Data used in the preparation of this article were obtained from the Alzheimer’s Disease Neuroimaging Initiative (ADNI) database.¹ The ADNI was launched in 2003 as a public–private partnership led by Principal Investigator Michael W. Weiner, MD. The primary goal of ADNI has been to test whether serial MRI, PET, other biological markers, and clinical and neuropsychological assessments can be combined to measure the progression of MCI and early AD. For up-to-date information, see www.adni-info.org. From the multiple phases of ADNI – ADNI 1, ADNI 2, ADNI GO, and ADNI 3 – we analyzed two sets of scans for the study of Aβ deposition and tau deposition. For the Aβ deposition study, we analyzed a total of 1,127 pairs of images from 1,109 subjects (18 of them have two pairs from different visiting dates), including 1,127 T1-weighted MR images and 1,127 florbetapir PET images. Similarly, we obtained 925 pairs from 688 subjects (191 of them have more than one pair from different visiting dates) of MRI scans and AV1451 PET images for the study of tau deposition.

In addition to each brain MRI scan, we also analyze the corresponding MMSE scores (Folstein et al., 1975). For amyloid PET, we utilize centiloid measures (Navitsky et al., 2018). Operationally, there have been widely accepted efforts to reconcile differences among different amyloid radiotracers using a norming approach called the centiloid scale (Klunk et al., 2015; Rowe et al., 2017). ADNI florbetapir PET data are processed using AVID pipeline (Navitsky et al., 2018), which are converted to the Centiloid scales according to their respective conversion equations (Navitsky et al., 2018; Su et al., 2019). For flortaucipir tau-PET – in a similar fashion to Aβ – tau data are reprocessed using a single pipeline consistent with (Sanchez et al., 2021), so that the standardized uptake value ratio (SUVR) from different ADNI study sites can be analyzed together. In this work, we examine two regional SUVR for tau deposition, corresponding to Braak12, and Braak34 (Schöll et al., 2016; Baker et al., 2017a,b; Maass et al., 2017). Table 1 shows the demographic information from the two cohorts that we analyzed.

In this work, we develop a FMFS model to detect the influence of Aβ and tau deposition on hippocampal shape deformity and to better support the future prediction of AD pathology as shown in Figure 1. In panel (1), each institution first extracts the morphometric features locally. The hippocampal structures are segmented from registered brain MR images and smoothed hippocampal surfaces are further generated. After the surface parameterization and fluid registration, the hippocampal radial distance (RD) and tensor-based morphometry (TBM) features are calculated at each surface point. Each institution selects patches on each hippocampal surface and reshapes the grouped features (RD or TBM on each patch are one group) of each subject to a vector. Next, in panel (2), taking each Aβ/tau measurement as the dependent variable, the institutions perform the federated feature selection model on these patches of features to generate local hippocampal ROIs for each Aβ/tau measurement.

To further validate whether these identified hippocampal ROIs are related to Aβ/tau deposition, we used RD and TBM features of these ROIs to predict MMSE scores based on random forest, multilayer perceptron (MLP), and LASSO regression models. Ten-fold cross-validation was adopted to evaluate the performance of the models, and root mean squared error (RMSE) was used for measuring the prediction accuracy. Meanwhile, we also compared the prediction results of ROI-related features with the results of the whole hippocampal features and Aβ/tau measures.

We also tested the computing efficiency with the 1,127 subjects for the study of Aβ. Firstly, we randomly assign the 1,127 subjects to five institutions, of which each has almost the same number of subjects and one computation node. After uniformly selecting 100 regularization parameters from 1.0 to 0.1, we performed stability selection with our proposed framework, FMFS, FBCD (FMFS without the screening rule), as well as the state-of-the-art distributed alternating direction method of multipliers (DADMMs) (Boyd et al., 2011). Besides this, we also repeated the same experiments with different dimensionality of features by randomly down-sampling and up-sampling the original features.

A significant innovation of FMFS is that we introduce a screening rule during the group LASSO feature selection stage, which highly improves the computation speed compared to the DADMMs algorithm (Boyd et al., 2011). Moreover, we also compare FMFS with the Gauss-Southwell-Lipschitz rules (GSL) for block coordinate descend in Nutini (2017). Besides, we also tested the running time of FBCD in our federated framework without the screening rule.

We simulated the distributed condition on a cluster with several conventional ×86 nodes, of which each contains two Intel Xeon E5-2680 v4 CPUs running at 2.40 GHz. Each parallel computing node has a full-speed Omni-Path connection to every other node in its partition. A total of 1,127 subjects for the Aβ deposition study were randomly assigned to five simulated institutions, each of which has almost the same number of subjects and one computation node. We uniformly selected 100 regularization parameters from 1.0 to 0.1 and ran all three methods with the same experimental set-up. Under different morphometry feature resolutions (where we randomly down-sampled or up-sampled the dimension of the features), our FMFS method achieved a speedup of 62–, 80–, 86–, and 89-fold, compared to DADMM as shown in Figure 2. For FBCD, our FMFS has a speedup of 54–, 72–, 80–, and 86-fold. For GSL, our model has a speedup of 12–, 15–, 15–, and 17-fold.

We employed stability selection with our FMFS model to select the ROIs (subregions of the hippocampal surfaces) related to Aβ and tau. We respectively standardize the two types of input features, RD and TBM, for each subject, using Z-scores, and adopt the centiloid value as the measure of Aβ burden and Braak12 and Braak34 measures for tau deposition. Since the regularization parameters can control the sparsity of the solution vector and further influence the area of the ROIs, we uniformly generated 100 regularization parameters between 0.01 and 0.001, which may lead to a reasonable size for the selected ROIs. After training the model, we got 100 solution vectors, of which the dimensionality is 60,000, since each of the left and right hippocampal surfaces contains 15,000 vertices, and each vertex has two features. Then, we performed stability selection by counting the non-zero entries for RD and TBM on the same vertex. The counted frequency on each vertex was normalized to 0–100 and then mapped to a color bar, as shown in Figures 3–5. For better visualization, we smoothed the values on each surface by a 2×3 averaging filter. The warmer color areas have a higher frequency value and have stronger associations with the responses, i.e., brain global Aβ and tau burden.

In this experiment, we first ran the proposed model on the cohorts for Aβ and tau deposition. As illustrated in the top left picture of Figures 3–5, the morphometric abnormalities mainly happen in specific hippocampal subregions, namely the subiculum and CA1. Additionally, we separately studied the ROIs for groups of CU, MCI, and AD subjects. As shown in the rest of the three panels in Figures 3–5, the morphometric associations are strongest in the subiculum and CA1 at the early stages; but with the progression of AD, the distortions are more focal in subiculum. Specifically, the results for CU subjects are shown in the top right panel of each figure, where the warmer colored regions are widespread in both the subiculum and CA1 areas. However, in the results for the AD group, the warmer colored regions mainly focus on the area of the subiculum.

In this experiment, we try to demonstrate the morphometric features of our selected ROIs have stronger correlations with the measures for Aβ and tau deposition than the other hippocampal surface features. After performing stability selection, we were able to rank the vertices related to each measurement of Aβ/tau deposition. We selected the 3,000 features from the 1,500 top-ranked vertices for each subject (1,500 RD and 1,500 TBM). For a fair comparison, we also selected 3,000 features from 1,500 randomly selected vertices for each subject and used them as features representing differences across the entire hippocampus. To fit the Pearson Correlation analysis, we converted the features on ROIs to a single value for each subject. First, as the features on the ROIs should have stronger predictive power, we used the frequency on each vertex as a weight to multiply the RD and TBM on the vertex. And then, we, respectively, summed up the weighted RD and weighted TBM on the ROIs for each subject. The value for RD and the value for TBM were further reduced to a scalar with principal components analysis (PCA). PCA is an unsupervised model to reduce the dimensionality of the data while minimizing information loss. It creates new uncorrelated features which maximize the variance successively. For the randomly selected features on the whole hippocampal surface, the RD and TBM were directly summed up without multiplying the frequency and reduced to a single value with PCA. In Figure 6, we illustrate the results of Pearson correlation between morphometric features and measures for Aβ and tau deposition. The top three subfigures illustrate the correlation between the values on our selected ROIs and the measure for Aβ or tau deposition. The bottom three are between the value on the whole hippocampal surface and the measure for Aβ or tau deposition. The correlation coefficients and p-values are shown in each subfigure. The correlation coefficient of Centiloid-related ROIs is −0.23, and the coefficient for the whole surface is only −0.1. For Braak12 and Braak34, the coefficients of our selected ROIs are −0.37 and −0.29 and the ones for the whole surface are −0.11 and −0.096. Consequently, the features on our selected ROIs have more associations to the measure for Aβ or tau deposition than the other features on the surface.

In the model of Jack et al. (2016), an abnormal level of Aβ and tau deposition tends to occur earlier than abnormal cognitive decline can be detected. In this experiment, we further validated the ROIs selected by our proposed model in terms of their prediction accuracy for MMSE score in cohorts where Aβ and tau deposition were measured separately. After performing stability selection, we were able to rank the vertices related to each measurement of Aβ/tau deposition. We selected the 3,000 features from the 1,500 top-ranked vertices for each subject (1,500 RD and 1,500 TBM). Then, we used these features to predict the MMSE score as described in section “Performance Evaluation Protocol.” For a fair comparison, we also selected 3,000 features from 1,500 randomly selected vertices for each subject and used them as features representing differences across the entire hippocampus. Moreover, we also leveraged the measurements for Aβ or tau deposition to predict MMSE. In addition, we compare our FMFS with recursive feature elimination (RFE) (Guyon et al., 2002). The feature dimensionality of our morphometry feature is 60,000 and RFE may take tens of days to rank features for such a big dataset. For equal comparison, we also selected 1,500 RD and 1,500 TBM for each measurement of Aβ/tau deposition. To accelerate the feature selection speed, we randomly select 300 features from the 30,000 RD and use RFE to select the top 15 RD. We repeated the step 100 times and selected 1,500 RD. With the same strategy, we also select 1,500 TBM. Then, we used these features to train machine learning models, including random forest, MLP, and LASSO regression. Ten-fold cross-validation was adopted to evaluate the performance of the models, and RMSE was used for measuring the prediction accuracy. In Table 2, the top five rows indicate the results for Aβ deposition, and the rest of the rows are for different measurements of tau deposition. Hippocampal ROIs represent the features on our selected ROIs and RFE-selected represents the features selected by RFE. The RMSEs of our framework are always the smallest. It is worth noting that comparing to the RFE method, our proposed FMFS framework demonstrated significant efficiency improvement. Specifically, the average running time of the RFE method is 49,319 s while ours FMFS method 22 s, roughly with 2,240-fold efficiency improvement. These results demonstrate that the features in the ROIs selected by our model can always have a stronger predictive power and predict the MMSE score better than the measurements of Aβ and tau deposition.

We also perform Pearson correlation between the morphometry features and MMSE and between the measure for Aβ or tau deposition and MMSE. We also utilize the same method as section “Association Analysis Between Features on Regions of Interest and Measure for Amyloid-β and Tau Deposition” to convert the multivariate features to a scalar. The results are shown in Figure 7. The first column is the correlation between the measures for Aβ and tau deposition and MMSE. And the second column is the correlation between the features on our selected ROIs and MMSE. The last column is between the feature on the whole surface and MMSE. The correlation coefficients and p-values are shown in each subfigure. In the study of Aβ deposition, the coefficient for centiloid is −0.36 and the ones for the features on centiloid-related ROIs and the whole surface are 0.3 and 0.11. In the study of tau deposition, the coefficient for Braak12 and Braak34 are −0.58 and −0.59. And the ones for the features on Braak12-related ROIs and Braak12-related ROIs are 0.29 and 0.28. The coefficient for the features on the whole surface is 0.057. The correlation of the features on our selected ROIs is stronger than the features on the whole surface, which demonstrates the effectiveness of our model. The measures for Aβ or tau deposition have the strongest correlation with MMSE. But our selected features are multivariate, which can have better performance in predicting MMSE. Our work validated the AD progression model and may provide unique insights for accurately estimating clinical disease burden.

In this experiment, we evaluated the performance of our features on the ROI in survival analysis by using 118 MCI participants’ data from a separate dataset (Wang et al., 2021) from ADNI (Table 3), including 63 MCI converters, who converted to probable AD in the next 6 years, and 55 MCI non-converters. Similar to section “Association Analysis Between Features on Regions of Interest and Measure for Amyloid-β and Tau Deposition,” we also chose 1,500 RD and 1,500 TBM from the four ROIs (Aβ, Braak12, and Braak34) and 3,000 features from 1,500 random-selected vertices on the whole hippocampal surface to predict the conversion rates from MCI to AD, respectively. For comparison, we also performed the same experiment with the surface area and volume of the hippocampus. The hippocampal volume and surface area were calculated with the smoothed hippocampal structures after linearly registered to the MNI imaging space (Patenaude et al., 2011; Shi et al., 2013a), and the sum of the bilateral hippocampal volume and the sum of the bilateral hippocampal surface area for each subject were used for this experiment.

To fit the univariate Cox model, we converted the features on ROIs to a single value for each subject. First, as the features on the ROIs should have stronger predictive power, we used the frequency on each vertex as a weight to multiply the RD and TBM on the vertex. And then, we, respectively, summed up the weighted RD and weighted TBM on the ROIs for each subject. The value for RD and the value for TBM were further reduced to a scalar with PCA. PCA is an unsupervised model to reduce the dimensionality of the data while minimizing information loss. It creates new uncorrelated features which maximize the variance successively. For the randomly selected features on the whole hippocampal surface, the RD and TBM were directly summed up without multiplying the frequency and reduced to a single value with PCA.

Then, the optimal cutoffs for these measurements were determined with the maximum sensitivity and specificity for distinguishing MCI converters and non-converters based on Receiver Operating Characteristic (ROC) analysis (Robin et al., 2011). The ROC curves are illustrated in Figure 8, and the AUC, 95% confidence interval (CI) of AUC, and the optimal cutoffs are shown in Table 4.

With the optimal cutoffs, we could divide the whole cohort into two groups with different measurements. For example, the subjects with hippocampal volume higher than 7814.9 mm^–3 were assigned to a high-value (HV) group, and the rest were into a low-value (LV) group. As expected, AD may decrease the hippocampal volume as well as the other measurements. Next, we fitted a Cox proportional hazard model (Moore, 2008) with the six measurements separately, and the regression beta coefficients (β), the hazard ratios (HRs), and statistical significance (p-values) are shown in Table 4.

Moreover, we calculated the survival probabilities for conversion to AD in the HV group and the LV group by fitting Kaplan–Meier curves. The survival probabilities of the subjects based on hippocampal surface area, volume, the whole hippocampal features, and the features on ROIs related to Aβ, Braak12, and Braak34 are shown in Figure 9. Each color represents the survival curve and 95% CI of one group. Here a log-rank test was used to compare the survival group differences based on a χ² test, and the p-values are illustrated in each plot. A result with a p-value < 0.05 indicates that the two groups are significantly different in terms of survival time. The features from our selected ROIs tended to always yield stronger significant results than the hippocampal surface area, volume, and the whole hippocampal features.

Amyloid-β and tau proteinopathies accelerate hippocampal atrophy leading to AD on MRI scans (Maass et al., 2017; Hanko et al., 2019; Wang et al., 2021). However, the influence of Aβ/tau deposition on hippocampal morphology in pathophysiological progression of AD is still not well understood. Some prior works (Shi et al., 2013a; Tsao et al., 2017; Adler et al., 2018) demonstrated that CA1 and the subiculum are the ROIs with the greatest abnormalities in the early stages of the AD pathophysiological process. Besides, the study of Hanko et al. (2019) reported a significant association between tau burden and atrophy in specific hippocampal ROIs (CA1 and the subiculum), but detected no Aβ-associated hippocampal ROIs in the 42 subjects they studied.

Our work applies two kinds of morphometry measures (RD and TBM) and the novel FMFS framework to two datasets to study fine-scale morphometric correlates of Aβ and tau deposition. Both results are consistent with the prior studies noted above. Besides, we also studied the influence of Aβ/tau burden on hippocampal morphometry at different stages of AD. As the results show in Figures 3–5, Aβ/tau associated hippocampal ROIs are more focal as AD pathology progresses, especially at the final stage of AD itself.

To verify the clinical value of these identified ROIs, we compared their prediction performances to global hippocampal morphometry and Aβ/tau measures using three different machine learning models. As shown in Table 2, the features on our identified ROIs have superior performance for predicting clinical scores, which followed our initial hypothesis. Compared to randomly selected features, the features on ROIs show stronger predictive power, which illustrates the promise of our FMFS model. Additionally, these Aβ/tau-associated features always performed better than the measurements of Aβ/tau, and could be used as a potential biomarker for Aβ/tau pathology, especially as a screening indicator.

In addition, the results in section “Predicting Mini-Mental State Exam Scores Based on Hippocampal Regions of Interest” further proved the stronger predictive power of the ROIs in survival analysis (of conversion from MCI to AD). Here, the univariate biomarker computed from our ROIs had better performance than the traditional hippocampal volume, which suggested the potential ability of our ROIs to study AD as a univariate biomarker. Consequently, both experiments demonstrated the effectiveness of the FMFS model.

To test whether the performance of our FMFS model could be affected by kinds of data distribution across institutions, we performed fivefold cross-validation on the dataset for the study of Aβ under three conditions, including a data-centralized condition and data distributed across three institutions and five institutions. We simulated the distributed condition on a cluster with several conventional ×86 nodes, of which each contains two Intel Xeon E5-2680 v4 CPUs running at 2.40 GHz. Each institution is assigned one computing node. For each training data set, we randomly assigned the subjects to three institutions, five institutions, or a single institution. Besides, we also compared the performance of FMFS with DADMM and FBCD under the five-institution conditions. We perform cross-validation a total of 10 times with a sequence of regularization parameters, 1, 0.5, and 0.1, and with all the other experimental set-ups being the same as in the previous experiment. The average RMSE for the prediction of MMSE was employed to evaluate the prediction accuracy during training and testing, as shown in Table 5.

Additionally, we tried to collect datasets from different institutions and studies to validate the stability of our federated model in the real-world condition. Besides ADNI, we also collected MRI scans from other institutions, including 307 cognitively unimpaired subjects from Open Access Series of Imaging Studies (OASIS) (Marcus et al., 2010) and 38 MCI patients from Arizona APOE cohort study (AZ) (Caselli et al., 2009). The datasets for the study of Aβ and tau are treated as two institutions’ data. Therefore, in this experiment, we have four institutions, Aβ for ADNI, tau for ADNI, OASIS, and AZ. In the four-institution condition, each institution was assigned one computing node and all the other parameter settings were the same. Then, we fit the features of these data and MMSE in our FMFS as well as FBCD and DADMM. FMFS are validated at data-centralized and the four-institution condition. FBCD and DADMM are only under the four-institution condition. The average RMSE for the prediction of MMSE was used to evaluate the prediction accuracy. The results of the training loss are shown in Table 6. The results indicated that different kinds of institutional distributions did not strongly influence our FMFS model.

Despite the promising results are obtained by applying FMFS, there are two important caveats. First, this work is based on cross-sectional data. It would also be valuable to track the longitudinal hippocampal ROIs deformity as Aβ/tau change over time. In the future, we plan to conduct longitudinal association analyses of hippocampal features and their relation to Aβ/tau burden. Second, This work only studied the hippocampal structures, but other structures, such as the ventricles, and cortical surface metrics such as gray matter thickness or volume (Chou et al., 2009; Doherty et al., 2015) are also affected by AD pathology. We hypothesize that our proposed framework will contribute more to these high-dimensional features. Therefore, in the future, we will collect more dataset to explore more Aβ/tau-associated brain regional abnormalities. This future work will help shed new light on the relationship of component biological processes in AD.