Advanced signal processing algorithms for fMRI

ADVANCED SIGNAL PROCESSING ALGORITHMS FOR fMRI TEY ENG TIAN NATIONAL UNIVERSITY OF SINGAPORE 2003 ADVANCED SIGNAL PROCESSING ALGORITHMS FOR fMRI TEY ENG TIAN (B.Eng.(Hons.), NUS) A THESIS SUBMITTED FOR THE DEGREE OF MASTER OF ENGINEERING DEPARTMENT OF ELECTRICAL AND COMPUTER ENGINEERING NATIONAL UNIVERSITY OF SINGAPORE 2003 ACKNOWLEDGEMENT I would like to thank everyone who has given me help and guidance throughout the duration of this project. In particular, special thanks go to i. My supervisor, Dr. Sadasivan Puthusserypady. ii. The fMRI Data Center for providing the fMRI data set, with speed and ease, free of charges too. iii. Researchers who have given me guidance through email like, Prof. Christian Jutten, Prof. Juha Karhunen, Asst. Prof. M.J. McKeown and Dr. John Ashburner iv. My father, mother, siblings and wife, yes I got one, who have shown tolerance and love for the duration of the project and especially thesis writing. v. Other post-graduate students who have been unwinding me with self-answered questions, jokes and more jokes. Hmm … where is the knowledge sharing … too chaotic, perhaps … i CONTENTS ACKNOWLEDGEMENT i CONTENTS ii SUMMARY iv LIST OF ABBREVIATIONS vi LIST OF FIGURES viii LIST OF TABLES xi CHAPTER INTRODUCTON 1.1 Background 1.1.1 Magnetic Resonance Imaging – A Brief History 1.1.2 Functional Magnetic Resonance Imaging 1.2 Motivation CHAPTER THEORY AND LITERATURE REVIEW 2.1 Magnetic Resonance Imaging 2.1.1 Larmor Frequency 2.1.2 Radio Frequency Pulse and Precession 8 11 2.1.3 T1, T2 and T2* Relaxation Times 16 2.1.4 Pulse Sequence 18 2.1.5 Spatial Encoding 23 2.1.6 Echo Planar Imaging 26 2.2 2.2.1 Functional Magnetic Resonance Imaging 28 Functional Magnetic Resonance Imaging Data Formation and Terminology 29 2.2.2 Blood Oxygenation Level Dependent (BOLD) Signal 31 2.2.3 Oxygen Limitation Model and Balloon Model 34 2.3 Independent Component Analysis 37 ii 2.3.1 Linear Independent Component Analysis 38 2.3.2 Nonlinear Independent Component Analysis 40 2.3.3 41 2.4 2.4.1 2.5 Post-Nonlinear Independent Component Analysis Kernel Density Estimation Cluster-Kernel Density Estimation Independent Component Analysis of fMRI data CHAPTER COMPUTER SIMULATION 43 44 45 48 3.1 Equipment for Simulations 48 3.2 fMRI Data 48 3.3 Generation of Reference Functions 50 3.4 Linear Independent Component Analysis on fMRI 53 3.5 Post-Nonlinear Independent Component Analysis on fMRI 55 3.5.1 Modification of the Original PNL-ICA Algorithm 55 3.5.2 Verification of Modified Kernel Density Estimation 57 3.5.3 Testing of Modified PNL-ICA Algorithm 62 3.5.4 Modified PNL-ICA Algorithm on fMRI data 66 3.5.5 Computational Complexity of the PNL-ICA Algorithm 66 3.6 Tools for Analysis of Results 67 CHAPTER RESULTS AND DISCUSSION 71 4.1 Preprocessing 71 4.2 Result of Linear ICA on fMRI 71 4.3 Result of PNL-ICA on fMRI 83 CHAPTER CONCLUSION 85 5.1 Conclusion 85 5.2 Future Work and Recommendation 86 REFERENCES 87 iii SUMMARY It is desirable to have systems which can noninvasively monitor the brain function of patients, especially coma patients, as they cannot communicate with their physicians. It is deemed that a hybrid imaging technique using functional magnetic resonance imaging (fMRI) and electroencephalogram (EEG), which complement each other’s strengths and weaknesses, can be used to achieve such a system. Moreover, both techniques are neither radioactive nor invasive and, thus are extremely safe for the patients. fMRI is a new technique for localising brain activity and independent component analysis (ICA) is a relatively new technique for blind source separation (BSS). The principle of brain modularity states that different regions of the brain perform different functions independently. Thus, spatial ICA can be applied on fMRI to localise the functions of the brain. Brain signal has long been shown to be nonlinear, so applying a nonlinear ICA method to analyse fMRI signals should yield improved results. However nonlinear ICA yields non-unique solutions, therefore alternative methods are needed. The post-nonlinear (PNL) ICA model has been used here because of its close resemblance to a simplified balloon model. The balloon model is a biomechanical model of the haemodynamic system, which includes transient states. Both linear and PNL-ICA was applied to the fMRI data. There are two purposes of applying linear ICA to fMRI data. Firstly, it served to familiarise fMRI data and ICA algorithms. Secondly, it provides a reference for comparison with the PNL-ICA algorithm at a later stage. Linear ICA was able to iv decompose the fMRI signals into their respective independent components in this study. The results also indicate that the choice of algorithm could be important to the success of decomposition. PNL-ICA was subsequently applied to the fMRI data and the results were compared with those from the linear ICA. The results of PNL-ICA were less satisfactory. There are two possible reasons for this. The simplest possibility is that the assumptions used to represent the simplified balloon model with the PNL model are incorrect. Another less likely possibility is that the PNL model cannot sufficiently represent the simplified balloon model, even though the simplified balloon model is correct. However to ascertain this, we need data sets with the CBF, CBV, CMRO2 and BOLD signal to compare the effect of simplifying the balloon model. Although the results obtained are not as encouraging as expected, it is premature to disregard the PNL-ICA technique for fMRI signal deconvolution. Further studies need to be conducted on more definitive fMRI data sets before any concrete conclusions can be drawn on the method tested. v LIST OF ABBREVIATIONS 2D Two Dimensional 3D Three Dimensional 4D Four Dimensional BCI Brain Computer Interface BIRCH Balanced Iterative Reducing and Clustering using Hierarchies BOLD Blood Oxygenation Level Dependent BSS Blind Source Separation CBF Cerebral Blood Flow CBV Cerebral Blood Volume CF Clustering Feature CMRO2 Cerebral Metabolic Rate of Oxygen CSF Cerebral Spinal Fluid CT Computer Tomography EEG Electroencephalogram EPI Echo planar imaging FDA Food and Drug Administration FID Free Induction Decay fMRI Functional Magnetic Resonance Imaging FSE Fast Spin Echo GE Gradient Echo GUI Graphic User Interface HRF Haemodynamic Response Function IC Independent Component vi ICA Independent Component Analysis IR Inversion Recovery MR Magnetic Resonance MRI Magnetic Resonance Imaging MSE Mean Square Error NMR Nuclear Magnetic Resonance PCA Principal Component Analysis PDW Proton Density Weighted PET Positron Emission Tomography PNL Post-Nonlinear rCBF Regional Cerebral Blood Flow RF Radiofrequency SE Spin Echo SPECT Single Photon Emission Computed Tomography SPM Statistical Parametric Mapping SNR Signal-to-Noise Ratio T1W T1 Weighted T2W T2 Weighted T2*W T2* Weighted TE Echo Delay Time TR Repetition Time vii LIST OF FIGURES Figure 1.1 Timeline of the development of fMRI Figure 2.1 Basic ideology of MRI Figure 2.2 (a) Proton rotate about its own axis (b) When external magnetic field, B0, is applied, the proton not only rotate about its own axis, but also rotates about the axis of B0. 11 Illustration of the nuclei’s alignment at equilibrium (a) before and (b) after B0 is applied 12 Figure 2.4 Net magnetisation (a) before and (b) after the RF pulse is applied 13 Figure 2.5 Illustration of nutation, the spiral motion of Mnet from z-axis towards x-y plane 14 Illustration of the spin dephasing. (a) Mxy just after RF pulse is removed, (b) spin-spin interaction caused inhomogeneities in magnetic field, (c) spins completely out of phase, with no net transverse magnetic field 17 Figure 2.7 Illustration of the spin echo pulse sequence 20 Figure 2.8 Illustration of the gradient echo pulse sequence 22 Figure 2.9 Usual direction of axes in a MRI machine. 23 Figure 2.3 Figure 2.6 Figure 2.10 Illustration of the changes (a) in phases when a phase encoding gradient is applied, (b) in precessional frequencies when a frequency encoding gradient is applied, and (c) in both phases and precessional frequencies when both phase and frequency encoding gradient are applied. 25 Figure 2.11 Chart showing the spatial, temporal resolution and invasive nature of various functional brain mapping technique 29 Figure 2.12 Illustration of fMRI scanning procedure and signal collected 30 Figure 2.13 Illustration of oxy and deoxy-haemoglobin concentration in blood vessels 33 Figure 2.14 BOLD signal strength vs time during stimulant onset 33 Figure 2.15 Block diagram of the balloon model 35 Figure 2.16 Simplified balloon model 36 Figure 2.17 PNL-ICA model based on simplified balloon model 36 viii not evident, or at least not obvious, in the time course of the IC map. This corresponds to the observation made by other researchers that, with a low magnetic field (1.5T) fMRI machine, these transients are not detected [21]. Although the shape of Figure 4.2 is a close resemblance to Figure 4.3, it is observed that the amplitude is different. This is an inherent issue with ICA, whereby the variance of the IC is normalised as mentioned in Section 2.3.1. Figure 4.4 is the scatter plot of the unfiltered time course of the independent components. From this figure, another characteristic of the task-related IC map is observed. The correlation coefficient of the task-related IC map stands out prominently from the rest, as seen in Figure 4.4. Component Map 44 Unfiltered Time Course with Corr Coeff of 0.70937 Intensity 10 50 100 150 Time/sec 200 250 300 Figure 4.2 Time course of Subject 01 with nonlinearity Component Map 42 Unfiltered Time Course with Corr Coeff of 0.73427 Intensity 10 −5 50 100 150 Time/sec 200 250 300 Figure 4.3 Time course of Subject 01 with Gaussian nonlinearity 75 Correlation Coefficients of Unfiltered Time Course 0.8 0.7 0.6 0.5 0.4 0.3 0.2 0.1 10 20 30 40 50 60 IC Map Number 70 80 90 100 Figure 4.4 Correlation coefficient of unfiltered task related IC map from Subject 01 Figure 4.5 shows the filtered time course of the task-related IC map. It is band-pass filtered using a Kaiser filter window with a cut-off of [1/90 1/15] Hz. Initially, a low-pass filter with a cut-off frequency of 1/90 Hz is used, however there is no observable difference between the filtered and unfiltered time course. Therefore, a band-pass filtering was attempted. Component Map 44 Filtered Time Course with Corr Coeff of 0.70937 Intensity −2 −4 50 100 150 Time/sec 200 250 300 Figure 4.5 Filtered time course of the task related IC map from Subject 01 76 As there is no guideline for choosing the low-pass cut-off frequency, it was arbitrarily set using trial and error method. However, all the tested cut-off frequencies, achieved either no noticeable difference with the unfiltered time course, or have a time course as in Figure 4.5. It is obvious that the time course in Figure 4.5 is over filtered, as it resembles simple mixtures of sine wave, rather than the expected reference wave. Thus, perhaps the suggestion of not doing a low-pass filtering to the time course is valid [21]. Figure 4.6 is the scatter plot of the filtered time course of the independent components. From this figure, it is clear that band-pass filtering destroyed the prominently displayed correlation coefficient of the task related IC map, as seen in Figure 4.4. The correlation coefficient of the task related IC map does not improve as significantly as the correlation coefficients of the other IC maps. In addition, since the high-pass filtering does not make any notable difference, it might be easier to access the results without any filtering. 77 Correlation Coefficients of Filtered Time Course 0.9 0.8 0.7 0.6 0.5 0.4 0.3 0.2 0.1 10 20 30 40 50 60 IC Map Number 70 80 90 100 Figure 4.6 Correlation coefficient of filtered task related IC map from Subject 01 Component Map 60 Unfiltered Time Course with Corr Coeff of 0.29292 −20 Intensity −30 −40 −50 −60 50 100 150 Time/sec 200 250 300 Figure 4.7 Time course of a poorly performed subject Figure 4.7 shows the time course of a poorly performing subject. It is clear that the time course does not resemble the reference wave. From the scatter plot of the correlation coefficient, shown in Figure 4.8, it is clear that none of the correlation coefficient is significantly higher than the rest. Thus, those poorly performing subjects can easily be identified from the scatter plot of the correlation coefficient and the time course. 78 Correlation Coefficients of Unfiltered TimeCourse 0.35 0.3 0.25 0.2 0.15 0.1 0.05 10 20 30 40 50 60 IC Map Number 70 80 90 100 Figure 4.8 Scatter plot course of a poorly performed subjects . The activated region of the subjects are detected by using the absolute of the z-score, zscore, which is defined as follows, zscore ( x) = x−µ σ (4.1) where x is the data point, µ and σ are the mean and variance of the ensemble of data respectively. The zscore cut-off is set at 3.3 to have a probability, p< 0.0001 of false activation. Thus, any voxel with a z-score of greater than 3.3 is considered to be activated. The final activation map is the average of IC map from the eight subjects, which are considered to be good samples. The z-score with a cut-off of is then used for the average activation map. The z-score is lower here because in a way, the average activation map has already been checked. The final activation map given in the figures below are further tuned by removing clusters that has less than activated 79 neighbours. Figure 4.9 shows the activated region using fastICA with hyperbolic tangent nonlinearity, whereas Figure 4.10 shows the activated region using fastICA with Gaussian nonlinearity. From both figures, we can see that both nonlinearities give similar activation regions. Figure 4.9 Activation regions detected by hyperbolic tangent nonlinearity 80 Figure 4.10 Activation regions detected by Gaussian nonlinearity Figure 4.11 shows the activation regions given by fastICA with Gaussian nonlinearity on Subject 16. It is clear that the activated regions are not clustered together, thus linear ICA failed to decompose the fMRI data. This is in contrast to what was suggested earlier, where Gaussian nonlinearity gave a better decomposition than hyperbolic tangent. Here, it is clear that the Gaussian nonlinearity has given an incorrect detection of the IC map. Thus the choice of nonlinearity type does affect the result, and both time course and activation map has to be examined before deciding if the IC map is task-related or not. The time course and scatter plot does however give a good indication of the quality of the decomposition. One observation from Figure 81 4.11, there is some similarity in the region of activation in the posterior part of the brain, as compared to Figure 4.9 and 4.10, though the clusters are smaller and deem insignificant. This might again be that the activation is at the nonlinear region of the BOLD-CBF transfer function. Thus, the linear ICA can only give some degree of decomposition as seen in Figure 3.14 and 3.15, where fastICA is applied on the PNL mixtures. Figure 4.11 Activation area for Subject 16 with Gaussian nonlinearity, IC map 25 82 4.3 Result of PNL-ICA on fMRI Due to the tremendous computing time required (about 2-3 weeks per subjects), only six subjects were tested with the modified PNL-ICA algorithm. Those tested were Subject 01, 02, 03, 04, 11 and 16. Unfortunately, the PNL-ICA result did not turn out to be consistent with the simplified balloon model. The results obtained indicate that each volume scanned is independent with respect to the stimulant, which is impossible. As the subjects form a good mix of both good and bad sample from the linear ICA analysis, it can be concluded the PNL-ICA algorithm failed to extract the independent components from the fMRI data set. The results (correlation coefficients of the unfiltered timecourse) of the PNL-ICA algorithm are shown in Table 4.3. It indicates that the correlation coefficient of the subjects are very low; all subjects’ correlation coefficient are well below 0.2. Figure 4.12 shows the typical correlation coefficients of the unfiltered timecourse of one of the subject we have analysed. From this figure, it is also clear that there is no independent component that stands out from the rest. Thus, it is impossible to pinpoint the desired component(s). Table 4.3 Maximum correlation coefficient of the unfiltered timecourse of the various subjects Subject Max Unfiltered Correlation Coefficient 01 02 03 04 11 16 0.1601 0.1735 0.1810 0.1637 0.1824 0.1781 83 Correlation Coefficients of Unfiltered TimeCourse 0.2 0.18 0.16 0.14 0.12 0.1 0.08 0.06 0.04 0.02 20 40 60 IC Map Number 80 100 Figure 4.12 Correlation coefficient of the unfiltered timecourse of Subject 11 With six subjects giving consistent results, this bring out two possibilities as follows, i. The simplified balloon model is invalid – one or more of the assumptions used to simplify the balloon model is invalid, hence the simplified balloon model might have become less accurate than the original balloon model. Therefore, even if the PNL-ICA model matches the simplified balloon model, it does not represent the underlying fMRI model, and thus the model failed to extract the independent components. ii. The simplified balloon model is correct, but is not adequately represented by the PNL-ICA model – from the discussion and analysis in Section 2.2.3, this should be quite unlikely. 84 CHAPTER CONCLUSION 5.1 Conclusion Motivated by the aspiration of having a continuous health monitoring system of the brain, analysis of the fMRI data was taken as the first step to achieve the final objective. In this thesis, both linear and PNL-ICA models were applied to the fMRI data set. The linear ICA has proved to be popular and successful signal processing algorithm in BSS applications. In particular, linear ICA has given good results for separation of fMRI data. Therefore, it is used as a comparison for the results of PNL-ICA on fMRI. The results of linear ICA showed that it is effective in detecting the task-related components from the fMRI data, although the choice of algorithm is also important. However, the results of PNL-ICA in this study are unsuccessful for the six subjects studied. There are two possible explanations for this. The simplest and most likely possibility is that the assumptions that were used to represent the simplified balloon model with the PNL model are wrong. If this was so, the PNL-ICA cannot be applied to fMRI data. Another less likely possibility is that the PNL model cannot adequately represent the simplified balloon model, although the simplified balloon model is correct. In short, these two questions need to be answered sequentially: Firstly, are the assumptions for the simplified balloon model correct? If so, can the PNL model sufficiently represent the simplified balloon model? 85 Therefore, it is premature to disregard the PNL-ICA model for analysis of fMRI. Further study needs to be conducted on more definitive fMRI data sets before drawing any concrete conclusion on the proposed model. 5.2 Future Work and Recommendation The following are suggested as possible future work: i. If the research is developing in this direction, then the two fundamental questions must be answered. That is, a) the correctness of the assumptions for the simplified balloon model and b) the effectiveness of PNL model to represent the resultant simplified balloon model. However, this might proved difficult if we cannot get another data set with the CBF, CBV, CMRO2 and the BOLD signal. ii. A more sophisticated segmentation algorithm can be developed to separate the brain from the unwanted portion. This is to reduce the size of fMRI data, so that computational time can be greatly reduced. 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[50] Esposito F., Formisano E., Seifritz E., Goebel R., Morrone R., Tedeschi G. and Di Salle F., "Spatial independent component analysis of functional MRI timeseries: to what extent results depend on the algorithm used?," Hum Brain Mapp, vol. 16, pp. 146-57, 2002. 90 [...]... applying nonlinear ICA to the fMRI signal data will result in better source separation of signals by their spatial origin of fMRI signals than linear ICA algorithm For this study, the PNL-ICA algorithm was applied to fMRI signal data and the results was compared to that from linear ICA algorithms for this application This project is focused on the development of nonlinear ICA algorithms 7 CHAPTER 2 THEORY... perform different functions and hence measured brain signals should be able to decomposed into their independent sources [8] Independent component analysis (ICA) is a powerful signal processing technique for blind source separation (BSS) which can decompose mixed signals into their independent sources [9,10] Therefore, ICA can be applied to fMRI data for extracting the independent components The fMRI. .. the linear ICA model 38 Figure 2.20 Mixing stage of signals and demixing stage of the nonlinear ICA model 40 Figure 2.21 Post-Nonlinear ICA model 42 Figure 2.22 Basic ideology of ICA, applied on fMRI data 46 Figure 2.23 The IC maps are linearly mixed, forming the measured signals 46 Figure 2.24 Plot of applied stimulant vs volume 47 Figure 3.1 The pre -processing steps 49 Figure 3.2 HRF model using a simple... Functional Magnetic Resonance Imaging fMRI is a technique for localising brain activity An fMRI machine is basically an advance magnetic resonance imaging (MRI) machine that is programmed to detect a functional signal rather than a structural signal fMRI usually measures the blood oxygenation level dependent (BOLD) signal on a voxel by voxel basis, which increases with increased brain activity With the... amplifying their signal as much as 10,000 times Ogawa called this effect blood oxygenation level dependent (BOLD) contrast imaging and published a 3 paper in 1990 [4] The BOLD contrast image is exceptionally good when acquired with magnet stronger than 4 Tesla Ogawa’s discovery leads to the development of effective fMRI 1.1.2 Functional Magnetic Resonance Imaging fMRI is a technique for localising brain... bi-Gaussian data 60 Figure 3.9 Magnified view of the Gaussian density estimation 60 Figure 3.10 Plot of computational time of the three algorithms 61 Figure 3.11 Plot of actual fMRI data density estimation 61 Figure 3.12 Plots showing the original signals and the mixed signals 63 Figure 3.13 Plot comparing the results of original and modified PNL-ICA algorithm 64 Figure 3.14 FastICA with Gaussian nonlinearity... Thus, a continuous monitoring of the patient’s brain should tell a lot about the patient’s health Unfortunately, due to the cost of the equipment and shielding requirements, it is not economical or practical to use fMRI for continuous monitoring Furthermore, it is technically impossible, as the BOLD signal will saturate under long exposure of a constant strong magnetic field Moreover, the use of RF... Table 2.2 Image contrast and their respective TR and TE 19 Table 3.1 Computational Time and the mean square error of the various algorithms 61 Table 3.2 Average computation time per iteration for the simulated data 64 Table 3.3 Average computation time per iteration for fMRI data 66 Table 4.1 Linear ICA result using tanh nonlinearity in fastICA 73 Table 4.2 Linear ICA result using Gaussian nonlinearity... the independent components The fMRI signals comprise effects from the applied stimulant, background activities (breathing, heartbeat etc) and motion of patient etc These effects are deemed to be independent events, which could be separated using ICA Linear ICA, because of its simplicity, has been applied to fMRI brain signal data and has shown reasonably good results for separating the brain’s activations... hybrid-techniques (e.g fMRI & EEG and fMRI & PET), where two or more different techniques are combined to achieve better imaging qualities [16-18] A hybrid method could prove to be possible to achieve the desired continuous monitoring especially in an intensive care unit environment Electroencephalogram (EEG) is a well-established method to 6 understand the conditions of the brain using 1D/2D signal processing . ADVANCED SIGNAL PROCESSING ALGORITHMS FOR fMRI TEY ENG TIAN NATIONAL UNIVERSITY OF SINGAPORE 2003 ADVANCED SIGNAL PROCESSING ALGORITHMS FOR fMRI. origin of fMRI signals than linear ICA algorithm. For this study, the PNL-ICA algorithm was applied to fMRI signal data and the results was compared to that from linear ICA algorithms for this. processing technique for blind source separation (BSS) which can decompose mixed signals into their independent sources [9,10]. Therefore, ICA can be applied to fMRI data for extracting the independent