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Iterative temporal clustering analysis for the detection of multiple response peaks in fMRI
Magnetic Resonance Imaging 21 (2003) 51–53
Iterative temporal clustering analysis for the detection of multiple response peaks in fMRI Jia-Hong Gao*, Seong-Hwan Yee Research Imaging Center, University of Texas Health Science Center at San Antonio, San Antonio, TX, USA Received 19 June 2002; accepted 5 October 2002
Abstract The temporal clustering analysis (TCA) is a novel and effective technique for obtaining brain activation maps when the timing and location of the activation are completely unknown. Performing the TCA method once can only detect the largest peak of the activation time windows well, if multiple response peaks at the same location of the brain occur. However, this limitation can be removed by using a TCA method in an iterative way in order for the smaller peaks to be detected. Our in vivo fMRI experiments with event-related visual tasks have demonstrated this ability. © 2003 Elsevier Science Inc. All rights reserved. Keywords: MRI; fMRI; Brain; Function; Temporal
1. Introduction
2. Methods
The temporal clustering analysis (TCA) has been introduced recently as a novel and effective technique for obtaining brain activation maps when the timing and location of the activation are completely unknown [1,2]. Performing TCA method once can only detect the largest peak of the activation time windows well, if multiple response peaks at the same location of the brain occur [2]. In another words, smaller peaks may not be able to be detected using the TCA method. In clinical practices, the multiple response peaks occurring at the same location of the brain is not unusual. fMRI studies involving drug stimulation or epileptic seizures are typical examples. This loss of information (the undetected smaller response peaks) will have a serious consequence in the evaluation and understanding of the brain function in response to various stimulation. To remove this limitation, an iterative TCA technique is proposed and its feasibility to detect multiple response peaks will be demonstrated in an event-related fMRI experiment with a visual stimulation paradigm.
In this section, the basic mathematical description of the TCA technique will be given first, then the fMRI experiment with event-related visual stimulation paradigm will be described. Finally, the concept and procedure of iterative TCA will be introduced.
* Corresponding author. Tel.: ⫹1-210-567-8058; fax: ⫹1-210-5678152. E-mail address: [email protected] (J.-H. Gao).
2.1. TCA method For simplicity, fMRI data can be represented by a matrix format. FMRI data having m ⫻ n spatial pixels (m rows, n columns) at each time point and p time points for each pixel can be represented as a 2-dimensional matrix S having m ⫻ n number of rows and p number of columns as follows:
S⫽
冢
S 1,1 S 2,1 S 3,1 · · · S mxn,1
S 1,2 S 2,2 S 3,2 · · · S mxn,2
S 1,3 S 2,3 S 3,3 · · · S msn,3
··· ··· ··· · · · ···
S 1,p S 2,p S 3,p · · · S mxn,p
冣
(1)
In Eq. (1), the matrix element Si,j is given by the pixel value at the i-th spatial and j-th temporal position (S ⫽ [Si,j], 1 ⱕ i ⱕ m ⫻ n, 1 ⱕ j ⱕ p). Further, a transient matrix W can be obtained from the matrix S using the following algorithm used for selecting pixels (W ⫽ [Wi,j], 1 ⱕ i ⱕ m ⫻ n, 1 ⱕ j ⱕ p):
0730-725X/03/$ – see front matter © 2003 Elsevier Science Inc. All rights reserved. PII: S 0 7 3 0 - 7 2 5 X ( 0 2 ) 0 0 6 2 7 - 6
52
J.-H. Gao and S.-H. Yee / Magnetic Resonance Imaging 21 (2003) 51–53
Fig. 1. The averaged TCA signal for each iteration (a, b and c) and the activation maps for the first peak (d) and the second peak (e). The detected TCA signals for 3 subjects were averaged after normalization. The gray rectangular blocks were used to denote excluded time points in each iteration of TCA processing.
W i, j ⫽
再
S i, j 0,
if S i, j ⫽ max兵S i,1, S i,2, S i,3, · · ·, S i,p其 otherwise. (2)
In Eq. (2), there is a selection criterion that states whether a pixel at the i-th spatial point reached maximum at the j-th time point among the whole changes in time. The result of the selection is weighted by the intensity (or amplitude) of the original pixel. Therefore, if the matrix elements at the same column of W are summed columnwise, the result will be the integrated intensity of a temporal cluster at each time point. Furthermore, the 1-dimensional (1-D) temporal change pattern (a pattern of intensity-weighted temporal cluster size change), K, can be obtained as follows, if all the elements of matrix W are summed column-wise:
冘W
2.2. fMRI and visual stimulation paradigm For testing the iterative TCA methods in actual fMRI experiments, a visual task with event-related paradigm was used. Experiments were performed on a whole-body 1.9 T GE/ Elscint Prestige MRI scanner (GE/Elscint, Haifa, Israel). Informed consent, approved by the Institutional Review Board at our institution was obtained from all three participating subjects. For different strengths of response peaks, 2 s and 5 s duration of visual stimuli with a flashing checkerboard pattern (8 Hz) were used. For each subject, duration of 2 s and 5 s visual stimuli were given at 40 s and at 90 s, respectively, during a fMRI scan with a total scan time of 140 s. For the functional scan, a single slice covering the visual cortex was imaged using single-shot T2*-weighted gradient-echo EPI pulse sequence. The imaging parameters were as follows: slice thickness ⫽ 10 mm, in-plane resolution ⫽ 3.0 mm ⫻ 3.0 mm, and TR/TE/ ⫽ 1000 ms/45 ms/90°.
m⫻n
K ⫽ 共K 1, K 2, K 3, · · ·, K p兲, where K j ⫽
i, j
2.3. Data processing using iterative TCA
i⫽1
(3) Consequently, the plot of K against time points can be used to detect time windows of activation peak without assuming the temporal response pattern of the brain.
In this study, the TCA technique, which was outlined in Eqs. (1)–(3), was applied to the fMRI data sets acquired for each subject. The procedure of iterative TCA is as follows: Perform TCA for the first time to the whole data sets that will enable us to detect the largest peak. After the largest
J.-H. Gao and S.-H. Yee / Magnetic Resonance Imaging 21 (2003) 51–53
53
peak is detected, the data points associated with the largest peak in the data sets should be removed, then the TCA should be performed again on the remaining data sets, which will result in the second largest peak being detected. If the third largest peak needs to be detected, TCA should be performed once more on the data sets which have already removed the data points that are associated with both the first and second largest peaks. In general, the TCA procedure can be iteratively repeated until no more clear peaks occur. A total of three iterative TCA procedures were performed in our fMRI data sets generated with the visual stimulation. It was expected and is shown in the results below that the first largest peak, corresponding to the visual stimulation with 5 s duration, will be detected after the first time of the TCA operation. The second largest peak, corresponding to the visual stimulation with 3 s duration, should be identified after the TCA was performed one more time in the data sets which have already excluded the first largest peak. The TCA performed a third time should not produce any apparent peaks. For each detected peak, an activation map was obtained using a spatial clustered analysis technique [3] by comparing the data points acquired within the time-window of the peak and those acquired prior-visual stimulation. The activation maps were obtained using a threshold of t ⫽ 2.5 and spatial clustered size ⫽ 5 [3].
by gray block in Fig. 1(b), which were associated with the first largest peak) were excluded, the TCA was operated a second time. This operation resulted in the second peak, which corresponds to the visual stimulation with a 3 s duration, was detected at around 48 s (see Fig. 1(b)). As expected, the processing of TCA for the third time by excluding the data points associated with both the first and second peaks (denoted by two gray blocks in Fig. 1(c)) will not detect any peaks in our data sets (see Fig. 1(c)). In addition, the activation maps which correspond to the first and the second largest TCA peaks are shown in Fig. 1(d) and Fig. 1(e), respectively. The activation pixels are located in the area of the visual cortex.
3. Results
References
The resultant averaged time series from all three subjects of the detected TCA signal (after normalization) for each iterating TCA is shown in Fig. 1. After performing the first TCA operation, the largest peak was identified at approximately 100 s as shown in Fig. 1(a), which was corresponding to the visual stimulation with a 5 s duration. After the 24 MRI data points (denoted
[1] Liu Y, Gao JH, Liu H, Fox PT. The temporal response of the brain after eating revealed by functional MRI. Nature 2000;405:1058 – 62. [2] Yee S, Gao JH. Improved detection of time windows of brain response in fMRI using modified temporal clustered analysis. Magn Reson Imag 2002;20:7–16. [3] Xiong J, Gao JH, Lancaster JL, Fox PT. Clustered pixels analysis for functional MRI activation studies in human brain. Human Brain Mapping 1995;3:287–301.
4. Conclusions The iterative TCA technique has been successful, experimentally, in validating its ability to detect the multiple response peaks in the human visual cortex in response to multiple visual stimulation. This improved capability of the TCA method will find a wide application in both basic neuroscience research and clinical practice. Acknowledgments This work was partially supported by NIH grants AG19844 and MH52176.
Iterative temporal clustering analysis for the detection of multiple response peaks in fMRI Jia-Hong Gao*, Seong-Hwan Yee Research Imaging Center, University of Texas Health Science Center at San Antonio, San Antonio, TX, USA Received 19 June 2002; accepted 5 October 2002
Abstract The temporal clustering analysis (TCA) is a novel and effective technique for obtaining brain activation maps when the timing and location of the activation are completely unknown. Performing the TCA method once can only detect the largest peak of the activation time windows well, if multiple response peaks at the same location of the brain occur. However, this limitation can be removed by using a TCA method in an iterative way in order for the smaller peaks to be detected. Our in vivo fMRI experiments with event-related visual tasks have demonstrated this ability. © 2003 Elsevier Science Inc. All rights reserved. Keywords: MRI; fMRI; Brain; Function; Temporal
1. Introduction
2. Methods
The temporal clustering analysis (TCA) has been introduced recently as a novel and effective technique for obtaining brain activation maps when the timing and location of the activation are completely unknown [1,2]. Performing TCA method once can only detect the largest peak of the activation time windows well, if multiple response peaks at the same location of the brain occur [2]. In another words, smaller peaks may not be able to be detected using the TCA method. In clinical practices, the multiple response peaks occurring at the same location of the brain is not unusual. fMRI studies involving drug stimulation or epileptic seizures are typical examples. This loss of information (the undetected smaller response peaks) will have a serious consequence in the evaluation and understanding of the brain function in response to various stimulation. To remove this limitation, an iterative TCA technique is proposed and its feasibility to detect multiple response peaks will be demonstrated in an event-related fMRI experiment with a visual stimulation paradigm.
In this section, the basic mathematical description of the TCA technique will be given first, then the fMRI experiment with event-related visual stimulation paradigm will be described. Finally, the concept and procedure of iterative TCA will be introduced.
* Corresponding author. Tel.: ⫹1-210-567-8058; fax: ⫹1-210-5678152. E-mail address: [email protected] (J.-H. Gao).
2.1. TCA method For simplicity, fMRI data can be represented by a matrix format. FMRI data having m ⫻ n spatial pixels (m rows, n columns) at each time point and p time points for each pixel can be represented as a 2-dimensional matrix S having m ⫻ n number of rows and p number of columns as follows:
S⫽
冢
S 1,1 S 2,1 S 3,1 · · · S mxn,1
S 1,2 S 2,2 S 3,2 · · · S mxn,2
S 1,3 S 2,3 S 3,3 · · · S msn,3
··· ··· ··· · · · ···
S 1,p S 2,p S 3,p · · · S mxn,p
冣
(1)
In Eq. (1), the matrix element Si,j is given by the pixel value at the i-th spatial and j-th temporal position (S ⫽ [Si,j], 1 ⱕ i ⱕ m ⫻ n, 1 ⱕ j ⱕ p). Further, a transient matrix W can be obtained from the matrix S using the following algorithm used for selecting pixels (W ⫽ [Wi,j], 1 ⱕ i ⱕ m ⫻ n, 1 ⱕ j ⱕ p):
0730-725X/03/$ – see front matter © 2003 Elsevier Science Inc. All rights reserved. PII: S 0 7 3 0 - 7 2 5 X ( 0 2 ) 0 0 6 2 7 - 6
52
J.-H. Gao and S.-H. Yee / Magnetic Resonance Imaging 21 (2003) 51–53
Fig. 1. The averaged TCA signal for each iteration (a, b and c) and the activation maps for the first peak (d) and the second peak (e). The detected TCA signals for 3 subjects were averaged after normalization. The gray rectangular blocks were used to denote excluded time points in each iteration of TCA processing.
W i, j ⫽
再
S i, j 0,
if S i, j ⫽ max兵S i,1, S i,2, S i,3, · · ·, S i,p其 otherwise. (2)
In Eq. (2), there is a selection criterion that states whether a pixel at the i-th spatial point reached maximum at the j-th time point among the whole changes in time. The result of the selection is weighted by the intensity (or amplitude) of the original pixel. Therefore, if the matrix elements at the same column of W are summed columnwise, the result will be the integrated intensity of a temporal cluster at each time point. Furthermore, the 1-dimensional (1-D) temporal change pattern (a pattern of intensity-weighted temporal cluster size change), K, can be obtained as follows, if all the elements of matrix W are summed column-wise:
冘W
2.2. fMRI and visual stimulation paradigm For testing the iterative TCA methods in actual fMRI experiments, a visual task with event-related paradigm was used. Experiments were performed on a whole-body 1.9 T GE/ Elscint Prestige MRI scanner (GE/Elscint, Haifa, Israel). Informed consent, approved by the Institutional Review Board at our institution was obtained from all three participating subjects. For different strengths of response peaks, 2 s and 5 s duration of visual stimuli with a flashing checkerboard pattern (8 Hz) were used. For each subject, duration of 2 s and 5 s visual stimuli were given at 40 s and at 90 s, respectively, during a fMRI scan with a total scan time of 140 s. For the functional scan, a single slice covering the visual cortex was imaged using single-shot T2*-weighted gradient-echo EPI pulse sequence. The imaging parameters were as follows: slice thickness ⫽ 10 mm, in-plane resolution ⫽ 3.0 mm ⫻ 3.0 mm, and TR/TE/ ⫽ 1000 ms/45 ms/90°.
m⫻n
K ⫽ 共K 1, K 2, K 3, · · ·, K p兲, where K j ⫽
i, j
2.3. Data processing using iterative TCA
i⫽1
(3) Consequently, the plot of K against time points can be used to detect time windows of activation peak without assuming the temporal response pattern of the brain.
In this study, the TCA technique, which was outlined in Eqs. (1)–(3), was applied to the fMRI data sets acquired for each subject. The procedure of iterative TCA is as follows: Perform TCA for the first time to the whole data sets that will enable us to detect the largest peak. After the largest
J.-H. Gao and S.-H. Yee / Magnetic Resonance Imaging 21 (2003) 51–53
53
peak is detected, the data points associated with the largest peak in the data sets should be removed, then the TCA should be performed again on the remaining data sets, which will result in the second largest peak being detected. If the third largest peak needs to be detected, TCA should be performed once more on the data sets which have already removed the data points that are associated with both the first and second largest peaks. In general, the TCA procedure can be iteratively repeated until no more clear peaks occur. A total of three iterative TCA procedures were performed in our fMRI data sets generated with the visual stimulation. It was expected and is shown in the results below that the first largest peak, corresponding to the visual stimulation with 5 s duration, will be detected after the first time of the TCA operation. The second largest peak, corresponding to the visual stimulation with 3 s duration, should be identified after the TCA was performed one more time in the data sets which have already excluded the first largest peak. The TCA performed a third time should not produce any apparent peaks. For each detected peak, an activation map was obtained using a spatial clustered analysis technique [3] by comparing the data points acquired within the time-window of the peak and those acquired prior-visual stimulation. The activation maps were obtained using a threshold of t ⫽ 2.5 and spatial clustered size ⫽ 5 [3].
by gray block in Fig. 1(b), which were associated with the first largest peak) were excluded, the TCA was operated a second time. This operation resulted in the second peak, which corresponds to the visual stimulation with a 3 s duration, was detected at around 48 s (see Fig. 1(b)). As expected, the processing of TCA for the third time by excluding the data points associated with both the first and second peaks (denoted by two gray blocks in Fig. 1(c)) will not detect any peaks in our data sets (see Fig. 1(c)). In addition, the activation maps which correspond to the first and the second largest TCA peaks are shown in Fig. 1(d) and Fig. 1(e), respectively. The activation pixels are located in the area of the visual cortex.
3. Results
References
The resultant averaged time series from all three subjects of the detected TCA signal (after normalization) for each iterating TCA is shown in Fig. 1. After performing the first TCA operation, the largest peak was identified at approximately 100 s as shown in Fig. 1(a), which was corresponding to the visual stimulation with a 5 s duration. After the 24 MRI data points (denoted
[1] Liu Y, Gao JH, Liu H, Fox PT. The temporal response of the brain after eating revealed by functional MRI. Nature 2000;405:1058 – 62. [2] Yee S, Gao JH. Improved detection of time windows of brain response in fMRI using modified temporal clustered analysis. Magn Reson Imag 2002;20:7–16. [3] Xiong J, Gao JH, Lancaster JL, Fox PT. Clustered pixels analysis for functional MRI activation studies in human brain. Human Brain Mapping 1995;3:287–301.
4. Conclusions The iterative TCA technique has been successful, experimentally, in validating its ability to detect the multiple response peaks in the human visual cortex in response to multiple visual stimulation. This improved capability of the TCA method will find a wide application in both basic neuroscience research and clinical practice. Acknowledgments This work was partially supported by NIH grants AG19844 and MH52176.