Functional Connectivity Mapping for Correlated Resting State Image Volumes

Transcription

1 Functional onnectivity Mapping for orrelated Resting State Image Volumes in hen, Long Meng, Man Qiu epartment of Electrical and omputer Engineering Purdue University alumet. Hammond, IN, Introduction Functional magnetic resonance imaging (fmri) measures the changes in blood flow and blood oxygenation in the brain related to neural activity of human beings or other animals. Resting state fmri which does not perform any tasks or stimuli during the experiment is to reveal a baseline or a default fundamental in understanding human brain functions [1]. he derived resting state connectivity maps reflect the underlying spontaneous neuronal activity within specific systems [2-4]. It has been shown applications in the examination of some neural diseases such as Alzheimer s disease and major depressive disorders. urrently, the most widely used techniques for resting state functional connectivity calculation are average signal based correlation analysis, Independent omponent Analysis (IA), Principal omponent Analysis (PA), and regression analysis [5]. In this project, Non-Negative Matrix Factorization (NMF) has been applied to the resting state data [6,7]. While most methods including IA rely on the assumptions that input signals are independent and non-gaussian noise, NMF only use the non-negative constrain during the data decomposition. herefore, NMF could be more suitable for MRI data analysis because MRI data are usually Gaussian noised and highly correlated. Methods he fmri data were preprocessed by Statistical Parametric Mapping (SPM). he image volumes were realigned, co-registrated, normalized and smoothed for artifact removal and movement error correction. he data were decomposed by NMF for connectivity map derivation. NMF is a group of algorithms in multivariate analysis and linear algebra. An n m matrix V could be decomposed into an n r matrix W and an r m matrix H. V WH while ( n + m) r < n m (1) Matrix W can be regarded as basic components, and matrix H contains the encoding information. o find an approximate factorization V WH, the Euclidean distance V-WH should be minimized: ( W V ) aµ ( VH ) ia H a µ H aµ W ia Wia (2) W WH WHH ( ) a µ ( ) ia

2 he Euclidean distance is invariant under these updates if and only if both W and H reach a stationary point. o compare the performance of IA and NMF in correlated and Gaussian noised data, three 1 artificial signals, square wave, sine wave, and cosine wave, were randomly mixed in three channels. he mixed signals then decomposed by IA and NMF respectively. he same methods applied to 1 functional data as and a 2 MRI image with additive Gaussian noise. Five resting state fmri datasets were acquired by a 3 Philips MRI scanner as well as one water data as reference. he datasets were processed by NMF and IA for default network calculation. A Figure1: A) Original input signals without strong correlations. ) Mixed signals from the input signals. ) Separated signals using IA. ) Separated signals using NMF. oth IA and NMF can decompose the mixed signals.

3 A Figure2: A) Original input signals with strong correlations. ) Mixed signals from the input signals. ) Separated signals using IA. ) Separated signals using NMF. IA decomposes the signals based on statistical independency while NMF can retrieve the original signals. Results Figure 1 shows the mixing of two signals with weak correlations. oth IA and NMF can retrieve the signals back. When the correlation increases as shown in Figure 2, IA can retrieve the first two signals back with a and phase offset, but it fails in the third signal. NMF decomposed all signals with correct magnitudes and phases. hree fmri time series randomly selected from a resting state fmri dataset (Figure 3A) and randomly mixed (Figure 3). he IA and NMF decomposition results are shown in Figure 3

4 and 3 respectively. NMF has higher fidelity in correlated source separations which is the situation of MRI data. Figure 4 is the resting state functional connectivity maps calculated by NMF which shows the default network. A Figure3: A) Original input fmri time series. ) Mixed signals from the inputs. ) Separated signals using IA. ) Separated signals using NMF. NMF matches the original fmri series better.

5 Figure 4. efault network overlaid on anatomical images. onclusions he results of all experiments above show that IA and NMF have shown comparable results when the input signals or images have little correlations. NMF has better performance when the signals are correlated. herefore, it is more suitable for fmri data processing because of the strong correlation in MRI data. References [1] iswal, Yetkin FZ, Haughton VM, and Hyde J, Functional connectivity in the motor cortex of resting human brain using echo-planar MRI, Magn Reson Med, vol. 34, pp , Oct [2] Lowe MJ, Mock J, and Sorenson JA, Functional connectivity in single and multislice echoplanar imaging using resting-state fluctuations, Neuroimage, vol. 7, pp , Feb [3] ordes, HaughtonVM, Arfanakis K, arew J, urski PA, Moritz H, Quigley MA, and Meyerand ME, Frequencies contributing to functional connectivity in the cerebral cortex in "resting-state" data, AJNR Am J Neuroradiol, vol. 22, pp , Aug [4] Hampson M, Peterson S, Skudlarski P, Gatenby J, and Gore J, etection of functional connectivity using temporal correlations in MR images, Hum rain Mapp, vol. 15, pp , Apr [5] Peter Fransson, Spontaneous low-frequency OL signal fluctuations: An fmri investigation of the resting-state default mode of brain function hypothesis, Human rain Mapping: Volume 26, Issue 1, pages 15 29, September 2005 [6] aniel. Lee & H. Sebastian Seung, Learning the parts of objects by non-negative matrix factorization, Nature 1999 v401 issue 6755 p [7] aniel. Lee & H. Sebastian Seung, Algorithms for Non-negative Matrix Factorization, Advanced in Neural Information Processing Systems, 13,