least a region of interest (ROI) in a subject arranged in the MRI system;

a plurality of gradient coils configured to apply a gradient field to the polarizing magnetic field;

a radio frequency (RF) system configured to apply an excitation field to the subject and acquire MR image data from a ROI;

a computer system programmed to:

control the plurality of gradient coils and the RF system according to an inversion recovery pulse sequence in order to acquire inversion-recovery data from the subject;

control the plurality of gradient coils and the RF system according to a pulse sequence in order to acquire spectral data of a phosphate-31 spectrum from the subject;

using the inversion-recovery data and the spectral data, determine adenosine triphosphate (ATP) hydrolysis rate of the subject without a quantification of inorganic phosphate.

10. The MRI system as recited in claim 9 in which acquiring the inversion-recovery data includes intrinsic longitudinal relaxation times of phosphocreatine (PCr) acquired with saturation of a gamma phosphate in adenosine triphosphate (ATPγ) and intrinsic longitudinal relaxation time of ATPγ acquired with both PCr and inorganic phosphate (Pi) saturation.

11. The MRI system as recited in claim 10 in which the processor is further programmed to measure of equilibrium magnetization of PCr, ATPγ, and Pi using a relaxed control phosphorous-31 (P-31) spectrum acquired without saturation.

12. The MRI system as recited in claim 11 in which the processor is further programmed to measure steady-state magnetization of PCr and Pi using a P-31 spectrum acquired with ATPγ saturation.

13. The MRI system as recited in claim 12 in which the processor is further programmed to measure steady-state magnetization of ATPγ using a P-31 spectrum acquired with both PCr and Pi saturation.

14. The MRI system of as recited in claim 13 in which the processor is further programmed to calculate an ATP hydrolysis rate using the intrinsic longitudinal relaxation times of PCr and ATPγ, the equilibrium magnetization of PCr and ATPγ, and the steady-state magnetization of PCr and ATPγ.

15. The MRI system as recited in claim 9 in which the processor is further programmed to calculate a forward rate constant of a PCr→ATP reaction and a total rate constant of combined PCr→ATP and Pi→ATP reactions to determine the ATP hydrolysis rate.

16. The MRI system of as recited in claim 15 in which the processor is further programmed to calculate the ATP hydrolysis rate by subtracting the forward rate constant of the PCr→ATP reaction from the total rate constant.

17. The MRI system of as recited in claim 15 in which the processor is further programmed to calculate the ATP hydrolysis rate according to:

k

ATP

->

Pi

=

k

ATP

,

tot

-

M

0

,

PCr

M

0

,

ATP

⁢

⁢

γ

⁢

k

PCr

->

ATP

.

18. The MRI system as recited in claim 9 in which the pulse sequence includes a B1-insensitive train to obliterate signal (BISTRO) pulse sequence.

19. The MRI system as recited in claim 9 in which the pulse sequence includes at least one of a chemical shift imaging (CSI) module and an image selected in vivo spectroscopy (ISIS) module.