This section summarizes our experiments and findings for SICE-based brain connectivity modeling of AD, MCI, and NC using FDG-PET data. Purposes of our study focus on how aspects of the connectivity patterns exhibited in the models relate to existing findings in the literature, and on how other aspects may suggest further investigations in brain connectivity research.
Data acquisition and preprocessing
The data used in our study include FDG-PET images from 49 AD, 348 116 MCI, and 67 NC subjects downloaded from the Alzheimer’s 349 disease neuroimaging initiative (ADNI) database. Demographic information and MMSE 352 scores of the subjects are summarized in . The ADNI was launched in 2003 by the National Institute on Aging (NIA), the National Institute of Biomedical Imaging and Bioengineering (NIBIB), the Food and Drug Administration (FDA), private pharmaceutical companies and non-profit organizations, as a $60 million, 5-year public-private partnership. The primary goal of ADNI has been to test whether serial MRI, PET, other biological markers, and clinical and neuropsychological assessment can be combined to measure the progression of MCI and early AD. The initial goal of ADNI was to recruit 800 adults, ages 55 to 90, to participate in the research – approximately 200 cognitively normal older individuals to be followed for 3 years, 400 people with MCI to be followed for 3 years, and 200 people with early AD to be followed for 2 years.
Demographic information and MMSE scores.
Preprocessing the images involves the following steps. Each subject’s FDG-PET image is spatially normalized to the MNI PET template, using the affine transformation and subsequent non-linear warping algorithm (Friston et al., 1995
) implemented in SPM. The affine deformation adjusts each whole brain image for its position, orientation, size, and global shape based upon minimizing the mean residual variance (Zhilkin and Alexander, 2004
). The non-linear warp, a linear combination of low spatial frequency basis discrete cosine functions, determines the optimal coefficients for each of the basis functions by minimizing the sum of squared differences between the raw MRI brain and the template image (Ashburner and Friston, 1999
). Simultaneously, the smoothness of the transformation is maximized using maximum a posterior (MAP). Once in the MNI template, Automated Anatomical Labeling (AAL) (Tzourio-Mazoyer et al., 2002
) is applied to extract data from each of the 116 anatomical volumes of interest (AVOI), and derived average of each AVOI for every subject based on the PET images.
Brain connectivity modeling by SICE and visualization techniques
42 AVOI are empirically chosen, which are brain regions known to be most affected by AD (Azari et al., 1992
; Horwitz et al., 1987
). These regions distribute in the frontal, parietal, occipital, and temporal lobes. Pease see for names of the AVOI and the lobe each of them belong to.
Names of the AVOI for connectivity modeling (L=Left hemisphere, R=Right hemisphere).
To build a brain connectivity model for AD, we first compute a sample covariance matrix, S
, of the 42 AVOI, based on the measurement data of the 42 AVOI from 49 AD patients. Then, we apply SICE to solve the optimization problem in Eq. (1)
based on the S
and a pre-selected λ. The solution
is further converted to a graph consisting of nodes (AVOI) and arcs (non-zero entries in
). Furthermore, considering that a graph of this kind may be too space-consuming for the paper, we adopt a matrix representation for the graph. Please see the first matrix in , for an example, which represents the brain connectivity model structure estimated by SICE at a certain λ. In the matrix, each row (column) corresponds to one of the 42 AVOI. A black cell corresponds to an arc. Because the matrix is symmetric, the total number of black cells is equal to twice the total number of arcs in the corresponding connectivity graph. Moreover, on each matrix, four red cubes are used to highlight the brain regions in each of the four lobes; that is, from top-left to bottom-right, the red cubes highlight the frontal, parietal, occipital, and temporal lobes, respectively.
(a) Brain connectivity models with total number of arcs equal to 60. (b) Brain connectivity models with total number of arcs equal to 120. (c) Brain connectivity models with total number of arcs equal to 180.
Furthermore, to facilitate the comparison between AD, MCI, and NC, connectivity models should also be developed for MCI and NC, respectively. The problem is how to select the λ value for each of three groups, so that the comparison between them will make sense. In this paper, we focus on comparing AD, MCI, and NC in terms of the distribution/organization of the connectivity, which has been less studied in the literature, but not in terms of the global scale of the connectivity, which has been studied substantially. To achieve this, we must factor out the connectivity difference between the three groups that is due to their difference at the global scale, so that the remaining difference will reflect their difference in the connectivity distribution/organization. A common strategy is to control the total number of arcs for each group to be the same, which has been adopted by a number of other studies (Supekar et al., 2008
; Stam et al., 2007
). We also adopt this strategy; specially, we adjust the λ in the estimation of the connectivity model of each group, such that the three models, corresponding to AD, MCI, and NC, respectively, will have the same total number of arcs. Also, by selecting different values for the total number of arcs, we can obtain models representing the brain connectivity at different strength levels. Specifically, given a small value for the total number of arcs, only strong arcs will show up in the resulting connectivity model, so the model is a model of strong brain connectivity; when increasing the total number of arcs, mild (or even weak) arcs will also show up in the resulting connectivity model, so the model is a model of mild-to-strong (or even weak-to-strong) brain connectivity. For example, shows the connectivity models for AD, MCI, and NC with the total number of arcs equal to 60, 120, and 180.
Finally, we introduce some other ways to visualize the connectivity models to facilitate the comparison between AD, MCI, and NC, such as graphs of nodes and arcs (e.g., ) and brain images (e.g., ):
Fig. 4 (i) Hippocampus and parahippcampus sub-network connectivity for AD, i.e., connectivity within the network and connectivity between the network and other regions in temporal lobe; green, blue, red arcs represent connectivity from strong to weak. (ii) Four (more ...)
displays a portion of the connectivity model for AD. Each node is an AVOI in in the temporal lobe. This graph focuses on the connectivity regarding the sub-network consisting of Hippocampus_L & R ((X39 & X40)) and ParaHippocampal_L & R (X41 & X42), so it only displays the arcs between each region in the sub-network and other regions in the temporal lobe, as well as the arcs between the regions in the sub-network. Other arcs are omitted. Furthermore, green arcs are arcs (black cells) appearing in the matrix plot of AD in , so they represent strong connectivity. Blue arcs are arcs not appearing in the matrix plot of AD in , but appearing in that in , so they represent less strong connectivity. Red arcs are arcs not appearing in the matrix plots of AD in , but appearing in that in , so they represent even less strong connectivity.
shows four axial slices of an AD brain. This graph focuses on displaying the connectivity between region X41, ParaHippocampal_L, and other regions in the temporal lobe. ParaHippocampal_L is highlighted in yellow. Regions highlighted in green, blue, and red are those in the temporal lobe that have strong, less strong, even less strong connectivity with ParaHippocampal_L, respectively. In a similar way, are developed for NC. Note that similar graphs to and can be developed for other portions of the brain connectivity model, or even the whole brain, which are not shown here due to space limits.
Fig. 5 (i) Hippocampus and parahippcampus sub-network connectivity for NC, i.e., connectivity within the network and connectivity between the network and other regions in temporal lobe; green, blue, red arcs represent connectivity from strong to weak. (ii) Four (more ...)
Comparison between AD, MCI, and NC in connectivity organization/distribution
The connectivity models estimated by SICE and various types of visualization techniques (matrix, graph, and brain slice) enable us to see the difference between AD, MCI, and NC in terms of connectivity organization/distribution. For example, shows fewer black cells in the temporal lobe of AD than NC, but more black cells in the frontal lobe of AD than NC, where black cells correspond to direct connections between brain regions. While visual comparison is an important initial step to pick out the differences, it should be followed by rigorous statistical hypothesis testing to check if the observed differences are statistically significant. Therefore, we perform hypothesis testing to check if the number of black cells within each lobe, used to represent the amount of direct connections within that lobe, is significantly different between each pair of the study groups (i.e., AD, MCI, and NC). The hypothesis testing is also performed for the number of black cells between lobes. Here, we show the steps for testing if the number of black cells within the temporal lobe of AD, nAD_T, is significantly different from that of NC, nNC_T.
- Draw samples of AD patients and samples of NC subjects, with replacement, from the original AD and NC datasets, respectively.
- Apply the SICE method to learn one connectivity model for AD and one for NC, based on the samples drawn. During the learning of each connectivity model, adjust the λ such that the two models have the same total number of arcs.
- Count the number of arcs (or equivalently, the number of black cells in the matrix representation) within the temporal lobe of the AD connectivity model. This number is a bootstrap sample for nAD_T; in a similar way, a bootstrap sample for nNC_T can be obtained.
- Repeat (i)–(iii) N times and obtain N bootstrap samples for nAD_T and nNC_T, respectively.
- Test the hypothesis that nAD_T and nNC_T are equal based on their respective bootstrap samples, and compute the P-value of the hypothesis test. Interpretation of the P-value is following: P-value <0.05 means strong evidence for nAD_T ≠ nAD_T; 0.05 < P <0.1 means some evidence (not strong though) for nAD_T ≠ nAD_T; P >0.1 means little evidence for nAD_T ≠ nAD_T, i.e., there is no significant difference between nAD_T and nNC_T.
Following similar steps to the above, we can also compare the amount of direct connections within other lobes as well as between lobes, for each pair of the study groups. The results are summarized in , which gives the P
-value of the hypothesis testing. Specifically, a P
-value is shown if it is smaller than 0.1 and replaced by a “–” otherwise. A P
-value is highlighted if it is smaller than 0.05. The P
-values presented here are those after correcting the effect of multiple testing using the standard False Discovery Rate (FDR) approach by Benjamini and Hochberg (1995)
. Note that because our multiple tests are not independent (the same datasets are used multiple times), the standard FDR approach might generate conservative results. This is a limitation of our current work and we will investigate how to overcome this limitation in future research. In addition to using P
-value for comparison, we also develop box plots, as shown in (only the box plots for AD vs. NC are shown due to the page limit).
P-value from the hypothesis test of connectivity difference between AD, MCI, and NC.
Box plots for comparing AD (yellow) vs. NC (green) in terms of the amount of intra-and inter-lobe direct connections (i.e., black cells or arcs).
Inspection of the results from visualizations, hypothesis testing, and box plots reveals the following interesting observations:
The temporal lobe of AD has a significantly lesser amount of direct connections than NC. This is true across the connectivity models at different strength levels (i.e., total arc number equal to 60, 120, and 180). In other words, even the direct connections between some strongly-connected brain regions in the temporal lobe may be disrupted by AD. In particular, it is clearly from that the regions “Hippocampus” and “ParaHippocampal” (numbered by 39–42, located at the right-bottom corner of ) are much more separated from other regions in AD than in NC. The decrease in the amount of connections in the temporal lobe of AD, especially between the Hippocampus and other regions, has been extensively reported in the literature (Supekar et al., 2008
; Wang et al., 2007
; Azari et al., 1992
; Horwitz et al., 1987
; Grady et al., 2001
). However, the temporal lobe of MCI does not show a significant decrease in the amount of direct connections, compared with NC. This may be because MCI does not disrupt the temporal lobe as severely as AD.
The frontal lobe of AD has a significantly more amount of direct connections than NC, which is true across the connectivity models at different strength levels. This is consistent with previous literature and has been interpreted as compensatory reallocation or recruitment of cognitive resources (Gould et al., 2006
; Stern, 2006
; Becker et al., 1996
; Woodard et al., 1998
; Saykin et al., 2004
; Grady et al., 2003
). Because the regions in the frontal lobe are typically affected later in the course of AD (our data are early AD), increase in the amount of connections in the frontal lobe may help preserve some cognitive functions in AD patients. Furthermore, the frontal lobe of MCI does not show a significant increase in the amount of direct connections, compared with NC. This indicates that the compensatory effect in MCI brain may not be as strong as that in AD brains.
There is no significant difference between AD, MCI, and NC in terms of the amount of direct connections within the parietal lobe and within the occipital lobe.
In general, human brains tend to have a less amount of between-lobe connections than within-lobe connections. A majority of the strong connections occurs within lobes, but rarely between lobes. These can be clearly seen from (especially ) in which there are a lot more black cells inside the red cubes than outside the red cubes, regardless of AD, MCI, and NC. Recall that the red cubes are used to highlight the four lobes.
AD has a significantly more amount of parietal-occipital direct connections than NC, which is true across the connectivity models at different strength levels. Increase in the amount of connections between the parietal and occipital lobes of AD has been previously reported in (Supekar, 2008
). It may also be interpreted as a compensatory effect. Furthermore, MCI also shows increase in the amount of direct connections between the parietal and occipital lobes, compared with NC, but the increase is not as significant as AD.
While the amount of direct connections between the frontal and occipital lobes shows little difference between AD and NC, this amount for MCI shows a significant decrease. Also, AD has a less amount of temporal-occipital connections, a less amount of frontal-parietal connections, but a more amount of parietal-temporal connections than NC.
We are also interested in knowing if there is a difference between AD, MCI, and NC, in terms of the amount of direct connections between hemispheres. To achieve this, we can count how many left–right pairs of the same regions have an arc (or black cell) between them in the connectivity models of AD, MCI, and NC, respectively. In addition to directly comparing the counts, we can also perform hypothesis testing (similar to the ones used for within-lobe and between-lobe comparisons). Results show that when the total number of arcs in the connectivity models is equal to 180 or 120, none of the tests is significant. However, when the total number of arcs is equal to 60, the P-value of the tests for “AD vs. NC”, “AD vs. MCI”, and “MCI vs. NC” are 0.038, 0.061, and 0.376, respectively. We further perform tests for the total number of arcs equal to 50 and find the P-value to be 0.026, 0.079, and 0.198 respectively. These results indicate that AD disrupts the strong connection between the same regions in the left and right hemispheres, whereas this disruption is not significant in MCI.
Comparison between AD, MCI, and NC in connection strength
We can use the quasi-measure developed in Section 2.2 to obtain an order for the inter-region connections in terms of the connection strength, for each of the three study groups. To present this order in a way that facilitates the comparison between the three groups, we propose a tree-like plot. As an illustrative example, is a tree-like plot developed from the brain connectivity models in . One way to read off information from is to look at it from right (small λ) to left (large λ). At a very small λ, i.e., λ=λ1, all regions are connected. As λ goes larger, i.e., λ1 < λ ≤λ2, X6, is the first region disconnected with other regions, so the connection between X6 and other regions is the weakest. As λ continues to go larger, i.e., λ2 − λ ≤ λ3, X4, X5, and the cluster of X1, X2, and X3 are disconnected, so the connection between them is the second weakest. Finally, with λ3 < λ, X1, X2, and X3 are disconnected, so the connectivity between them is the strongest.
A tree-like plot showing the order of connections between the brain regions in .
Following a similar manner, we develop a tree-like plot for AD, as shown in . Specially, the range of λ is determined such that the lower bound (λ=λL
) corresponds to a “fully-connected” graph, i.e., every node has at least one arc attached, and the upper bound (λ=λU
) corresponds to a “null” graph which has no arcs. Starting from the lower bound λ=λL
, as λ goes larger, i.e., λL
< λ ≤λ2
, region “Tempora_Sup_L” is the first one disconnected with the rest of the brain, so “Tempora_Sup_L” may be the weakest connected region. As λ continues to go larger, i.e., λ2
, the rest of the brain further splits into three disconnected clusters, including the cluster of “Cingulum_Post_R” and “Cingulum_Post_L”, the cluster of “Fusiform_R” up to “Temporal_Sup_R”, and the cluster of the other regions. As λ continuously increases, each current cluster further splits into smaller clusters. Eventually, when λ reaches λU
, all regions become disconnected. The sequence of the splitting gives an order for the inter-region connections in terms of the connection strength. Specifically, the earlier (i.e., smaller λ) a region or a cluster of regions becomes disconnected with the rest of the brain, the weaker it is connected with the rest of the brain. For example, in , it can be known that “Tempora_Sup_L” may be weakest connected with the rest of the brain in the brain network of AD; the second weakest ones are the cluster of “Cingulum_Post_R” and “Cingulum_Post_L”, and the cluster of “Fusiform_R” up to “Temporal_Sup_R”. It is very interesting to see that the weakest and second weakest connected brain regions in the brain network of AD include “Cingulum_Post_R” and “Cingulum_Post_L” as well as regions all in the temporal lobe, all of which have been found to be affected by AD early and severely (Supekar et al., 2008
; Wang et al., 2007
; Azari et al., 1992
; Horwitz et al., 1987
; Grady et al., 2001
A tree-like plot for AD, showing the order of connections in terms of connection strength.
Next, to facilitate the comparison between AD and NC, a tree-like plot is also constructed for NC, as shown in . By comparing the plots for AD and NC, we can observe the following two distinct phenomena: First, in AD, between-lobe connections tend to be weaker than within-lobe connections. This can be seen from which shows a clear pattern that the lobes become disconnected with each other before the regions within each lobe become disconnected with each other, as λ goes from small to large. This pattern does not show in for NC. Second, the same brain regions in the left and right hemispheres are connected much weaker in AD than in NC. This can be seen from for NC, in which the same brain regions in the left and right hemispheres are still connected even at a very large. However, this pattern does not show in for AD.
A tree-like plot for NC, showing the order of connections in terms of connection strength.
Furthermore, a tree-like plot is also constructed for MCI () and compared with the plots for AD and NC. In terms of the two phenomena discussed previously, MCI shows similar patterns to AD, but these patterns are not as distinct from NC as AD. Specifically, in terms of the first phenomenon, MCI also shows weaker between-lobe connections than within-lobe connections, which is similar to AD. However, this phenomenon is not as distinctive as AD. For example, a few regions in the temporal lobe of MCI, including “Temporal_Mid_R” and “Temporal_Sup_R”, appear to be more strongly connected with the occipital lobe than with other regions in the temporal lobe. In terms of the second phenomenon, MCI also shows weaker between-hemisphere connections in the same brain region than NC. However, this phenomenon is not as distinctive as AD. For example, several left–right pairs of the same brain regions are still connected even at a very large λ, such as “Rectus_R” and “Rectus_L”, “Frontal_Mid_Orb_R” and “Frontal_Mid_Orb _L”, “Parietal_Sup_R” and “Parietal_Sup_L”, as well as “Precuneus_R” and “Precuneus_L”. All above findings are consistent with the knowledge that MCI may be considered as a transition stage between normal aging and AD. Note that the tree-like plots in , and reveal the “observed” differences between AD, MCI, and NC. This serves as a starting point for comparing AD, MCI, and NC in terms of the connection strength. A challenging task following this may be to formulate an appropriate hypothesis testing to test the statistical significance of the observed difference, which will be investigated in future research.
A tree-like plot for MCI, showing the order of connections in terms of connection strength.
Use of SICE for classification of AD and NC
The purpose of this experiment is to assess the classification accuracy of the proposed method in Section 2.3. The experiment is performed on the PET dataset of 49 AD and 67 NC subjects. Leave-one-out cross-validation is applied. Specifically, we use each of the 116 (49 AD plus 67 NC) subjects as the “new” subject and the remaining subjects as the training data. Then, we apply the proposed method in Section 2.3 and obtain a “predicted” class (AD or NC) for the new subject. In this manner, we can obtain predicted classes for all 116 subjects. The predicted classes are compared with the true classes and classification accuracy is computed.
Results from the experiment are shown in and . In particular, shows the classification accuracy (vertical axis) of the 49 AD vs. λ values (horizontal axis), based on all 42 regions (blue curve), frontal regions only (red curve), and temporal regions only (green curve). Note that the classification accuracy varies with different λ’s, because different λ’s lead to different estimates for the inverse covariance matrices, θAD and θNC, which further affect performance of the classification based on them. In practice, we can choose a value for λ that achieves the desired classification accuracy for AD and NC, i.e., the desired sensitivity and specificity; and keep this λ for classifying future subjects.
Classification accuracy of AD.
Classification accuracy of NC.
Some observations can be made based on the results in and . The best sensitivity and specificity the proposed method can achieve are 88% and 88%, respectively. However, they are not achieved at the same λ, because gain in sensitivity is associated with loss in specificity. Furthermore, performance of the classification based on all 42 regions is much better than that based on frontal or temporal regions alone. This may be because both frontal and temporal connectivity, as well as other connectivity patterns identified in the previous section of the paper (e.g., left-right hemisphere connectivity), have some discriminating power. Thus, using all 42 regions in the classification takes advantage of the combinatory effect of the discriminating powers of these local connectivity patterns.