The 21st Annual Conference of the Japanese Neural Network Society (December, 2011)

Iterative Dual-Regression with Sparse Prior to Estimate Individual Neuronal Activations from Group Functional Magnetic Resonance Imaging (fMRI) Data

Yong-Hwan Kim,�Dong-Youl Kim,�and Jong-Hwan Lee

Department of Brain and Cognitive Engineering, Korea University, Seoul, Korea E-mail: jonghwan_lee@korea.ac.kr

Abstract―An iterative dual-regression (DR) with a sparse prior was proposed to estimate individual neuronal activations from an ICA application to a group functional magnetic resonance imaging (fMRI) data. Compared to an original DR with two steps of least-squares to estimate both spatial and temporal patterns, our approach showed enhanced true positive rates while reducing false positive rates across all individual results as quantitatively evaluated using semi-artificial fMRI data.

Keywords― Independent component analysis, ICA, Group ICA, Dual Regression, Alternating Least- Squares, Sparse Prior

1. Introduction A group of functional magnetic resonance imaging

(fMRI) data from multiple subjects has successfully been analyzed using an independent component analysis (ICA) with an extension to temporally–concatenated (TC) 2-dimensional (2-D) BOLD fMRI data matrix, in which the column vectors are BOLD time-series (TC) (i.e. time points × voxels) from multiple subjects (i.e. TC group ICA, or TC-GICA) [1]. Once the spatial and temporal patterns (i.e. independent components, or ICs) from this TC 2-D data matrix (i.e. group-level ICs) were estimated, two steps of alternating least-squares (LS) algorithms (i.e. dual-regression, or DR) were deployed to estimate the individual-level ICs [1]. In detail, firstly the temporal patterns maximally fitted to an individual data set were obtained using the resulting group-level spatial patterns via the minimization of LS residual error [1]. Then, the spatial patterns associated with the individual data were subsequently estimated using the individual temporal patterns [1]. However, we claim that these patterns would need to be fine-tuned iteratively using the modified spatial and temporal patterns, respectively, while keeping the independence between spatial patterns (i.e. super- Gaussian) to minimize the false positive rate (FPR) and to maintain the true positive rate (TPR).

In this context, we propose an iterative DR method with an additional sparse prior (i.e. Laplacian) [2] to estimate and further refine the temporal and spatial patterns of neuronal activations better fitted to the individual fMRI data. To quantitatively evaluate the results from the proposed method compared to the original form of DR and a popular general linear model (GLM) [3], semi-artificial fMRI data sets with pre-defined spatial and temporal patterns of neuronal activations were generated from a real fMRI data without an explicit task paradigm (i.e. resting-state fMRI data [4]). The TPR and FPR of determined active voxels along with the Pearson’s correlation coefficient (CC) were

subsequently calculated to quantitatively evaluate the estimated spatial and temporal patterns, respectively.

2. Methods Fig. 1 shows an overall flow diagram. Once

semi-artificial data sets were generated, the TC-GICA was applied to these data to extract group-level spatial and temporal patterns. Then, individual spatial and temporal patterns were estimated from (1) original DR, and (2) proposed iterative DR with a sparse prior.

2.1. Semi-Artificial fMRI Data Preparation The publicly available resting-state fMRI data

(www.nitrc.org/projects/nyu_trt; 25 subjects) without any specific target tasks were used as baseline fMRI data across a whole brain [5]. The BOLD TC corresponding to “target task” were generated from a canonical hemodynamic response function (HRF) by controlling parameters such as delay to peak and duration in the SPM2 (www.fil.ion.ucl.ac.uk/spm) and were added to the brain regions randomly selected (i.e. semi-artificial fMRI data). In detail, the baseline fMRI data consist of various non-neuronal components that include a static positive level, MRI systematic noises including slow time drift, cardiac-respiratory physiological noises, and Gaussian thermal noises [3], were extracted using a parametric bootstrap model [6]. After the normalization of individual fMRI data to standard template space, the HRFs were artificially designed based on the pre-defined block-based task-paradigms convolved with the randomly perturbed HRF model parameters and added to the randomly selected seed voxel and the neighboring 99 voxels (i.e. total of 100 voxels; max. of 2% BOLD increase similar to the real fMRI data from a commercial 3-T MRI scanner) for each subject. Since the TC-GICA approach may particularly be vulnerable to the level of spatial overlap across subjects [7], only a single voxel was overlapping across all 25 subjects to put a stringent condition on spatial patterns (i.e. 1% overlap). The generated spatial patterns and BOLD TS were exemplified in the step 1 of Fig. 1.

2.2. TC-GICA Application The TC-GICA method was applied to the 2-D matrix

of artificially generated BOLD TS across all the 25 subjects using the MELODIC tool in the FSL (www.fmrib.ox.ac.uk/fsl). One of the 17 (determined based on Laplace approximation available in the FSL tool) ICs was successfully estimated the task-related group-level spatial and temporal patterns as shown in the step 2 of Fig. 1.

[P3-11]

Fig. 1. An illustration of overall steps

2.3. Estimating Individual Spatial/Temporal Patterns Original DR

As shown in Eq. (1), original DR is based on two steps of LS solution [1], in which the individual-level temporal patterns (Ai) were firstly obtained using group-level spatial patterns (SG) and individual data (Xi). Then, the individual-level spatial patterns (Si) were subsequently estimated using Ai.

Ai =Xi SGT SG SG

T( )−1, Si = Ai

TAi( )−1AiTXi

(1)

where an i (=1, 2, …, 25) indicates an subject index. Iterative DR with a sparse prior

An iterative approach of the DR was proposed as Eq. (2&3). Moreover, the spatial patterns are further refined to maximize its sparseness adopting the first order derivative of the Laplace distribution (i.e. sign function) via a gradient descent scheme as shown in Eq. (4) [2].

Aik = 1−α( )Ai

k−1 +αXi Sik−1,T Si

k−1Sik−1,T( )

−1 (2)

Sik = 1−β( )Sik +β Ai

k,T Aik( )

−1Ai

k,T Xi(3)

Sik = Si

k −γ sign(Sik ) (4)

where k (=1, 2, …) is an iteration index, group-level spatial patterns (SG) are used as an initial condition Si

0, and α, β, and γ are learning rates to control the update speed of temporal, spatial patterns, and sparseness, respectively. In this work, to show the feasibility of the method, α and β were fixed at 10-2 and γ was tested for several values (10-2, 10-3, 10-4 & 10-5) to control relative importance of sparseness criterion compared to regression update over the course of 1000 iterations.

3. Experimental Results Fig. 2 showed the resulting performance. Overall, the

proposed method with an appropriate weight for the sparse prior (i.e. γ=10-4) showed the best performance, in which almost perfect TPRs (=1) across all the subjects and significantly reduced FPRs (<0.001) along with superior

estimation of the temporal patterns (i.e. CC = 0.90 ± 0.06) were observed from the proposed method. The estimated spatial/temporal patterns from one subject (i.e. subject 8) were exemplified in the step 3 of Fig. 1 (true/false positive voxels at p<0.05 denoted as gray/dark; original/estimated HRF as dotted/solid lines). Note that the true positive voxels (within circles) from the proposed approach are almost same as the reference voxels of the subject 8 in the step 1 of Fig. 1 and false positive voxels were drastically reduced compared to these from the original DR.

Fig. 2. Boxplots of resulting performance

4. Discussion In this study, we proposed an iterative DR method with

a sparse prior. From the quantitative evaluation via semi-artificial fMRI data, our proposed DR model showed almost perfect estimation of true neuronal activations along with significantly reduced false activations compared to the original DR and GLM methods. The performance seems to be vulnerable depending on update speed of the sparse prior (i.e. γ) relative to the regression (i.e. α & β), and thus it would need to be adaptively changed using such as hierachical Bayesian algorithm. Significantly increased estimation power in temporal domain was also observed using the temporal CCs between the original and estimated HRFs. A further study is warranted to show whether the proposed model can also benefit to better estimate neuronal activation patterns from real fMRI data. References [1] Beckmann, C.F., Mackay, C.E., Filippini, N., & Smith,

S.M. (2009). Group comparison of resting-state fMRI data using multi-subject ICA and dual regression, 15th Annual Meeting of Organization for Human Brain Mapping, poster 441 SU-AM.

[2] Cichocki, A. & Zdunek, R. (2007). Regularized alternating least squares algorithms for non-negative matrix/tensor factorization. Lecture Notes in Computer Science (LNCS), 4493, 793-802.

[3] Huettel, S.A., Song, A.W., & McCarthy, G. (2008). Functional magnetic resonance imaging, 2nd ed. Sinauer Associates, Sunderland, MA, 2008.

[4] Fox, M.D., & Raichle, M.E. (2007). Spontaneous fluctuations in brain activity observed with functional magnetic resonance imaging. Nat Rev Neurosci. 8, 700-711.

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[6] Bellec, P., Perlbarg, V. & Evans, A.C. (2009). Bootstrap generation and evaluation of an fMRI simulation database. Magn. Reson. Imaging, 27, 1382-1396.

[7] Lee, J.H., Lee, T.W., Jolesz, F.A., & Yoo, S.S. (2008). Independent vector analysis (IVA): multivariate approach for fMRI group study. NeuroImage. 40, 86-109.