Correlation transfer function analysis as a biomarker for Alzheimer brain plasticity using longitudinal resting-state fMRI data

Neural plasticity is the ability of the brain to alter itself functionally and structurally as a result of its experience. However, longitudinal changes in functional connectivity of the brain are still unrevealed in Alzheimer’s disease (AD). This study aims to discover the significant connections (SCs) between brain regions for AD stages longitudinally using correlation transfer function (CorrTF) as a new biomarker for the disease progression. The dataset consists of: 29 normal controls (NC), and 23, 24, and 23 for early, late mild cognitive impairments (EMCI, LMCI), and ADs, respectively, along three distant visits. The brain was divided into 116 regions using the automated anatomical labeling atlas, where the intensity time series is calculated, and the CorrTF connections are extracted for each region. Finally, the standard t-test and ANOVA test were employed to investigate the SCs for each subject’s visit. No SCs, along three visits, were found For NC subjects. The most SCs were mainly directed from cerebellum in case of EMCI and LMCI. Furthermore, the hippocampus connectivity increased in LMCI compared to EMCI whereas missed in AD. Additionally, the patterns of longitudinal changes among the different AD stages compared to Pearson Correlation were similar, for SMC, VC, DMN, and Cereb networks, while differed for EAN and SN networks. Our findings define how brain changes over time, which could help detect functional changes linked to each AD stage and better understand the disease behavior.


Dataset
The dataset was taken from the Alzheimer's Disease Neuroimaging Initiative (ADNI) database.The ADNI was launched in 2003 as a public-private partnership, led by principal investigator Michael W. Weiner, MD.ADNI consisted of participants enrolled at 57 clinical centers in the US and Canada, funded as a private-public partnership.All ADNI studies are conducted according to the Good Clinical Practice guidelines, the Declaration of Helsinki, and U.S. 21 CFR Part 50 (Protection of Human Subjects), and Part 56 (Institutional Review Boards).Written informed consent was obtained from all participants before protocol-specific procedures were performed.The ADNI protocol was approved by the Institutional Review Boards of all of the participating institutions.The main objective of ADNI is to test whether combining different diagnosing techniques can be pooled to characterize the progression of MCI and early AD.For up-to-date information, see www.adni-info.org.A complete description of ADNI is available at http:// adni.loni.usc.edu/.Moreover, the data access requests are to be sent to http:// adni.loni.usc.edu/ data-sampl es/ access-data/.
The rs-fMRI images were collected at baseline, three months, six months, 12 months from baseline, and annually afterward.We did exclude the patients who had not at least two follow-up visits following the baseline scan.In this study, 99 subjects were downloaded from ADNI, formed of four classes: NCs, EMCI, LMCI, and AD patients, as reported in Table 1.The rs-fMRI images were acquired using 3.0 Tesla Philips Achieva scanners.The scanning protocol parameters are reported in Table 2.According to ADNI2 inclusion criteria https:// adni.loni.usc.edu/ wp-conte nt/ uploa ds/ 2008/ 07/ adni2-proce dures-manual.pdf, the Mini-Mental State Exam (MMSE) score for CN, EMCI, and LMCI is between 24 and 30.While the exam score for AD is between 20 and 26.For all groups, exceptions may be made for subjects with less than 8 years of education at the discretion of the project director.

Methodology Data preprocessing and brain network analysis
The typical preprocessing procedures for rs-fMRI are carried out, as shown in Fig. 1, using the software tool Statistical Parametric Mapping SPM12 (Welcome Trust Centre for Neuroimaging, London, UK) 16 .It involves discarding the first ten time-point volumes for each subject in order to ensure magnetization equilibrium.The remaining volumes are then corrected for the interleaved order of slices, in which the all odd-number slices were collected first and then all even-numbered slices.Registration for head motion artifact elimination, and co-registration of functional and structural images has been later applied.The images are then normalized to standard space using the SPM12 MNI/EPI (Montreal Neurological Institute/Echo Planer Image) template.The images were spatially smoothed using a 5 mm FWHM Gaussian kernel to increase the signal to noise ratio.Each volume was then segmented into 116 regions of interest (ROIs), as found in 9 , according to automatic anatomical atlas labeling (AAL) [17][18][19] .The different ROI's mean intensity time series was then obtained and band-pass-filtered at 0.01-0.08Hz to better localize the rs-fMRI while removing the noise signals as a result of some psychological artifacts such as breathing, and heartbeat.Finally, each subject was expressed by a matrix with 116 (number of regions) × 130 (time points), defining the time signal for each ROI.

CorrTF feature extraction
The correlation transfer function (CorrTF) quantifies the amount of information transmitted between the input and output ROIs.Therefore, the properties of the functional connection path between any two regions can be anticipated.AD is characterized by nerve cell death, affecting the region's connection path.As a result, alterations in the connection path may potentially differentiate between healthy and diseased cases 9,20,21 and provide critical information about changes in brain connectivity over time.CorrTF feature extraction technique can be considered as a biomarker for AD stage identification 9 .
Theoretically, the transfer function models the system's output for each possible input 9 .The relationship between output y(t) and input x(t), for any system, can be modeled using where the h(t) is the impulse response that defines the system behavior.While the relationship in the frequency domain can be modeled using where Y(f), X(f) and H(f) are the Fourier transform of the y(t), x(t), and h(t) respectively.Similarly, this definition can be interpreted to model the connectivity path between any pair of brain regions, as illustrated in where CorrTF (ROI 1 , ROI 2 ) is the transfer function calculated between the mean time series of ROI 1 and ROI 2 , Ƒ is the discrete Fourier Transform.

Statistical analysis
A standard t-test and ANOVA were employed to explore the between-group changes in CorrTF connections activation over time at a significance level of p < 0.05.The data were normalized, so that the sum of the squares equal one, to fulfill the normal distribution condition for the t-test.For NC and each disease stage, the statistical significance of every CorrTF connection, along three visits, was examined.The connection is considered significant if there were significant differences in activation between both pairs; baseline-visit1 and visit1-visit2.

Results
In this paper, we are interested in extracting the significant connections that characterize the progression of AD in each stage.A standard t-test and ANOVA test were employed to explore the between-group changes in CorrTF connections activation over time, at a significance level of p < 0.05.Almost all connections extracted using t-test included within connections extracted using ANOVA test.Consequently, we will discuss the common connections extracted using both tests.The connections regions names and their abbreviations have been listed in Table 3.
Figure 2 shows the 133 significant CorrTF connections that characterize the EMCI progression.Among these connections, we found that the connections were mainly directed only from eight brain regions which are; Vermis_3, Left CAL, Left PCL, Right TPOmid, Right TPOsup, Left HES, Right HIP, and Left SPG.The number of connections directed from each region are: 101, 12, 10, 3, 3, 2, 1, and 1 respectively.
Figure 3 shows the 79 significant CorrTF connections that characterize the LMCI progression.Among these connections, we found that the connections were mainly directed only from five brain regions which are; Left CRBL10, Right HIP, Left CRBLCrus1, Left ACG, and Left CRBL3.The number of connections directed from each region are: 61, 13, 2, 2, and 1 respectively.
Figure 4 presents the 41 significant CorrTF connections that characterize the AD progression.Among these connections, we found that the connections were mainly directed only from four brain regions: left TPOsup, Right STG, Right PCL, and Right REC.The number of connections directed from each region are: 34, 4, 2, and 1 respectively.At all connections, the t-test critical value sign changed from positive to negative for the difference between baseline-visit1 and visit1-visit2, respectively, except the connections directed from Right STG changed in the opposite direction.In contrast to the previously mentioned stages of AD, the NC showed no significant statistical difference in any CorrTF connections between baseline-visit1 and between visit1-visit2.
In Fig. 5, we grouped the significant connections to highlight the most altered network pairs among all AD stages.As observed from Fig. 5., the Cerebellum network has the highest contribution with 178 connections.It is worth noting that Figs. 2, 3, and 4 were generated using the CIRCOS tool 22 .
A comparison between the proposed method using CorrTF and Pearson correlation (PC) 23 is found in Fig. 6.The comparison was done to validate our results using CorrTF vs PC, the conventional method used in the literature.To increase the normality of the correlation coefficients, we first computed the PC for interregional connectivity.Fisher's z-transformation was then applied to standardize the PC feature values.Figure 6 presents the percentage of contribution for each functional network acquired using PC vs. CorrTF for each disease stage.

Discussion
This longitudinal fMRI study demonstrates the significant CorrTF connections that characterize the progression of each AD stage.It is worth noting that, while MCI is a risk factor for AD it is not a guarantee of developing the disease.In fact, most people with MCI will not go on to develop AD 24 .There are a number of things that people with MCI can do to reduce their risk of developing AD, such as staying mentally and physically active, eating a healthy diet, and getting enough sleep.In our manuscript, the progression of AD stages is represented by tracking the longitudinal changes in cognitive cohorts occurred such as those with probable AD dementia (established clinically rather than biologically) and a potential prodromal cohort (E/L MCI).

Analysis of EMCI progression
Figure 2 shows the significant connections that characterize the EMCI progression.Among these connections, there are 101 connections between different brain regions and Vermis_3.The Vermis is a part of the cerebellum involved in motor control, cognition, and emotional regulation 25 .Several studies suggest the relation between cerebellum Vermis and cognitive impairment and other symptoms of neurodegenerative diseases [26][27][28] .As Cerebellum Vermis may be involved in the visuospatial functions 26 , which may be impaired at the early stages of AD 29 .Consequently, we interpret that the significant contribution of vermis may be a compensatory activation related to the cognitive changes occurred to the EMCI subjects.Besides the Vermis, areas of SMC, such as the Left Paracentral Lobule, Left Superior Parietal Gyrus, Left Heschl Gyrus, and Right Superior Temporal Pole, are significantly contributed by 16 connections.Several studies investigated the role of SMC in the early AD stages [30][31][32][33][34] .Moreover, the connections within these particular regions are consistent with the literature [35][36][37][38][39][40][41][42] .Gupta et al. 43 demonstrate that the increased significance in Paracentral Lobule could be attributed to maintaining  www.nature.com/scientificreports/

Analysis of LMCI progression
Figure 3 presents the significant connections that characterize the LMCI progression.The most significant connections were directed from areas of the cerebellum; Left Cerebellum_10, Left Cerebellum_3 and Left Cerebellum Crus_1.This is consistent with the symptoms of decline in motor, cognition, and emotional activities since the cerebellum regulate these functions 50 .Recently, researchers have given attention to the alterations of cerebellum regions during AD's different stages 51 .Tang et al. 52 indicate significant changes regarding the FC of cerebellar cognitive subregions within the AD and MCI groups.The strength of left cerebellar FC is positively associated with certain cognitive subsites; memory, executive function, visuospatial function, and global cognition in AD and aMCI 53 .Hoxha et al. 54 concluded that the Cerebellum region is vulnerable to amyloid-β toxic destruction, even at the onset of the disease, resulting in impaired motor function.Jacobs et al. 55 state that the cerebellum is more than a silent witness in the pathophysiology of AD and its clinical phenomenology.Besides the cerebellum, there are 13 connections directed from Right Hippocampus.Compared to EMCI, the HIP connections participate more in the LMCI progression.This may be considered a compensatory action from the brain to restore the  loss of memory function, as suggested by Ref. 11 .Figure 3, also, shows the significant connections directed from Left Anterior Cingulate Gyrus.The Cingulate Gyrus is an essential part of the limbic system involved in regulating cognitive function 56 .Various studies investigate the relation between cognition impairment and Cingulate Cortex [56][57][58][59] .Wei et al. 60 found that the progressive MCI group had smaller left posterior and caudal Anterior Cingulate than the stable MCI group at baseline.The Anterior Cingulate Cortex is involved in central cognitive functions, such as motivation, decision-making, education, cost-benefit analysis, and conflict and problem solving 56 , which match the disease symptoms.

Analysis of AD progression
Figure 4 shows the significant CorrTF connections that identify the AD progression.The most significant connections were directed from the Left Superior Temporal Pole (TPOsup), a region of the EAN.The EAN is required for active maintenance of and manipulation of information in working memory as well as for principle problem solving and decision making 61 .Authors in 61 found that the FC within the EAN increased a bit in the MCI patient while declined significantly in the AD patients.Chen et al. 62 found that AD patients suffer from abnormal left TPOsup.Besides left TPOsup, Right Superior Temporal Gyrus, and Right Paracentral Lobule, areas of SMC are also associated with AD, as shown in figure.Zhan et al. 63 indicated abnormal network components in DMN, SMC, visual-sensory network, and visual-attention network during AD progression.Different researches demonstrate the abnormality of STG in AD patients [64][65][66][67] .Xiao et al. 64 reported that during a span of one year, individuals diagnosed with AD had notable degeneration in both STG and the left caudate.Furthermore, a reduction in grey matter volume in the right STG and left caudate was found to be associated with a drop in cognitive function.Clarke et al. 68 concluded that the high-risk AD group was related to a hub in the right paracentral lobe, a medial frontoparietal cortical area with sensorimotor functions.Figure 4 also shows a significant connection directed from the Right Rectus Gyrus, the area of DMN.Li et al. 69 stated that MCI patients exhibited considerably lower clustering coefficients in the right inferior parietal gyrus, right superior parietal gyrus, right rectus and, left middle frontal gyrus as well as lower shortest path length in the left paracentral lobule, compared to NC. Yang et al. 70 demonstrated that following donepezil treatment, patients with AD exhibited increased amplitude of low-frequency fluctuations, measured using rs-fMRI, in the right gyrus rectus, which decreased after treatment.
Among the significant connections in our findings, the t-test critical value changed from positive to negative except for the connection to Right STG in AD progression.Thus, we can interpret that this connection gets worth after specific compensation, whereas the other connections compensate for function loss as time progresses.In this context and according to the findings of Xiao et al. 64 , people diagnosed with Alzheimer's disease (AD) saw significant degradation in both the STG and the left caudate over the course of one year.Moreover, a decrease in grey matter volume in the right STG and left caudate nucleus was observed to be correlated with a decline in cognitive performance.

Analysis across different AD stages
The number of significant connections extracted for EMCI, LMCI, and AD was 133, 79, and 41, respectively, as observed in Figs. 2, 3, and 4.This observation interprets that the number of connections employed by the brain to transfer information is inversely proportional to the disease severity.With the disease progression, the brain FC may lose some of its compensation ability due to pathological changes.This may relate to the disease's progressive nature, which means its symptoms become worse with time.
Figure 5 presents the number of significant connections between each pair of networks for all AD stages with directionality ignored.We observed that the significant connections decrease with disease severity in six groups: SMC-Cereb, VC-DMN, EAN-Cereb, DMN-Cereb, SN-Cereb, and Cereb-Cereb, highlighted by red rectangles.These results define the clinical relationship between motor and cognitive function deterioration in AD progression [71][72][73] .Zheng et al. 73 reported that The Crus II of the cerebellum was functionally connected to several DMN regions and frontoparietal network (FPN) regions.It was also reported that the lobule IX of the cerebellum was involved in the DMN, FPN, VC, and SMC regions.While Halko et al. 72 reveal that altering activity in the lateral cerebellar Crus I/II impacts the cerebral DMN, however vermal lobule VII stimulation affects the cerebral dorsal attention system.We can also observe that the Cerebellum regions are highly affected by AD.Hoxha et al. 54 stated that the cerebellum is considered a region exposed to amyloid-β toxic destruction, even at the onset of the disease, with motor function implications.
In contrast, we observed, from Fig. 5, that the number of significant connections increased in LMCI from EMCI in the relation between the SN network and three other networks: SMC, VC, and EAN, highlighted by black rectangles.Generally, We observed an increase in the hippocampus, area of SN network, connectivity in LMCI compared to EMCI that was missed in the final AD stage.This may be considered a compensation action during the AD progression, which failed at the AD final stage, similar conclusion suggested by authors in 13 .
Figure 6 shows the percentage of significant contribution by each functional network obtained using Pearson Correlation vs. CorrTF.The percentage of contribution is the ratio of contributed regions to the total significant regions.For both techniques, the pattern of longitudinal changes among disease progression was quite similar in SMC, VC, DMN, and Cereb networks.However, the longitudinal pattern of change differed for EAN and SN networks.This comparison supports our interpretations and understanding of the longitudinal changes during the disease progression.

Limitations
There are several limitations in our study.First the dataset doesn't include subjects who known to be progressed to next severe stage e.g.subjects progressed from EMCI to LMCI or from LMCI to AD.Second, the proposed work investigates only the significance of one factor which is the CorrTF features.It will be very valuable to

Figure 2 .
Figure 2. The significant CorrTF connections that characterize the EMCI progression.Connection were colored based on the originated ROI color.The figure has been generated using the CIRCOS online tool (http:// mkweb.bcgsc.ca/ table viewer/).

Figure 3 .
Figure 3.The significant CorrTF connections that characterize the LMCI progression.Connection were colored based on the originated ROI color.The figure has been generated using the CIRCOS online tool (http:// mkweb.bcgsc.ca/ table viewer/).

Figure 4 .
Figure 4.The significant CorrTF connections that characterize the AD progression.Connection were colored based on the originated ROI color.The figure has been generated using the CIRCOS online tool (http:// mkweb.bcgsc.ca/ table viewer/).

Figure 5 .
Figure 5.Comparison between the numbers of significant connections, grouped by input-output networks with connection's directionality ignored, for different AD stages.SMC sensorimotor cortex, EAN executive attention network, VC visual cortex, Cereb cerebellum, DMN DefaultMode network, SN subcortical nuclei.

Table 3 .
List of the 116 brain regions and their abbreviations.