Deviation From Model of Normal Aging in Alzheimer’s Disease: Application of Deep Learning to Structural MRI Data and Cognitive Tests

Background. Psychophysiological and cognitive tests as well as other functional studies can detect pre-symptomatic stages of dementia. When assembled with structural data, cognitive tests diagnose NDs more reliably thus becoming a multimodal diagnostic tool. Objective. Our main goal is to improve screening for dementia by studying an association between the brain structure and its function. Hypothetically, the brain structure-function association has features specific for either disease-related cognitive deterioration or normal neurocognitive slowing while aging. Materials and methods. We studied a total number of 287 cognitively normal cases, 646 of mild cognitive impairment, and 369 of Alzheimer’s disease. To work out a new marker of neurodegeneration, we created a convolutional neural network-based regression model and predicted the cognitive status of the cognitively preserved examinee from the brain MRI data. This was a model of normal aging. A big deviation from the model suggests a high risk of accelerated cognitive decline. Results. The deviation from the model of normal aging can accurately distinguish cognitively normal subjects from MCI patients (AUC = 0.9957). We also achieved creditable performance in the MCI-versus-AD classification (AUC = 0.9793). We identified a considerable difference in the MMSE test between A-positive and A-negative demented individuals according to ATN-criteria (6.27±1.82 vs 5.32±1.9; $p< 0.05$ ). Conclusion. The deviation from the model of normal aging can be potentially used as a marker of dementia and as a tool for differentiating Alzheimer’s disease from non-Alzheimer’s dementia. To find and justify a reliable threshold levels, further research is required


I. INTRODUCTION
A typical topic of studies in cognitive neuroscience is distinguishing between normal and accelerated aging manifesting itself with dementia. The primary goal is to explain operation of the human mind in the healthy condition and in pathology [1]. There are different ways to perform studies on cognition. The model-based cognitive neuroscience approach is the most commonly used routine. The models predict brain measures from some parameters and provide a potential explanation of brain functioning [2]. Depending on the study issues, researchers use symbolic, neural, connectionist, dynamical and other models. The conceptual framework selected for the study influences the issue of the study, the research questions we address, the experiments we perform, and the ways in which we interpret the results [3]. We intend to improve diagnostics of cognitive disorders and focus on the difference between the brain structure and function in normal and accelerated aging. Multimodal techniques for diagnosis and prognosis of Alzheimer's disease (AD) deserve particular attention as they are more sensitive and promote screening and early management strategies [4]. To use the advances of multimodal diagnostics, we resort to models of structurefunction association (SFA). These models accumulate information from both structural and functional findings, which makes them more specific for norm or pathology. Dementia is a disturbance of higher mental functions, such as reasoning, planning, judging and memorizing. The most common reason for dementia is Alzheimer's disease (AD). Currently, 57 million people worldwide suffer from dementia. This number is predicted to triple by 2050 and reach 152 million cases [5]. The reason for this exponential increment in dementia is aging of society which raises the incidence of neurodegenerative diseases (NDs). Diagnostics of NDs is challenging since neither structural signs nor functional tests are sensitive enough and specific. There is a big list of unresolved issues to cover. First, there is no reliable tool to predict whether the pre-dementia will progress. Second, it is impossible to perform the differential diagnostics of exact neurodegenerative diseases (ND) with non-invasive tests. For instance, the early differentiation between mild cognitive impairment (MCI) due to AD and MCI caused by other ND conditions is particularly challenging in clinical settings.
To improve the current situation, we propose a combined analysis of structural and functional data with machine learning (ML) [6]. The strengths and limitations of brain structural and functional assessment are briefly discussed below. As seen from the references, there is no agreement between researchers on which non-invasive diagnostic modality is more promising for screening purposes. We chose to focus on multimodal diagnostics to benefit from both types of data.

A. FUNCTIONAL TESTS FOR COGNITIVE ASSESSMENT
Physicians can use functional tests to improve early diagnostics of NDs. However, there are some clear disadvantages of the tests: they are time-consuming; they require a special testing environment to keep the subject focused. Besides these, their interpretation is challenging as there is no understanding of the pathophysiological mechanisms underlying cognitive decline, whose structural bases are not studied well [7]. At the same time, psychophysiological, cognitive tests and evoked potentials studies can detect purely pre-symptomatic stages of dementia. Many models of developing dementia include cognitive test scores as predictors [8]. The most commonly used cognitive tests are the Mini-Mental State Examination (MMSE) [9], Rey Auditory-Verbal Learning Test (RAVLT) [10], Alzheimer's Disease Assessment Scale cognitive subscale (ADAS-cog) [11], Digit Symbol Substitution Test (DSST) [12], Trail Making Test (TMT) [13], Clinical Dementia Rating (CDR) [14], Logical Memory Tests (LMT), Immediate and Delayed Recall Test [15].
When assembled with structural data, cognitive tests indentify NDs more reliably thus becoming a multimodal diagnostic tool [16], [17]. Few studies focused on the prediction of the cognitive status from brain structural images (see Table 1). Some authors predicted MMSE scores from resting state functional MRI of patients with AD [18]. While others calculated MMSE, ADAS-cog, and CDR scores from structural MRI [19]. The prediction of the results of the tests that reflect a lower number of cognitive domains (e.g., RAVLT) was less accurate than of the tests covering a larger set of the domains (ADAS or MMSE). Another research team predicted MMSE and ADAS-cog scores with the model that integrated spatial-temporal features of the brain received from MRI findings [20]. Recent studies provided an insight into neurophysiological and morphological characteristics of the brain in patients with dementia [16]- [20]. However, the clinical utility of the proposed models remains limited.

B. BRAIN MORPHOLOGY STUDIES WITH MRI
The current study is dedicated to automatic analysis of MRI findings which can be used for screening. Structural MRI is a valid marker of the late stages of AD [21], but at an early stage it is not particularly revealing about the difference of the brain structural change in normal and accelerated aging. For this reason, some authors believe that a reliable means of identifying individuals at risk of AD should derive from electrophysiological diagnostics (e.g., event-related potentials) [8], [22].
Contrarily, there is evidence that neuropathological changes can be detected with neuroimaging much earlier than cognitive decline becomes apparent [23]. Structural MRI examinations reveal that the extent of age-related brain change varies markedly across individuals [24]. Studies on brain functioning bare inconsistencies in both the onset and the rate of episodic memory loss among the elderly. Inherited and lifestyle factors may account for these discrepancies. There is no direct link between structural and functional impairment. Researchers try to discover the structure-function relationship in the brain with advanced methods of neuroimaging [7], [25]. They show the importance of visual rating scales, volumetric assessment, and structured reporting.
A few brain regions are vulnerable to atrophy in NDs: hippocampus, amygdala, entorhinal cortex, fusiform gyrus, putamen, medial temporal lobe, etc. The aforementioned structures are neural centers responsible for learning, memory, navigation, processing information, emotions, behavior and time perception. Some authors study the brain at the macrostructural level. With MRI they assess the enlargement of gray matter, white matter (WM), ventricles, and accumulation of WM lesions -hyperintensitive areas in the T2-weighted sequence [26], [27]. Other researches focus on microstructural effects of NDs, e.g. neuronal death, accumulation of β-amyloid and τ -protein in hippocampus, etc. [28], [29]. Macrostructural characteristics of the brain (tissue volumes) can be identified with MRI and used for screening for NDs. Microstructural features (tissue organization) serve as golden standards of diagnostics.

C. MACHINE LEARNING METHODS
Processing biomedical images with ML techniques is a field of ongoing studies [30]. It has been already shown that an association between structural and functional changes of the brain can be studied with ML [6]. Numerous conventional ML and deep learning (DL) methods were proposed to discriminate AD patients from cognitively preserved people with structural MRI data [31]. For instance, Altaf et al. used a combination of textures (i.e., gray level co-occurrence matrix) and clinical features (i.e., MMSE) to predict the final diagnosis [32]. Ahmed et al. resorted to the bag-ofvisual-words approach to generate a unique signature of an individual brain from hippocampus and posterior cingulate cortex [33]. Khedher et al. analyzed tissue-segmented MRI (i.e., white and gray matter images) to diagnose AD at an early stage [34]. Other authors used slices or 2D patches extracted from T1-weighted MRI as predictors in designed 2D-convolutional neural network (CNN) models [35]- [38]. Recently, 3D patches extracted from MRI were used to segregate healthy individuals from patients with MCI or AD [39]. The authors extracted voxels corresponding to hippocampus and used them as an input to 3DCNN classification model [40]. 3D images of the whole brain also served as an input to 3D subject-level CNNs [36], [41]- [47]. Qiao et al. used a 3DCNN with sharing weights to extract the features from MRI, followed by multiple sub-networks which transformed the MMSE regression models into a series of binary classification models [46]. All the methods discussed are summarized in Table 1. We presume that new findings on the brain structure-function association may foster further research on earlier detection and treatment of NDs. Multimodal diagnostics that we develop with ML accumulates the advantages of morphological and functional findings.

D. OBJECTIVE AND SUB-OBJECTIVES
Our main goal is to improve screening for dementia by studying an association between the brain structure and its function. Hypothetically, the brain SFA has features specific for either disease-related cognitive deterioration or normal neurocognitive slowing in aging. To address this objective, we formulate the following tasks: • Conduct an exploratory analysis of structural and functional change in cognitively preserved population and in subjects diagnosed with MCI or dementia.
• Propose a reliable marker of disease-related cognitive decline.
• Justify the proposed marker as a screening tool for MCI and dementia.
• Test if the proposed marker can prognosticate the conversion of pre-dementia to dementia and differentiate cognitive decline due to AD from other NDs.

A. DATASET
The data used in this study were obtained from the Alzheimer's Disease Neuroimaging Initiative (ADNI) database [62]. • Clinical data on the final diagnosis.
• Morphometric data (i.e., volumes of brain areas mostly affected by ND).
• Pre-processed T1-weighted MRI files. Figure 2 shows the general idea of proposed SFA model and Figure 3 illustrates the proposed framework. The first objective was to conduct a comparative analysis of the brain structure and function in CN subjects, MCI and AD groups. We evaluated the separability of the three groups with non-parametric statistical methods, i.e. Kruskal-Wallis test for the continuous features and the Chi-square test for the quantitative ones.

B. PROPOSED FRAMEWORK
The second objective was to propose a new marker of accelerated cognitive decline. In line with the hypothesis of the study, we proposed to predict the cognitive status of the cognitively preserved examinee from the brain MRI data and worked out the SFA model. Then we applied the SFA model to the findings of the study group. When the findings of a scanned individual did not fit the standard SFA model, accelerated aging was suspected. We calculated the deviation from the model of normal aging (DMNA) as the error of cognitive score prediction (see Equation 1).
where y is a result of the cognitive test. Modeling cognitive performance from MRI is a complex problem. To reduce its computational complexity, we transformed MRI images into two-dimensional data (see subsection II-C). Then we designed CNN model and trained it on images of CN individuals. To generalize the model to a true rate error, we utilized the five-fold cross-validation technique.
As an input, we used the pre-processed MRI data (D

1) THE THIRD OBJECTIVE WAS TO JUSTIFY THE RELIABILITY OF DMNA)
It was a three-fold task. First, we employed non-parametric statistical tests to compare DMNA values of the CN group with MCI and AD patients. Second, we created ML models that distinguish the following study cohorts by DMNA values: CN people from patients with MCI, and patients with MCI from those with AD. The models were trained with the ten-fold cross-validation technique. Finally, we evaluated their performance. The performance of the regression models VOLUME 10, 2022 was expressed as mean absolute error (MAE). The accuracy of the classification model was assessed with Sensitivity, Specificity, F-measure, ROC, AUC, Accuracy, and Balanced Accuracy.

2) THE FOURTH OBJECTIVE WAS TWO-FOLD
In the first part of sub-objective four, we tested if the proposed marker can prognosticate the conversion of pre-dementia to dementia. To find the cases of stable and progressive MCI, we did an exhaustive search in all longitudinal studies: ADNI1, ADNI2, ADNI-GO, ADNI3. Then, we built the conventional ML model segregating the cases according to stability/progression. We used DMNA in MMSE and ADAS-cog as more reliable predictors because the tests covered the global cognitive functioning. To compare the distribution of DMNA in two groups, we applied the non-parametric Kruskal-Wallis test. We also assessed sensitivity and specificity of the model classifying MCI cases into stable and progressive ones.
The second part of sub-objective four was to check if DMNA could differentiate cognitive decline due to AD from other NDs. To address the research question, we resorted to ATN criteria [65] and adopted a two-step analysis. Firstly, we dichotomized each biomarker category as either normal (-) or abnormal (+) with the following cutoff thresholds. A case was considered as A-if the CSF concentration of beta-amyloid was higher than 81/ml [66], [67], T-if the level of p-tau was less than 56 pg/ml [66], [68], and N-if FDG-PET uptake was larger than 1.21 [69]. Secondly, we classified all the cases with MCI and dementia into groups and calculated mean values of DMNA for them (see Table 6). Finally, we identified the difference in DMNA between demented individuals with Alzheimer's continuum (A+) and those with either normal AD biomarkers or non-AD pathologic change (A-).

C. DATA PRE-PROCESSING
All the retrieved images passed through grad-warping and intensity correction and were scaled to gradient drift with the phantom data (for more details, see [63]). The pre-processed T1 weighted structural MRI images were downloaded in NIFTI format. We also retrieved the corresponding clinical data from the dataset. Then the images were registered to an MNI152 space with FLIRT tool from FSL package [70]. As brains differ in size and shape, each brain image was translated into a common reference space (normalized) to ensure consistency of orientation. To correct low-frequency intensity non-uniformity, we used N4 bias field correction algorithm [71]. Then we normalized the voxel intensities by scaling them to the standard normal distribution parameters. To enhance the predictive performance, we extracted the brain parenchyma with Brain Extraction Tool (BET) from FSL package [70].
One of the major challenges of studies on MRI is a high dimensionality of data [72]. We used the following approach to reduce it. An MRI image was defined as where X ,Y ,Z were the dimensions of the MRI scan in axes x, y and z. Then the j th sagittal, coronal or axial slice s of the I image could be defined as: The corresponding averaged images were generated as follows: In this way, we averaged voxel intensities along the sagittal, coronal and axial axes and created two-dimensional datasets D axial , D sagittal , and D coronal : coronal , I 2 coronal , . . . , I N coronal } Then, we removed the background by cropping the image to the size of the brain mask. We down-sampled brain images with nearest-neighbor interpolation to the size of 150 by 150 pixels, normalized them within the range of 0 to 1, and stored in JPEG format as shown in Figure 1. To unify the pre-processing workflow, we used Nipype which is an opensource community-developed initiative under the umbrella of NiPy [73]. To automate the deployment of the applications within the software containers, we installed Neurodocker which wraps up the aforementioned software in a complete file system.

D. STATISTICAL ANALYSIS AND MACHINE LEARNING
We calculated volumes of WM hyperintensities and the following structures: interventricular CSF, hippocampus, putamen, caudate nucleus, amygdala, WM, enthorinal cortex, fusiform gyrus, middle temporal lobe, gray matter, its cortex and total intracranial volume. Subcortical and cortical 53238 VOLUME 10, 2022 parcellation volumes were computed with FreeSurfer 7.1.0 software [74]. We resorted to Desikan/Killiany atlas as a reference. All features were expressed as percentage to the total intracranial volume and used as an input to the ML model predicting the cognitive scores.
The functional data were presented with the results of the following cognitive tests: MMSE, DSST, TMT (part B), ADAS-cog (ADAS Q4 , ADAS 11 , and ADAS 13 ) and RAVLT (RAVLT immediate , RAVLT learning , and RAVLT forgetting ) [62]. The associations between CSF% and performance in ADAS-cog and RAVLT were stronger for ADAS-13 and RAVLT immediate compared to the other scores in these test. For this reason we used ADAS-13 and RAVLT immediate for further analysis (see section III-A).
We started the statistical analysis by looking at the relationship among the attributes. The associations of the cognitive test scores with age, functional and structural data in healthy cohort and subjects diagnosed with MCI and AD were assessed with Pearson's correlation coefficient. Then, we inspected the attributes for Gaussianity. Shapiro-Wilk test revealed the non-normal distribution of all the attributes. Therefore, we utilized non-parametric statistical tests for further analysis. To check if the data from the studied groups (CN, MCI, AD) came from a common distribution we used Kruskal-Wallis test with the continuous features and the Chi-square test with the quantitative ones. The results were expressed as IQR, mean ± std or the number of cases, and their percentage in the observed group.
To predict cognitive scores from the structural data, we designed a CNN model. The proposed CNN regression model consisted of six convolution layers followed by two fully connected dense layers. The model was regularized with L2 penalty and α = 0.0001. We used RMSProp optimizer and trained the network for 200 epochs or until convergence. To optimize a learning rate hyperparameter, we monitored the validation loss during the training process. When the metric stopped improving for 10 continuous epochs, we multiplied the learning rate value by 0.2. To optimize the training time, we also monitored the validation loss. If it did not decrease for 20 continuous epochs, we terminated the training process. 20% of the training data was used for validation purposes. The model was trained on the CN cohort in the five-fold crossvalidation technique. There were several arguments in favor of the necessity to train models of SFA on non-demented cases exceptionally. As the model reflected the brain SFA for the healthy controls, it could be used as a reference norm. If trained on a mixed cohort of healthy individuals and patients, the model would fail to identify the patients out of the reference range and would lose its diagnostic value. The trained model from the last fold was tested on MCI and AD groups.
For each case we had 2D images obtained by averaging brain MRI in three planes: axial (A), coronal (B), and sagittal (C). We could use them either separately or in combination. For the combined approach we used two options: data and model blending. The first one was fusing predictions, which was an ensemble estimator or voting regressor that averaged model outcomes. The second method was model blending. We trained the linear regression (LR) model on the outcomes of three CNN models trained on axial, coronal, and sagittal averaged images. The outcomes of the predictive algorithm were the results of mental status tests such as MMSE, RAVLT, DSST, ADAS-cog, and TMT (Part B).
We compared the distribution of the DMNA absolute values in the healthy population and patients with MCI and Dementia. We also calculated 95% confidence intervals for DMNA values with the t-test. To control the familywise error rate related to multiple comparisons we employed Bonferroni correction. All statistical tests were performed in Python v. 3.6.9 with SciPy v. 1.16.4 library [75].
The experimental work was performed with the help of Linux Ubuntu 18.04 Nvidia DGX-1 deep learning server with 40 CPU cores and 8x NVIDIA Tesla V100 GPU with 32 GB memory each, accessed with a web-based multiuser concurrent job scheduling system [76]. The tensorflowgpu v.2.3.1 library was utilized to implement the proposed solution.

A. DEMOGRAPHIC, FUNCTIONAL, AND STRUCTURAL DATA IN STUDIED COHORTS
The structural data are presented in terms of percentage of the volume of a specific brain area to the total intracranial volume. There are significant differences among the studied cohorts in the structures most vulnerable to change in ND (see Table 2). The data reveal shrinkage of the brain parts (hippocampus, entorhinal cortex, fusiform gyrus, medial  temporal lobe) and enlargement of ventricles in accelerated aging. No significant differences in age among CN, MCI and AD groups was detected (p = 0.1109).
In the MCI cohort, the ADAS-cog score is negatively associated with the major part of the analyzed relative volumes. The exception is the relative volume of WM, CSF, WM lession, and caudate nucleus. The association of performance in ADAS-cog with the relative volume of caudate nucleus is almost significant (p = 0.061). The portion of TIV occupied by WM lesions does not correlate with ADAS-cog scores in this group (r = 0.03; p = 0.38). WM lesions are a typical sign of brain aging. They result from chronic small vessel disease and can be seen well as foci or areas hypointensive on T1-weighted images and hyperintensive on T2-weighted images including FLAIR. There are different patterns of the emergence of the WM lesions in MCI and AD groups.  The functional data in ADNI1 are obtained with cognitive tests such as MMSE, ADAS-cog (ADAS Q4 , ADAS 11 , ADAS 13 ), DSST, RAVLT (RAVLT immediate , RAVLT learning , RAVLT forgetting ), and TMT (part B) [62]. The association between the major marker of brain atrophy -CSF% -and performance in ADAS-cog tests is stronger for ADAS 13 (r = 0.18; p < 0.05) than for ADAS Q4 (r = 0.15; p < 0.05) and ADAS 11 (r = 0.15; p < 0.05). This goes in line with a research which evidenced a more pronounced annual decline in ADAS 13 than in ADAS 11 in AD patients [77]. Similarly, the association of CSF% score with RAVLT immediate is stronger than with RAVLT learning and RAVLT forgetting scores (r = −0.19 vs −0.10 and 0.12; p < 0.05). Other authors also showed that the accuracy of the model predicting RAVLT scores from gray matter density is higher for RAVLT immediate score than for RAVLT forgetting [78]. Therefore, we used ADAS 13 and RAVLT immediate in this study. Figure 5 shows the associations of the test results with age and structural data.
SFA. ADAS-cog and MMSE are primary cognitive tests required in all recent Food and Drug Administration clinical drug trials for AD in the USA [79]. From our data, the results in ADAS-cog and RAVLT had the strongest association with the structural markers of brain atrophy in the CN group. For instance, the coefficient of correlation between hippocampal volume and ADAS 13 score was −0.18 in the CN cohort, −0.34 in patients with MCI, and −0.20 in the AD group. The same coefficient in RAVLT immediate was 0.13, 0.24, and 0.18 in the correspondent cohorts (see Figure 5).

B. PROPOSED MARKER OF DISEASE-RELATED COGNITIVE DECLINE
When applied to distinct cognitive test scores, the proposed CNN model shows the best prediction performance in the CN cohort (see Table 3). The worst performance was monitored in the AD group. Data-blending did not boost the performance considerably, i.e., there was no evident advantage in using several image reconstructions. In contrast to this, the modelblending approach showed the top accuracy. It allowed us to retrieve maximum data for assessing SFA (see Figure 4). The variability of the results in the studied cohorts is most apparent in ADAS-cog and MMSE tests and less evident in RAVLT, DSST, and TMT. The distribution of MAE differs significantly among the cohorts (see Table 4). This justifies that cognitively-normal people and patients with NDs have different SFA patterns, which can aid to diagnostics of MCI and AD.

C. JUSTIFICATION OF DMNA AS MARKER OF DEMENTIA
To determine a diagnosis from DMNA values, we employed nine conventional ML classifiers (SVM linear and non-linear, Gaussian NB, Extra Trees, Bagging, Random Forest, Logistic Regression, Ridge Regression, Neural Network). DMNA values were obtained from skull-stripped brain images averaged along the axial, coronal, and sagittal axes. The ML models were evaluated with the ROC AUC metric. 53242 VOLUME 10, 2022   Table 4, Figures 6 and 7).
The performance of the CN-versus-AD classification model (AUC = 1.0) was comparable to the accuracy of state-ofthe-art models trained on ADNI dataset (see Table 6). From the table, DMNA can accurately distinguish CN subjects from MCI patients (AUC = 0.9957). We also achieved creditable performance in the MCI-versus-AD classification (AUC = 0.9793). Therefore, DMNA can be potentially used as a marker of dementia and can help to identify the disease. Moreover, to use the proposed approach in clinics, we assessed the possible threshold values of DMNA markers. We undertook sequential values of DMNA and calculated the accuracy of the CN vs MCI and MCI vs AD classification. Table 5 lists the thresholds of DMNA markers in the binary classification models. The optimal performance is noted in the models based on ADAS-cog scores. These models allowed us to distinguish normal aging from MCI and the latter from AD with a high accuracy (above 90%). Table 7 shows the sensitivity and specificity of the conventional model that classifies MCI cases into stable and VOLUME 10, 2022  progressive ones. As seen from the table, there is no considerable difference in DMNA values between the groups (p=0.16÷0.21). Though the balanced accuracy of binary classification is above 80%, low specificity can be considered as a strong limitation of the models. We also identified the difference in DMNA between demented individuals with A+ and A-subjects (see Table 8). Only in MMSE tests the distinction in DMNA was considerable (6.27±1.82 vs 5.32±1.9; p < 0.05). At the same time, there was no difference between A+ and Apatients with MCI (p = 0.75 − 0.98).

A. ASSOCIATION OF COGNITIVE TESTS AND STRUCTURAL DATA
In our study the structural markers of brain aging demonstrated a stronger correlation with the results in ADAS-cog than in the other tests. Other authors also justified the informative value of ADAS-cog by predicting the ADAS-cog score with a regression model from morphometric features [20], [80]. We found an obvious correlation of MMSE score with hippocampal volume (r = 0.44, p = 7.25e − 86). This goes in line with another study that showed their close association (r = 0.51, p < 0.001) [49].
The results we received suggest the presence of a distinct SFA in healthy aging and ND. For instance, the proportion of WM lesions to TIV does not show a linear association with ADAS-cog score in subjects diagnosed with MCI. In contrast to this, the relationship is strong in AD patients (r = 0.22; p = 2.61e − 05). Other authors showed that WM lesions enlarged with age and with the development of dementia [29], [81]. It remains unclear why the emergence of WM lesions has a common pattern in the CN adults and patients with AD.
We reported a prominent relationship between cognitive functioning and the volumes of hippocampus, amygdala, entorhinal cortex, and middle temporal lobe. Other studies also justified the importance of the hippocampal area, amygdala, and the middle temporal lobe for intellectual activities [82]- [93].

B. DEVIATION FROM THE MODEL OF NORMAL AGING
Some authors found marked correlations between the predicted and actual scores in MMSE (r = 0.44, p =< 0.0001) and ADAS-cog tests (r = 0.57, p =< 0.0001) [19], [20]. We also observed a significant linear association between the predicted and actual values in the combined group of the CN subjects, MCI, and AD patients (MMSE r = 0.09, p = 2.28e − 4, ADAS r = 0.05, p = 2.87e − 2, RAVLT r = 0.11, p = 2.24e − 05, TMT r = 0.22, p = 2.34e − 18). We recorded conflicting findings (a non-correlation) in the CN group due to distinct study design. Stonington et. al [19] trained the model on three cohorts (CN, MCI, and AD), while we fed the predictive model exceptionally with the CN cases. Other researchers managed to predict MMSE results from fMRI data accurately [18]. The calculation of cognitive scores is more precise from the radiomics data than from the images (see Table 3). The first reason for this is the noise of the 2D images averaged along distinct axes. The second reason is the relatively low number of cases used for training the deep learning model. The high-dimensional computational model needs a larger number of training samples because of the dimensionally cursed phenomena [94].
The idea of using the deviation between the model and actual values is not new for diagnostics. There is a large body of evidence that the difference between the computed and actual age -biological age gap -is a reliable marker of dementia [95]- [97]. A study suggested an association between the gap and cognitive performance. It also reported that BAG is related to worsening in performance on the DSST and TMT tests [98]. We applied the same idea to prediction of cognitive performance.

C. DISTINCTION BETWEEN HEALTHY POPULATION, PATIENTS WITH MCI AND WITH AD
Many papers reported a high accuracy of the models that classify healthy and demented subjects [32], [33], [35], [36], [39], [40], [42], [43]. All the deep learning models were trained on pre-processed MRI images of the cognitively preserved and those with cognitive deterioration. In contrast to the studies, we trained the model exclusively on CN people.
From our data, the predictive power of an SFA model depends on the complexity of the cognitive test used for its training. The accuracy is higher for the tests covering several cognitive domains (MMSE, ADAS, TMT vs information processing in DSST, memory in RAVLT). This supports the results of a study by Stonnington et. al. [19].
A limitation of the current research is that we did not study convertible and non-convertible to AD MCI cases separately, although some researchers suggest this [42]. Advances in DL technology allowed neuroscientists to improve the classification accuracy of CN-versus-MCI and MCI-versus-AD models [43]. However, the models were biased because of the data leakage related to the late split [99]. Thus, substantial work is required to use such algorithms as a diagnostic tool.

D. DMNA AS A MARKER OF PROGRESSIVE MCI AND DIFFERENTIATION DIAGNOSTIC TOOL
From our data, DMNA cannot be recommended as a tool for predicting the conversion of MCI to dementia because of its low specificity (up to 75%). Other existing CSF markers of progressive MCI also do not ensure the necessary level of prediction: mean diffusivity (average accuracy of 77%), tau concentration (74%), volumetry data retrieved from the brain MRI (66%) [100]. There is a considerable distinction in DMNA between demented individuals with Alzheimer's continuum (A+) and those with either normal AD biomarkers or non-AD pathologic change (A-). Hence, the proposed marker can be potentially used for differentiating dementia due to AD from non-AD dementia. To find and justify a reliable threshold level, further research is required. We failed to identify a strong distinction between MCI due to the accumulation of beta-amyloid and because of other pathologies (p > 0.05). From our data, the biomarker is not applicable for discriminating MCI cases by underlying pathology (AD vs non-AD).

V. CONCLUSION
• There is a strong association between the brain structure of a subject and his/her performance in cognitive tests. However, the patterns of the structure-function association differ among cognitively preserved people, patients with MCI and with dementia. For instance, the coefficient of correlation between hippocampal volume and ADAS 13 score was −0.18 in the CN cohort, −0.34 in patients with MCI, and −0.20 in the AD group. The same coefficient in RAVLT immediate was 0.13, 0.24, and 0.18 in the correspondent cohorts • To work out a new marker of neurodegeneration, we predicted the cognitive status of the cognitively preserved examinee from the brain MRI data. This was an SFA model of normal aging. A big deviation from the model of normal aging suggests a high risk of accelerated cognitive decline, i.e., a high level of the error of cognitive score prediction should rise awareness of a neurodegenerative disease.
• The results in the tests reflecting global cognitive functioning -ADAS-cog and RAVLT -had the strongest association with the structural markers of brain atrophy.
In line with this, the variability of the deviation from the model of normal aging in the cognitively preserved subjects, patients with MCI and dementia is most apparent in ADAS-cog and MMSE tests and less evident in the tests covering several cognitive subdomains -RAVLT, DSST, and TMT. Diagnosing dementia from DMNA values was most accurate with Random Forest classifier jointly trained on DMNA MMSE and DMNA ADAS-cog. DMNA can accurately distinguish CN subjects from MCI patients. We also achieved creditable performance in the MCI-versus-AD classification.
• There is no considerable difference in DMNA values between stable and progressive MCI cases. DMNA as a prognostic criterium of progressive MCI has strong limitation. Both the proposed and the existing markers of progressive MCI do not ensure the necessary level of prediction.
• The proposed marker can be potentially used for differentiating dementia due to AD from non-AD dementia. We

AUTHOR CONTRIBUTIONS
All the authors contributed to the conceptual idea of the article, wrote the manuscript, and planned the experiments. Tetiana Habuza formulated the methodology of the study, conducted the experimental work. Nazar Zaki, Yauhen Statsenko, and Elfadil A. Mohamed contributed to the critical data analysis, discussion, and interpretation of the results.

ETHICAL APPROVAL
The current study is a retrospective analysis of data that were recently collected either as a standard of care or for other research purposes. This totally complies currently existing ethical policies. The original data collection procedures were done in accordance with an institutional review board, also known as an independent ethics committee. According to ADNI: ''All procedures performed in studies involving human participants were in accordance with the ethical standards of the institutional and/or national research committee and with the 1964 Helsinki declaration and its later amendments or comparable ethical standards.'' All necessary patient/participant consent has been obtained. Any clinical trials involved have been registered with an ICMJE-approved registry.
TETIANA HABUZA received the bachelor's degree in applied mathematics and the master's degree in informatics from Yuriy Fedkovych Chernivtsi National University, Chernivtsi, Ukraine, in 2004 and 2005, respectively. She is currently pursuing the Ph.D. degree in computer science with United Arab Emirates University (UAEU).
In 2018, having a strong interest in data science and research, she returned to academia and joined UAEU. Currently, she mainly focuses on using advanced machine learning techniques to automatically detect valuable biomarkers from medical images. Her research interests include artificial intelligence, machine learning (deep learning), bioinformatics, and control theory.
NAZAR ZAKI is a Professor of computer science with the Department of Computer Science and Software Engineering, United Arab Emirates University (UAEU). He is the Founder and the Director of the Big Data Analytics Center, UAEU. He mainly focuses on developing intelligent algorithms to solve problems in domains, such as education, biology, and healthcare. He has published more than 120 scientific results in reputable journals and conferences. His research interests include data mining and machine learning. He received several scholarship awards, such as the College Recognition Award for Excellence in Scholarship and the Chancellor's Annotation Award in technology. He is also a frequent recipient of certificates of achievement for publishing in top journals and bringing recognition to the UAEU. ELFADIL A. MOHAMED has received the Ph.D. degree in computer science from Universiti Teknologi Malaysia, Malaysia, in 2002. He is currently working as an Assistant Professor with the College of Engineering and Information Technology, Ajman University, United Arab Emirates. He has published several scientific results in reputable journals and leading conferences. His research interests include data analysis, data mining, and databases.
YAUHEN STATSENKO is an Associate Professor with the Radiology Department, College of Medicine and Health Sciences, UAEU. He has published more than 100 scientific results in reputable journals and conferences. His research interests include mathematical modeling of aging, regeneration process, early diagnostics methods of maladjustment diseases (acupuncture diagnosing, psychophysiological testing), and prediction and treatment sport overtraining syndrome (decrease in adaptation reserve and athletic performance). VOLUME 10, 2022