Apparatus and method for analysing functional MRI data
A system and method are provided for analysing a functional magnetic resonance imaging (MRI) scan representing a time-sequence, comprising t time points, of images comprising v voxels, where each scan can be represented by a data matrix X ∈ t×v . The method comprises modelling the scan data X as the convolution of neural activation time courses N ∈ + t×v and a haemodynamic filter Ψ, and performing an inverse operation to estimate N from X and Ψ. The method further compasses decomposing the neural activation time courses N into multiple brain network components by representing N as the product of a first matrix H defining, for each component, a spatial map of the voxels belonging to that component, and a second matrix W defining, for each component, the time sequence of activation of that component during the scan. In other implementations, the matrix decomposition may be performed before the deconvolution.
1. A method for analysing a functional magnetic resonance imaging (fMRI) scan representing a time-sequence, comprising t time points, of images comprising v voxels, where each scan can be represented by a data matrix X∈ t×v the method comprising:
modelling the scan data X as the convolution of a neural activation time course N∈ + t×v and a haemodynamic filter Ψ, and performing an inverse operation to estimate N from X and Ψ; and
decomposing the neural activation time course N into multiple brain network components by representing N as the product of a first matrix H defining, for each component, a spatial map of the voxels belonging to that component, and a second matrix W defining, for each component, the time sequence of activation of that component during the scan.
2. The method of claim 1 , wherein decomposing the neural activation comprises a non-negative matrix factorisation.
3. The method of claim 1 , further comprising adopting a probabilistic approach for decomposing the neural activation time course into multiple brain network components by defining prior probability distributions over individual elements in W and H.
4. The method of claim 3 , further comprising using the prior probability distributions to estimate an uncertainty associated with the individual elements in W and H.
5. A method for analysing a functional magnetic resonance imaging (fMRI) scan representing a time-sequence, comprising t time points, of images comprising v voxels, where each scan can be represented by a data matrix X∈ t×x the method comprising:
decomposing the data matrix X into multiple brain network components by representing X as the product of a first matrix H defining, for each component, a spatial map of the voxels belonging to that component, and a second matrix W*, where W* is formed by convolving a haemodynamic filter with a third matrix N*, defining, for each component, the time sequence of activation of that component during the scan; and
performing an inverse operation to estimate N* from W*.
6. The method of claim 5 , wherein decomposing the data matrix comprises a matrix factorisation.
7. The method of claim 1 , wherein the inverse operation comprises a nonlinear deconvolution.
8. The method of claim 1 , wherein the inverse operation and/or the matrix H are known.
9. The method of claim 1 , further comprising determining the inverse operation and/or the matrix H during a training phase, based on analysing a cohort of multiple scans.
10. The method of claim 9 , wherein the inverse operation is determined during the training phase by minimising, for the cohort of scans, differences between (i) the observed data X; and (ii) reconstructed data {circumflex over (X)}.
11. The method of claim 10 , wherein the reconstructed data is generated by applying a trial inverse operation to the observed data followed by the haemodynamic filter and performing an optimisation to determine a trial inverse operation that minimises said differences and that is then used as the inverse operation.
12. The method of claim 9 , wherein during the training phase, the matrix H is consistent across the cohort of multiple scans.
13. The method of claim 12 , wherein determining the matrix H includes determining the smallest number of components of H such that WH corresponds to N or W*H corresponds to X across the cohort of multiple scans.
14. The method of claim 13 , wherein determining the smallest number of components is performed using a cross-validation technique.
15. The method of claim 9 , wherein the cohort of multiple scans all relate to a specific task.
16. The method of claim 1 , further comprising preprocessing each fMRI scan to perform motion alignment.
17. The method of claim 1 , further comprising preprocessing each fMRI scan to perform co-registration with a structural scan so as to relate functional and anatomical brain regions.
18. The method of claim 1 , further comprising acquiring said fMRI scan.
19. Apparatus for analysing a functional magnetic resonance imaging (fMRI) scan representing a time-sequence, comprising t time points, of images comprising v voxels, where each scan can be represented by a data matrix X∈ t×v the apparatus including a computer processing system configured to:
model the scan data X as the convolution of a neural activation time course N∈ + t×v and a haemodynamic filter Ψ, and
perform an inverse operation with respect to Ψ and a matrix decomposition into multiple brain network components using a matrix H defining, for each component, a spatial map of the voxels belonging to that component, to derive for each component, the time sequence of activation of that component during the scan.