Methods, apparatuses, systems, and computer-readable mediums for biomarker quantification using free-breathing stack-of-radial imaging

1 . A method of generating at least one image using a magnetic resonance imaging (MRI) system, the method comprising:

generating, for each contrast of a plurality of contrasts, an image by

forming a first multi-dimensional data matrix by dividing MRI imaging data for a contrast into a plurality of bins, each bin of the plurality of bins corresponding to one of a plurality of respiratory motion states and the first multi-dimensional data matrix including acquired k-space data assigned to k-space and motion state dimensions, and

generating the image by evaluating an optimization function based on the MRI imaging data, the first multi-dimensional data matrix, a transformation matrix, and an image regularization.

2 . The method of claim 1 , further comprising:

generating the transformation matrix for each contrast of the plurality of contrasts.

3 . The method of claim 2 , wherein the transformation matrix includes at least one of an undersampling pattern, a coil sensitivity map, or a non-uniform Fourier transform.

4 . The method of claim 2 , further comprising:

determining the image regularization involving a linear transformation for each contrast of the plurality of contrasts.

5 . The method of claim 4 , wherein the image regularization includes at least one regularization factor.

6 . The method of claim 5 , wherein the at least one regularization factor is at least one of a regularization factor for spatial regularization or motion-state regularization.

7 . The method of claim 2 , further comprising, for each contrast of the plurality of contrasts:

applying the transformation matrix to the first multi-dimensional data matrix for the contrast to obtain a transformed multi-dimensional data matrix;

wherein the generating generates the image based on the MRI imaging data and the transformed multi-dimensional data matrix.

8 . The method of claim 1 , wherein the optimization function is based on an optimization equation given by

1

2

⁢



Ax

-

y



2

2

+



W

⁡

(

α

,

β

)

⁢

x



1

,

wherein

A is the transformation matrix,

x is a second multi-dimensional data matrix of the MRI imaging data to be reconstructed, the second multi-dimensional data matrix including at least a spatial dimension and a motion-state dimension,

y is the first multi-dimensional data matrix of the acquired k-space data assigned to k-space and motion-state dimensions, and

W is the image regularization.

9 . The method of claim 1 , further comprising:

acquiring the MRI imaging data from an MRI system, wherein the MRI imaging data is acquired for each contrast of the plurality of contrasts resulting from application of a pulse of the MRI system.

10 . The method of claim 9 , further comprising:

extracting a self-gating signal from the MRI imaging data; and

determining, based on the self-gating signal, the plurality of respiratory motion states associated with acquisition of the MRI imaging data,

wherein a separate self-gating signal is extracted for each contrast included in the plurality of contrasts.

11 . The method of claim 9 , wherein the MRI imaging data is acquired using a stack-of-star trajectory and a self-gating signal is extracted from the MRI imaging data by sampling a plurality of radial views included in the MRI imaging data.

12 . The method of claim 9 , further comprising:

determining the plurality of respiratory motion states associated with acquisition of the MRI imaging data by measuring one or more physiological signals with the MRI system.

13 . The method of claim 1 , further comprising:

calculating one or more biomarker parameter maps based on the images generated for the plurality of contrasts.

14 . The method of claim 13 , wherein the one or more biomarker parameter maps comprise at least one of a proton density fat fraction (PDFF) parameter map or a transverse relaxation rate (R 2 *) parameter map.

15 . A system for generating at least one image, the system comprising:

at least one processor; and

at least one memory including instructions that, when executed by the at least one processor, cause the system to

generate, for each contrast of a plurality of contrasts, an image by

forming a first multi-dimensional data matrix by dividing MRI imaging data for a contrast into a plurality of bins, each bin of the plurality of bins corresponding to one of a plurality of respiratory motion states and the first multi-dimensional data matrix including acquired k-space data assigned to k-space and motion state dimensions, and

generating the image by evaluating an optimization function based on the MRI imaging data, the first multi-dimensional data matrix, a transformation matrix, and an image regularization.

16 . The system of claim 15 , wherein the system is further caused to:

calculate one or more biomarker parameter maps based on the images generated for the plurality of contrasts.

17 . A non-transitory computer readable medium system storing computer readable instruction that, when executed by one or more processors of a system, cause the system to perform a method of generating at least one image, the method comprising:

generating, for each contrast of a plurality of contrasts, an image by

forming a first multi-dimensional data matrix by dividing MRI imaging data for a contrast into a plurality of bins, each bin of the plurality of bins corresponding to one of a plurality of respiratory motion states and the first multi-dimensional data matrix including acquired k-space data assigned to k-space and motion state dimensions, and

generating the image by evaluating an optimization function based on the MRI imaging data, the first multi-dimensional data matrix, a transformation matrix, and an image regularization.

18 . The non-transitory computer readable medium of claim 17 , wherein the method further comprises:

calculating one or more biomarker parameter maps based on the images generated for the plurality of contrasts.