System, method and computer-accessible medium for determining brain microstructure parameters from diffusion magnetic resonance imaging signal's rotational invariants
An exemplary system, method and computer-accessible medium for determining a plurality of tissue parameters of a tissue(s), can include, for example, receiving information related to a plurality of rotational invariants contained within a diffusion magnetic resonance (dMR) image(s) of the tissue(s), and generating the tissue parameters using a set of rotational invariants related to the plurality of tissue parameters using such information. The tissue parameters can be generated by factorizing a response of an individual fiber segment of the tissue(s) based on the set of rotational invariants. The response of the individual fiber segments can be factorized from an orientational distribution function (“ODF”). The individual fiber segments can be factorized using a scalar tensor factorization(s) of the rotational invariants. The set of rotational invariants can be of a rotation group SO(3).
1. A non-transitory computer-accessible medium having stored thereon computer-executable instructions for determining a plurality of tissue parameters of at least one tissue, wherein, when a computer arrangement executes the instructions, the computer arrangement is configured to perform procedures comprising:
receiving information related to a set of rotational invariants related to the tissue parameters that are contained within at least one diffusion magnetic resonance (dMR) image of the at least one tissue;
generating the tissue parameters using (i) the set of rotational invariants based on the information, and (ii) at least one non-linear fitting procedure applied to each voxel of an image of at the least one tissue, wherein the generation of the tissue parameters using the generating procedure is performed by factorizing a response of individual fiber segments of the at least one tissue from an orientation distribution function (ODF) based on the set of rotational invariants; and
constructing the orientation distribution function using an exact factorization relation.
2. The computer-accessible medium of claim 1 , wherein the computer arrangement is further configured to determine a plurality of tensor tissue parameters based on a plurality of scalar tissue parameters and a plurality of diffusion moments.
3. The computer-accessible medium of claim 2 , wherein:
the scalar tissue parameters include at least one of (i) a diffusivity inside neurites of the at least one tissue, (ii) the diffusivities outside the neurites, or (iii) a neurite water fraction of the at least one tissue; and
the tensor tissue parameters include an orientation distribution function of the at least one tissue.
4. The computer-accessible medium of claim 2 , wherein a number of the tissue parameters are based on a maximum order of the diffusion moments.
5. The computer-accessible medium of claim 1 , wherein the computer arrangement is further configured to cause an activation of a magnetic resonance imaging apparatus to acquire the dMR image.
6. The computer-accessible medium of claim 1 , wherein diffusion rotational invariants include diffusion moments and wherein the computer arrangement is configured to factorize the response of the individual fiber segments using at least one scalar tensor factorization of the diffusion moments, and relations between the tissue parameters and the rotational invariants that are based on the diffusion moments.
7. The computer-accessible medium of claim 1 , wherein the set of rotational invariants are of a rotation group SO(3).
8. The computer-accessible medium of claim 1 , wherein the computer arrangement is further configured to estimate the information using a plurality of cumulant tensors.
9. The computer-accessible medium of claim 8 , wherein the tissue parameters include at least two branches of tissue parameters, and wherein the computer arrangement is further configured to select one of the branches based on prior information about a range of model parameters values.
10. The computer-accessible medium of claim 1 , wherein the computer arrangement is configured to generate the tissue parameters using at least one minimization function with respect to a plurality of model parameters.
11. The computer-accessible medium of claim 1 , wherein the diffusion rotational invariants include diffusion moments, and wherein the computer arrangement is configured to factorize the response of the individual fiber segments using at least one scalar-tensor factorization of the diffusion moments, and relations between the tissue parameters and the rotational invariants that are based on the diffusion moments.
12. The computer-accessible medium of claim 11 , wherein the computer arrangement is further configured to initialize the at least one non-linear fitting procedure based on the tissue parameters.
13. The computer-accessible medium of claim 1 , wherein the at least one non-linear fitting procedure is based on a prevalence procedure.
14. The computer-accessible medium of claim 13 , wherein the prevalence procedure includes (i) beginning at a number of random initializations, (ii) clustering outcomes of the prevalence procedure, and (iii) and selecting a largest cluster.
15. The computer-accessible medium of claim 1 , wherein the computer arrangement is further configured to initialize the at least one non-linear fitting procedure using fit outcomes related by a duality transformation.
16. The computer-accessible medium of claim 1 , wherein the computer arrangement is further configured to determine a plurality of tensor tissue parameters based on scalar tissue parameters and the rotational invariants.
17. The computer-accessible medium of claim 1 , wherein the computer arrangement is further configured to receive at least one signal related to the at least one dMR image.
18. The computer-accessible medium of claim 17 , wherein the computer arrangement is further configured to construct the rotational invariants based on the at least one dMR signal.
19. The computer-accessible medium of claim 18 , wherein the computer arrangement is further configured to:
generate at least one training set; and
generate the tissue parameters based on the at least one training set.
20. The computer-accessible medium of claim 19 , wherein the computer arrangement is further configured to generate the tissue parameters using at least one further non-linear fitting procedure.
21. The computer-accessible medium of claim 20 , wherein the computer arrangement is further configure to initialize the at least one further non-linear fitting procedure based on the tissue parameters using the at least one training set.
22. A system for determining a plurality of tissue parameters of at least one tissue, comprising:
a computer hardware arrangement configured to:
receive information related to a set of rotational invariants related to the tissue parameters that are contained within at least one diffusion magnetic resonance (dMR) image of the at least one tissue;
generate the tissue parameters using (i) the set of rotational invariants based on the information, and (ii) at least one non linear fitting procedure applied to each voxel of an image of at the least one tissue, wherein the generation of the tissue parameters using the generating procedure is performed by factorizing a response of individual fiber segments of the at least one tissue from an orientation distribution function (ODF) based on the set of rotational invariants; and
construct the orientation distribution function using an exact factorization relation.
23. A method for determining a plurality of tissue parameters of at least one tissue, comprising:
receiving information related to a set of rotational invariants related to the tissue parameters that are contained within at least one diffusion magnetic resonance (dMR) image of the at least one tissue;
with a computer hardware arrangement, generating the tissue parameters using (i) the set of rotational invariants based on the information, and (ii) at least one non-linear fitting procedure applied to each voxel of an image of at the least one tissue, wherein the generation of the tissue parameters is performed by factorizing a response of individual fiber segments of the at least one tissue from an orientation distribution function (ODF) based on the set of rotational invariants; and
constructing the orientation distribution function using an exact factorization relation.
24. A non-transitory computer-accessible medium having stored thereon computer executable instructions for determining a plurality of tissue parameters of at least one tissue, wherein, when a computer arrangement executes the instructions, the computer arrangement is configured to perform procedures comprising:
receiving information related to a plurality of diffusion rotational invariants contained within at least one diffusion magnetic resonance (dMR) image of the at least one tissue;
generating the tissue parameters using (i) a set of rotational invariants related to the tissue parameters based on the information, and (ii) at least one non-linear fitting procedure applied to each voxel of an image of at the least one tissue; and
determining a plurality of tensor tissue parameters based on a plurality of scalar tissue parameters and a plurality of diffusion moments,
wherein the scalar tissue parameters include at least one of (i) a diffusivity inside neurites of the at least one tissue, (ii) the diffusivities outside the neurites, or (iii) a neurite water fraction of the at least one tissue, and
wherein the tensor tissue parameters include an orientation distribution function of the at least one tissue.
25. The computer-accessible medium of claim 24 , wherein the diffusion rotational invariants include the diffusion moments, and wherein the computer arrangement is further configured to factorize a response of individual fiber segments using at least one scalar tensor factorization of the diffusion moments and relations between the tissue parameters and the rotational invariants that are based on the diffusion moments.
26. A system for determining a plurality of tissue parameters of at least one tissue, comprising:
a computer hardware arrangement configured to:
receive information related to a plurality of diffusion rotational invariants contained within at least one diffusion magnetic resonance (dMR) image of the at least one tissue;
generate the tissue parameters using (i) a set of rotational invariants related to the tissue parameters based on the information, and (ii) at least one non-linear fitting procedure applied to each voxel of an image of at the least one tissue; and
determine a plurality of tensor tissue parameters based on a plurality of scalar tissue parameters and a plurality of diffusion moments,
wherein the scalar tissue parameters include at least one of (i) a diffusivity inside neurites of the at least one tissue, (ii) the diffusivities outside the neurites, or (iii) a neurite water fraction of the at least one tissue, and
wherein the tensor tissue parameters include an orientation distribution function of the at least one tissue.
27. The system of claim 26 , wherein the diffusion rotational invariants include the diffusion moments, and wherein the computer hardware arrangement is further configured to factorize a response of individual fiber segments using at least one scalar tensor factorization of the diffusion moments and relations between the tissue parameters and the rotational invariants that are based on the diffusion moments.
28. A method for determining a plurality of tissue parameters of at least one tissue, comprising:
receiving information related to a plurality of diffusion rotational invariants contained within at least one diffusion magnetic resonance (dMR) image of the at least one tissue;
generating the tissue parameters using (i) a set of rotational invariants related to the tissue parameters based on the information, and (ii) at least one non-linear fitting procedure applied to each voxel of an image of at the least one tissue; and
using a computer hardware arrangement, determining a plurality of tensor tissue parameters based on a plurality of scalar tissue parameters and a plurality of diffusion moments,
wherein the scalar tissue parameters include at least one of (i) a diffusivity inside neurites of the at least one tissue, (ii) the diffusivities outside the neurites, or (iii) a neurite water fraction of the at least one tissue, and
wherein the tensor tissue parameters include an orientation distribution function of the at least one tissue.
29. The method of claim 28 , wherein the diffusion rotational invariants include the diffusion moments, and further comprising factorizing a response of individual fiber segments using at least one scalar tensor factorization of the diffusion moments and relations between the tissue parameters and the rotational invariants that are based on the diffusion moments.